From fa89fb0395b92d2d09003500d65e11448bc7f810 Mon Sep 17 00:00:00 2001 From: Corentin Lemasson <95612140+clemasso@users.noreply.github.com> Date: Thu, 6 Jul 2023 16:23:40 +0200 Subject: [PATCH 01/56] Update DESCRIPTION --- DESCRIPTION | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index 40f1880..c81b52d 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,7 +1,7 @@ Package: rjd3revisions Type: Package Title: Revision analysis with 'JDemetra+ 3.0' -Version: 1.0.0 +Version: 1.0.1 Authors@R: person(given = "Corentin", family = "Lemasson", @@ -17,7 +17,7 @@ Depends: R (>= 3.6.0) Imports: rJava (>= 1.0-6), - rjd3toolkit (>= 3.0.0), + rjd3toolkit (>= 3.0.1), knitr, rmarkdown Suggest: From 2439154eeaae7843ad86292b1f4e1f03ab9b207f Mon Sep 17 00:00:00 2001 From: Lemasson Corentin Date: Mon, 28 Aug 2023 09:29:52 +0200 Subject: [PATCH 02/56] vignette + bug fix --- .gitignore | 3 +- DESCRIPTION | 3 +- R/vintages.R | 15 +- man/create_vintages_from_csv.Rd | 6 +- man/create_vintages_from_xlsx.Rd | 9 +- vignettes/.gitignore | 2 + vignettes/rjd3revisions.Rmd | 340 +++++++++++++++++++++++++++++++ 7 files changed, 370 insertions(+), 8 deletions(-) create mode 100644 vignettes/.gitignore create mode 100644 vignettes/rjd3revisions.Rmd diff --git a/.gitignore b/.gitignore index e79678f..1cecb41 100644 --- a/.gitignore +++ b/.gitignore @@ -2,4 +2,5 @@ .Rbuildignore .Rhistory .RData -.Ruserdata \ No newline at end of file +.Ruserdata +inst/doc diff --git a/DESCRIPTION b/DESCRIPTION index 40f1880..15929c7 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,7 +1,7 @@ Package: rjd3revisions Type: Package Title: Revision analysis with 'JDemetra+ 3.0' -Version: 1.0.0 +Version: 1.1.0 Authors@R: person(given = "Corentin", family = "Lemasson", @@ -38,3 +38,4 @@ Collate: 'vintages.R' 'zzz.R' RoxygenNote: 7.2.3 +VignetteBuilder: knitr diff --git a/R/vintages.R b/R/vintages.R index b935778..e55b1e8 100644 --- a/R/vintages.R +++ b/R/vintages.R @@ -175,7 +175,11 @@ create_vintages<- function(df, periodicity, vintage.selection = NULL, revdate.fo #' @examples #' \dontrun{ #' file.name<-"myinput.csv" -#' vintages<-create_vintages_from_csv(file.name, 12, separator = ";", revdate.format="%d/%m/%Y") +#' vintages<-create_vintages_from_csv(file.name, +#' periodicity=12, +#' separator = ";", +#' vintage.selection=NULL, +#' revdate.format="%Y-%m-%d") #' } create_vintages_from_csv<-function(file, periodicity, separator = ",", vintage.selection=NULL, revdate.format="%Y.%m.%d"){ @@ -210,9 +214,14 @@ create_vintages_from_csv<-function(file, periodicity, separator = ",", vintage.s #' @examples #' \dontrun{ #' file.name<-"myinput.xlsx" -#' vintages<-create_vintages_from_xlsx(file.name, 12, separator = ";", revdate.format="%d/%m/%Y") +#' sheet.name<-"Sheet1" +#' vintages<-create_vintages_from_xlsx(file.name, +#' sheet.name, +#' periodicity=12, +#' vintage.selection=NULL, +#' revdate.format="%d/%m/%Y")) #' } -create_vintages_from_xlsx<-function(file, sheetname, periodicity, vintage.selection, revdate.format= "%Y.%m.%d"){ +create_vintages_from_xlsx<-function(file, sheetname, periodicity, vintage.selection = NULL, revdate.format= "%Y.%m.%d"){ if(! require(readxl)){stop("package 'readxl' must be installed to run the function 'create_vintages_from_xlsx'")} diff --git a/man/create_vintages_from_csv.Rd b/man/create_vintages_from_csv.Rd index f24fb80..e31a2c6 100644 --- a/man/create_vintages_from_csv.Rd +++ b/man/create_vintages_from_csv.Rd @@ -40,7 +40,11 @@ Create vintages table from CSV or TXT files \examples{ \dontrun{ file.name<-"myinput.csv" -vintages<-create_vintages_from_csv(file.name, 12, separator = ";", revdate.format="\%d/\%m/\%Y") +vintages<-create_vintages_from_csv(file.name, + periodicity=12, + separator = ";", + vintage.selection=NULL, + revdate.format="\%Y-\%m-\%d") } } \seealso{ diff --git a/man/create_vintages_from_xlsx.Rd b/man/create_vintages_from_xlsx.Rd index 7143b83..1e6440e 100644 --- a/man/create_vintages_from_xlsx.Rd +++ b/man/create_vintages_from_xlsx.Rd @@ -8,7 +8,7 @@ create_vintages_from_xlsx( file, sheetname, periodicity, - vintage.selection, + vintage.selection = NULL, revdate.format = "\%Y.\%m.\%d" ) } @@ -40,7 +40,12 @@ Create vintages table from XLSX files \examples{ \dontrun{ file.name<-"myinput.xlsx" -vintages<-create_vintages_from_xlsx(file.name, 12, separator = ";", revdate.format="\%d/\%m/\%Y") +sheet.name<-"Sheet1" +vintages<-create_vintages_from_xlsx(file.name, + sheet.name, + periodicity=12, + vintage.selection=NULL, + revdate.format="\%d/\%m/\%Y")) } } \seealso{ diff --git a/vignettes/.gitignore b/vignettes/.gitignore new file mode 100644 index 0000000..097b241 --- /dev/null +++ b/vignettes/.gitignore @@ -0,0 +1,2 @@ +*.html +*.R diff --git a/vignettes/rjd3revisions.Rmd b/vignettes/rjd3revisions.Rmd new file mode 100644 index 0000000..c3fb18b --- /dev/null +++ b/vignettes/rjd3revisions.Rmd @@ -0,0 +1,340 @@ +--- +title: "Revision analysis tool with JDemetra+ version 3.x algorithms" +output: + html_vignette: + toc: true + toc_depth: 2 +vignette: > + %\VignetteIndexEntry{Revision analysis tool with JDemetra+ version 3.x algorithms} + %\VignetteEngine{knitr::rmarkdown} + %\VignetteEncoding{UTF-8} +author: Corentin Lemasson +abstract: Revision analyses provides important information on the efficiency of preliminary estimates, allowing to identify potential issues and/or improvements that could be made in the compilation process. This package provides a tool to automatically perform a battery of relevant tests on revisions and submit a visual report including both the main results and their interpretation. The tool can perform analysis on different types of revision intervals and on different vintage views. +--- + +```{r, include = FALSE} +knitr::opts_chunk$set( + collapse = TRUE, + eval = FALSE, + comment = "#>" +) +``` + +# Introduction + +This package performs revision analysis and offers both detailed and summary output including the generation of a visual report. It is composed on a selection of parametric tests which enable the users to detect potential bias (both mean and regression bias) and other sources of inefficiency in preliminary estimates. What we mean by inefficiency in preliminary estimates is whether further revisions are predictable in some way. + +This package uses the efficient libraries of [JDemetra+ v3](https://github.com/jdemetra/jdplus-main). It was built mostly based on Eurostat’s technical reports from D. Ares and L. Pitton (2013). + +The next section helps with the installation of the package. The third section describes how to use the tool and give some important details on the main functions. In particular, it is important to mention beforehand that your input data must first be set in a specific format described in the sub-section on the [input data](#input_format). The fourth section is theoretical and describes each test being performed by the main function `revision_analysis()` (they could also be performed individually) and how to interpret them. Finally, you will find out all the reference papers in the last section. + +# Installation settings + +This package relies on the Java libraries of [JDemetra+ v3](https://github.com/jdemetra/jdplus-main) and on the package [rjd3toolkit](https://github.com/rjdemetra/rjd3toolkit) of [RJDemetra](https://github.com/rjdemetra). Prior the installation, you must ensure to have a Java version >= 17.0 on your computer. If you need to use a portable version of Java to fill this request, you can follow the instructions in the [installation manual](https://github.com/jdemetra/rjdemetra/wiki/Installation-manual) of RJDemetra. + +In addition to a Java version >= 17.0, you must have a recent version of the R packages rJava (>= 1.0.6) and RProtobuf (>=0.4.17) that you can download from CRAN. Depending on your current version of R, you might also need to install another version of Rtools. (>= 3.6). + +This package also depends on the package [rjd3toolkit](https://github.com/rjdemetra/rjd3toolkit) that you must install from GitHub prior to [rjd3revsions](https://github.com/rjdemetra/rjd3revisions). +```{r} +remotes::install_github("rjdemetra/rjd3toolkit") +remotes::install_github("rjdemetra/rjd3revisions") +``` + +Note that depending on the R packages that are already installed on your computer, you might also be asked to install or re-install a few other packages from CRAN. + +Finally, this package also suggests the R packages `formattable` and `kableExtra` (and `readxl` if you import your input data from Excel) downloadable from CRAN. You are invited to install them for an enhanced formatting of the output (i.e., meaningful colors). + +# Usage + +## Input data {#input_format} + +Your input data must be in a specific format taken from the reference documents of Ares and Pitton (2013). It must have specific column names and date formats as in the table below. Note that missing values can either be mentioned as NA (as in the example below) or not be included in the input at the best convenience of the user. + +| rev_date | time_period | obs_values | +| ----------- | ----------- | ----------- | +| 2022-07-31 | 2022Q1 | 0.8 | +| 2022-07-31 | 2022Q2 | 0.2 | +| 2022-07-31 | 2022Q3 | NA | +| 2022-07-31 | 2022Q4 | NA | +| 2022-08-31 | 2022Q1 | 0.8 | +| ... | ... | ... | + +Depending on the location of your input data, you can use `create_vintages_from_xlsx()` or `create_vintages_from_csv()`, or the more generic function `create_vintages()` to create the vintages (see section [vintages & revisions](#vintages)) later on. If you plan to use the generic function, you'll first need to put your input data in a data.frame in R as in the example below. + +```{r, eval = TRUE} +# Example +input_df<-data.frame(rev_date = c(rep("2022-07-31",4), rep("2022-08-31",4), + rep("2022-09-30",4), rep("2022-10-31",4), + rep("2022-11-30",4), rep("2022-12-31",4), + rep("2023-01-31",4), rep("2023-02-28",4)), + time_period = c(rep(c("2022Q1","2022Q2","2022Q3","2022Q4"),8)), + obs_values = c(.8,.2,NA,NA, .8,.1,NA,NA, + .7,.1,NA,NA, .7,.2,.5,NA, + .7,.2,.5,NA, .7,.3,.7,NA, + .7,.2,.7,.4, .7,.3,.7,.3)) +``` + +## Processing + +```{r} +library(rjd3revisions) +``` + +Once your input data are in the right format, you create the vintages, possibly inspect the revisions and perform the revision analysis +```{r} +vintages<-create_vintages(input_df, periodicity = 4) +# vintages<-create_vintages_from_xlsx("myinput.xlsx", "Sheet1", periodicity=4, vintage.selection=NULL, revdate.format="%d/%m/%Y") +# vintages<-create_vintages_from_csv("myinput.csv", periodicity=4, separator="\t", vintage.selection=NULL, revdate.format="%Y-%m-%d") +revisions<-get_revisions(vintages, gap = 1) +rslt<-revision_analysis(vintages, gap = 1, view = "diagonal", n.releases = 3) +``` + +Finally to create the report and get a summary of the results, you can use +```{r} +get_report(rslt) + +summary(rslt) +print(rslt) +plot(rslt) +``` + +## Details on the main functions + +### Vintages & revisions {#vintages} + +Once your input data are in the right format, you must first create an object of the class `rjd3rev_vintages` before you can run your revision analysis. The function `create_vintages()` (or, alternatively, `create_vintages_from_xlsx()` or `create_vintages_from_csv()`) will create this object from the input data and display the vintages considering three different data structures or views: vertical, horizontal and diagonal. + +1. The **vertical view** shows the observed values at each time period by the different vintages. This approach is robust to changes of base year and data redefinition and could for example be used to analyse revisions resulting from a benchmark revision. A drawback of this approach is that for comparing the same historical series for different vintages, we need to look at the smallest common number of observations and consequently the number of observations is in some circumstances very small. Moreover, it is often the case that most of the revision is about the last few points of the series so that the number of observations is too small to test anything. + +| Period | 2023/03/31 | 2023/04/30 | 2023/05/31 | +| -------- | ---------- | ---------- | ---------- | +| 2022M01 | 15.2 | 15.1 | 15.0 | +| 2022M02 | 15.0 | 14.9 | 14.9 | +| ... | ... | ... | ... | +| 2023M01 | 13.0 | 13.1 | 13.2 | +| 2023M02 | | 12.1 | 12.1 | +| 2023M03 | | | 12.3 | + +Table: Example of vertical view + +2. The **horizontal view** shows the observed values of the different vintages by the period. A quick analysis can be performed by rows in order to see how for the same data point (e.g. 2023Q1), figures are first estimated, then forecasted and finally revised. The main findings are usually obvious: in most cases the variance decreases, namely data converge towards the 'true value'. Horizontal tables are just a transpose of vertical tables and are not used in the tests in 'revision_analysis'. + +| Period | 2022M01 | 2022M02 | ... | 2023M01 | 2023M02 | 2023M03 | +| ---------- | ------- | ------- | ------- | ------- | ------- | ------- | +| 2023/03/31 | 15.2 | 15.0 | ... | 13.0 | | | +| 2023/04/30 | 15.1 | 14.9 | ... | 13.1 | 12.1 | | +| 2023/05/31 | 15.0 | 14.9 | ... | 13.2 | 12.1 | 12.3 | + +Table: Example of horizontal view + +3. The **diagonal view** shows subsequent releases of a given time period, without regard for the date of publication. The advantage of the diagonal approach is that it gives a way to analyse the trade between the timing of the release and the accuracy of the published figures. It is particularly informative when regular estimation intervals exist for the data under study (as it is the case for most of the official statistics). However, this approach requires to be particularly vigilant in case there is a change in base year or data redefinition. + +| Period | Release1 | Release2 | Release3 | +| -------- | ---------- | ---------- | ---------- | +| 2023M01 | 13.0 | 13.1 | 13.2 | +| 2023M02 | 12.1 | 12.1 | | +| 2023M03 | 12.3 | | | + +Table: Example of diagonal view + +Note that in the argument of the function `create_vintages()`, the argument `vintage.selection` allows you to limit the range of revision dates to consider if needed. See ?create_vintages for more details. + +Revisions are easily calculated from vintages by choosing the gap to consider. The function `get_revisions()` will display the revisions according to each view. It is just an informative function that does not need to be run prior the revision analysis. + +### Revision analysis & reporting + +The function `revision_analysis()` is the main function of the package. It provides some descriptive statistics and performs a battery of parametric tests which enable the users to detect potential bias (both mean and regression bias) and sources of inefficiency in preliminary estimates. We would conclude to inefficiency in the preliminary estimates when revisions are predictable in some way. Parametric tests are divided into 5 categories: relevancy (check whether preliminary estimates are even worth it), bias, efficiency, orthogonality (correlation at higher lags), and signalVSnoise. This function is robust. If for some reasons, a test fails to process, it is just skipped and a warning is sent to users with the possible cause of failure. The other tests are then performed as usual. + +For some of the parametric tests, prior transformation of the vintage data may be important to avoid misleading results. By default, the decision to differentiate the vintage data is performed automatically based on unit root and co-integration tests. More specifically, we focus on the augmented Dickey-Fuller (ADF) test to test the presence of unit root and, for cointegration, we proceed to an ADF test on the residuals of an OLS regression between the two vintages. The results of those tests are also made available in the output of the function (section 'varbased'). By constrast, the choice of log-transformation is left to the discretion of the users based on their knowledge of the series and the diagnostics of the various tests. By default, no log-transformation is considered. + +As part of the arguments of the `revision_analysis()` function, you can choose the view and the gap to consider, restrict the number of releases under investigation when diagonal view is selected and/or change the default setting about the prior transformation of the data (including the possibility to add a prior log-transformation of your data). + +The function `get_report()` applied on the output of `revision_analysis()` will generate an enhanced HTML report including both a formatted summary of the results and full explanations about each tests (which are also included in the vignette below). The formatted summary of the results display the p-value of each test (except for Theil's tests where the value of the statistics is provided) and their interpretation. An appreciation 'good', 'uncertain', 'bad' and 'severe' is indeed associated to each test following the usual statistical interpretation of p-values and the orientation of the tests. This allows a quick visual interpretation of the results and is similar to what is done in the GUI of JDemetra+. + +In addition to the function `revision_analysis()`, the user can also perform tests individually if they want to. To list all functions available in the package (and therefore finding the different functions corresponding to the individual tests), you can do + +```{r} +ls("package:rjd3revisions") +``` + +Use help(‘name of the functions’) or ?‘name of the functions’ for more information and examples over the various functions. + +## Output + +The detailed results of each test are part of the output returned by the function `revision_analysis()`. Alternatively, the functions associated with the individual test will give you the same result specific to this test. + +In addition to the visual report that you can get by applying the function `get_report()` on the output of the function `revision_analysis()`, you can also apply the usual `summary()`, `print()` and `plot()` functions to this output. The function `summary()`, in particular, will print only the formatted table of the report with the main results. The `print()` will provide the same unformatted information together with some extra ones and `plot()` will plot the revisions over time. + +# Tests description and interpretation + +Recall that the purpose of the parametric tests described below are: + +- To check the *relevancy* of preliminary estimates +- To detect potential mean and regression *bias* +- To measure *efficiency* of preliminary estimates (i.e., whether revisions are somehow predictable) + +## Relevancy + +### Theil’s Inequality Coefficient + +In the context of revision analysis, Theil's inequality coefficient, also known as Theil's U, provides a measure of the accuracy of a set of preliminary estimates (P) compared to a latter version (L). There exists a few definitions of Theil's statistics leading to different interpretation of the results. In this package, two definitions are considered. The first statistic, U1, is given by +$$ +U_1=\frac{\sqrt{\frac{1}{n}\sum^n_{t=1}(L_t-P_t)^2}}{\sqrt{\frac{1}{n}\sum^n_{t=1}L_t^2}+\sqrt{\frac{1}{n}\sum^n_{t=1}P_t^2}} \\ \\ +$$ +U1 is bounded between 0 and 1. The closer the value of U1 is to zero, the better the forecast method. However, this classic definition of Theil's statistic suffers from a number of limitations. In particular, a set of near zero preliminary estimates would always give a value of the U1 statistic close to 1 even though they are close to the latter estimates. + +The second statistic, U2, is given by +$$ +U_2=\frac{\sqrt{\sum^n_{t=1}\left(\frac{P_{t+1}-L_{t+1}}{L_t}\right)^2}}{\sqrt{\sum^n_{t=1}\left(\frac{L_{t+1}-L_t}{L_t}\right)^2}} +$$ +The interpretation of U2 differs from U1. The value of 1 is no longer the upper bound of the statistic but a threshold above (below) which the preliminary estimates is less (more) accurate than the naïve random walk forecast repeating the last observed value (considering $P_{t+1}=L_t$). Whenever it can be calculated ($L_t \neq 0 ~\forall t$), the U2 statistic is the preferred option to evaluate the relevancy of the preliminary estimates. + + +## Bias + +A bias in preliminary estimates may indicate inaccurate initial data or inefficient compilation methods. However, we must be cautious if a bias is shown to be statistically significant and we intend to correct it. Biases may change overtime, so we might correct for errors that no longer apply. Over a long interval, changes in methodology or definitions may also occur so that there are valid reasons to expect a non-zero mean revision. + +### T-test and Augmented T-test + +To test whether the mean revision is statistically different from zero for a sample of n, we employ a conventional t-statistic +$$ +t=\frac{\overline{R}}{\sqrt{s^2/n}} +$$ +If the null hypothesis that the bias is equal to zero is rejected, it may give an insight of whether a bias exists in the earlier estimates. + +The t-test is equivalent to fitting a linear regression of the revisions on only a constant (i.e. the mean). Assumptions such as the gaussianity of the revisions are implied. One can release the assumption of no autocorrelation by adding it into the model. Hence we have +$$ +R_t=\mu+\varepsilon_t, ~~t=1,...,n +$$ +And the errors are thought to be serially correlated according to an AR(1) model, that is +$$ +\varepsilon_t=\gamma\varepsilon_t+u_t, ~~with~ |\gamma|<1 ~and ~u_t \sim{iid} +$$ +The auto-correlation in the error terms reduces the number of independent observations (and the degrees of freedom) by a factor of $n\frac{(1-\gamma)}{(1+\gamma)}$ and thus, the variance of the mean should be adjusted upward accordingly. + +Hence, the Augmented t-test is calculated as +$$ +t_{adj}=\frac{\overline{R}}{\sqrt{\frac{s^2(1+\hat{\gamma})}{n(1-\hat{\gamma})}}} +$$ +where +$$ +\hat{\gamma}=\frac{\sum^{n-1}_{t=1}(R_t-\overline{R})(R_{t+1}-\overline{R})}{\sum^n_{t=1}(R_t-\overline{R})^2} +$$ + +### Slope and drift + +We assume a linear regression model of a latter vintage (L) on a preliminary vintage (P) and estimate the intercept (drift) $\beta_0$ and slope coefficient $\beta_1$ by OLS. The model is + +$$ +L_t=\beta_0+\beta_1P_t+\varepsilon_t +$$ +While the (augmented) t-test on revisions only gives information about mean bias, this regression enables to assess both mean and regression bias. A regression bias would occur, for example, if preliminary estimates tend to be too low when latter estimates are relatively high and too high when latter estimates are relatively low. In this case, this may result in a positive value of the intercept and a value of $\beta_1<1$. To evaluate whether a mean or regression bias is present, we employ a conventional t-test on the parameters with the null hypothesis $\beta_0 = 0$ and $\hat{\beta}_1 = 1$. + +Recall that OLS regressions always come along with rather strict assumptions. Users should check the diagnostics and draw the necessary conclusions from them. + +## Efficiency + +Efficiency tests evaluate whether preliminary estimates are "efficient" forecast of the latter estimates. If all information were used efficiently at the time of the preliminary estimate, revisions should not be predictable and therefore neither be correlated with preliminary estimates or display any relationship from one vintage to another. This section focuses on these two points. Predictability of revisions is tested even further in the Orthogonality and SignalVSNoise sections. + +### Regression of revisions on previous estimates + +We assume a linear regression model of the revisions (R) on a preliminary vintage (P) and estimate the intercept $\beta_0$ and slope coefficient $\beta_1$ by OLS. The model is + +$$ +R_t=\beta_0+\beta_1P_t+\varepsilon_t, ~~t=1,...,n +$$ +If revisions are affected by preliminary estimates, it means that those are not efficient and could be improved. We employ a conventional t-test on the parameters with the null hypothesis $\beta_0 = 0$ and $\beta_1 = 0$. Diagnostics on the residuals should be verified. + +### Regression of revisions from latter vintages on revisions from the previous vintages + +We assume a linear regression model of the revisions between latter vintages ($R_v$) on the revisions between the previous vintages ($R_{v-1}$) and estimate the intercept $\beta_0$ and slope coefficient $\beta_1$ by OLS. The model is + +$$ +R_{v,t}=\beta_0+\beta_1R_{v-1,t}+\varepsilon_t, ~~t=1,...,n +$$ +If latter revisions are predictable from previous revisions, it means that preliminary estimates are not efficient and could be improved. We employ a conventional t-test on the parameters with the null hypothesis $\beta_0 = 0$ and $\beta_1 = 0$. Diagnostics on the residuals should be verified. + + +## Orthogonality + +Orthogonality tests evaluate whether revisions from older vintages affect the latter revisions. This section also includes autocorrelation and seasonality tests for a given set of revisions. If there is significant correlation in the revisions for subsequent periods, this may witness some degree of predictability in the revision process. + +### Regression of latter revisions (Rv) on previous revisions (Rv_1, Rv_2,...Rv_p) + +We assume a linear regression model of the revisions from latter vintages ($R_v$) on the revisions from p previous vintages ($R_{v-1}, ..., R_{v-p}$) and estimate the intercept $\beta_0$ and slope coefficients of $\beta_1, ..., \beta_p$ by OLS. The model is + +$$ +R_{v,t}=\beta_0+\sum^p_{i=1}\beta_{i}R_{v-i,t}+\varepsilon_t, ~~t=1,...,n +$$ +If latter revisions are predictable from previous revisions, it means that preliminary estimates are not efficient and could be improved. We employ a conventional t-test on the intercept parameter with the null hypothesis $\beta_0 = 0$ and a F-test to check the null hypothesis that $\beta_1 = \beta_2=...=\beta_p=0$. Diagnostics on the residuals should be verified + +### Regression of latter revisions (Rv) on revisions from a specific vintage (Rv_k) + +We assume a linear regression model of the revisions from latter vintages ($R_v$) on the revisions from a specific vintage ($R_{v-k}$) and estimate the intercept $\beta_0$ and slope coefficient $\beta_1$ by OLS. The model is + +$$ +R_{v,t}=\beta_0+\beta_1R_{v-k,t}+\varepsilon_t, ~~t=1,...,n +$$ +If latter revisions are predictable from previous revisions, it means that preliminary estimates are not efficient and could be improved. We employ a conventional t-test on the parameters with the null hypothesis $\beta_0 = 0$ and $\beta_1 = 0$. Diagnostics on the residuals should be verified. + +### Test of autocorrelations in revisions + +To test whether autocorrelation is present in revisions, we employ the Ljung-Box test. The Ljung-Box test considers together a group of autocorrelation coefficients up to a certain lag k and is therefore sometimes referred to as a portmanteau test. For the purpose of revision analysis, as we expect a relatively small number of observations, we decided to restrict the number of lags considered to $k=2$. Hence, the users can also make the distinction with autocorrelation at seasonal lags (see seasonality tests below). + +The null hypothesis is no autocorrelation. The test statistic is given by +$$ +Q=n(n+2)\sum^k_{i=1}\frac{\hat{\rho}_i^2}{n-i} +$$ +where n is the sample size, $\hat{\rho}_i^2$ is the sample autocorrelation at lag in and $k=2$ is the number of lags being tested. Under the null hypothesis, $Q\sim\chi^2(k)$. + +If Q is statistically different from zero, the revision process may be locally biased in the sense that latter revisions are related to the previous ones. + +### Test of seasonality in revisions + +To test whether seasonality is present in revisions, we employ two tests: the parametric QS test and the non-parametric Friedman test. Note that seasonality tests are always performed on first-differentiated series to avoid misleading results. + +The QS test is a variant of the Ljung-Box test computed on seasonal lags, where we only consider positive auto-correlations +$$ +QS=n(n+2)\sum^k_{i=1}\frac{\left[max(0,\hat{\gamma}_{i.l})\right]^2}{n-i.l} +$$ +where $k=2$, so only the first and second seasonal lags are considered. Thus, the test would checks the correlation between the actual observation and the observations lagged by one and two years. Note that $l=12$ when dealing with monthly observations, so we consider the auto-covariances $\hat{\gamma}_{12}$ and $\hat{\gamma}_{24}$ alone. In turn $k=4$ in the case of quarterly data. + +Under the null hypothesis of no autocorrelation at seasonal lags, $QS\sim \chi_{modified}^2(k)$. The elimination of negative correlations calls indeed for a modified $\chi^2$ distribution. This was done using simulation techniques. + +The Friedman test requires no distributional assumptions. It uses the rankings of the observations. It is constructed as follows. Consider first the matrix of data $\{x_{ij}\}_{nxk}$ with n rows (the blocks, i.e. the number of years in the sample), k columns (the treatments, i.e., either 12 months or 4 quarters, depending on the frequency of the data). The data matrix needs to be replaced by a new matrix $\{r_{ij}\}_{nxk}$, where the entry $r_{ij}$ is the rank of $x_{ij}$ within the block i. The test statistic is given by + +$$ +Q=\frac{n\sum^k_{j=1}(\tilde{r}_{.j}-\tilde{r})^2}{\frac{1}{n(k-1)}\sum^n_{i=1}\sum^k_{j=1}(r_{ij}-\tilde{r})^2} +$$ +The denominator represents the variance of the average ranking across treatments j relative to the total. Under the null hypothesis of no (stable) seasonality, $Q\sim \chi^2(k-1)$. + +As for non-seasonal autocorrelation tests at lower lags, if QS and Q are significantly different from zero, the revision process may be locally biased in the sense that latter revisions are related to the previous ones. + + +## Signal vs Noise + +Regression techniques can also be used to determine whether revisions should be classified as ‘news’ or ‘noise’. Those are also closely related to the notion of efficiency developed earlier. + +If the correlation between revisions and preliminary estimates is significantly different from zero, this implies that we did not fully utilize all the information available at the time of the preliminary estimates. In that sense, we would conclude that the preliminary estimates could have been better and that revisions embody noise. The model to test whether revisions are "noise" is similar to the first model established earlier to test efficiency: +$$ +R_t=\beta_0+\beta_1P_t+\varepsilon_t, ~~t=1,...,n +$$ +We employ a F-test on the parameters to test jointly that $\beta_0 = 0$ and $\beta_1 = 0$. If the null hypothesis is rejected, this suggest that revisions are likely to include noise. Diagnostics on the residuals should be verified. + +On the other hand, revisions should be correlated to the latter estimates. If this is the case, it means that information which becomes +available between the compilation of the preliminary and the latter estimates are captured in the estimation process of the latter estimates. In that sense, the revision process is warranted and we conclude that revisions embody news. The model to test whether revisions are "news" is + +$$ +R_t=\beta_0+\beta_1L_t+\varepsilon_t, ~~t=1,...,n +$$ +We employ a F-test on the parameters to test jointly that $\beta_0 = 0$ and $\beta_1 = 0$. If the null hypothesis is rejected, this is a good thing as it suggests that revisions incorporate news. Note that even if we reject the null hypothesis and conclude that revisions incorporate news, it does not necessarily mean that revisions are efficient as those might still be predicted by other variables not included in the estimation process. + +# References + +- Ares, David. 2013. “Tool for Revision Analysis : Technical Report.” DI/06769. DG ESTAT. +- Cook, Steve. 2019. “Forecast Evaluation Using Theil’s Inequality Coefficients.” Swansea University; https://www.economicsnetwork.ac.uk/showcase/cook_theil. +- Fixler, Dennis. 2007. “How to Interpret Whether Revisions to Economic Variables Reflect ‘News’ or ‘Noise’.” OECD. +- McKenzie, Richard, and Michela Gamba. 2007. “Interpreting the Results of Revision Analyses: Recommended Summary Statistics.” OECD. +- Pitton, Laurent, and David Ares. 2013a. “Tool for Revision Analysis : Regression Based Parametric Analysis.” DI/06769. DG ESTAT. +- Pitton, Laurent, and David Ares. 2013b. “Tool for Revision Analysis : VAR Based Models and Final Equation.” DI/06769. DG ESTAT. +- Smyk, Anna, Alain Quartier-la-Tente, Tanguy Barthelemy, and Karsten Webel. 2023. “JDemetra+ Documentation.” INSEE; https://jdemetra-new-documentation.netlify.app/. From 35ce4953babe6e6de8c76e1c70f1865ba4b13a79 Mon Sep 17 00:00:00 2001 From: Corentin Lemasson <95612140+clemasso@users.noreply.github.com> Date: Mon, 28 Aug 2023 09:57:26 +0200 Subject: [PATCH 03/56] Update README.md --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index a2c722f..50c571b 100644 --- a/README.md +++ b/README.md @@ -48,5 +48,5 @@ plot(rslt) ``` ## Additional information -This README.md file gives you an example of how to proceed. Then, you can consult the documentation of each function separately (for example: `?create_vintages`, `?revision_analysis`) to see the current possibilities of the tool. Finally, the function `get_report()` generates a report that includes a summary of the results but also explanation about all the tests being performed. +This README.md file gives you a quick example of how to proceed. Consult the vignette and the documentation of each function (for example: `?create_vintages`, `?revision_analysis`) to see the current possibilities of the tool. From 9fc5088b305f178cc558db4340f7af9d2df73f94 Mon Sep 17 00:00:00 2001 From: Tanguy BARTHELEMY Date: Fri, 29 Sep 2023 13:48:47 +0200 Subject: [PATCH 04/56] Update DESCRIPTION file with Remotes field --- DESCRIPTION | 2 ++ 1 file changed, 2 insertions(+) diff --git a/DESCRIPTION b/DESCRIPTION index 8973d9b..528cb63 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -20,6 +20,8 @@ Imports: rjd3toolkit (>= 3.0.1), knitr, rmarkdown +Remotes: + github::rjdemetra/rjd3toolkit Suggest: readxl, formattable, From cdd718d87f3b554a2a2a185dfe53732f2a08e9ba Mon Sep 17 00:00:00 2001 From: Tanguy BARTHELEMY Date: Wed, 18 Oct 2023 12:40:02 +0200 Subject: [PATCH 05/56] Update Readme with stable installation of last release version --- README.md | 13 +++++++++++++ vignettes/rjd3revisions.Rmd | 2 +- 2 files changed, 14 insertions(+), 1 deletion(-) diff --git a/README.md b/README.md index 50c571b..17c0064 100644 --- a/README.md +++ b/README.md @@ -1,11 +1,24 @@ # rjd3revisions ## Installation + +To get the current stable version (from the latest release): + ``` r +# install.packages("remotes") +remotes::install_github("rjdemetra/rjd3toolkit@v3.1.0") +remotes::install_github("rjdemetra/rjd3revisions@v1.0.0") +``` + +To get the current development version from GitHub: + +``` r +# install.packages("remotes") remotes::install_github("rjdemetra/rjd3revisions") ``` ## Usage + First you need to get your input data set as a data.frame in R in a specific format as below. | rev_date | time_period | obs_values | | ----------- | ----------- | ----------- | diff --git a/vignettes/rjd3revisions.Rmd b/vignettes/rjd3revisions.Rmd index c3fb18b..75fb38c 100644 --- a/vignettes/rjd3revisions.Rmd +++ b/vignettes/rjd3revisions.Rmd @@ -77,7 +77,7 @@ input_df<-data.frame(rev_date = c(rep("2022-07-31",4), rep("2022-08-31",4), ## Processing ```{r} -library(rjd3revisions) +library("rjd3revisions") ``` Once your input data are in the right format, you create the vintages, possibly inspect the revisions and perform the revision analysis From 59fa8887199e6e13affa8bfd595358c4ad9e3152 Mon Sep 17 00:00:00 2001 From: Tanguy Barthelemy Date: Thu, 19 Oct 2023 12:49:16 +0200 Subject: [PATCH 06/56] Update README.md --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 17c0064..99c8522 100644 --- a/README.md +++ b/README.md @@ -7,7 +7,7 @@ To get the current stable version (from the latest release): ``` r # install.packages("remotes") remotes::install_github("rjdemetra/rjd3toolkit@v3.1.0") -remotes::install_github("rjdemetra/rjd3revisions@v1.0.0") +remotes::install_github("rjdemetra/rjd3revisions@v1.1.0") ``` To get the current development version from GitHub: From acbb65f55f74708647947ca0f342fcbaa2909426 Mon Sep 17 00:00:00 2001 From: Tanguy BARTHELEMY Date: Thu, 19 Oct 2023 15:10:13 +0200 Subject: [PATCH 07/56] Update README file with stable installation of last release version --- README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index 17c0064..4ddce70 100644 --- a/README.md +++ b/README.md @@ -6,8 +6,8 @@ To get the current stable version (from the latest release): ``` r # install.packages("remotes") -remotes::install_github("rjdemetra/rjd3toolkit@v3.1.0") -remotes::install_github("rjdemetra/rjd3revisions@v1.0.0") +remotes::install_github("rjdemetra/rjd3toolkit@*release") +remotes::install_github("rjdemetra/rjd3revisions@*release") ``` To get the current development version from GitHub: From 2c83114a246df68f7ca0ced4f74c2cea56d53dd2 Mon Sep 17 00:00:00 2001 From: Tanguy Barthelemy Date: Fri, 10 Nov 2023 11:22:42 +0100 Subject: [PATCH 08/56] Update README.md --- README.md | 35 ++++++++++++++++++++--------------- 1 file changed, 20 insertions(+), 15 deletions(-) diff --git a/README.md b/README.md index 4ddce70..da4c3fa 100644 --- a/README.md +++ b/README.md @@ -30,25 +30,31 @@ First you need to get your input data set as a data.frame in R in a specific for | ... | ... | ... | ``` r -#Example -df<-data.frame(rev_date = c(rep("2022-07-31",4), rep("2022-08-31",4), - rep("2022-09-30",4), rep("2022-10-31",4), - rep("2022-11-30",4), rep("2022-12-31",4), - rep("2023-01-31",4), rep("2023-02-28",4)), - time_period = c(rep(c("2022Q1","2022Q2","2022Q3","2022Q4"),8)), - obs_values = c(.8,.2,NA,NA, .8,.1,NA,NA, - .7,.1,NA,NA, .7,.2,.5,NA, - .7,.2,.5,NA, .7,.3,.7,NA, - .7,.2,.7,.4, .7,.3,.7,.3)) +# Example +df <- data.frame( + rev_date = c( + rep("2022-07-31", 4), rep("2022-08-31", 4), + rep("2022-09-30", 4), rep("2022-10-31", 4), + rep("2022-11-30", 4), rep("2022-12-31", 4), + rep("2023-01-31", 4), rep("2023-02-28", 4) + ), + time_period = c(rep(c("2022Q1", "2022Q2", "2022Q3", "2022Q4"), 8)), + obs_values = c( + .8, .2, NA, NA, .8, .1, NA, NA, + .7, .1, NA, NA, .7, .2, .5, NA, + .7, .2, .5, NA, .7, .3, .7, NA, + .7, .2, .7, .4, .7, .3, .7, .3 + ) +) ``` Then you can create your vintages, inspect revisions if you want and make the analysis ``` r library("rjd3revisions") -vintages<-create_vintages(df, periodicity = 4) -#revisions<-get_revisions(vintages, gap = 2) -rslt<-revision_analysis(vintages, gap = 1, view = "diagonal", n.releases = 3) +vintages <- create_vintages(df, periodicity = 4) +# revisions<-get_revisions(vintages, gap = 2) +rslt <- revision_analysis(vintages, gap = 1, view = "diagonal", n.releases = 3) ``` Finally to create a report and get a summary of the results, you can use @@ -61,5 +67,4 @@ plot(rslt) ``` ## Additional information -This README.md file gives you a quick example of how to proceed. Consult the vignette and the documentation of each function (for example: `?create_vintages`, `?revision_analysis`) to see the current possibilities of the tool. - +This README.md file gives you a quick example of how to proceed. Consult the vignette (with `browseVignettes("rjd3revisions")`) and the documentation of each function (for example: `?create_vintages`, `?revision_analysis`) to see the current possibilities of the tool. From a57bf93de57ec79351fdf56dca523b792754acb3 Mon Sep 17 00:00:00 2001 From: Tanguy BARTHELEMY Date: Fri, 22 Dec 2023 17:34:20 +0100 Subject: [PATCH 09/56] change T in TRUE and F in FALSE --- .Rbuildignore | 2 + .gitignore | 2 + R/jd3_rslts.R | 1 - R/output.R | 4 +- R/report.R | 30 ++-- R/revision_analysis.R | 352 +++++++++++++++++++------------------- R/revisions.R | 28 +-- R/tests.R | 290 +++++++++++++++---------------- R/vintages.R | 16 +- R/zzz.R | 4 +- inst/templates/report.Rmd | 16 +- rjd3revisions.Rproj | 6 +- 12 files changed, 377 insertions(+), 374 deletions(-) diff --git a/.Rbuildignore b/.Rbuildignore index 5f21cd5..60b8d9d 100644 --- a/.Rbuildignore +++ b/.Rbuildignore @@ -1,2 +1,4 @@ ^rjd3revisions\.Rproj$ ^\.Rproj\.user$ +^doc$ +^Meta$ diff --git a/.gitignore b/.gitignore index 1cecb41..99ac7be 100644 --- a/.gitignore +++ b/.gitignore @@ -4,3 +4,5 @@ .RData .Ruserdata inst/doc +/doc/ +/Meta/ diff --git a/R/jd3_rslts.R b/R/jd3_rslts.R index ab38961..a18dde9 100644 --- a/R/jd3_rslts.R +++ b/R/jd3_rslts.R @@ -153,4 +153,3 @@ proc_likelihood<-function(jrslt, prefix){ hannanquinn=proc_numeric(jrslt, paste(prefix,"hannanquinn", sep=""))) ) } - diff --git a/R/output.R b/R/output.R index d8983df..827f8b9 100644 --- a/R/output.R +++ b/R/output.R @@ -29,7 +29,7 @@ summary.rjd3rev_revision_analysis<- function(x){ font.weight = ifelse(substr(x,1,1) == "S", "bold", "plain"))) } nc<-ncol(x$summary) - return(list(formattable::formattable(x$summary, apply(x$summary[,2:nc,drop=F], 2, format_font)))) + return(list(formattable::formattable(x$summary, apply(x$summary[,2:nc,drop=FALSE], 2, format_font)))) } } @@ -51,5 +51,3 @@ plot.rjd3rev_revision_analysis <- function(x, ...){ legend("topleft", bty="n", lty=1,lwd=2, col=c(1:nc), legend=colnames(rev)) title(main = "Size of Revisions") } - - diff --git a/R/report.R b/R/report.R index 30b03a9..0acf0ef 100644 --- a/R/report.R +++ b/R/report.R @@ -1,14 +1,14 @@ #' Generate report on Revision Analysis #' -#' @param rslt an object of class `"rjd3rev_vintages"` which is the output +#' @param rslt an object of class `"rjd3rev_vintages"` which is the output #' of the function `revision_analysis()` #' @param path.out path of the output HTML file containing the report. Default #' is NULL meaning that the report will be saved in the working -#' directory with a generic name. +#' directory with a generic name. #' @param open.report Boolean. Default is TRUE meaning that the report will #' open automatically after being generated. #' @seealso `revision_analysis()` to create the input object -#' +#' #' @export #' #' @examples @@ -17,7 +17,7 @@ #' qtr<-(as.numeric(substr(period_range,6,7))+2)/3 #' time_period<-rep(paste0(format(period_range, "%Y"), "Q", qtr),5) #' np<-length(period_range) -#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), #' rep("2022-12-31",np), rep("2023-06-30",np)) #' set.seed(1) #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) @@ -28,21 +28,21 @@ #' obs_values<-c(obs_values,xt) #' } #' df<-data.frame(rev_date, time_period, obs_values) -#' +#' #' ## Make analysis and generate the report #' vintages<-create_vintages(df, periodicity = 4) #' rslt<-revision_analysis(vintages, view = "diagonal") #' \dontrun{ #' get_report(rslt) #' } -#' +#' get_report <- function(rslt, path.out = NULL, - open.report=T) { - + open.report=TRUE) { + #template_file<-"report.Rmd" template_file<-system.file("templates/report.Rmd", package = "rjd3revisions") - + if(is.null(path.out)){ path.out<-paste0(getwd(),"/","revisions_report.html") }else{ @@ -50,15 +50,15 @@ get_report <- function(rslt, paste0(path.out,".html"), path.out) } - + e<-new.env(parent = baseenv()) assign("descriptive_statistics", rslt$descriptive.statistics, envir = e) assign("main_results", rslt$summary, envir = e) - - rmarkdown::render(input = template_file, + + rmarkdown::render(input = template_file, output_file = path.out, - output_options = list(self_contained = F, mathjax = "local"), + output_options = list(self_contained = FALSE, mathjax = "local"), envir = e) - - if(open.report) utils::browseURL(path.out) + + if(open.report) utils::browseURL(path.out) } diff --git a/R/revision_analysis.R b/R/revision_analysis.R index edc7eaa..911305d 100644 --- a/R/revision_analysis.R +++ b/R/revision_analysis.R @@ -1,5 +1,5 @@ #' Revision analysis through a battery of tests -#' +#' #' The function perform parametric tests which enable the users to detect #' potential bias (both mean and regression bias) and sources of inefficiency in #' preliminary estimates. We would conclude to inefficiency in the preliminary @@ -15,50 +15,50 @@ #' running the function `get_report()` on the output of `revision_analysis()` #' would give you both a formatted summary of the results and full explanations #' about each tests. -#' -#' @param vintages an object of class `"rjd3rev_vintages"` which is the output +#' +#' @param vintages an object of class `"rjd3rev_vintages"` which is the output #' of the function `create_vintages()` -#' @param gap Integer. Gap to consider between each vintages. Default is 1 +#' @param gap Integer. Gap to consider between each vintages. Default is 1 #' which means that revisions are calculated and tested for each #' vintages consecutively. #' @param view Selected view. Can be "vertical" (the default) or "diagonal". -#' Vertical view shows the observed values at each time period by +#' Vertical view shows the observed values at each time period by #' the different vintages. Diagonal view shows subsequent releases -#' of a given time period, without regard for the date of -#' publication, which can be particularly informative when regular +#' of a given time period, without regard for the date of +#' publication, which can be particularly informative when regular #' estimation intervals exist. See `?create_vintages()` for more #' information about interests and drawbacks of each view. -#' @param n.releases only used when `view = "diagonal"`. Ignored otherwise. -#' Allow the user to limit the number of releases under +#' @param n.releases only used when `view = "diagonal"`. Ignored otherwise. +#' Allow the user to limit the number of releases under #' investigation). When `view = "vertical"`, the user is #' invited to limit the number of vintages upstream through #' the parameter `vintage.selection` in `create_vintages()` #' whenever necessary. -#' @param transf.diff differentiation to apply to the data prior testing. Only +#' @param transf.diff differentiation to apply to the data prior testing. Only #' used for regressions including vintage data as regressor -#' and/or regressand. Regression including revision data only -#' are never differentiated even if `transf.diff = "forced"`. +#' and/or regressand. Regression including revision data only +#' are never differentiated even if `transf.diff = "forced"`. #' Options are "automatic" (the default), "forced" and "none". -#' @param transf.log Boolean whether a log-transformation should first be -#' applied to the data. Default is FALSE. -#' @param descriptive.rounding Integer. Number of decimals to display for +#' @param transf.log Boolean whether a log-transformation should first be +#' applied to the data. Default is FALSE. +#' @param descriptive.rounding Integer. Number of decimals to display for #' descriptive statistics. Default is 3. -#' @param nrevs,ref Integer. Number of lags to consider for orthogonality tests +#' @param nrevs,ref Integer. Number of lags to consider for orthogonality tests #' 1 and 2 respectively. -#' @param na.zero Boolean whether missing values should be considered as 0 or +#' @param na.zero Boolean whether missing values should be considered as 0 or #' rather as data not yet available (the default). -#' +#' #' @import rJava rjd3toolkit -#' -#' @seealso `create_vintages()` to create the input object, -#' `get_report()` to get a summary and information the tests -#' +#' +#' @seealso `create_vintages()` to create the input object, +#' `get_report()` to get a summary and information the tests +#' #' @return an object of class `"rjd3rev_revision_analysis"` -#' +#' #' @export -#' +#' #' @examples -#' +#' #' ## Simulated data #' period_range<-seq(as.Date('2011-01-01'),as.Date('2020-10-01'),by='quarter') #' qtr<-(as.numeric(substr(period_range,6,7))+2)/3 @@ -75,16 +75,16 @@ #' obs_values<-c(obs_values,xt) #' } #' df<-data.frame(rev_date, time_period, obs_values) -#' +#' #' ## Create a `"rjd3rev_vintages"` object with the input #' vintages<-create_vintages(df, periodicity = 4, revdate.format= "%Y-%m-%d") #' # revisions<-get_revisions(vintages, gap = 1) # just to get a first insight of the revisions -#' +#' #' ## Call using all default parameters #' rslt1<-revision_analysis(vintages) #' #get_report(rslt1) #' #summary(rslt1) # formatted summary only -#' +#' #' ## Calls using diagonal view (suited in many situations such as to evaluate GDP estimates) #' ## Note: when input are not growth rates but the gross series, differentiation is #' ## performed automatically (if transf.diff is let to its default option) but `transf.log` @@ -92,94 +92,94 @@ #' rslt2<-revision_analysis(vintages, gap = 1, view = "diagonal", n.releases = 3) #' #get_report(rslt2) #' #summary(rslt2) -#' +#' #' ## Call to evaluate revisions for a specific range of vintage periods #' vintages<-create_vintages(df, periodicity = 4, vintage.selection = list(start="2021-12-31", end="2023-06-30")) #' rslt3<-revision_analysis(vintages, gap=2, view = "vertical") #' #get_report(rslt3) #' #summary(rslt3) #' -revision_analysis<-function(vintages, +revision_analysis<-function(vintages, gap = 1, view = c("vertical", "diagonal"), n.releases = 3, transf.diff = c("auto", "forced", "none"), - transf.log = F, - descriptive.rounding = 3, - nrevs = 1, + transf.log = FALSE, + descriptive.rounding = 3, + nrevs = 1, ref = 1, - na.zero=F){ - + na.zero=FALSE){ + options(scipen = 999) - + cl<-match.call() - + out <- list() class(out) <- "rjd3rev_revision_analysis" - + view<-match.arg(view) transf.diff<-match.arg(transf.diff) - + if(is.null(vintages)) stop("No vintage found!") if(n.releases<(1+gap)) stop("'n.releases' must be >= (1+gap)") - + # Input selection - + ## Select vintage view if(view == "vertical"){ vt<-vintages$vertical_view }else if (view == "diagonal"){ vt<-vintages$diagonal_view[,1:n.releases] } - - ## Revisions and Vintages Transformation + + ## Revisions and Vintages Transformation rv_notrf<-get_vd_rev(vt, gap) freq<-frequency(vt) - + ### Log transformation if(transf.log){ if(length(vt[vt[!is.na(vt)] < 0])>0){ - warning("Logarithm transformation incompatible with negative data. No transformation considered.",call.=F) + warning("Logarithm transformation incompatible with negative data. No transformation considered.",call.=FALSE) rv<-rv_notrf - is_log<-F + is_log<-FALSE }else{ vt<-log(vt) rv<-get_vd_rev(vt, gap) - is_log<-T + is_log<-TRUE } }else{ rv<-rv_notrf - is_log<-F + is_log<-FALSE } - + ### Differentiation ur<-unitroot(vt, adfk=1, na.zero) # H0: non-stationary if(!is.null(ur)){ ur_rslt<-t(round(ur,3)) ur_ADFpvals<-ur[,"ADF.pvalue"] pc_signif_ur<-length(ur_ADFpvals[ur_ADFpvals<.05])/length(ur_ADFpvals) - is_stationary<-ifelse(pc_signif_ur>.8,T,F) + is_stationary<-ifelse(pc_signif_ur>.8,TRUE,FALSE) }else{ ur_rslt<-NULL - is_stationary<-T + is_stationary<-TRUE } - + coint<-cointegration(vt, adfk=1, na.zero) # H0: no-cointegration if(is_stationary){ - is_cointegrated<-T + is_cointegrated<-TRUE }else{ if(!is.null(coint)){ coint_pvals<-coint[,"pvalue"] pc_signif_coint<-length(coint_pvals[coint_pvals<.05])/length(coint_pvals) - is_cointegrated<-ifelse(pc_signif_coint>.8,T,F) + is_cointegrated<-ifelse(pc_signif_coint>.8,TRUE,FALSE) }else{ - is_cointegrated<-F + is_cointegrated<-FALSE } } - + seasonality<-apply(vt,2,check_seasonality) nt<-sum(seasonality) - is_seasonal<-ifelse(nt/ncol(vt)>.8,T,F) + is_seasonal<-ifelse(nt/ncol(vt)>.8,TRUE,FALSE) if(is_seasonal){ vt_diff<-diff(vt, freq) delta_diff<-freq @@ -187,28 +187,28 @@ revision_analysis<-function(vintages, vt_diff<-diff(vt) delta_diff<-1 } - + if(transf.diff == "auto"){ vts<-if(is_stationary) vt else vt_diff vtc<-if(is_cointegrated) vt else vt_diff }else if(transf.diff == "forced"){ vts<-vtc<-vt_diff - is_stationary<-is_cointegrated<-F + is_stationary<-is_cointegrated<-FALSE }else if(transf.diff == "none"){ vts<-vtc<-vt if(!is_stationary | !is_cointegrated){ - warning("No differentiation considered even though stationarity and/or cointegration might not be present. This can lead to spurious regression.",call.=F) + warning("No differentiation considered even though stationarity and/or cointegration might not be present. This can lead to spurious regression.",call.=FALSE) } - is_stationary<-is_cointegrated<-T + is_stationary<-is_cointegrated<-TRUE } - + # Descriptive statistics ds<-descriptive_statistics(rv_notrf,descriptive.rounding) - + # Parametric analysis - + ## I. Relevancy - + ### Theil U1 and U2 N<-apply(rv_notrf,2,function(x) length(x[!is.na(x)])) U_det<-"U" @@ -217,181 +217,181 @@ revision_analysis<-function(vintages, U2<-theil2(vt, gap, na.zero) if(!is.null(U1)){ theil_rslt<-round(rbind(N,U1),3) - if(!is.null(U2) && !all(is.nan(U2))==T){ + if(!is.null(U2) && !all(is.nan(U2))==TRUE){ theil_rslt<-rbind(theil_rslt,U2=round(U2,3)) theil_q<-eval_U(U2) U_det<-"U2" }else{ theil_rslt<-rbind(theil_rslt,U2=rep(NA,length(U1))) - theil_q<-eval_U(U1,U2=F) + theil_q<-eval_U(U1,U2=FALSE) U_det<-"U1" - warning("Theil U2 could not be calculated. Theil U1 is considered instead in summary().",call.=F) + warning("Theil U2 could not be calculated. Theil U1 is considered instead in summary().",call.=FALSE) } }else{ theil_rslt<-NULL theil_q<-rep(NA,length(colnames(rv))) - } - + } + ## II. Bias (mean and regression bias) - + ### II.1_2. T-test and Augmented T-test ta_trf<-ifelse(is_log,"Log","None") ta<-bias(rv, na.zero) if(!is.null(ta)){ - ta_rslt<-t(round(ta,3)) - t_q<-eval_pvals(ta[,"pvalue"], h0_good=T) - ta_q<-eval_pvals(ta[,"pvalue.adjusted"], h0_good=T) + ta_rslt<-t(round(ta,3)) + t_q<-eval_pvals(ta[,"pvalue"], h0_good=TRUE) + ta_q<-eval_pvals(ta[,"pvalue.adjusted"], h0_good=TRUE) }else{ ta_rslt<-NULL t_q<-ta_q<-rep(NA,length(colnames(rv))) } - + ### II.3. Slope and drift sd_trf<-if (is_cointegrated && !is_log) "None" else if (is_cointegrated && is_log) "Log" else - if (!is_cointegrated && !is_log) paste("Delta", delta_diff) else + if (!is_cointegrated && !is_log) paste("Delta", delta_diff) else paste("Delta-Log", delta_diff) sd<-slope_and_drift(vtc, gap, na.zero) if(!is.null(sd)){ sd_rslt<-format_reg_output(sd,is_log,!is_cointegrated) - sd_m_q<-eval_pvals(sd[,"intercept.pvalue"], h0_good=T) - sd_r_q<-eval_pvals(sd[,"slope.pvalue"], h0_good=T) + sd_m_q<-eval_pvals(sd[,"intercept.pvalue"], h0_good=TRUE) + sd_r_q<-eval_pvals(sd[,"slope.pvalue"], h0_good=TRUE) sd_diagnostics<-regression_diagnostics(sd) }else{ sd_rslt<-sd_diagnostics<-NULL sd_m_q<-sd_r_q<-rep(NA,length(colnames(vtc)[-c(1:gap)])) } - + ## III. Efficiency - + ### III.1. Regression of revision on previous estimate (=noise) eff1_trf<-if (is_stationary && !is_log) "None" else if (is_stationary && is_log) "Log" else - if (!is_stationary && !is_log) paste("Delta", delta_diff) else + if (!is_stationary && !is_log) paste("Delta", delta_diff) else paste("Delta-Log", delta_diff) eff1<-efficiencyModel1(vts, gap, na.zero) if(!is.null(eff1)){ eff1_rslt<-format_reg_output(eff1, is_log, !is_stationary) - eff1_m_q<-eval_pvals(eff1[,"intercept.pvalue"],h0_good=T) - eff1_r_q<-eval_pvals(eff1[,"slope.pvalue"],h0_good=T) + eff1_m_q<-eval_pvals(eff1[,"intercept.pvalue"],h0_good=TRUE) + eff1_r_q<-eval_pvals(eff1[,"slope.pvalue"],h0_good=TRUE) eff1_diagnostics<-regression_diagnostics(eff1) }else{ eff1_rslt<-eff1_diagnostics<-NULL eff1_m_q<-eff1_r_q<-rep(NA,length(colnames(rv))) } - + ### III.2. Regression of latter revisions (Rv) on previous revisions (Rv_1) eff2_trf<-ifelse(is_log,"Log","None") eff2<-efficiencyModel2(vt, gap, na.zero) if(!is.null(eff2)){ - eff2_rslt<-format_reg_output(eff2, is_log, F) - eff2_m_q<-c("",eval_pvals(eff2[,"intercept.pvalue"],h0_good=T)) - eff2_r_q<-c("",eval_pvals(eff2[,"slope.pvalue"],h0_good=T)) + eff2_rslt<-format_reg_output(eff2, is_log, FALSE) + eff2_m_q<-c("",eval_pvals(eff2[,"intercept.pvalue"],h0_good=TRUE)) + eff2_r_q<-c("",eval_pvals(eff2[,"slope.pvalue"],h0_good=TRUE)) eff2_diagnostics<-regression_diagnostics(eff2) }else{ eff2_rslt<-eff2_diagnostics<-NULL eff2_m_q<-eff2_r_q<-c("",rep(NA,length(colnames(rv)[-1]))) } - + ## IV. Orthogonality - + ### IV.1. Regression of latter revisions (Rv) on previous revisions (Rv_1, Rv_2,...Rv_p) orth1_trf<-ifelse(is_log,"Log","None") orth1<-orthogonallyModel1(rv, nrevs, na.zero) if(!is.null(orth1)){ - orth1_rslt<-format_reg_output(orth1,is_log, F) - orth1_m_q<-c(rep("",nrevs),eval_pvals(orth1[,"intercept.pvalue"],h0_good=T)) - orth1_r_q<-c(rep("",nrevs),eval_pvals(pf(orth1[,"F"], nrevs, orth1[,"N"]-nrevs-1),h0_good=T)) + orth1_rslt<-format_reg_output(orth1,is_log, FALSE) + orth1_m_q<-c(rep("",nrevs),eval_pvals(orth1[,"intercept.pvalue"],h0_good=TRUE)) + orth1_r_q<-c(rep("",nrevs),eval_pvals(pf(orth1[,"F"], nrevs, orth1[,"N"]-nrevs-1),h0_good=TRUE)) orth1_diagnostics<-regression_diagnostics(orth1) }else{ orth1_rslt<-orth1_diagnostics<-NULL if(ncol(rv)>nrevs) orth1_m_q<-orth1_r_q<-c(rep("",nrevs),rep(NA,length(colnames(rv)[-c(1:nrevs)]))) else orth1_m_q<-orth1_r_q<-rep("",nrevs) } - + ### IV.2. Regression model of latter revisions (Rv) on previous revisions at a specific version (Rv_k) orth2_trf<-ifelse(is_log,"Log","None") orth2<-orthogonallyModel2(rv, ref, na.zero) if(!is.null(orth2)){ - orth2_rslt<-format_reg_output(orth2, is_log, F) - orth2_m_q<-c(rep("",ref),eval_pvals(orth2[,"intercept.pvalue"],h0_good=T)) - orth2_r_q<-c(rep("",ref),eval_pvals(orth2[,"slope.pvalue"],h0_good=T)) + orth2_rslt<-format_reg_output(orth2, is_log, FALSE) + orth2_m_q<-c(rep("",ref),eval_pvals(orth2[,"intercept.pvalue"],h0_good=TRUE)) + orth2_r_q<-c(rep("",ref),eval_pvals(orth2[,"slope.pvalue"],h0_good=TRUE)) orth2_diagnostics<-regression_diagnostics(orth2) }else{ orth2_rslt<-orth2_diagnostics<-NULL if(ncol(rv)>ref) orth2_m_q<-orth2_r_q<-c(rep("",ref),rep(NA,length(colnames(rv)[-c(1:ref)]))) else orth2_m_q<-orth2_r_q<-rep("",ref) } - + ### IV.3. Autocorrelation test ac_trf<-ifelse(is_log,"Log","None") - ac_trf_str<-ifelse(ac_trf == "Log", get_info_transformation(T,F), get_info_transformation(F,F)) - pm_test<-try(apply(rv,2,function(x) ljungbox(x[!is.na(x)],k=2)),silent=T) # Ljung-Box up to k - + ac_trf_str<-ifelse(ac_trf == "Log", get_info_transformation(TRUE,FALSE), get_info_transformation(FALSE,FALSE)) + pm_test<-try(apply(rv,2,function(x) ljungbox(x[!is.na(x)],k=2)),silent=TRUE) # Ljung-Box up to k + if(!"try-error" %in% class(pm_test)){ - pm_test_mat<-matrix(unlist(pm_test), ncol=2, byrow=T)[,,drop=F] - dimnames(pm_test_mat)<-list(colnames(rv), c("value","p.value")) + pm_test_mat<-matrix(unlist(pm_test), ncol=2, byrow=TRUE)[,,drop=FALSE] + dimnames(pm_test_mat)<-list(colnames(rv), c("value","p.value")) ac_rslt<-list(info_transformation=ac_trf_str, estimates_ljungbox=pm_test_mat) - ac_q<-eval_pvals(ac_rslt$estimates_ljungbox[,"p.value"], h0_good=T) + ac_q<-eval_pvals(ac_rslt$estimates_ljungbox[,"p.value"], h0_good=TRUE) }else{ ac_rslt<-NULL ac_q<-rep(NA, length(colnames(rv))) } - + ### IV.4. Seasonality test seas_trf<- ifelse(is_log,"Delta-Log 1","Delta 1") - seas_trf_str<-ifelse(seas_trf == "Delta-Log 1", get_info_transformation(T,T), get_info_transformation(F,T)) - lb_test<-try(apply(diff(rv),2,function(x) seasonality_qs(x,freq)),silent=T) # Ljung-Box - fd_test<-try(apply(diff(rv),2,function(x) seasonality_friedman(x,freq)),silent=T) # Friedman non-parametric test - + seas_trf_str<-ifelse(seas_trf == "Delta-Log 1", get_info_transformation(TRUE,TRUE), get_info_transformation(FALSE,TRUE)) + lb_test<-try(apply(diff(rv),2,function(x) seasonality_qs(x,freq)),silent=TRUE) # Ljung-Box + fd_test<-try(apply(diff(rv),2,function(x) seasonality_friedman(x,freq)),silent=TRUE) # Friedman non-parametric test + if(!"try-error" %in% class(lb_test) & !"try-error" %in% class(fd_test) & freq>1){ seas_rslt<-list(info_transformation=seas_trf_str, - estimates_ljungbox=matrix(unlist(lb_test), ncol=2, byrow = T, dimnames = list(colnames(rv), c("value","p.value"))), - estimates_friedman=matrix(unlist(fd_test), ncol=2, byrow = T, dimnames = list(colnames(rv), c("value","p.value")))) - seas_lb_q<-eval_pvals(seas_rslt$estimates_ljungbox[,"p.value"], h0_good=T) - seas_fd_q<-eval_pvals(seas_rslt$estimates_friedman[,"p.value"], h0_good=T) + estimates_ljungbox=matrix(unlist(lb_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value","p.value"))), + estimates_friedman=matrix(unlist(fd_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value","p.value")))) + seas_lb_q<-eval_pvals(seas_rslt$estimates_ljungbox[,"p.value"], h0_good=TRUE) + seas_fd_q<-eval_pvals(seas_rslt$estimates_friedman[,"p.value"], h0_good=TRUE) }else if(!"try-error" %in% class(lb_test) & freq>1){ seas_rslt<-list(info_transformation=seas_trf_str, - estimates_ljungbox=matrix(unlist(lb_test), ncol=2, byrow = T, dimnames = list(colnames(rv), c("value","p.value"))), + estimates_ljungbox=matrix(unlist(lb_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value","p.value"))), estimates_friedman=NULL) - seas_lb_q<-eval_pvals(seas_rslt$estimates_ljungbox[,"p.value"], h0_good=T) + seas_lb_q<-eval_pvals(seas_rslt$estimates_ljungbox[,"p.value"], h0_good=TRUE) seas_fd_q<-rep(NA, length(colnames(rv))) }else if(!"try-error" %in% class(fd_test) & freq>1){ seas_rslt<-list(info_transformation=seas_trf_str, estimates_ljungbox=NULL, - estimates_friedman=matrix(unlist(fd_test), ncol=2, byrow = T, dimnames = list(colnames(rv), c("value","p.value")))) + estimates_friedman=matrix(unlist(fd_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value","p.value")))) seas_lb_q<-rep(NA, length(colnames(rv))) - seas_fd_q<-eval_pvals(seas_rslt$estimates_friedman[,"p.value"], h0_good=T) + seas_fd_q<-eval_pvals(seas_rslt$estimates_friedman[,"p.value"], h0_good=TRUE) }else{ seas_rslt<-NULL seas_lb_q<-seas_fd_q<-rep(NA, length(colnames(rv))) } - + ## V. Signal vs Noise sn_trf<-if(is_stationary && !is_log) "None" else if(is_stationary && is_log) "Log" else - if(!is_stationary && !is_log) paste("Delta", delta_diff) else + if(!is_stationary && !is_log) paste("Delta", delta_diff) else paste("Delta-Log", delta_diff) sn<-signalnoise(vts, gap, na.zero) if(!is.null(sn)){ sn_rslt<-list(info_transformation=get_info_transformation(is_log, !is_stationary), estimates=t(round(sn,3))) - sn_noise_q<-eval_pvals(sn[,"Noise.pvalue"], h0_good=T) - sn_news_q<-eval_pvals(sn[,"News.pvalue"], h0_good=F) + sn_noise_q<-eval_pvals(sn[,"Noise.pvalue"], h0_good=TRUE) + sn_news_q<-eval_pvals(sn[,"News.pvalue"], h0_good=FALSE) }else{ sn_rslt<-NULL sn_noise_q<-sn_news_q<-rep(NA,colnames(rv)) } - - + + # VAR-based Analysis - + ## 1. Unit root test - ## see before - + ## see before + ## 2. Cointegration test if(!is.null(coint)) coint_rslt<-round(coint, 3) - + ## 3. VECM errcorr<-vecm(vt, lag=2, model="none", na.zero) if(!is.null(errcorr)){ @@ -399,35 +399,35 @@ revision_analysis<-function(vintages, }else{ vecm_rslt<-NULL } - + var_based_rslt<-list(unit_root_test = ur_rslt, cointegration_test = coint_rslt, vecm = vecm_rslt) - - + + # Output - lbl<-c(paste("Relevancy - Theil", U_det), "Bias1 T-test", "Bias2 Augmented T-test", - "Bias3 SlopeAndDrift (Ols L on P) - Mean", "Bias3 SlopeAndDrift (Ols L on P) - Reg.", + lbl<-c(paste("Relevancy - Theil", U_det), "Bias1 T-test", "Bias2 Augmented T-test", + "Bias3 SlopeAndDrift (Ols L on P) - Mean", "Bias3 SlopeAndDrift (Ols L on P) - Reg.", "Efficiency1 (Ols R on P) - Mean", "Efficiency1 (Ols R on P) - Reg.", "Efficiency2 (Ols Rv on Rv_1) - Mean", "Efficiency2 (Ols Rv on Rv_1) - Reg.", "Orthogonality1 (Ols Rv on Rv_(1:p)) - Mean", "Orthogonality1 (Ols Rv on Rv_(1:p)) - Reg.", "Orthogonality2 (Ols Rv on Rv_k.) - Mean", "Orthogonality2 (Ols Rv on Rv_k) - Reg.", - "Orthogonality3 AutoCorrelation (Ljung-Box)", + "Orthogonality3 AutoCorrelation (Ljung-Box)", "Orthogonality4 Seasonality (Ljung-Box)", "Orthogonality4 Seasonality (Friedman)", "SignalVsNoise1 - Noise (Ols R on P)", "SignalVsNoise2 - Signal (Ols R on L)") transformation<-c(theil_trf,rep(ta_trf,2),rep(sd_trf,2),rep(eff1_trf,2), - rep(eff2_trf,2), rep(orth1_trf,2), rep(orth2_trf,2), + rep(eff2_trf,2), rep(orth1_trf,2), rep(orth2_trf,2), ac_trf, rep(seas_trf,2) ,rep(sn_trf,2)) - evals<-rbind(theil_q, t_q, ta_q, sd_m_q, sd_r_q, eff1_m_q, eff1_r_q, eff2_m_q, - eff2_r_q, orth1_m_q, orth1_r_q, orth2_m_q, orth2_r_q, - ac_q, seas_lb_q, seas_fd_q, sn_noise_q, sn_news_q) + evals<-rbind(theil_q, t_q, ta_q, sd_m_q, sd_r_q, eff1_m_q, eff1_r_q, eff2_m_q, + eff2_r_q, orth1_m_q, orth1_r_q, orth2_m_q, orth2_r_q, + ac_q, seas_lb_q, seas_fd_q, sn_noise_q, sn_news_q) summary_table<-data.frame(transformation, evals, row.names = lbl) - colnames(summary_table)<- c("Transf.",colnames(rv)) - + colnames(summary_table)<- c("Transf.",colnames(rv)) + diagnostics_table <- list(slope_and_drift = sd_diagnostics, efficiency1 = eff1_diagnostics, efficiency2 = eff2_diagnostics, orthogonality1 = orth1_diagnostics, orthogonality2 = orth2_diagnostics) - + out$call <- cl out$revisions <- rv_notrf out$descriptive.statistics <- ds @@ -436,13 +436,13 @@ revision_analysis<-function(vintages, out$relevancy <- list(theil=theil_rslt) out$bias <- list(t_ta_test=ta_rslt, slope_and_drift=sd_rslt) out$efficiency <- list(efficiency1=eff1_rslt, efficiency2=eff2_rslt) - out$orthogonality <- list(orthogonality1=orth1_rslt, orthogonality2=orth2_rslt, + out$orthogonality <- list(orthogonality1=orth1_rslt, orthogonality2=orth2_rslt, autocorrelation_test=ac_rslt, seasonality_test=seas_rslt) - out$signalnoise <- list(signal_noise=sn_rslt) + out$signalnoise <- list(signal_noise=sn_rslt) out$varbased<-var_based_rslt - + options(scipen = 0) - + return(out) } @@ -459,9 +459,9 @@ get_rownames_diag <- function(vt, gap){ } -eval_pvals<-function(pval, h0_good = T, residuals = F){ +eval_pvals<-function(pval, h0_good = TRUE, residuals = FALSE){ pval<-as.numeric(pval) - + if(! residuals){ if(h0_good){ quality<-ifelse(pval>.05, "Good", @@ -479,13 +479,13 @@ eval_pvals<-function(pval, h0_good = T, residuals = F){ } } quality[is.na(quality)]<-"Good" - + return(paste0(quality, " (", trimws(format(round(pval,3), nsmall=3)), ")")) } -eval_U<-function(U, U2=T){ +eval_U<-function(U, U2=TRUE){ U<-as.numeric(U) - + if(U2){ quality<-ifelse(U>=1, "Severe", ifelse(U>.9, "Bad", @@ -496,21 +496,21 @@ eval_U<-function(U, U2=T){ ifelse(U>.8, "Uncertain", "Good"))) } quality[is.na(quality)]<-"Good" - + return(paste0(quality, " (", trimws(format(round(U,3), nsmall=3)), ")")) } format_reg_output<-function(x, is_log, is_diff){ info_transformation<-get_info_transformation(is_log, is_diff) - - x_df<-as.data.frame(t(round(x,3))) + + x_df<-as.data.frame(t(round(x,3))) n<-nrow(x_df) - estim<-x_df[1:(n-13),,drop=F] - - norm_test<-list(Jarque_Bera_test=x_df[(n-12):(n-9),,drop=F]) - hsk_test<-list(Breusch_Pagan_test=x_df[(n-8):(n-6),,drop=F],White_test=x_df[(n-5):(n-3),,drop=F],ARCH_test=x_df[(n-2):n,,drop=F]) + estim<-x_df[1:(n-13),,drop=FALSE] + + norm_test<-list(Jarque_Bera_test=x_df[(n-12):(n-9),,drop=FALSE]) + hsk_test<-list(Breusch_Pagan_test=x_df[(n-8):(n-6),,drop=FALSE],White_test=x_df[(n-5):(n-3),,drop=FALSE],ARCH_test=x_df[(n-2):n,,drop=FALSE]) tests<-list(normality=norm_test, homoskedasticity=hsk_test) - + return(list(info_transformation=info_transformation,estimates=estim,residuals=tests)) } @@ -529,52 +529,52 @@ get_info_transformation<-function(is_log, is_diff){ } regression_diagnostics<-function(reg_output){ - - jb<-eval_pvals(reg_output[,"JarqueBera.pvalue"], residuals=T) - bp<-eval_pvals(reg_output[,"BreuschPagan.pvalue"], residuals=T) - wh<-eval_pvals(reg_output[,"White.pvalue"], residuals=T) - arch<-eval_pvals(reg_output[,"arch.pvalue"], residuals=T) - + + jb<-eval_pvals(reg_output[,"JarqueBera.pvalue"], residuals=TRUE) + bp<-eval_pvals(reg_output[,"BreuschPagan.pvalue"], residuals=TRUE) + wh<-eval_pvals(reg_output[,"White.pvalue"], residuals=TRUE) + arch<-eval_pvals(reg_output[,"arch.pvalue"], residuals=TRUE) + lbl<-c("Jarque-Bera", "Breusch-Pagan", "White", "ARCH") tests<-c("Normality", rep("Homoskedasticity",3)) tests_rslts<-rbind(jb,bp,wh,arch) - + rslt<-`colnames<-`(data.frame(tests, tests_rslts, row.names = lbl), c("Test",rownames(reg_output))) - + return(rslt) } get_vd_rev <- function(vt, gap){ n<-dim(vt)[2] - + idx1<-(gap+1):n idx0<-1:(n-gap) - - rev<-vt[,idx1,drop=F]-vt[,idx0,drop=F] - + + rev<-vt[,idx1,drop=FALSE]-vt[,idx0,drop=FALSE] + w<-sapply(colnames(vt), function(s){paste0('[', s, ']')}) rw<-mapply(function(a,b){paste(a,b,sep='-')}, w[idx1],w[idx0]) - + rev<-`colnames<-`(rev, rw) return (rev) } check_seasonality <- function(x){ - + if(frequency(x)>1){ x_diff<-diff(x) - lb_pval<-try(seasonality_qs(x_diff,frequency(x))$pvalue, silent=T) # Ljung-Box - fd_pval<-try(seasonality_friedman(x_diff,frequency(x))$pvalue, silent=T) # Friedman non-parametric test - + lb_pval<-try(seasonality_qs(x_diff,frequency(x))$pvalue, silent=TRUE) # Ljung-Box + fd_pval<-try(seasonality_friedman(x_diff,frequency(x))$pvalue, silent=TRUE) # Friedman non-parametric test + test_succeeded<-c(!"try-error" %in% class(lb_pval), !"try-error" %in% class(fd_pval)) if(all(test_succeeded)){ pvals<-c(lb_pval, fd_pval) - seasonality<-ifelse(length(pvals[which(pvals<.05)])==2, T, F) + seasonality<-ifelse(length(pvals[which(pvals<.05)])==2, TRUE, FALSE) }else if(any(test_succeeded)){ if(test_succeeded[1]){ - seasonality<-ifelse(lb_pval<.01,T,F) + seasonality<-ifelse(lb_pval<.01,TRUE,FALSE) }else if(test_succeeded[2]){ - seasonality<-ifelse(fd_pval<.01,T,F) + seasonality<-ifelse(fd_pval<.01,TRUE,FALSE) } }else{ seasonality<-FALSE diff --git a/R/revisions.R b/R/revisions.R index 9b10360..67fc490 100644 --- a/R/revisions.R +++ b/R/revisions.R @@ -1,14 +1,14 @@ #' Calculate revisions from vintages #' -#' @param vintages an object of class `"rjd3rev_vintages"` +#' @param vintages an object of class `"rjd3rev_vintages"` #' @param gap Integer. Gap to consider between each vintages to calculate #' revision. Default is 1 which means that revisions are #' calculated for each vintages consecutively. -#' +#' #' @seealso `create_vintages()` -#' +#' #' @return a list with revisions calculated for the three vintage views -#' +#' #' @export #' #' @examples @@ -23,31 +23,31 @@ #' .7,.2,.7,.4, .7,.3,.7,.3)) #' vintages<-create_vintages(df, periodicity = 4) #' revisions<-get_revisions(vintages, gap=1) -#' +#' get_revisions<-function(vintages, gap=1){ if(!class(vintages)=="rjd3rev_vintages"){ warning("Wrong input. vintages must be an object of class 'rjd3rev_vintages'.") return(NULL) } - + get_vd_rev <- function(vt, gap){ n<-dim(vt)[2] - + idx1<-(gap+1):n idx0<-1:(n-gap) - - rev<-vt[,idx1,drop=F]-vt[,idx0,drop=F] - + + rev<-vt[,idx1,drop=FALSE]-vt[,idx0,drop=FALSE] + w<-sapply(colnames(vt), function(s){paste0('[', s, ']')}) rw<-mapply(function(a,b){paste(a,b,sep='-')}, w[idx1],w[idx0]) - + rev<-`colnames<-`(rev, rw) return (rev) } - + vr<-get_vd_rev(vintages$vertical_view, gap) hr<-`colnames<-`(t(vr),colnames(vintages$horizontal_view)) dr<-get_vd_rev(vintages$diagonal_view, gap) - + return (list(vertical_view=vr, horizontal_view=hr, diagonal_view=dr)) -} \ No newline at end of file +} diff --git a/R/tests.R b/R/tests.R index 148dc51..23f6a74 100644 --- a/R/tests.R +++ b/R/tests.R @@ -4,19 +4,19 @@ biasNames<-c("N", "estimate", "stderr", "tstat", "pvalue", "ar(1)", "stderr.adju OlsNames<-c("N", "R2", "F", "intercept.estimate", "intercept.stderr", "intercept.pvalue", "slope.estimate", "slope.stderr", "slope.pvalue", - "skewness", "kurtosis", "JarqueBera.value", "JarqueBera.pvalue", + "skewness", "kurtosis", "JarqueBera.value", "JarqueBera.pvalue", "BreuschPagan.R2", "BreuschPagan.value", "BreuschPagan.pvalue", - "White.R2", "White.value", "White.pvalue", + "White.R2", "White.value", "White.pvalue", "arch.R2", "arch.value", "arch.pvalue") -OlsTestNames<-c("skewness", "kurtosis", "JarqueBera.value", "JarqueBera.pvalue", +OlsTestNames<-c("skewness", "kurtosis", "JarqueBera.value", "JarqueBera.pvalue", "BreuschPagan.R2", "BreuschPagan.value", "BreuschPagan.pvalue", - "White.R2", "White.value", "White.pvalue", + "White.R2", "White.value", "White.pvalue", "arch.R2", "arch.value", "arch.pvalue") OlsAdjNames<-c("N", "R2", "F") -acNames<-c("BreuschGodfrey.R2", "BreuschGodfrey.value", "BreuschGodfrey.pvalue", +acNames<-c("BreuschGodfrey.R2", "BreuschGodfrey.value", "BreuschGodfrey.pvalue", "LungBox.value", "LungBox.pvalue") urNames<-c("DF.value", "DF.stderr", "DF.statistic", "DF.pvalue", @@ -30,13 +30,13 @@ snNames<-c("News.R2", "News.F", "News.pvalue", "Noise.R2", "Noise.F", "Noise.pva OlsCNames<-function(nregs){ - n<-c("intercept.estimate", "intercept.stderr", "intercept.pvalue") + n<-c("intercept.estimate", "intercept.stderr", "intercept.pvalue") for (i in 1:nregs){ cur<-paste0("x(", i, ")") - n<-c(n, paste0(cur, ".estimate"), paste0(cur, ".stderr"), paste0(cur, ".pvalue")) + n<-c(n, paste0(cur, ".estimate"), paste0(cur, ".stderr"), paste0(cur, ".pvalue")) } return (n) -} +} OlsAllNames<-function(nregs){ return (c(OlsAdjNames, OlsCNames(nregs), OlsTestNames)) @@ -53,7 +53,7 @@ vecmAllNames<-function(lag){ #' Descriptive statistics #' -#' @param revisions.view mts object. Vertical or diagonal view of the +#' @param revisions.view mts object. Vertical or diagonal view of the #' `get_revisions()` output #' @param rounding number of decimals to display #' @@ -64,7 +64,7 @@ vecmAllNames<-function(lag){ #' qtr<-(as.numeric(substr(period_range,6,7))+2)/3 #' time_period<-rep(paste0(format(period_range, "%Y"), "Q", qtr),5) #' np<-length(period_range) -#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), #' rep("2022-12-31",np), rep("2023-06-30",np)) #' set.seed(1) #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) @@ -75,17 +75,17 @@ vecmAllNames<-function(lag){ #' obs_values<-c(obs_values,xt) #' } #' df<-data.frame(rev_date, time_period, obs_values) -#' -#' ## Create vintage and get descriptive statistics of revisions +#' +#' ## Create vintage and get descriptive statistics of revisions #' vintages<-create_vintages(df, periodicity = 4) #' revisions<-get_revisions(vintages, gap=1) #' descriptive_statistics(revisions$diagonal_view, rounding=1) -#' +#' descriptive_statistics<-function(revisions.view, rounding=3){ - + descriptive_statistics_one<-function(r){ rc<-as.numeric(r[!is.na(r)]) - + n<-length(rc) mn<-mean(rc) sd<-sd(rc) @@ -99,25 +99,25 @@ descriptive_statistics<-function(revisions.view, rounding=3){ pn<-1-pp-p0 mar<-mean(abs(rc)) rmsr<-sqrt(mean(rc^2)) - + return(c(n,mn,sd,min,q10,q50,q90,max,pp,p0,pn,mar,rmsr)) } - + ds<-apply(revisions.view, 2, descriptive_statistics_one) - + return (`rownames<-`(round(ds,rounding), descriptiveStatNames)) } #' Theil's Inequality Coefficient U1 #' -#' @param vintages.view mts object. Vertical or diagonal view of the +#' @param vintages.view mts object. Vertical or diagonal view of the #' `create_vintages()` output -#' @param gap Integer. Gap to consider between each vintages. Default is 1 +#' @param gap Integer. Gap to consider between each vintages. Default is 1 #' which means that revisions are calculated and tested for each #' vintages consecutively. -#' @param na.zero Boolean whether missing values should be considered as 0 or +#' @param na.zero Boolean whether missing values should be considered as 0 or #' rather as data not (yet) available (the default). -#' +#' #' @seealso `revision_analysis()`, `get_report()` #' #' @export @@ -128,7 +128,7 @@ descriptive_statistics<-function(revisions.view, rounding=3){ #' qtr<-(as.numeric(substr(period_range,6,7))+2)/3 #' time_period<-rep(paste0(format(period_range, "%Y"), "Q", qtr),5) #' np<-length(period_range) -#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), #' rep("2022-12-31",np), rep("2023-06-30",np)) #' set.seed(1) #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) @@ -139,18 +139,18 @@ descriptive_statistics<-function(revisions.view, rounding=3){ #' obs_values<-c(obs_values,xt) #' } #' df<-data.frame(rev_date, time_period, obs_values) -#' +#' #' ## Create vintage and test #' vintages<-create_vintages(df, periodicity = 4) #' theil(vintages$diagonal_view) -#' -theil<-function(vintages.view, gap=1, na.zero=F){ +#' +theil<-function(vintages.view, gap=1, na.zero= FALSE){ q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) - theil<-try(.jcall("jdplus/revisions/base/r/Utility", "[D", "theil", jq, as.integer(gap)),silent=T) + theil<-try(.jcall("jdplus/revisions/base/r/Utility", "[D", "theil", jq, as.integer(gap)),silent= TRUE) if("try-error" %in% class(theil)){ - warning("theil could not be performed",call.=F) + warning("theil could not be performed",call.= FALSE) return(NULL) } return (theil) @@ -158,12 +158,12 @@ theil<-function(vintages.view, gap=1, na.zero=F){ #' Theil's Inequality Coefficient U2 #' -#' @param vintages.view mts object. Vertical or diagonal view of the +#' @param vintages.view mts object. Vertical or diagonal view of the #' `create_vintages()` output -#' @param gap Integer. Gap to consider between each vintages. Default is 1 +#' @param gap Integer. Gap to consider between each vintages. Default is 1 #' which means that revisions are calculated and tested for each #' vintages consecutively.. -#' @param na.zero Boolean whether missing values should be considered as 0 or +#' @param na.zero Boolean whether missing values should be considered as 0 or #' rather as data not (yet) available (the default). #' @seealso `revision_analysis()`, `get_report()` #' @@ -175,7 +175,7 @@ theil<-function(vintages.view, gap=1, na.zero=F){ #' qtr<-(as.numeric(substr(period_range,6,7))+2)/3 #' time_period<-rep(paste0(format(period_range, "%Y"), "Q", qtr),5) #' np<-length(period_range) -#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), #' rep("2022-12-31",np), rep("2023-06-30",np)) #' set.seed(1) #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) @@ -186,18 +186,18 @@ theil<-function(vintages.view, gap=1, na.zero=F){ #' obs_values<-c(obs_values,xt) #' } #' df<-data.frame(rev_date, time_period, obs_values) -#' +#' #' ## Create vintage and test #' vintages<-create_vintages(df, periodicity = 4) #' theil2(vintages$diagonal_view) -#' -theil2<-function(vintages.view, gap=1, na.zero=F){ +#' +theil2<-function(vintages.view, gap=1, na.zero= FALSE){ q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) - theil2<-try(.jcall("jdplus/revisions/base/r/Utility", "[D", "theil2", jq, as.integer(gap)),silent=T) + theil2<-try(.jcall("jdplus/revisions/base/r/Utility", "[D", "theil2", jq, as.integer(gap)),silent= TRUE) if("try-error" %in% class(theil2)){ - warning("theil2 could not be performed",call.=F) + warning("theil2 could not be performed",call.= FALSE) return(NULL) } return (theil2) @@ -205,9 +205,9 @@ theil2<-function(vintages.view, gap=1, na.zero=F){ #' Estimate bias using t-test and augmented t-test #' -#' @param revisions.view mts object. Vertical or diagonal view of the +#' @param revisions.view mts object. Vertical or diagonal view of the #' `get_revisions()` output -#' @param na.zero Boolean whether missing values should be considered as 0 or +#' @param na.zero Boolean whether missing values should be considered as 0 or #' rather as data not (yet) available (the default). #' @seealso `revision_analysis()`, `get_report()` #' @@ -230,25 +230,25 @@ theil2<-function(vintages.view, gap=1, na.zero=F){ #' obs_values<-c(obs_values,xt) #' } #' df<-data.frame(rev_date, time_period, obs_values) -#' +#' #' ## Create vintage and test #' vintages<-create_vintages(df, periodicity = 4) #' revisions<-get_revisions(vintages, gap=1) #' bias(revisions$diagonal_view) -#' -bias<-function(revisions.view, na.zero=F){ +#' +bias<-function(revisions.view, na.zero= FALSE){ r<-revisions.view if(na.zero) r[is.na(r)]<-0 jrevs<-matrix_r2jd(r) - jbias<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "bias", jrevs),silent=T) + jbias<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "bias", jrevs),silent= TRUE) if("try-error" %in% class(bias)){ - warning("bias could not be performed",call.=F) + warning("bias could not be performed",call.= FALSE) return(NULL) } bias=matrix_jd2r(jbias) bias[rowSums(bias[])==0,]<-NaN # fix non-calculable cases if(all(is.nan(bias))){ - warning("bias could not be performed",call.=F) + warning("bias could not be performed",call.= FALSE) return(NULL) } colnames(bias)<-biasNames @@ -258,15 +258,15 @@ bias<-function(revisions.view, na.zero=F){ #' Slope and Drift -#' +#' #' Linear regression model of a latter vintage (L) on a preliminary vintage (P) #' -#' @param vintages.view mts object. Vertical or diagonal view of the +#' @param vintages.view mts object. Vertical or diagonal view of the #' `create_vintages()` output -#' @param gap Integer. Gap to consider between each vintages. Default is 1 +#' @param gap Integer. Gap to consider between each vintages. Default is 1 #' which means that revisions are calculated and tested for each #' vintages consecutively. -#' @param na.zero Boolean whether missing values should be considered as 0 or +#' @param na.zero Boolean whether missing values should be considered as 0 or #' rather as data not (yet) available (the default). #' #' @seealso `revision_analysis()`, `get_report()` @@ -279,7 +279,7 @@ bias<-function(revisions.view, na.zero=F){ #' qtr<-(as.numeric(substr(period_range,6,7))+2)/3 #' time_period<-rep(paste0(format(period_range, "%Y"), "Q", qtr),5) #' np<-length(period_range) -#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), #' rep("2022-12-31",np), rep("2023-06-30",np)) #' set.seed(1) #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) @@ -290,24 +290,24 @@ bias<-function(revisions.view, na.zero=F){ #' obs_values<-c(obs_values,xt) #' } #' df<-data.frame(rev_date, time_period, obs_values) -#' +#' #' ## Create vintage and test #' vintages<-create_vintages(df, periodicity = 4) #' slope_and_drift(vintages$diagonal_view) -#' -slope_and_drift<-function(vintages.view, gap=1, na.zero=F){ +#' +slope_and_drift<-function(vintages.view, gap=1, na.zero= FALSE){ q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) - jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "slopeAndDrift", jq, as.integer(gap)),silent=T) + jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "slopeAndDrift", jq, as.integer(gap)),silent= TRUE) if("try-error" %in% class(jsd)){ - warning("Slope and drift could not be performed",call.=F) + warning("Slope and drift could not be performed",call.= FALSE) return(NULL) } slope_and_drift=matrix_jd2r(jsd) slope_and_drift[rowSums(slope_and_drift[])==0,]<-NaN # fix non-calculable cases if(all(is.nan(slope_and_drift))){ - warning("slope_and_drift could not be performed",call.=F) + warning("slope_and_drift could not be performed",call.= FALSE) return(NULL) } colnames(slope_and_drift)<-OlsNames @@ -317,18 +317,18 @@ slope_and_drift<-function(vintages.view, gap=1, na.zero=F){ #' Efficiency Model 1 -#' +#' #' Linear regression model of the revisions (R) on a preliminary vintage (P) -#' -#' @param vintages.view mts object. Vertical or diagonal view of the +#' +#' @param vintages.view mts object. Vertical or diagonal view of the #' `create_vintages()` output -#' @param gap Integer. Gap to consider between each vintages. Default is 1 +#' @param gap Integer. Gap to consider between each vintages. Default is 1 #' which means that revisions are calculated and tested for each #' vintages consecutively. -#' @param na.zero Boolean whether missing values should be considered as 0 or +#' @param na.zero Boolean whether missing values should be considered as 0 or #' rather as data not (yet) available (the default). -#' -#' @seealso `revision_analysis()`, `get_report()` +#' +#' @seealso `revision_analysis()`, `get_report()` #' #' @export #' @@ -338,7 +338,7 @@ slope_and_drift<-function(vintages.view, gap=1, na.zero=F){ #' qtr<-(as.numeric(substr(period_range,6,7))+2)/3 #' time_period<-rep(paste0(format(period_range, "%Y"), "Q", qtr),5) #' np<-length(period_range) -#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), #' rep("2022-12-31",np), rep("2023-06-30",np)) #' set.seed(1) #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) @@ -349,24 +349,24 @@ slope_and_drift<-function(vintages.view, gap=1, na.zero=F){ #' obs_values<-c(obs_values,xt) #' } #' df<-data.frame(rev_date, time_period, obs_values) -#' +#' #' ## Create vintage and test #' vintages<-create_vintages(df, periodicity = 4) #' efficiencyModel1(vintages$diagonal_view) -#' -efficiencyModel1<-function(vintages.view, gap=1, na.zero=F){ +#' +efficiencyModel1<-function(vintages.view, gap=1, na.zero= FALSE){ q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) - jef1<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "efficiencyModel1", jq, as.integer(gap)),silent=T) + jef1<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "efficiencyModel1", jq, as.integer(gap)),silent= TRUE) if("try-error" %in% class(jef1)){ - warning("efficiencyModel1 could not be performed",call.=F) + warning("efficiencyModel1 could not be performed",call.= FALSE) return(NULL) } efficiencyModel1=matrix_jd2r(jef1) efficiencyModel1[rowSums(efficiencyModel1[])==0,]<-NaN # fix non-calculable cases if(all(is.nan(efficiencyModel1))){ - warning("efficiencyModel1 could not be performed",call.=F) + warning("efficiencyModel1 could not be performed",call.= FALSE) return(NULL) } colnames(efficiencyModel1)<-OlsNames @@ -378,15 +378,15 @@ efficiencyModel1<-function(vintages.view, gap=1, na.zero=F){ } #' Efficiency Model 2 -#' +#' #' Linear regression model of Rv on R{v-1} #' -#' @param vintages.view mts object. Vertical or diagonal view of the +#' @param vintages.view mts object. Vertical or diagonal view of the #' `create_vintages()` output -#' @param gap Integer. Gap to consider between each vintages. Default is 1 +#' @param gap Integer. Gap to consider between each vintages. Default is 1 #' which means that revisions are calculated and tested for each #' vintages consecutively. -#' @param na.zero Boolean whether missing values should be considered as 0 or +#' @param na.zero Boolean whether missing values should be considered as 0 or #' rather as data not (yet) available (the default). #' @seealso `revision_analysis()`, `get_report()` #' @@ -398,7 +398,7 @@ efficiencyModel1<-function(vintages.view, gap=1, na.zero=F){ #' qtr<-(as.numeric(substr(period_range,6,7))+2)/3 #' time_period<-rep(paste0(format(period_range, "%Y"), "Q", qtr),5) #' np<-length(period_range) -#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), #' rep("2022-12-31",np), rep("2023-06-30",np)) #' set.seed(1) #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) @@ -409,28 +409,28 @@ efficiencyModel1<-function(vintages.view, gap=1, na.zero=F){ #' obs_values<-c(obs_values,xt) #' } #' df<-data.frame(rev_date, time_period, obs_values) -#' +#' #' ## Create vintage and test #' vintages<-create_vintages(df, periodicity = 4) #' efficiencyModel2(vintages$diagonal_view) -#' -efficiencyModel2<-function(vintages.view, gap=1, na.zero=F){ +#' +efficiencyModel2<-function(vintages.view, gap=1, na.zero= FALSE){ q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) - jef2<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "efficiencyModel2", jq, as.integer(gap)),silent=T) + jef2<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "efficiencyModel2", jq, as.integer(gap)),silent= TRUE) if("try-error" %in% class(jef2)){ - warning("efficiencyModel2 could not be performed",call.=F) + warning("efficiencyModel2 could not be performed",call.= FALSE) return(NULL) } efficiencyModel2=matrix_jd2r(jef2) if(length(efficiencyModel2)==0) { - warning("efficiencyModel2 could not be performed: Too few number of vintages",call.=F) + warning("efficiencyModel2 could not be performed: Too few number of vintages",call.= FALSE) return(NULL) } efficiencyModel2[rowSums(efficiencyModel2[])==0,]<-NaN # fix non-calculable cases if(all(is.nan(efficiencyModel2))){ - warning("efficiencyModel2 could not be performed",call.=F) + warning("efficiencyModel2 could not be performed",call.= FALSE) return(NULL) } colnames(efficiencyModel2)<-OlsNames @@ -445,10 +445,10 @@ efficiencyModel2<-function(vintages.view, gap=1, na.zero=F){ #' #' Linear regression model of Rv on R_{v-1},...,R_{v-p}. (p=nrevs) #' -#' @param revisions.view mts object. Vertical or diagonal view of the +#' @param revisions.view mts object. Vertical or diagonal view of the #' `get_revisions()` output #' @param nrevs Integer. Number of lags to consider. -#' @param na.zero Boolean whether missing values should be considered as 0 or +#' @param na.zero Boolean whether missing values should be considered as 0 or #' rather as data not (yet) available (the default). #' @seealso `revision_analysis()`, `get_report()` #' @@ -460,7 +460,7 @@ efficiencyModel2<-function(vintages.view, gap=1, na.zero=F){ #' qtr<-(as.numeric(substr(period_range,6,7))+2)/3 #' time_period<-rep(paste0(format(period_range, "%Y"), "Q", qtr),5) #' np<-length(period_range) -#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), #' rep("2022-12-31",np), rep("2023-06-30",np)) #' set.seed(1) #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) @@ -471,29 +471,29 @@ efficiencyModel2<-function(vintages.view, gap=1, na.zero=F){ #' obs_values<-c(obs_values,xt) #' } #' df<-data.frame(rev_date, time_period, obs_values) -#' +#' #' ## Create vintage and test #' vintages<-create_vintages(df, periodicity = 4) #' revisions<-get_revisions(vintages, gap=1) #' orthogonallyModel1(revisions$diagonal_view) -#' -orthogonallyModel1<-function(revisions.view, nrevs=1, na.zero=F){ +#' +orthogonallyModel1<-function(revisions.view, nrevs=1, na.zero= FALSE){ r<-revisions.view if(na.zero) r[is.na(r)]<-0 jr<-matrix_r2jd(as.matrix(r)) - jom<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "orthogonallyModel1", jr, as.integer(nrevs)),silent=T) + jom<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "orthogonallyModel1", jr, as.integer(nrevs)),silent= TRUE) if("try-error" %in% class(jom)){ - warning("orthogonallyModel1 could not be performed",call.=F) + warning("orthogonallyModel1 could not be performed",call.= FALSE) return(NULL) } om=matrix_jd2r(jom) if (length(om)==0) { - warning("orthogonallyModel1 could not be performed: Too few number of vintages",call.=F) + warning("orthogonallyModel1 could not be performed: Too few number of vintages",call.= FALSE) return(NULL) } om[rowSums(om[])==0,]<-NaN # fix non-calculable cases if(all(is.nan(om))){ - warning("orthogonallyModel1 could not be performed",call.=F) + warning("orthogonallyModel1 could not be performed",call.= FALSE) return(NULL) } colnames(om)<-OlsAllNames(nrevs) @@ -502,13 +502,13 @@ orthogonallyModel1<-function(revisions.view, nrevs=1, na.zero=F){ } #' Orthogonally Model 2 -#' +#' #' Linear regression model of R_v on R_{v-k} (k = reference) #' -#' @param revisions.view mts object. Vertical or diagonal view of the +#' @param revisions.view mts object. Vertical or diagonal view of the #' `get_revisions()` output #' @param reference Integer. Number of lags to consider. -#' @param na.zero Boolean whether missing values should be considered as 0 or +#' @param na.zero Boolean whether missing values should be considered as 0 or #' rather as data not (yet) available (the default). #' @seealso `revision_analysis()`, `get_report()` #' @@ -520,7 +520,7 @@ orthogonallyModel1<-function(revisions.view, nrevs=1, na.zero=F){ #' qtr<-(as.numeric(substr(period_range,6,7))+2)/3 #' time_period<-rep(paste0(format(period_range, "%Y"), "Q", qtr),5) #' np<-length(period_range) -#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), #' rep("2022-12-31",np), rep("2023-06-30",np)) #' set.seed(1) #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) @@ -531,29 +531,29 @@ orthogonallyModel1<-function(revisions.view, nrevs=1, na.zero=F){ #' obs_values<-c(obs_values,xt) #' } #' df<-data.frame(rev_date, time_period, obs_values) -#' +#' #' ## Create vintage and test #' vintages<-create_vintages(df, periodicity = 4) #' revisions<-get_revisions(vintages, gap=1) #' orthogonallyModel2(revisions$diagonal_view) -#' -orthogonallyModel2<-function(revisions.view, reference=1, na.zero=F){ +#' +orthogonallyModel2<-function(revisions.view, reference=1, na.zero= FALSE){ r<-revisions.view if(na.zero) r[is.na(r)]<-0 jr<-matrix_r2jd(as.matrix(r)) - jom<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "orthogonallyModel2", jr, as.integer(reference)),silent=T) + jom<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "orthogonallyModel2", jr, as.integer(reference)),silent= TRUE) if("try-error" %in% class(jom)){ - warning("orthogonallyModel2 could not be performed",call.=F) + warning("orthogonallyModel2 could not be performed",call.= FALSE) return(NULL) } om=matrix_jd2r(jom) if (length(om)==0) { - warning("orthogonallyModel2 could not be performed: Too few number of vintages",call.=F) + warning("orthogonallyModel2 could not be performed: Too few number of vintages",call.= FALSE) return(NULL) } om[rowSums(om[])==0,]<-NaN # fix non-calculable cases if(all(is.nan(om))){ - warning("orthogonallyModel2 could not be performed",call.=F) + warning("orthogonallyModel2 could not be performed",call.= FALSE) return(NULL) } colnames(om)<-OlsNames @@ -563,16 +563,16 @@ orthogonallyModel2<-function(revisions.view, reference=1, na.zero=F){ #' Signal VS Noise #' -#' Linear regression models to determine whether revisions are ‘news’ or ‘noise’. -#' For 'noise': R (revisions) on P (preliminary estimate). -#' For 'news': R on L (latter estimate). +#' Linear regression models to determine whether revisions are ‘news’ or ‘noise’. +#' For 'noise': R (revisions) on P (preliminary estimate). +#' For 'news': R on L (latter estimate). #' -#' @param vintages.view mts object. Vertical or diagonal view of the +#' @param vintages.view mts object. Vertical or diagonal view of the #' `create_vintages()` output -#' @param gap Integer. Gap to consider between each vintages. Default is 1 +#' @param gap Integer. Gap to consider between each vintages. Default is 1 #' which means that revisions are calculated and tested for each #' vintages consecutively. -#' @param na.zero Boolean whether missing values should be considered as 0 or +#' @param na.zero Boolean whether missing values should be considered as 0 or #' rather as data not (yet) available (the default). #' @seealso `revision_analysis()`, `get_report()` #' @@ -584,7 +584,7 @@ orthogonallyModel2<-function(revisions.view, reference=1, na.zero=F){ #' qtr<-(as.numeric(substr(period_range,6,7))+2)/3 #' time_period<-rep(paste0(format(period_range, "%Y"), "Q", qtr),5) #' np<-length(period_range) -#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), #' rep("2022-12-31",np), rep("2023-06-30",np)) #' set.seed(1) #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) @@ -595,24 +595,24 @@ orthogonallyModel2<-function(revisions.view, reference=1, na.zero=F){ #' obs_values<-c(obs_values,xt) #' } #' df<-data.frame(rev_date, time_period, obs_values) -#' +#' #' ## Create vintage and test #' vintages<-create_vintages(df, periodicity = 4) #' signalnoise(vintages$diagonal_view) -#' -signalnoise<-function(vintages.view, gap=1, na.zero=F){ +#' +signalnoise<-function(vintages.view, gap=1, na.zero= FALSE){ q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) - jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "signalNoise", jq, as.integer(gap)),silent=T) + jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "signalNoise", jq, as.integer(gap)),silent= TRUE) if("try-error" %in% class(jsd)){ - warning("signalnoise could not be performed",call.=F) + warning("signalnoise could not be performed",call.= FALSE) return(NULL) } sn<-matrix_jd2r(jsd) sn[rowSums(sn[])==0,]<-NaN # fix non-calculable cases if(all(is.nan(sn))){ - warning("SignalNoise could not be performed",call.=F) + warning("SignalNoise could not be performed",call.= FALSE) return(NULL) } colnames(sn)<-snNames @@ -625,10 +625,10 @@ signalnoise<-function(vintages.view, gap=1, na.zero=F){ #' Unit root test #' -#' @param vintages.view mts object. Vertical or diagonal view of the +#' @param vintages.view mts object. Vertical or diagonal view of the #' `create_vintages()` output #' @param adfk Number of lags to consider for Augmented Dicky-Fuller (ADF) test -#' @param na.zero Boolean whether missing values should be considered as 0 or +#' @param na.zero Boolean whether missing values should be considered as 0 or #' rather as data not (yet) available (the default). #' @seealso `revision_analysis()`, `get_report()` #' @@ -640,7 +640,7 @@ signalnoise<-function(vintages.view, gap=1, na.zero=F){ #' qtr<-(as.numeric(substr(period_range,6,7))+2)/3 #' time_period<-rep(paste0(format(period_range, "%Y"), "Q", qtr),5) #' np<-length(period_range) -#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), #' rep("2022-12-31",np), rep("2023-06-30",np)) #' set.seed(1) #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) @@ -651,18 +651,18 @@ signalnoise<-function(vintages.view, gap=1, na.zero=F){ #' obs_values<-c(obs_values,xt) #' } #' df<-data.frame(rev_date, time_period, obs_values) -#' +#' #' ## Create vintage and test #' vintages<-create_vintages(df, periodicity = 4) #' unitroot(vintages$diagonal_view) -#' -unitroot<-function(vintages.view, adfk=1, na.zero=F){ +#' +unitroot<-function(vintages.view, adfk=1, na.zero= FALSE){ q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) - jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "unitroot", jq, as.integer(adfk)),silent=T) + jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "unitroot", jq, as.integer(adfk)),silent= TRUE) if("try-error" %in% class(jsd)){ - warning("unit root test could not be performed",call.=F) + warning("unit root test could not be performed",call.= FALSE) return(NULL) } ur<-matrix_jd2r(jsd) @@ -673,10 +673,10 @@ unitroot<-function(vintages.view, adfk=1, na.zero=F){ #' Cointegration tests (Engle-Granger) #' -#' @param vintages.view mts object. Vertical or diagonal view of the +#' @param vintages.view mts object. Vertical or diagonal view of the #' `create_vintages()` output #' @param adfk Number of lags to consider for ADF -#' @param na.zero Boolean whether missing values should be considered as 0 or +#' @param na.zero Boolean whether missing values should be considered as 0 or #' rather as data not (yet) available (the default). #' @seealso `revision_analysis()`, `get_report()` #' @@ -688,7 +688,7 @@ unitroot<-function(vintages.view, adfk=1, na.zero=F){ #' qtr<-(as.numeric(substr(period_range,6,7))+2)/3 #' time_period<-rep(paste0(format(period_range, "%Y"), "Q", qtr),5) #' np<-length(period_range) -#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), #' rep("2022-12-31",np), rep("2023-06-30",np)) #' set.seed(1) #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) @@ -699,18 +699,18 @@ unitroot<-function(vintages.view, adfk=1, na.zero=F){ #' obs_values<-c(obs_values,xt) #' } #' df<-data.frame(rev_date, time_period, obs_values) -#' +#' #' ## Create vintage and test #' vintages<-create_vintages(df, periodicity = 4) #' cointegration(vintages$diagonal_view) -#' -cointegration<-function(vintages.view, adfk=1, na.zero=F){ +#' +cointegration<-function(vintages.view, adfk=1, na.zero= FALSE){ q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) - jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "cointegration", jq, as.integer(adfk)),silent=T) + jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "cointegration", jq, as.integer(adfk)),silent= TRUE) if("try-error" %in% class(jsd)){ - warning("cointegration test could not be performed",call.=F) + warning("cointegration test could not be performed",call.= FALSE) return(NULL) } eg<-matrix_jd2r(jsd) @@ -720,15 +720,15 @@ cointegration<-function(vintages.view, adfk=1, na.zero=F){ } #' Vector error correction model (VECM) -#' +#' #' Can lead to a better understanding of the nature of any nonstationary process #' among the different component series. #' -#' @param vintages.view mts object. Vertical or diagonal view of the +#' @param vintages.view mts object. Vertical or diagonal view of the #' `create_vintages()` output #' @param lag Number of lags #' @param model Character. Must be "none" (the default), "cnt" or "trend". -#' @param na.zero Boolean whether missing values should be considered as 0 or +#' @param na.zero Boolean whether missing values should be considered as 0 or #' rather as data not (yet) available (the default). #' @export #' @@ -738,7 +738,7 @@ cointegration<-function(vintages.view, adfk=1, na.zero=F){ #' qtr<-(as.numeric(substr(period_range,6,7))+2)/3 #' time_period<-rep(paste0(format(period_range, "%Y"), "Q", qtr),5) #' np<-length(period_range) -#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +#' rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), #' rep("2022-12-31",np), rep("2023-06-30",np)) #' set.seed(1) #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) @@ -749,19 +749,19 @@ cointegration<-function(vintages.view, adfk=1, na.zero=F){ #' obs_values<-c(obs_values,xt) #' } #' df<-data.frame(rev_date, time_period, obs_values) -#' +#' #' ## Create vintage and test #' vintages<-create_vintages(df, periodicity = 4) #' vecm(vintages$diagonal_view) -#' -vecm<-function(vintages.view, lag=2, model = c("none", "cnt", "trend"), na.zero=F){ +#' +vecm<-function(vintages.view, lag=2, model = c("none", "cnt", "trend"), na.zero= FALSE){ model<-match.arg(model) q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) - jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "vecm", jq, as.integer(lag), model),silent=T) + jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "vecm", jq, as.integer(lag), model),silent= TRUE) if("try-error" %in% class(jsd)){ - warning("vecm could not be performed",call.=F) + warning("vecm could not be performed",call.= FALSE) return(NULL) } vecm<-matrix_jd2r(jsd) @@ -771,15 +771,15 @@ vecm<-function(vintages.view, lag=2, model = c("none", "cnt", "trend"), na.zero= } # Auto-correlation tests on OLS residuals -# -# auto_correlation<-function(vintages.view, nbreuschgodfrey=1, nljungbox=1, na.zero=F){ +# +# auto_correlation<-function(vintages.view, nbreuschgodfrey=1, nljungbox=1, na.zero= FALSE){ # q<-vintages.view # if(na.zero) q[is.na(q)]<-0 # jq<-matrix_r2jd(q) # jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "autoCorrelation", jq -# , as.integer(nbreuschgodfrey), as.integer(nljungbox)),silent=T) +# , as.integer(nbreuschgodfrey), as.integer(nljungbox)),silent= TRUE) # if("try-error" %in% class(jsd)){ -# warning("auto_correlation test on OLS residuals could not be performed",call.=F) +# warning("auto_correlation test on OLS residuals could not be performed",call.= FALSE) # return(NULL) # } # ac<-matrix_jd2r(jsd) diff --git a/R/vintages.R b/R/vintages.R index e55b1e8..2b6483e 100644 --- a/R/vintages.R +++ b/R/vintages.R @@ -175,15 +175,15 @@ create_vintages<- function(df, periodicity, vintage.selection = NULL, revdate.fo #' @examples #' \dontrun{ #' file.name<-"myinput.csv" -#' vintages<-create_vintages_from_csv(file.name, -#' periodicity=12, +#' vintages<-create_vintages_from_csv(file.name, +#' periodicity=12, #' separator = ";", -#' vintage.selection=NULL, +#' vintage.selection=NULL, #' revdate.format="%Y-%m-%d") #' } create_vintages_from_csv<-function(file, periodicity, separator = ",", vintage.selection=NULL, revdate.format="%Y.%m.%d"){ - df<-as.data.frame(read.csv(file, sep = separator, stringsAsFactors = F)) + df<-as.data.frame(read.csv(file, sep = separator, stringsAsFactors = FALSE)) return(create_vintages(df, periodicity, vintage.selection, revdate.format)) } @@ -215,10 +215,10 @@ create_vintages_from_csv<-function(file, periodicity, separator = ",", vintage.s #' \dontrun{ #' file.name<-"myinput.xlsx" #' sheet.name<-"Sheet1" -#' vintages<-create_vintages_from_xlsx(file.name, -#' sheet.name, -#' periodicity=12, -#' vintage.selection=NULL, +#' vintages<-create_vintages_from_xlsx(file.name, +#' sheet.name, +#' periodicity=12, +#' vintage.selection=NULL, #' revdate.format="%d/%m/%Y")) #' } create_vintages_from_xlsx<-function(file, sheetname, periodicity, vintage.selection = NULL, revdate.format= "%Y.%m.%d"){ diff --git a/R/zzz.R b/R/zzz.R index e0b8c70..13aadb5 100644 --- a/R/zzz.R +++ b/R/zzz.R @@ -2,11 +2,11 @@ NULL .onLoad <- function(libname, pkgname) { - if (! requireNamespace("rjd3toolkit", quietly = T)) stop("Loading rjd3 libraries failed") + if (! requireNamespace("rjd3toolkit", quietly = TRUE)) stop("Loading rjd3 libraries failed") result <- rJava::.jpackage(pkgname, lib.loc=libname) if (!result) stop("Loading java packages failed") # reload extractors .jcall("jdplus/toolkit/base/api/information/InformationExtractors", "V", "reloadExtractors") -} \ No newline at end of file +} diff --git a/inst/templates/report.Rmd b/inst/templates/report.Rmd index 32ab1f7..d658935 100644 --- a/inst/templates/report.Rmd +++ b/inst/templates/report.Rmd @@ -27,17 +27,17 @@ For some parametric tests, transformation may be important to avoid misleading r ```{r descriptivetable, echo = FALSE} selection<-c("N","mean revision", "st.dev.", "% positive", "% zero", "% negative") -if (! requireNamespace("kableExtra", quietly=T)) { - knitr::kable(descriptive_statistics[selection,,drop=F], format="html") +if (! requireNamespace("kableExtra", quietly=TRUE)) { + knitr::kable(descriptive_statistics[selection,,drop=FALSE], format="html") warning("Please install kableExtra: install.packages('kableExtra') to get more visual table output") }else{ - kableExtra::kable_minimal(knitr::kable(descriptive_statistics[selection,,drop=F], format="html")) + kableExtra::kable_minimal(knitr::kable(descriptive_statistics[selection,,drop=FALSE], format="html")) } ``` # Main Results ```{r summarytable, echo = FALSE} -if (! requireNamespace("kableExtra", quietly=T)) { +if (! requireNamespace("kableExtra", quietly=TRUE)) { knitr::kable(main_results, format="html") }else{ format_font <- function(x){ @@ -45,12 +45,12 @@ if (! requireNamespace("kableExtra", quietly=T)) { color = ifelse(is.na(x),"black", ifelse(substr(x,1,1) == "G", "green", ifelse(substr(x,1,1) == "U", "orange", "red"))), - bold = ifelse(is.na(x),F, - ifelse(substr(x,1,1) == "S", T, F))) + bold = ifelse(is.na(x),FALSE, + ifelse(substr(x,1,1) == "S", TRUE, FALSE))) } nc<-ncol(main_results) - main_results[,2:nc]<-apply(main_results[,2:nc,drop=F], 2, format_font) - kableExtra::kable_minimal(knitr::kable(main_results, format="html", escape = F)) + main_results[,2:nc]<-apply(main_results[,2:nc,drop=FALSE], 2, format_font) + kableExtra::kable_minimal(knitr::kable(main_results, format="html", escape = FALSE)) } ``` diff --git a/rjd3revisions.Rproj b/rjd3revisions.Rproj index cba1b6b..7e81b12 100644 --- a/rjd3revisions.Rproj +++ b/rjd3revisions.Rproj @@ -2,11 +2,11 @@ Version: 1.0 RestoreWorkspace: No SaveWorkspace: No -AlwaysSaveHistory: Default +AlwaysSaveHistory: No EnableCodeIndexing: Yes UseSpacesForTab: Yes -NumSpacesForTab: 2 +NumSpacesForTab: 4 Encoding: UTF-8 RnwWeave: Sweave @@ -19,3 +19,5 @@ BuildType: Package PackageUseDevtools: Yes PackageInstallArgs: --no-multiarch --with-keep.source PackageRoxygenize: rd,collate,namespace + +UseNativePipeOperator: Yes From 754d8411d3fcafc0941fc5acfbb3791e17f17db9 Mon Sep 17 00:00:00 2001 From: Tanguy BARTHELEMY Date: Thu, 8 Feb 2024 14:23:56 +0100 Subject: [PATCH 10/56] lint assignation sign = to <- --- R/jd3_rslts.R | 2 +- R/tests.R | 12 ++++++------ R/vintages.R | 2 +- 3 files changed, 8 insertions(+), 8 deletions(-) diff --git a/R/jd3_rslts.R b/R/jd3_rslts.R index a18dde9..3bdbab7 100644 --- a/R/jd3_rslts.R +++ b/R/jd3_rslts.R @@ -131,7 +131,7 @@ proc_dictionary<-function(name){ keys<-array(dim=size) jiter<-.jcall(jkeys, "Ljava/util/Iterator;", "iterator") for (i in 1:size){ - keys[i]=.jcall(.jcall(jiter, "Ljava/lang/Object;", "next"), "Ljava/lang/String;", "toString") + keys[i] <- .jcall(.jcall(jiter, "Ljava/lang/Object;", "next"), "Ljava/lang/String;", "toString") } return (keys) } diff --git a/R/tests.R b/R/tests.R index 23f6a74..10487e6 100644 --- a/R/tests.R +++ b/R/tests.R @@ -245,7 +245,7 @@ bias<-function(revisions.view, na.zero= FALSE){ warning("bias could not be performed",call.= FALSE) return(NULL) } - bias=matrix_jd2r(jbias) + bias <- matrix_jd2r(jbias) bias[rowSums(bias[])==0,]<-NaN # fix non-calculable cases if(all(is.nan(bias))){ warning("bias could not be performed",call.= FALSE) @@ -304,7 +304,7 @@ slope_and_drift<-function(vintages.view, gap=1, na.zero= FALSE){ warning("Slope and drift could not be performed",call.= FALSE) return(NULL) } - slope_and_drift=matrix_jd2r(jsd) + slope_and_drift <- matrix_jd2r(jsd) slope_and_drift[rowSums(slope_and_drift[])==0,]<-NaN # fix non-calculable cases if(all(is.nan(slope_and_drift))){ warning("slope_and_drift could not be performed",call.= FALSE) @@ -363,7 +363,7 @@ efficiencyModel1<-function(vintages.view, gap=1, na.zero= FALSE){ warning("efficiencyModel1 could not be performed",call.= FALSE) return(NULL) } - efficiencyModel1=matrix_jd2r(jef1) + efficiencyModel1 <- matrix_jd2r(jef1) efficiencyModel1[rowSums(efficiencyModel1[])==0,]<-NaN # fix non-calculable cases if(all(is.nan(efficiencyModel1))){ warning("efficiencyModel1 could not be performed",call.= FALSE) @@ -423,7 +423,7 @@ efficiencyModel2<-function(vintages.view, gap=1, na.zero= FALSE){ warning("efficiencyModel2 could not be performed",call.= FALSE) return(NULL) } - efficiencyModel2=matrix_jd2r(jef2) + efficiencyModel2 <- matrix_jd2r(jef2) if(length(efficiencyModel2)==0) { warning("efficiencyModel2 could not be performed: Too few number of vintages",call.= FALSE) return(NULL) @@ -486,7 +486,7 @@ orthogonallyModel1<-function(revisions.view, nrevs=1, na.zero= FALSE){ warning("orthogonallyModel1 could not be performed",call.= FALSE) return(NULL) } - om=matrix_jd2r(jom) + om <- matrix_jd2r(jom) if (length(om)==0) { warning("orthogonallyModel1 could not be performed: Too few number of vintages",call.= FALSE) return(NULL) @@ -546,7 +546,7 @@ orthogonallyModel2<-function(revisions.view, reference=1, na.zero= FALSE){ warning("orthogonallyModel2 could not be performed",call.= FALSE) return(NULL) } - om=matrix_jd2r(jom) + om <- matrix_jd2r(jom) if (length(om)==0) { warning("orthogonallyModel2 could not be performed: Too few number of vintages",call.= FALSE) return(NULL) diff --git a/R/vintages.R b/R/vintages.R index 2b6483e..5f3813e 100644 --- a/R/vintages.R +++ b/R/vintages.R @@ -261,7 +261,7 @@ yp<-function(s){ if(nchar(as.character(s))[1] == 4){ return (ymd(y,1)) }else{ - p=substr(s,5,5) + p <- substr(s,5,5) if (all(p == 'Q') | all(p == 'q')){ q<-as.integer(substr(s, 6, 6)) return (yq(y,q)) From a5f4989588707730c806c91fcad5a0802a3c7abe Mon Sep 17 00:00:00 2001 From: Tanguy BARTHELEMY Date: Fri, 9 Feb 2024 14:53:49 +0100 Subject: [PATCH 11/56] seq linter --- R/jd3_rslts.R | 2 +- R/vintages.R | 4 ++-- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/R/jd3_rslts.R b/R/jd3_rslts.R index 3bdbab7..b852100 100644 --- a/R/jd3_rslts.R +++ b/R/jd3_rslts.R @@ -125,7 +125,7 @@ proc_data<-function(rslt, name){ proc_dictionary<-function(name){ jmapping<-.jcall(name, "Ldemetra/information/InformationMapping;", "getMapping") jmap<-.jnew("java/util/LinkedHashMap") - .jcall(jmapping, "V", "fillDictionary", .jnull("java/lang/String"), .jcast(jmap, "java/util/Map"), TRUE ) + .jcall(jmapping, "V", "fillDictionary", .jnull("java/lang/String"), .jcast(jmap, "java/util/Map"), TRUE) jkeys<-.jcall(jmap, "Ljava/util/Set;", "keySet") size<-.jcall(jkeys, "I", "size") keys<-array(dim=size) diff --git a/R/vintages.R b/R/vintages.R index 5f3813e..20ef955 100644 --- a/R/vintages.R +++ b/R/vintages.R @@ -118,7 +118,7 @@ create_vintages<- function(df, periodicity, vintage.selection = NULL, revdate.fo } # format input - input<-split(df, seq(nrow(df))) + input<-split(df, seq_len(nrow(df))) add_to_JD3revisions <- function(x) { revdate<-x[[1]] @@ -139,7 +139,7 @@ create_vintages<- function(df, periodicity, vintage.selection = NULL, revdate.fo ## diagonal view vd_mat<-t(apply(t(vv), 2, function(x) x[order(is.na(x))])) - releases_name<-sprintf("Release[%s]",seq(1:ncol(vd_mat))) + releases_name<-sprintf("Release[%s]",seq_len(ncol(vd_mat))) vd<-`colnames<-`(ts(vd_mat, start = start(vv), frequency = periodicity),releases_name) vintages <- list(vertical_view = vv, horizontal_view = vh, diagonal_view = vd) From 4177033620830622b50dbb68e49797fcd0f03d9a Mon Sep 17 00:00:00 2001 From: Tanguy BARTHELEMY Date: Fri, 9 Feb 2024 15:16:32 +0100 Subject: [PATCH 12/56] linter commas --- R/jd3_rslts.R | 32 +++--- R/jd3_ts.R | 8 +- R/output.R | 16 +-- R/report.R | 4 +- R/revision_analysis.R | 190 ++++++++++++++++++------------------ R/revisions.R | 6 +- R/tests.R | 108 ++++++++++---------- R/vintages.R | 20 ++-- inst/templates/report.Rmd | 18 ++-- vignettes/rjd3revisions.Rmd | 18 ++-- 10 files changed, 210 insertions(+), 210 deletions(-) diff --git a/R/jd3_rslts.R b/R/jd3_rslts.R index b852100..1e73004 100644 --- a/R/jd3_rslts.R +++ b/R/jd3_rslts.R @@ -34,7 +34,7 @@ proc_ts<-function(rslt, name){ if (is.jnull(s)) return (NULL) if (.jinstanceof(s, "demetra/timeseries/TsData")) - return(ts_jd2r(.jcast(s,"demetra/timeseries/TsData"))) + return(ts_jd2r(.jcast(s, "demetra/timeseries/TsData"))) else return (NULL) } @@ -98,11 +98,11 @@ proc_data<-function(rslt, name){ if (is.jnull(s)) return (NULL) if (.jinstanceof(s, "demetra/timeseries/TsData")) - return(ts_jd2r(.jcast(s,"demetra/timeseries/TsData"))) + return(ts_jd2r(.jcast(s, "demetra/timeseries/TsData"))) else if (.jinstanceof(s, "java/lang/Number")) return (.jcall(s, "D", "doubleValue")) else if (.jinstanceof(s, "demetra/math/matrices/MatrixType")) - return(matrix_jd2r(.jcast(s,"demetra/math/matrices/MatrixType"))) + return(matrix_jd2r(.jcast(s, "demetra/math/matrices/MatrixType"))) else if (.jinstanceof(s, "demetra/data/Parameter")){ val<-.jcall(s, "D", "getValue") return (c(val)) @@ -138,18 +138,18 @@ proc_dictionary<-function(name){ proc_likelihood<-function(jrslt, prefix){ return (list( - ll=proc_numeric(jrslt, paste(prefix,"ll", sep="")), - ssq=proc_numeric(jrslt, paste(prefix,"ssq", sep="")), - ser=proc_numeric(jrslt, paste(prefix,"ser", sep="")), - nobs=proc_int(jrslt, paste(prefix,"nobs", sep="")), - neffective=proc_int(jrslt, paste(prefix,"neffective", sep="")), - nparams=proc_int(jrslt, paste(prefix,"nparams", sep="")), - df=proc_int(jrslt, paste(prefix,"df", sep="")), - aic=proc_numeric(jrslt, paste(prefix,"aic", sep="")), - aicc=proc_numeric(jrslt, paste(prefix,"aicc", sep="")), - bic=proc_numeric(jrslt, paste(prefix,"bic", sep="")), - bic2=proc_numeric(jrslt, paste(prefix,"bic2", sep="")), - bicc=proc_numeric(jrslt, paste(prefix,"bicc", sep="")), - hannanquinn=proc_numeric(jrslt, paste(prefix,"hannanquinn", sep=""))) + ll=proc_numeric(jrslt, paste(prefix, "ll", sep="")), + ssq=proc_numeric(jrslt, paste(prefix, "ssq", sep="")), + ser=proc_numeric(jrslt, paste(prefix, "ser", sep="")), + nobs=proc_int(jrslt, paste(prefix, "nobs", sep="")), + neffective=proc_int(jrslt, paste(prefix, "neffective", sep="")), + nparams=proc_int(jrslt, paste(prefix, "nparams", sep="")), + df=proc_int(jrslt, paste(prefix, "df", sep="")), + aic=proc_numeric(jrslt, paste(prefix, "aic", sep="")), + aicc=proc_numeric(jrslt, paste(prefix, "aicc", sep="")), + bic=proc_numeric(jrslt, paste(prefix, "bic", sep="")), + bic2=proc_numeric(jrslt, paste(prefix, "bic2", sep="")), + bicc=proc_numeric(jrslt, paste(prefix, "bicc", sep="")), + hannanquinn=proc_numeric(jrslt, paste(prefix, "hannanquinn", sep=""))) ) } diff --git a/R/jd3_ts.R b/R/jd3_ts.R index aca5523..acf59f9 100644 --- a/R/jd3_ts.R +++ b/R/jd3_ts.R @@ -4,12 +4,12 @@ ts_r2jd<-function(s){ } freq<-frequency(s) start<-start(s) - .jcall("jdplus/toolkit/base/r/timeseries/TsUtility", "Ljdplus/toolkit/base/r/timeseries/TsData;", "of", + .jcall("jdplus/toolkit/base/r/timeseries/TsUtility", "Ljdplus/toolkit/base/r/timeseries/TsData;", "of", as.integer(freq), as.integer(start[1]), as.integer(start[2]), as.double(s)) } tsdomain_r2jd<-function(period, startYear, startPeriod, length){ - .jcall("jdplus/toolkit/base/r/timeseries/TsUtility", "Ljdplus/toolkit/base/r/timeseries/TsDomain;", "of", + .jcall("jdplus/toolkit/base/r/timeseries/TsUtility", "Ljdplus/toolkit/base/r/timeseries/TsDomain;", "of", as.integer(period), as.integer(startYear), as.integer(startPeriod), as.integer(length)) } @@ -21,7 +21,7 @@ ts_jd2r<-function(s){ pstart<-.jcall("jdplus/toolkit/base/r/timeseries/TsUtility", "[I", "startPeriod", s) jx<-.jcall(s, "Ljdplus/toolkit/base/api/data/DoubleSeq;", "getValues") x<-.jcall(jx, "[D", "toArray") - ts(x,start=pstart[2:3], frequency=pstart[1]) + ts(x, start=pstart[2:3], frequency=pstart[1]) } matrix_jd2r<-function(s){ @@ -41,5 +41,5 @@ matrix_r2jd<-function(s){ s<-matrix(s, nrow=length(s), ncol=1) } sdim<-dim(s) - return (.jcall("jdplus/toolkit/base/api/math/matrices/Matrix","Ljdplus/toolkit/base/api/math/matrices/Matrix;", "of", as.double(s), as.integer(sdim[1]), as.integer(sdim[2]))) + return (.jcall("jdplus/toolkit/base/api/math/matrices/Matrix", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "of", as.double(s), as.integer(sdim[1]), as.integer(sdim[2]))) } diff --git a/R/output.R b/R/output.R index 827f8b9..f4c824a 100644 --- a/R/output.R +++ b/R/output.R @@ -4,11 +4,11 @@ #' @param \dots further arguments passed to or from other methods. #' @export #' -print.rjd3rev_revision_analysis <- function(x,...){ +print.rjd3rev_revision_analysis <- function(x, ...){ print(list(call=x$call, descriptive_statistics=x$descriptive.statistics, - parametric_analysis=x$summary,...)) + parametric_analysis=x$summary, ...)) } #' Summary function for objects of class "rjd3rev_revision_analysis" @@ -24,12 +24,12 @@ summary.rjd3rev_revision_analysis<- function(x){ }else{ format_font <- function(x){ formattable::formatter('span', - style = x ~ formattable::style(color = ifelse(substr(x,1,1) == "G", "green", - ifelse(substr(x,1,1) == "U", "orange", "red")), - font.weight = ifelse(substr(x,1,1) == "S", "bold", "plain"))) + style = x ~ formattable::style(color = ifelse(substr(x, 1, 1) == "G", "green", + ifelse(substr(x, 1, 1) == "U", "orange", "red")), + font.weight = ifelse(substr(x, 1, 1) == "S", "bold", "plain"))) } nc<-ncol(x$summary) - return(list(formattable::formattable(x$summary, apply(x$summary[,2:nc,drop=FALSE], 2, format_font)))) + return(list(formattable::formattable(x$summary, apply(x$summary[, 2:nc, drop=FALSE], 2, format_font)))) } } @@ -43,11 +43,11 @@ plot.rjd3rev_revision_analysis <- function(x, ...){ rev<-x$revisions nc<-ncol(rev) if(nc>4){ - rev<-rev[,1:4] + rev<-rev[, 1:4] nc<-4 } ts.plot(rev, gpars=list(xlab="", ylab="", col=c(1:nc), type="h", lwd=2, ...)) - legend("topleft", bty="n", lty=1,lwd=2, col=c(1:nc), legend=colnames(rev)) + legend("topleft", bty="n", lty=1, lwd=2, col=c(1:nc), legend=colnames(rev)) title(main = "Size of Revisions") } diff --git a/R/report.R b/R/report.R index 0acf0ef..b858956 100644 --- a/R/report.R +++ b/R/report.R @@ -44,10 +44,10 @@ get_report <- function(rslt, template_file<-system.file("templates/report.Rmd", package = "rjd3revisions") if(is.null(path.out)){ - path.out<-paste0(getwd(),"/","revisions_report.html") + path.out<-paste0(getwd(), "/", "revisions_report.html") }else{ path.out<-ifelse(substr(path.out, length(path.out)-5, length(path.out)) != ".html", - paste0(path.out,".html"), + paste0(path.out, ".html"), path.out) } diff --git a/R/revision_analysis.R b/R/revision_analysis.R index 911305d..c70f4e4 100644 --- a/R/revision_analysis.R +++ b/R/revision_analysis.R @@ -129,7 +129,7 @@ revision_analysis<-function(vintages, if(view == "vertical"){ vt<-vintages$vertical_view }else if (view == "diagonal"){ - vt<-vintages$diagonal_view[,1:n.releases] + vt<-vintages$diagonal_view[, 1:n.releases] } ## Revisions and Vintages Transformation @@ -139,7 +139,7 @@ revision_analysis<-function(vintages, ### Log transformation if(transf.log){ if(length(vt[vt[!is.na(vt)] < 0])>0){ - warning("Logarithm transformation incompatible with negative data. No transformation considered.",call.=FALSE) + warning("Logarithm transformation incompatible with negative data. No transformation considered.", call.=FALSE) rv<-rv_notrf is_log<-FALSE }else{ @@ -155,10 +155,10 @@ revision_analysis<-function(vintages, ### Differentiation ur<-unitroot(vt, adfk=1, na.zero) # H0: non-stationary if(!is.null(ur)){ - ur_rslt<-t(round(ur,3)) - ur_ADFpvals<-ur[,"ADF.pvalue"] + ur_rslt<-t(round(ur, 3)) + ur_ADFpvals<-ur[, "ADF.pvalue"] pc_signif_ur<-length(ur_ADFpvals[ur_ADFpvals<.05])/length(ur_ADFpvals) - is_stationary<-ifelse(pc_signif_ur>.8,TRUE,FALSE) + is_stationary<-ifelse(pc_signif_ur>.8, TRUE, FALSE) }else{ ur_rslt<-NULL is_stationary<-TRUE @@ -169,17 +169,17 @@ revision_analysis<-function(vintages, is_cointegrated<-TRUE }else{ if(!is.null(coint)){ - coint_pvals<-coint[,"pvalue"] + coint_pvals<-coint[, "pvalue"] pc_signif_coint<-length(coint_pvals[coint_pvals<.05])/length(coint_pvals) - is_cointegrated<-ifelse(pc_signif_coint>.8,TRUE,FALSE) + is_cointegrated<-ifelse(pc_signif_coint>.8, TRUE, FALSE) }else{ is_cointegrated<-FALSE } } - seasonality<-apply(vt,2,check_seasonality) + seasonality<-apply(vt, 2, check_seasonality) nt<-sum(seasonality) - is_seasonal<-ifelse(nt/ncol(vt)>.8,TRUE,FALSE) + is_seasonal<-ifelse(nt/ncol(vt)>.8, TRUE, FALSE) if(is_seasonal){ vt_diff<-diff(vt, freq) delta_diff<-freq @@ -197,53 +197,53 @@ revision_analysis<-function(vintages, }else if(transf.diff == "none"){ vts<-vtc<-vt if(!is_stationary | !is_cointegrated){ - warning("No differentiation considered even though stationarity and/or cointegration might not be present. This can lead to spurious regression.",call.=FALSE) + warning("No differentiation considered even though stationarity and/or cointegration might not be present. This can lead to spurious regression.", call.=FALSE) } is_stationary<-is_cointegrated<-TRUE } # Descriptive statistics - ds<-descriptive_statistics(rv_notrf,descriptive.rounding) + ds<-descriptive_statistics(rv_notrf, descriptive.rounding) # Parametric analysis ## I. Relevancy ### Theil U1 and U2 - N<-apply(rv_notrf,2,function(x) length(x[!is.na(x)])) + N<-apply(rv_notrf, 2, function(x) length(x[!is.na(x)])) U_det<-"U" theil_trf<-"None" U1<-theil(vt, gap, na.zero) U2<-theil2(vt, gap, na.zero) if(!is.null(U1)){ - theil_rslt<-round(rbind(N,U1),3) + theil_rslt<-round(rbind(N, U1), 3) if(!is.null(U2) && !all(is.nan(U2))==TRUE){ - theil_rslt<-rbind(theil_rslt,U2=round(U2,3)) + theil_rslt<-rbind(theil_rslt, U2=round(U2, 3)) theil_q<-eval_U(U2) U_det<-"U2" }else{ - theil_rslt<-rbind(theil_rslt,U2=rep(NA,length(U1))) - theil_q<-eval_U(U1,U2=FALSE) + theil_rslt<-rbind(theil_rslt, U2=rep(NA, length(U1))) + theil_q<-eval_U(U1, U2=FALSE) U_det<-"U1" - warning("Theil U2 could not be calculated. Theil U1 is considered instead in summary().",call.=FALSE) + warning("Theil U2 could not be calculated. Theil U1 is considered instead in summary().", call.=FALSE) } }else{ theil_rslt<-NULL - theil_q<-rep(NA,length(colnames(rv))) + theil_q<-rep(NA, length(colnames(rv))) } ## II. Bias (mean and regression bias) ### II.1_2. T-test and Augmented T-test - ta_trf<-ifelse(is_log,"Log","None") + ta_trf<-ifelse(is_log, "Log", "None") ta<-bias(rv, na.zero) if(!is.null(ta)){ - ta_rslt<-t(round(ta,3)) - t_q<-eval_pvals(ta[,"pvalue"], h0_good=TRUE) - ta_q<-eval_pvals(ta[,"pvalue.adjusted"], h0_good=TRUE) + ta_rslt<-t(round(ta, 3)) + t_q<-eval_pvals(ta[, "pvalue"], h0_good=TRUE) + ta_q<-eval_pvals(ta[, "pvalue.adjusted"], h0_good=TRUE) }else{ ta_rslt<-NULL - t_q<-ta_q<-rep(NA,length(colnames(rv))) + t_q<-ta_q<-rep(NA, length(colnames(rv))) } ### II.3. Slope and drift @@ -253,13 +253,13 @@ revision_analysis<-function(vintages, paste("Delta-Log", delta_diff) sd<-slope_and_drift(vtc, gap, na.zero) if(!is.null(sd)){ - sd_rslt<-format_reg_output(sd,is_log,!is_cointegrated) - sd_m_q<-eval_pvals(sd[,"intercept.pvalue"], h0_good=TRUE) - sd_r_q<-eval_pvals(sd[,"slope.pvalue"], h0_good=TRUE) + sd_rslt<-format_reg_output(sd, is_log, !is_cointegrated) + sd_m_q<-eval_pvals(sd[, "intercept.pvalue"], h0_good=TRUE) + sd_r_q<-eval_pvals(sd[, "slope.pvalue"], h0_good=TRUE) sd_diagnostics<-regression_diagnostics(sd) }else{ sd_rslt<-sd_diagnostics<-NULL - sd_m_q<-sd_r_q<-rep(NA,length(colnames(vtc)[-c(1:gap)])) + sd_m_q<-sd_r_q<-rep(NA, length(colnames(vtc)[-c(1:gap)])) } ## III. Efficiency @@ -272,96 +272,96 @@ revision_analysis<-function(vintages, eff1<-efficiencyModel1(vts, gap, na.zero) if(!is.null(eff1)){ eff1_rslt<-format_reg_output(eff1, is_log, !is_stationary) - eff1_m_q<-eval_pvals(eff1[,"intercept.pvalue"],h0_good=TRUE) - eff1_r_q<-eval_pvals(eff1[,"slope.pvalue"],h0_good=TRUE) + eff1_m_q<-eval_pvals(eff1[, "intercept.pvalue"], h0_good=TRUE) + eff1_r_q<-eval_pvals(eff1[, "slope.pvalue"], h0_good=TRUE) eff1_diagnostics<-regression_diagnostics(eff1) }else{ eff1_rslt<-eff1_diagnostics<-NULL - eff1_m_q<-eff1_r_q<-rep(NA,length(colnames(rv))) + eff1_m_q<-eff1_r_q<-rep(NA, length(colnames(rv))) } ### III.2. Regression of latter revisions (Rv) on previous revisions (Rv_1) - eff2_trf<-ifelse(is_log,"Log","None") + eff2_trf<-ifelse(is_log, "Log", "None") eff2<-efficiencyModel2(vt, gap, na.zero) if(!is.null(eff2)){ eff2_rslt<-format_reg_output(eff2, is_log, FALSE) - eff2_m_q<-c("",eval_pvals(eff2[,"intercept.pvalue"],h0_good=TRUE)) - eff2_r_q<-c("",eval_pvals(eff2[,"slope.pvalue"],h0_good=TRUE)) + eff2_m_q<-c("", eval_pvals(eff2[, "intercept.pvalue"], h0_good=TRUE)) + eff2_r_q<-c("", eval_pvals(eff2[, "slope.pvalue"], h0_good=TRUE)) eff2_diagnostics<-regression_diagnostics(eff2) }else{ eff2_rslt<-eff2_diagnostics<-NULL - eff2_m_q<-eff2_r_q<-c("",rep(NA,length(colnames(rv)[-1]))) + eff2_m_q<-eff2_r_q<-c("", rep(NA, length(colnames(rv)[-1]))) } ## IV. Orthogonality ### IV.1. Regression of latter revisions (Rv) on previous revisions (Rv_1, Rv_2,...Rv_p) - orth1_trf<-ifelse(is_log,"Log","None") + orth1_trf<-ifelse(is_log, "Log", "None") orth1<-orthogonallyModel1(rv, nrevs, na.zero) if(!is.null(orth1)){ - orth1_rslt<-format_reg_output(orth1,is_log, FALSE) - orth1_m_q<-c(rep("",nrevs),eval_pvals(orth1[,"intercept.pvalue"],h0_good=TRUE)) - orth1_r_q<-c(rep("",nrevs),eval_pvals(pf(orth1[,"F"], nrevs, orth1[,"N"]-nrevs-1),h0_good=TRUE)) + orth1_rslt<-format_reg_output(orth1, is_log, FALSE) + orth1_m_q<-c(rep("", nrevs), eval_pvals(orth1[, "intercept.pvalue"], h0_good=TRUE)) + orth1_r_q<-c(rep("", nrevs), eval_pvals(pf(orth1[, "F"], nrevs, orth1[, "N"]-nrevs-1), h0_good=TRUE)) orth1_diagnostics<-regression_diagnostics(orth1) }else{ orth1_rslt<-orth1_diagnostics<-NULL - if(ncol(rv)>nrevs) orth1_m_q<-orth1_r_q<-c(rep("",nrevs),rep(NA,length(colnames(rv)[-c(1:nrevs)]))) - else orth1_m_q<-orth1_r_q<-rep("",nrevs) + if(ncol(rv)>nrevs) orth1_m_q<-orth1_r_q<-c(rep("", nrevs), rep(NA, length(colnames(rv)[-c(1:nrevs)]))) + else orth1_m_q<-orth1_r_q<-rep("", nrevs) } ### IV.2. Regression model of latter revisions (Rv) on previous revisions at a specific version (Rv_k) - orth2_trf<-ifelse(is_log,"Log","None") + orth2_trf<-ifelse(is_log, "Log", "None") orth2<-orthogonallyModel2(rv, ref, na.zero) if(!is.null(orth2)){ orth2_rslt<-format_reg_output(orth2, is_log, FALSE) - orth2_m_q<-c(rep("",ref),eval_pvals(orth2[,"intercept.pvalue"],h0_good=TRUE)) - orth2_r_q<-c(rep("",ref),eval_pvals(orth2[,"slope.pvalue"],h0_good=TRUE)) + orth2_m_q<-c(rep("", ref), eval_pvals(orth2[, "intercept.pvalue"], h0_good=TRUE)) + orth2_r_q<-c(rep("", ref), eval_pvals(orth2[, "slope.pvalue"], h0_good=TRUE)) orth2_diagnostics<-regression_diagnostics(orth2) }else{ orth2_rslt<-orth2_diagnostics<-NULL - if(ncol(rv)>ref) orth2_m_q<-orth2_r_q<-c(rep("",ref),rep(NA,length(colnames(rv)[-c(1:ref)]))) - else orth2_m_q<-orth2_r_q<-rep("",ref) + if(ncol(rv)>ref) orth2_m_q<-orth2_r_q<-c(rep("", ref), rep(NA, length(colnames(rv)[-c(1:ref)]))) + else orth2_m_q<-orth2_r_q<-rep("", ref) } ### IV.3. Autocorrelation test - ac_trf<-ifelse(is_log,"Log","None") - ac_trf_str<-ifelse(ac_trf == "Log", get_info_transformation(TRUE,FALSE), get_info_transformation(FALSE,FALSE)) - pm_test<-try(apply(rv,2,function(x) ljungbox(x[!is.na(x)],k=2)),silent=TRUE) # Ljung-Box up to k + ac_trf<-ifelse(is_log, "Log", "None") + ac_trf_str<-ifelse(ac_trf == "Log", get_info_transformation(TRUE, FALSE), get_info_transformation(FALSE, FALSE)) + pm_test<-try(apply(rv, 2, function(x) ljungbox(x[!is.na(x)], k=2)), silent=TRUE) # Ljung-Box up to k if(!"try-error" %in% class(pm_test)){ - pm_test_mat<-matrix(unlist(pm_test), ncol=2, byrow=TRUE)[,,drop=FALSE] - dimnames(pm_test_mat)<-list(colnames(rv), c("value","p.value")) + pm_test_mat<-matrix(unlist(pm_test), ncol=2, byrow=TRUE)[, , drop=FALSE] + dimnames(pm_test_mat)<-list(colnames(rv), c("value", "p.value")) ac_rslt<-list(info_transformation=ac_trf_str, estimates_ljungbox=pm_test_mat) - ac_q<-eval_pvals(ac_rslt$estimates_ljungbox[,"p.value"], h0_good=TRUE) + ac_q<-eval_pvals(ac_rslt$estimates_ljungbox[, "p.value"], h0_good=TRUE) }else{ ac_rslt<-NULL ac_q<-rep(NA, length(colnames(rv))) } ### IV.4. Seasonality test - seas_trf<- ifelse(is_log,"Delta-Log 1","Delta 1") - seas_trf_str<-ifelse(seas_trf == "Delta-Log 1", get_info_transformation(TRUE,TRUE), get_info_transformation(FALSE,TRUE)) - lb_test<-try(apply(diff(rv),2,function(x) seasonality_qs(x,freq)),silent=TRUE) # Ljung-Box - fd_test<-try(apply(diff(rv),2,function(x) seasonality_friedman(x,freq)),silent=TRUE) # Friedman non-parametric test + seas_trf<- ifelse(is_log, "Delta-Log 1", "Delta 1") + seas_trf_str<-ifelse(seas_trf == "Delta-Log 1", get_info_transformation(TRUE, TRUE), get_info_transformation(FALSE, TRUE)) + lb_test<-try(apply(diff(rv), 2, function(x) seasonality_qs(x, freq)), silent=TRUE) # Ljung-Box + fd_test<-try(apply(diff(rv), 2, function(x) seasonality_friedman(x, freq)), silent=TRUE) # Friedman non-parametric test if(!"try-error" %in% class(lb_test) & !"try-error" %in% class(fd_test) & freq>1){ seas_rslt<-list(info_transformation=seas_trf_str, - estimates_ljungbox=matrix(unlist(lb_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value","p.value"))), - estimates_friedman=matrix(unlist(fd_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value","p.value")))) - seas_lb_q<-eval_pvals(seas_rslt$estimates_ljungbox[,"p.value"], h0_good=TRUE) - seas_fd_q<-eval_pvals(seas_rslt$estimates_friedman[,"p.value"], h0_good=TRUE) + estimates_ljungbox=matrix(unlist(lb_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value", "p.value"))), + estimates_friedman=matrix(unlist(fd_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value", "p.value")))) + seas_lb_q<-eval_pvals(seas_rslt$estimates_ljungbox[, "p.value"], h0_good=TRUE) + seas_fd_q<-eval_pvals(seas_rslt$estimates_friedman[, "p.value"], h0_good=TRUE) }else if(!"try-error" %in% class(lb_test) & freq>1){ seas_rslt<-list(info_transformation=seas_trf_str, - estimates_ljungbox=matrix(unlist(lb_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value","p.value"))), + estimates_ljungbox=matrix(unlist(lb_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value", "p.value"))), estimates_friedman=NULL) - seas_lb_q<-eval_pvals(seas_rslt$estimates_ljungbox[,"p.value"], h0_good=TRUE) + seas_lb_q<-eval_pvals(seas_rslt$estimates_ljungbox[, "p.value"], h0_good=TRUE) seas_fd_q<-rep(NA, length(colnames(rv))) }else if(!"try-error" %in% class(fd_test) & freq>1){ seas_rslt<-list(info_transformation=seas_trf_str, estimates_ljungbox=NULL, - estimates_friedman=matrix(unlist(fd_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value","p.value")))) + estimates_friedman=matrix(unlist(fd_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value", "p.value")))) seas_lb_q<-rep(NA, length(colnames(rv))) - seas_fd_q<-eval_pvals(seas_rslt$estimates_friedman[,"p.value"], h0_good=TRUE) + seas_fd_q<-eval_pvals(seas_rslt$estimates_friedman[, "p.value"], h0_good=TRUE) }else{ seas_rslt<-NULL seas_lb_q<-seas_fd_q<-rep(NA, length(colnames(rv))) @@ -375,12 +375,12 @@ revision_analysis<-function(vintages, sn<-signalnoise(vts, gap, na.zero) if(!is.null(sn)){ sn_rslt<-list(info_transformation=get_info_transformation(is_log, !is_stationary), - estimates=t(round(sn,3))) - sn_noise_q<-eval_pvals(sn[,"Noise.pvalue"], h0_good=TRUE) - sn_news_q<-eval_pvals(sn[,"News.pvalue"], h0_good=FALSE) + estimates=t(round(sn, 3))) + sn_noise_q<-eval_pvals(sn[, "Noise.pvalue"], h0_good=TRUE) + sn_news_q<-eval_pvals(sn[, "News.pvalue"], h0_good=FALSE) }else{ sn_rslt<-NULL - sn_noise_q<-sn_news_q<-rep(NA,colnames(rv)) + sn_noise_q<-sn_news_q<-rep(NA, colnames(rv)) } @@ -395,7 +395,7 @@ revision_analysis<-function(vintages, ## 3. VECM errcorr<-vecm(vt, lag=2, model="none", na.zero) if(!is.null(errcorr)){ - vecm_rslt<-round(errcorr,3) + vecm_rslt<-round(errcorr, 3) }else{ vecm_rslt<-NULL } @@ -415,14 +415,14 @@ revision_analysis<-function(vintages, "Orthogonality3 AutoCorrelation (Ljung-Box)", "Orthogonality4 Seasonality (Ljung-Box)", "Orthogonality4 Seasonality (Friedman)", "SignalVsNoise1 - Noise (Ols R on P)", "SignalVsNoise2 - Signal (Ols R on L)") - transformation<-c(theil_trf,rep(ta_trf,2),rep(sd_trf,2),rep(eff1_trf,2), - rep(eff2_trf,2), rep(orth1_trf,2), rep(orth2_trf,2), - ac_trf, rep(seas_trf,2) ,rep(sn_trf,2)) + transformation<-c(theil_trf, rep(ta_trf, 2), rep(sd_trf, 2), rep(eff1_trf, 2), + rep(eff2_trf, 2), rep(orth1_trf, 2), rep(orth2_trf, 2), + ac_trf, rep(seas_trf, 2), rep(sn_trf, 2)) evals<-rbind(theil_q, t_q, ta_q, sd_m_q, sd_r_q, eff1_m_q, eff1_r_q, eff2_m_q, eff2_r_q, orth1_m_q, orth1_r_q, orth2_m_q, orth2_r_q, ac_q, seas_lb_q, seas_fd_q, sn_noise_q, sn_news_q) summary_table<-data.frame(transformation, evals, row.names = lbl) - colnames(summary_table)<- c("Transf.",colnames(rv)) + colnames(summary_table)<- c("Transf.", colnames(rv)) diagnostics_table <- list(slope_and_drift = sd_diagnostics, efficiency1 = eff1_diagnostics, efficiency2 = eff2_diagnostics, orthogonality1 = orth1_diagnostics, @@ -452,9 +452,9 @@ get_rownames_diag <- function(vt, gap){ # Example for n=4: v1_v2, v1_v3, v1_v4, v2_v3, v2_v4, v3_v4 n<-ncol(vt) idx1<-rep(1:(n-gap), (n-gap):1) - idx0<-sequence((n-gap):1)+rep(1:(n-gap),(n-gap):1) + idx0<-sequence((n-gap):1)+rep(1:(n-gap), (n-gap):1) w<-sapply(colnames(vt), function(s){paste0('[', s, ']')}) - rw<-mapply(function(a,b){paste(a,b,sep='_')}, w[idx1],w[idx0]) + rw<-mapply(function(a, b){paste(a, b, sep='_')}, w[idx1], w[idx0]) return(rw) } @@ -473,14 +473,14 @@ eval_pvals<-function(pval, h0_good = TRUE, residuals = FALSE){ }else{ if(h0_good){ quality<-ifelse(pval>.1, "Good", - ifelse(pval>.01, "Uncertain","Bad")) + ifelse(pval>.01, "Uncertain", "Bad")) }else{ quality<-ifelse(pval<.05, "Good", "Uncertain") } } quality[is.na(quality)]<-"Good" - return(paste0(quality, " (", trimws(format(round(pval,3), nsmall=3)), ")")) + return(paste0(quality, " (", trimws(format(round(pval, 3), nsmall=3)), ")")) } eval_U<-function(U, U2=TRUE){ @@ -497,21 +497,21 @@ eval_U<-function(U, U2=TRUE){ } quality[is.na(quality)]<-"Good" - return(paste0(quality, " (", trimws(format(round(U,3), nsmall=3)), ")")) + return(paste0(quality, " (", trimws(format(round(U, 3), nsmall=3)), ")")) } format_reg_output<-function(x, is_log, is_diff){ info_transformation<-get_info_transformation(is_log, is_diff) - x_df<-as.data.frame(t(round(x,3))) + x_df<-as.data.frame(t(round(x, 3))) n<-nrow(x_df) - estim<-x_df[1:(n-13),,drop=FALSE] + estim<-x_df[1:(n-13), , drop=FALSE] - norm_test<-list(Jarque_Bera_test=x_df[(n-12):(n-9),,drop=FALSE]) - hsk_test<-list(Breusch_Pagan_test=x_df[(n-8):(n-6),,drop=FALSE],White_test=x_df[(n-5):(n-3),,drop=FALSE],ARCH_test=x_df[(n-2):n,,drop=FALSE]) + norm_test<-list(Jarque_Bera_test=x_df[(n-12):(n-9), , drop=FALSE]) + hsk_test<-list(Breusch_Pagan_test=x_df[(n-8):(n-6), , drop=FALSE], White_test=x_df[(n-5):(n-3), , drop=FALSE], ARCH_test=x_df[(n-2):n, , drop=FALSE]) tests<-list(normality=norm_test, homoskedasticity=hsk_test) - return(list(info_transformation=info_transformation,estimates=estim,residuals=tests)) + return(list(info_transformation=info_transformation, estimates=estim, residuals=tests)) } get_info_transformation<-function(is_log, is_diff){ @@ -530,16 +530,16 @@ get_info_transformation<-function(is_log, is_diff){ regression_diagnostics<-function(reg_output){ - jb<-eval_pvals(reg_output[,"JarqueBera.pvalue"], residuals=TRUE) - bp<-eval_pvals(reg_output[,"BreuschPagan.pvalue"], residuals=TRUE) - wh<-eval_pvals(reg_output[,"White.pvalue"], residuals=TRUE) - arch<-eval_pvals(reg_output[,"arch.pvalue"], residuals=TRUE) + jb<-eval_pvals(reg_output[, "JarqueBera.pvalue"], residuals=TRUE) + bp<-eval_pvals(reg_output[, "BreuschPagan.pvalue"], residuals=TRUE) + wh<-eval_pvals(reg_output[, "White.pvalue"], residuals=TRUE) + arch<-eval_pvals(reg_output[, "arch.pvalue"], residuals=TRUE) lbl<-c("Jarque-Bera", "Breusch-Pagan", "White", "ARCH") - tests<-c("Normality", rep("Homoskedasticity",3)) - tests_rslts<-rbind(jb,bp,wh,arch) + tests<-c("Normality", rep("Homoskedasticity", 3)) + tests_rslts<-rbind(jb, bp, wh, arch) - rslt<-`colnames<-`(data.frame(tests, tests_rslts, row.names = lbl), c("Test",rownames(reg_output))) + rslt<-`colnames<-`(data.frame(tests, tests_rslts, row.names = lbl), c("Test", rownames(reg_output))) return(rslt) } @@ -550,10 +550,10 @@ get_vd_rev <- function(vt, gap){ idx1<-(gap+1):n idx0<-1:(n-gap) - rev<-vt[,idx1,drop=FALSE]-vt[,idx0,drop=FALSE] + rev<-vt[, idx1, drop=FALSE]-vt[, idx0, drop=FALSE] w<-sapply(colnames(vt), function(s){paste0('[', s, ']')}) - rw<-mapply(function(a,b){paste(a,b,sep='-')}, w[idx1],w[idx0]) + rw<-mapply(function(a, b){paste(a, b, sep='-')}, w[idx1], w[idx0]) rev<-`colnames<-`(rev, rw) return (rev) @@ -563,8 +563,8 @@ check_seasonality <- function(x){ if(frequency(x)>1){ x_diff<-diff(x) - lb_pval<-try(seasonality_qs(x_diff,frequency(x))$pvalue, silent=TRUE) # Ljung-Box - fd_pval<-try(seasonality_friedman(x_diff,frequency(x))$pvalue, silent=TRUE) # Friedman non-parametric test + lb_pval<-try(seasonality_qs(x_diff, frequency(x))$pvalue, silent=TRUE) # Ljung-Box + fd_pval<-try(seasonality_friedman(x_diff, frequency(x))$pvalue, silent=TRUE) # Friedman non-parametric test test_succeeded<-c(!"try-error" %in% class(lb_pval), !"try-error" %in% class(fd_pval)) if(all(test_succeeded)){ @@ -572,9 +572,9 @@ check_seasonality <- function(x){ seasonality<-ifelse(length(pvals[which(pvals<.05)])==2, TRUE, FALSE) }else if(any(test_succeeded)){ if(test_succeeded[1]){ - seasonality<-ifelse(lb_pval<.01,TRUE,FALSE) + seasonality<-ifelse(lb_pval<.01, TRUE, FALSE) }else if(test_succeeded[2]){ - seasonality<-ifelse(fd_pval<.01,TRUE,FALSE) + seasonality<-ifelse(fd_pval<.01, TRUE, FALSE) } }else{ seasonality<-FALSE diff --git a/R/revisions.R b/R/revisions.R index 67fc490..7a9c708 100644 --- a/R/revisions.R +++ b/R/revisions.R @@ -36,17 +36,17 @@ get_revisions<-function(vintages, gap=1){ idx1<-(gap+1):n idx0<-1:(n-gap) - rev<-vt[,idx1,drop=FALSE]-vt[,idx0,drop=FALSE] + rev<-vt[, idx1, drop=FALSE]-vt[, idx0, drop=FALSE] w<-sapply(colnames(vt), function(s){paste0('[', s, ']')}) - rw<-mapply(function(a,b){paste(a,b,sep='-')}, w[idx1],w[idx0]) + rw<-mapply(function(a, b){paste(a, b, sep='-')}, w[idx1], w[idx0]) rev<-`colnames<-`(rev, rw) return (rev) } vr<-get_vd_rev(vintages$vertical_view, gap) - hr<-`colnames<-`(t(vr),colnames(vintages$horizontal_view)) + hr<-`colnames<-`(t(vr), colnames(vintages$horizontal_view)) dr<-get_vd_rev(vintages$diagonal_view, gap) return (list(vertical_view=vr, horizontal_view=hr, diagonal_view=dr)) diff --git a/R/tests.R b/R/tests.R index 10487e6..d9dfaff 100644 --- a/R/tests.R +++ b/R/tests.R @@ -1,4 +1,4 @@ -descriptiveStatNames<-c("N", "mean revision", "st.dev.", "min", "q.10", "median","q.90", "max", "% positive", "% zero", "% negative", "mean absolute revision", "root mean square revision") +descriptiveStatNames<-c("N", "mean revision", "st.dev.", "min", "q.10", "median", "q.90", "max", "% positive", "% zero", "% negative", "mean absolute revision", "root mean square revision") biasNames<-c("N", "estimate", "stderr", "tstat", "pvalue", "ar(1)", "stderr.adjusted", "tstat.adjusted", "pvalue.adjusted") @@ -45,10 +45,10 @@ OlsAllNames<-function(nregs){ vecmAllNames<-function(lag){ t<-m<-c() for (i in lag:1){ - t<-c(t,paste0("trace(", i, ")")) - m<-c(m,paste0("max(", i, ")")) + t<-c(t, paste0("trace(", i, ")")) + m<-c(m, paste0("max(", i, ")")) } - return(c(t,m)) + return(c(t, m)) } #' Descriptive statistics @@ -90,9 +90,9 @@ descriptive_statistics<-function(revisions.view, rounding=3){ mn<-mean(rc) sd<-sd(rc) min<-min(rc) - q10<-quantile(rc,.1) + q10<-quantile(rc, .1) q50<-median(rc) - q90<-quantile(rc,.9) + q90<-quantile(rc, .9) max<-max(rc) pp<-length(rc[rc>0])/n p0<-length(rc[rc==0])/n @@ -100,12 +100,12 @@ descriptive_statistics<-function(revisions.view, rounding=3){ mar<-mean(abs(rc)) rmsr<-sqrt(mean(rc^2)) - return(c(n,mn,sd,min,q10,q50,q90,max,pp,p0,pn,mar,rmsr)) + return(c(n, mn, sd, min, q10, q50, q90, max, pp, p0, pn, mar, rmsr)) } ds<-apply(revisions.view, 2, descriptive_statistics_one) - return (`rownames<-`(round(ds,rounding), descriptiveStatNames)) + return (`rownames<-`(round(ds, rounding), descriptiveStatNames)) } #' Theil's Inequality Coefficient U1 @@ -148,9 +148,9 @@ theil<-function(vintages.view, gap=1, na.zero= FALSE){ q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) - theil<-try(.jcall("jdplus/revisions/base/r/Utility", "[D", "theil", jq, as.integer(gap)),silent= TRUE) + theil<-try(.jcall("jdplus/revisions/base/r/Utility", "[D", "theil", jq, as.integer(gap)), silent= TRUE) if("try-error" %in% class(theil)){ - warning("theil could not be performed",call.= FALSE) + warning("theil could not be performed", call.= FALSE) return(NULL) } return (theil) @@ -195,9 +195,9 @@ theil2<-function(vintages.view, gap=1, na.zero= FALSE){ q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) - theil2<-try(.jcall("jdplus/revisions/base/r/Utility", "[D", "theil2", jq, as.integer(gap)),silent= TRUE) + theil2<-try(.jcall("jdplus/revisions/base/r/Utility", "[D", "theil2", jq, as.integer(gap)), silent= TRUE) if("try-error" %in% class(theil2)){ - warning("theil2 could not be performed",call.= FALSE) + warning("theil2 could not be performed", call.= FALSE) return(NULL) } return (theil2) @@ -240,15 +240,15 @@ bias<-function(revisions.view, na.zero= FALSE){ r<-revisions.view if(na.zero) r[is.na(r)]<-0 jrevs<-matrix_r2jd(r) - jbias<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "bias", jrevs),silent= TRUE) + jbias<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "bias", jrevs), silent= TRUE) if("try-error" %in% class(bias)){ - warning("bias could not be performed",call.= FALSE) + warning("bias could not be performed", call.= FALSE) return(NULL) } bias <- matrix_jd2r(jbias) - bias[rowSums(bias[])==0,]<-NaN # fix non-calculable cases + bias[rowSums(bias[])==0, ]<-NaN # fix non-calculable cases if(all(is.nan(bias))){ - warning("bias could not be performed",call.= FALSE) + warning("bias could not be performed", call.= FALSE) return(NULL) } colnames(bias)<-biasNames @@ -299,15 +299,15 @@ slope_and_drift<-function(vintages.view, gap=1, na.zero= FALSE){ q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) - jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "slopeAndDrift", jq, as.integer(gap)),silent= TRUE) + jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "slopeAndDrift", jq, as.integer(gap)), silent= TRUE) if("try-error" %in% class(jsd)){ - warning("Slope and drift could not be performed",call.= FALSE) + warning("Slope and drift could not be performed", call.= FALSE) return(NULL) } slope_and_drift <- matrix_jd2r(jsd) - slope_and_drift[rowSums(slope_and_drift[])==0,]<-NaN # fix non-calculable cases + slope_and_drift[rowSums(slope_and_drift[])==0, ]<-NaN # fix non-calculable cases if(all(is.nan(slope_and_drift))){ - warning("slope_and_drift could not be performed",call.= FALSE) + warning("slope_and_drift could not be performed", call.= FALSE) return(NULL) } colnames(slope_and_drift)<-OlsNames @@ -358,21 +358,21 @@ efficiencyModel1<-function(vintages.view, gap=1, na.zero= FALSE){ q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) - jef1<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "efficiencyModel1", jq, as.integer(gap)),silent= TRUE) + jef1<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "efficiencyModel1", jq, as.integer(gap)), silent= TRUE) if("try-error" %in% class(jef1)){ - warning("efficiencyModel1 could not be performed",call.= FALSE) + warning("efficiencyModel1 could not be performed", call.= FALSE) return(NULL) } efficiencyModel1 <- matrix_jd2r(jef1) - efficiencyModel1[rowSums(efficiencyModel1[])==0,]<-NaN # fix non-calculable cases + efficiencyModel1[rowSums(efficiencyModel1[])==0, ]<-NaN # fix non-calculable cases if(all(is.nan(efficiencyModel1))){ - warning("efficiencyModel1 could not be performed",call.= FALSE) + warning("efficiencyModel1 could not be performed", call.= FALSE) return(NULL) } colnames(efficiencyModel1)<-OlsNames n<-dim(q)[2] w<-sapply(colnames(q), function(s){paste0('[', s, ']')}) - rw<-mapply(function(a,b){paste(a,b,sep='-')}, w[(gap+1):n],w[1:(n-gap)]) + rw<-mapply(function(a, b){paste(a, b, sep='-')}, w[(gap+1):n], w[1:(n-gap)]) rownames(efficiencyModel1)<-rw return (efficiencyModel1) } @@ -418,25 +418,25 @@ efficiencyModel2<-function(vintages.view, gap=1, na.zero= FALSE){ q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) - jef2<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "efficiencyModel2", jq, as.integer(gap)),silent= TRUE) + jef2<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "efficiencyModel2", jq, as.integer(gap)), silent= TRUE) if("try-error" %in% class(jef2)){ - warning("efficiencyModel2 could not be performed",call.= FALSE) + warning("efficiencyModel2 could not be performed", call.= FALSE) return(NULL) } efficiencyModel2 <- matrix_jd2r(jef2) if(length(efficiencyModel2)==0) { - warning("efficiencyModel2 could not be performed: Too few number of vintages",call.= FALSE) + warning("efficiencyModel2 could not be performed: Too few number of vintages", call.= FALSE) return(NULL) } - efficiencyModel2[rowSums(efficiencyModel2[])==0,]<-NaN # fix non-calculable cases + efficiencyModel2[rowSums(efficiencyModel2[])==0, ]<-NaN # fix non-calculable cases if(all(is.nan(efficiencyModel2))){ - warning("efficiencyModel2 could not be performed",call.= FALSE) + warning("efficiencyModel2 could not be performed", call.= FALSE) return(NULL) } colnames(efficiencyModel2)<-OlsNames n<-dim(q)[2] w<-sapply(colnames(q), function(s){paste0('[', s, ']')}) - rw<-mapply(function(a,b){paste(a,b,sep='-')}, w[(gap+1):n],w[1:(n-gap)]) + rw<-mapply(function(a, b){paste(a, b, sep='-')}, w[(gap+1):n], w[1:(n-gap)]) rownames(efficiencyModel2)<-rw[-1] return (efficiencyModel2) } @@ -481,19 +481,19 @@ orthogonallyModel1<-function(revisions.view, nrevs=1, na.zero= FALSE){ r<-revisions.view if(na.zero) r[is.na(r)]<-0 jr<-matrix_r2jd(as.matrix(r)) - jom<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "orthogonallyModel1", jr, as.integer(nrevs)),silent= TRUE) + jom<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "orthogonallyModel1", jr, as.integer(nrevs)), silent= TRUE) if("try-error" %in% class(jom)){ - warning("orthogonallyModel1 could not be performed",call.= FALSE) + warning("orthogonallyModel1 could not be performed", call.= FALSE) return(NULL) } om <- matrix_jd2r(jom) if (length(om)==0) { - warning("orthogonallyModel1 could not be performed: Too few number of vintages",call.= FALSE) + warning("orthogonallyModel1 could not be performed: Too few number of vintages", call.= FALSE) return(NULL) } - om[rowSums(om[])==0,]<-NaN # fix non-calculable cases + om[rowSums(om[])==0, ]<-NaN # fix non-calculable cases if(all(is.nan(om))){ - warning("orthogonallyModel1 could not be performed",call.= FALSE) + warning("orthogonallyModel1 could not be performed", call.= FALSE) return(NULL) } colnames(om)<-OlsAllNames(nrevs) @@ -541,19 +541,19 @@ orthogonallyModel2<-function(revisions.view, reference=1, na.zero= FALSE){ r<-revisions.view if(na.zero) r[is.na(r)]<-0 jr<-matrix_r2jd(as.matrix(r)) - jom<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "orthogonallyModel2", jr, as.integer(reference)),silent= TRUE) + jom<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "orthogonallyModel2", jr, as.integer(reference)), silent= TRUE) if("try-error" %in% class(jom)){ - warning("orthogonallyModel2 could not be performed",call.= FALSE) + warning("orthogonallyModel2 could not be performed", call.= FALSE) return(NULL) } om <- matrix_jd2r(jom) if (length(om)==0) { - warning("orthogonallyModel2 could not be performed: Too few number of vintages",call.= FALSE) + warning("orthogonallyModel2 could not be performed: Too few number of vintages", call.= FALSE) return(NULL) } - om[rowSums(om[])==0,]<-NaN # fix non-calculable cases + om[rowSums(om[])==0, ]<-NaN # fix non-calculable cases if(all(is.nan(om))){ - warning("orthogonallyModel2 could not be performed",call.= FALSE) + warning("orthogonallyModel2 could not be performed", call.= FALSE) return(NULL) } colnames(om)<-OlsNames @@ -604,21 +604,21 @@ signalnoise<-function(vintages.view, gap=1, na.zero= FALSE){ q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) - jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "signalNoise", jq, as.integer(gap)),silent= TRUE) + jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "signalNoise", jq, as.integer(gap)), silent= TRUE) if("try-error" %in% class(jsd)){ - warning("signalnoise could not be performed",call.= FALSE) + warning("signalnoise could not be performed", call.= FALSE) return(NULL) } sn<-matrix_jd2r(jsd) - sn[rowSums(sn[])==0,]<-NaN # fix non-calculable cases + sn[rowSums(sn[])==0, ]<-NaN # fix non-calculable cases if(all(is.nan(sn))){ - warning("SignalNoise could not be performed",call.= FALSE) + warning("SignalNoise could not be performed", call.= FALSE) return(NULL) } colnames(sn)<-snNames n<-dim(q)[2] w<-sapply(colnames(q), function(s){paste0('[', s, ']')}) - rw<-mapply(function(a,b){paste(a,b,sep='-')}, w[(gap+1):n],w[1:(n-gap)]) + rw<-mapply(function(a, b){paste(a, b, sep='-')}, w[(gap+1):n], w[1:(n-gap)]) rownames(sn)<-rw return (sn) } @@ -660,9 +660,9 @@ unitroot<-function(vintages.view, adfk=1, na.zero= FALSE){ q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) - jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "unitroot", jq, as.integer(adfk)),silent= TRUE) + jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "unitroot", jq, as.integer(adfk)), silent= TRUE) if("try-error" %in% class(jsd)){ - warning("unit root test could not be performed",call.= FALSE) + warning("unit root test could not be performed", call.= FALSE) return(NULL) } ur<-matrix_jd2r(jsd) @@ -708,9 +708,9 @@ cointegration<-function(vintages.view, adfk=1, na.zero= FALSE){ q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) - jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "cointegration", jq, as.integer(adfk)),silent= TRUE) + jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "cointegration", jq, as.integer(adfk)), silent= TRUE) if("try-error" %in% class(jsd)){ - warning("cointegration test could not be performed",call.= FALSE) + warning("cointegration test could not be performed", call.= FALSE) return(NULL) } eg<-matrix_jd2r(jsd) @@ -759,9 +759,9 @@ vecm<-function(vintages.view, lag=2, model = c("none", "cnt", "trend"), na.zero= q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) - jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "vecm", jq, as.integer(lag), model),silent= TRUE) + jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "vecm", jq, as.integer(lag), model), silent= TRUE) if("try-error" %in% class(jsd)){ - warning("vecm could not be performed",call.= FALSE) + warning("vecm could not be performed", call.= FALSE) return(NULL) } vecm<-matrix_jd2r(jsd) @@ -777,9 +777,9 @@ vecm<-function(vintages.view, lag=2, model = c("none", "cnt", "trend"), na.zero= # if(na.zero) q[is.na(q)]<-0 # jq<-matrix_r2jd(q) # jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "autoCorrelation", jq -# , as.integer(nbreuschgodfrey), as.integer(nljungbox)),silent= TRUE) +# , as.integer(nbreuschgodfrey), as.integer(nljungbox)), silent= TRUE) # if("try-error" %in% class(jsd)){ -# warning("auto_correlation test on OLS residuals could not be performed",call.= FALSE) +# warning("auto_correlation test on OLS residuals could not be performed", call.= FALSE) # return(NULL) # } # ac<-matrix_jd2r(jsd) diff --git a/R/vintages.R b/R/vintages.R index 20ef955..36e5091 100644 --- a/R/vintages.R +++ b/R/vintages.R @@ -86,7 +86,7 @@ create_vintages<- function(df, periodicity, vintage.selection = NULL, revdate.fo return(NULL) } - colnames(df)<-c("revdate","time","obs_value") + colnames(df)<-c("revdate", "time", "obs_value") df$revdate<-as.Date(as.character(df$revdate), revdate.format) if (any(is.na(df$revdate))){ @@ -139,8 +139,8 @@ create_vintages<- function(df, periodicity, vintage.selection = NULL, revdate.fo ## diagonal view vd_mat<-t(apply(t(vv), 2, function(x) x[order(is.na(x))])) - releases_name<-sprintf("Release[%s]",seq_len(ncol(vd_mat))) - vd<-`colnames<-`(ts(vd_mat, start = start(vv), frequency = periodicity),releases_name) + releases_name<-sprintf("Release[%s]", seq_len(ncol(vd_mat))) + vd<-`colnames<-`(ts(vd_mat, start = start(vv), frequency = periodicity), releases_name) vintages <- list(vertical_view = vv, horizontal_view = vh, diagonal_view = vd) class(vintages) <- "rjd3rev_vintages" @@ -259,16 +259,16 @@ yq<-function(y, q){ yp<-function(s){ y<-as.integer(substr(s, 1, 4)) if(nchar(as.character(s))[1] == 4){ - return (ymd(y,1)) + return (ymd(y, 1)) }else{ - p <- substr(s,5,5) + p <- substr(s, 5, 5) if (all(p == 'Q') | all(p == 'q')){ q<-as.integer(substr(s, 6, 6)) - return (yq(y,q)) + return (yq(y, q)) } if (all(p == 'M') | all(p == 'm')){ m<-as.integer(substr(s, 6, length(s))) - return (ymd(y,m)) + return (ymd(y, m)) } } return (NULL) @@ -277,11 +277,11 @@ yp<-function(s){ d2t<-function(d, periodicity){ y<-floor(d) frac<-d%%1 - date<-ymd(y,1,1)+(ymd(y+1,1,1)-ymd(y,1,1))*frac + date<-ymd(y, 1, 1)+(ymd(y+1, 1, 1)-ymd(y, 1, 1))*frac if (periodicity == 12){ - return (paste0(y,"M",format(date,"%m"))) + return (paste0(y, "M", format(date, "%m"))) }else if (periodicity == 4){ - return (paste0(y,"Q",(as.numeric(format(date,"%m"))+2)/3)) + return (paste0(y, "Q", (as.numeric(format(date, "%m"))+2)/3)) }else if (periodicity == 1){ return (y) } diff --git a/inst/templates/report.Rmd b/inst/templates/report.Rmd index d658935..db497bc 100644 --- a/inst/templates/report.Rmd +++ b/inst/templates/report.Rmd @@ -25,13 +25,13 @@ For some parametric tests, transformation may be important to avoid misleading r # Descriptive statistics ```{r descriptivetable, echo = FALSE} -selection<-c("N","mean revision", "st.dev.", "% positive", "% zero", "% negative") +selection<-c("N", "mean revision", "st.dev.", "% positive", "% zero", "% negative") if (! requireNamespace("kableExtra", quietly=TRUE)) { - knitr::kable(descriptive_statistics[selection,,drop=FALSE], format="html") + knitr::kable(descriptive_statistics[selection, , drop=FALSE], format="html") warning("Please install kableExtra: install.packages('kableExtra') to get more visual table output") }else{ - kableExtra::kable_minimal(knitr::kable(descriptive_statistics[selection,,drop=FALSE], format="html")) + kableExtra::kable_minimal(knitr::kable(descriptive_statistics[selection, , drop=FALSE], format="html")) } ``` @@ -42,14 +42,14 @@ if (! requireNamespace("kableExtra", quietly=TRUE)) { }else{ format_font <- function(x){ kableExtra::cell_spec(x, - color = ifelse(is.na(x),"black", - ifelse(substr(x,1,1) == "G", "green", - ifelse(substr(x,1,1) == "U", "orange", "red"))), - bold = ifelse(is.na(x),FALSE, - ifelse(substr(x,1,1) == "S", TRUE, FALSE))) + color = ifelse(is.na(x), "black", + ifelse(substr(x, 1, 1) == "G", "green", + ifelse(substr(x, 1, 1) == "U", "orange", "red"))), + bold = ifelse(is.na(x), FALSE, + ifelse(substr(x, 1, 1) == "S", TRUE, FALSE))) } nc<-ncol(main_results) - main_results[,2:nc]<-apply(main_results[,2:nc,drop=FALSE], 2, format_font) + main_results[, 2:nc]<-apply(main_results[, 2:nc, drop=FALSE], 2, format_font) kableExtra::kable_minimal(knitr::kable(main_results, format="html", escape = FALSE)) } ``` diff --git a/vignettes/rjd3revisions.Rmd b/vignettes/rjd3revisions.Rmd index 75fb38c..c9bf576 100644 --- a/vignettes/rjd3revisions.Rmd +++ b/vignettes/rjd3revisions.Rmd @@ -63,15 +63,15 @@ Depending on the location of your input data, you can use `create_vintages_from_ ```{r, eval = TRUE} # Example -input_df<-data.frame(rev_date = c(rep("2022-07-31",4), rep("2022-08-31",4), - rep("2022-09-30",4), rep("2022-10-31",4), - rep("2022-11-30",4), rep("2022-12-31",4), - rep("2023-01-31",4), rep("2023-02-28",4)), - time_period = c(rep(c("2022Q1","2022Q2","2022Q3","2022Q4"),8)), - obs_values = c(.8,.2,NA,NA, .8,.1,NA,NA, - .7,.1,NA,NA, .7,.2,.5,NA, - .7,.2,.5,NA, .7,.3,.7,NA, - .7,.2,.7,.4, .7,.3,.7,.3)) +input_df<-data.frame(rev_date = c(rep("2022-07-31", 4), rep("2022-08-31", 4), + rep("2022-09-30", 4), rep("2022-10-31", 4), + rep("2022-11-30", 4), rep("2022-12-31", 4), + rep("2023-01-31", 4), rep("2023-02-28", 4)), + time_period = c(rep(c("2022Q1", "2022Q2", "2022Q3", "2022Q4"), 8)), + obs_values = c(.8, .2, NA, NA, .8, .1, NA, NA, + .7, .1, NA, NA, .7, .2, .5, NA, + .7, .2, .5, NA, .7, .3, .7, NA, + .7, .2, .7, .4, .7, .3, .7, .3)) ``` ## Processing From f84bbc71c99cd9bd80924837fde8acde8832fdbb Mon Sep 17 00:00:00 2001 From: Corentin Lemasson <95612140+clemasso@users.noreply.github.com> Date: Tue, 20 Feb 2024 16:11:53 +0100 Subject: [PATCH 13/56] Update README.md --- README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index da4c3fa..6dd5f65 100644 --- a/README.md +++ b/README.md @@ -7,14 +7,14 @@ To get the current stable version (from the latest release): ``` r # install.packages("remotes") remotes::install_github("rjdemetra/rjd3toolkit@*release") -remotes::install_github("rjdemetra/rjd3revisions@*release") +remotes::install_github("rjdemetra/rjd3revisions@*release", build_vignettes = TRUE) ``` To get the current development version from GitHub: ``` r # install.packages("remotes") -remotes::install_github("rjdemetra/rjd3revisions") +remotes::install_github("rjdemetra/rjd3revisions", build_vignettes = TRUE) ``` ## Usage From fb91035e742d21d0ef65f37be2fd4bee0bc86bdc Mon Sep 17 00:00:00 2001 From: AQLT Date: Sat, 9 Mar 2024 19:11:25 +0100 Subject: [PATCH 14/56] correction of error when is.null(sn) --- R/revision_analysis.R | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/R/revision_analysis.R b/R/revision_analysis.R index c70f4e4..cdf1414 100644 --- a/R/revision_analysis.R +++ b/R/revision_analysis.R @@ -380,7 +380,7 @@ revision_analysis<-function(vintages, sn_news_q<-eval_pvals(sn[, "News.pvalue"], h0_good=FALSE) }else{ sn_rslt<-NULL - sn_noise_q<-sn_news_q<-rep(NA, colnames(rv)) + sn_noise_q<-sn_news_q<-rep(NA, length(colnames(rv))) } From 373c50e2c13d891b8514218217765da8e85bd761 Mon Sep 17 00:00:00 2001 From: AQLT Date: Sat, 9 Mar 2024 19:22:19 +0100 Subject: [PATCH 15/56] n.releases correction when ncol(vintages$diagonal_view) < n.releases --- R/revision_analysis.R | 1 + 1 file changed, 1 insertion(+) diff --git a/R/revision_analysis.R b/R/revision_analysis.R index cdf1414..4ff02b7 100644 --- a/R/revision_analysis.R +++ b/R/revision_analysis.R @@ -129,6 +129,7 @@ revision_analysis<-function(vintages, if(view == "vertical"){ vt<-vintages$vertical_view }else if (view == "diagonal"){ + n.releases <- min(n.releases, ncol(vintages$diagonal_view)) vt<-vintages$diagonal_view[, 1:n.releases] } From 26ea5481636db6687455fc8748e53d6de1cf4d72 Mon Sep 17 00:00:00 2001 From: Tanguy BARTHELEMY Date: Mon, 18 Mar 2024 10:08:30 +0100 Subject: [PATCH 16/56] document package --- DESCRIPTION | 2 +- man/bias.Rd | 6 +++--- man/cointegration.Rd | 8 ++++---- man/create_vintages_from_csv.Rd | 6 +++--- man/create_vintages_from_xlsx.Rd | 8 ++++---- man/descriptive_statistics.Rd | 10 +++++----- man/efficiencyModel1.Rd | 10 +++++----- man/efficiencyModel2.Rd | 10 +++++----- man/get_report.Rd | 6 +++--- man/orthogonallyModel1.Rd | 8 ++++---- man/orthogonallyModel2.Rd | 8 ++++---- man/revision_analysis.Rd | 32 ++++++++++++++++---------------- man/signalnoise.Rd | 14 +++++++------- man/slope_and_drift.Rd | 10 +++++----- man/theil.Rd | 10 +++++----- man/theil2.Rd | 12 ++++++------ man/unitroot.Rd | 8 ++++---- man/vecm.Rd | 13 +++++++++---- rjd3revisions.Rproj | 2 +- 19 files changed, 94 insertions(+), 89 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index 528cb63..3dc055e 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -39,5 +39,5 @@ Collate: 'tests.R' 'vintages.R' 'zzz.R' -RoxygenNote: 7.2.3 +RoxygenNote: 7.3.1 VignetteBuilder: knitr diff --git a/man/bias.Rd b/man/bias.Rd index 75b22d2..26304c0 100644 --- a/man/bias.Rd +++ b/man/bias.Rd @@ -4,13 +4,13 @@ \alias{bias} \title{Estimate bias using t-test and augmented t-test} \usage{ -bias(revisions.view, na.zero = F) +bias(revisions.view, na.zero = FALSE) } \arguments{ -\item{revisions.view}{mts object. Vertical or diagonal view of the +\item{revisions.view}{mts object. Vertical or diagonal view of the `get_revisions()` output} -\item{na.zero}{Boolean whether missing values should be considered as 0 or +\item{na.zero}{Boolean whether missing values should be considered as 0 or rather as data not (yet) available (the default).} } \description{ diff --git a/man/cointegration.Rd b/man/cointegration.Rd index 53b0184..73b166e 100644 --- a/man/cointegration.Rd +++ b/man/cointegration.Rd @@ -4,15 +4,15 @@ \alias{cointegration} \title{Cointegration tests (Engle-Granger)} \usage{ -cointegration(vintages.view, adfk = 1, na.zero = F) +cointegration(vintages.view, adfk = 1, na.zero = FALSE) } \arguments{ -\item{vintages.view}{mts object. Vertical or diagonal view of the +\item{vintages.view}{mts object. Vertical or diagonal view of the `create_vintages()` output} \item{adfk}{Number of lags to consider for ADF} -\item{na.zero}{Boolean whether missing values should be considered as 0 or +\item{na.zero}{Boolean whether missing values should be considered as 0 or rather as data not (yet) available (the default).} } \description{ @@ -24,7 +24,7 @@ period_range<-seq(as.Date('2011-01-01'),as.Date('2020-10-01'),by='quarter') qtr<-(as.numeric(substr(period_range,6,7))+2)/3 time_period<-rep(paste0(format(period_range, "\%Y"), "Q", qtr),5) np<-length(period_range) -rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), rep("2022-12-31",np), rep("2023-06-30",np)) set.seed(1) xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) diff --git a/man/create_vintages_from_csv.Rd b/man/create_vintages_from_csv.Rd index e31a2c6..0079cd1 100644 --- a/man/create_vintages_from_csv.Rd +++ b/man/create_vintages_from_csv.Rd @@ -40,10 +40,10 @@ Create vintages table from CSV or TXT files \examples{ \dontrun{ file.name<-"myinput.csv" -vintages<-create_vintages_from_csv(file.name, - periodicity=12, +vintages<-create_vintages_from_csv(file.name, + periodicity=12, separator = ";", - vintage.selection=NULL, + vintage.selection=NULL, revdate.format="\%Y-\%m-\%d") } } diff --git a/man/create_vintages_from_xlsx.Rd b/man/create_vintages_from_xlsx.Rd index 1e6440e..756ebb1 100644 --- a/man/create_vintages_from_xlsx.Rd +++ b/man/create_vintages_from_xlsx.Rd @@ -41,10 +41,10 @@ Create vintages table from XLSX files \dontrun{ file.name<-"myinput.xlsx" sheet.name<-"Sheet1" -vintages<-create_vintages_from_xlsx(file.name, - sheet.name, - periodicity=12, - vintage.selection=NULL, +vintages<-create_vintages_from_xlsx(file.name, + sheet.name, + periodicity=12, + vintage.selection=NULL, revdate.format="\%d/\%m/\%Y")) } } diff --git a/man/descriptive_statistics.Rd b/man/descriptive_statistics.Rd index d24f2cc..fb127a1 100644 --- a/man/descriptive_statistics.Rd +++ b/man/descriptive_statistics.Rd @@ -7,7 +7,7 @@ descriptive_statistics(revisions.view, rounding = 3) } \arguments{ -\item{revisions.view}{mts object. Vertical or diagonal view of the +\item{revisions.view}{mts object. Vertical or diagonal view of the `get_revisions()` output} \item{rounding}{number of decimals to display} @@ -21,7 +21,7 @@ period_range<-seq(as.Date('2011-01-01'),as.Date('2020-10-01'),by='quarter') qtr<-(as.numeric(substr(period_range,6,7))+2)/3 time_period<-rep(paste0(format(period_range, "\%Y"), "Q", qtr),5) np<-length(period_range) -rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), rep("2022-12-31",np), rep("2023-06-30",np)) set.seed(1) xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) @@ -32,10 +32,10 @@ for(i in 1:4){ obs_values<-c(obs_values,xt) } df<-data.frame(rev_date, time_period, obs_values) - -## Create vintage and get descriptive statistics of revisions + +## Create vintage and get descriptive statistics of revisions vintages<-create_vintages(df, periodicity = 4) revisions<-get_revisions(vintages, gap=1) descriptive_statistics(revisions$diagonal_view, rounding=1) - + } diff --git a/man/efficiencyModel1.Rd b/man/efficiencyModel1.Rd index e6f6f8c..ef068c3 100644 --- a/man/efficiencyModel1.Rd +++ b/man/efficiencyModel1.Rd @@ -4,17 +4,17 @@ \alias{efficiencyModel1} \title{Efficiency Model 1} \usage{ -efficiencyModel1(vintages.view, gap = 1, na.zero = F) +efficiencyModel1(vintages.view, gap = 1, na.zero = FALSE) } \arguments{ -\item{vintages.view}{mts object. Vertical or diagonal view of the +\item{vintages.view}{mts object. Vertical or diagonal view of the `create_vintages()` output} -\item{gap}{Integer. Gap to consider between each vintages. Default is 1 +\item{gap}{Integer. Gap to consider between each vintages. Default is 1 which means that revisions are calculated and tested for each vintages consecutively.} -\item{na.zero}{Boolean whether missing values should be considered as 0 or +\item{na.zero}{Boolean whether missing values should be considered as 0 or rather as data not (yet) available (the default).} } \description{ @@ -26,7 +26,7 @@ period_range<-seq(as.Date('2011-01-01'),as.Date('2020-10-01'),by='quarter') qtr<-(as.numeric(substr(period_range,6,7))+2)/3 time_period<-rep(paste0(format(period_range, "\%Y"), "Q", qtr),5) np<-length(period_range) -rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), rep("2022-12-31",np), rep("2023-06-30",np)) set.seed(1) xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) diff --git a/man/efficiencyModel2.Rd b/man/efficiencyModel2.Rd index 169d112..3e33ec2 100644 --- a/man/efficiencyModel2.Rd +++ b/man/efficiencyModel2.Rd @@ -4,17 +4,17 @@ \alias{efficiencyModel2} \title{Efficiency Model 2} \usage{ -efficiencyModel2(vintages.view, gap = 1, na.zero = F) +efficiencyModel2(vintages.view, gap = 1, na.zero = FALSE) } \arguments{ -\item{vintages.view}{mts object. Vertical or diagonal view of the +\item{vintages.view}{mts object. Vertical or diagonal view of the `create_vintages()` output} -\item{gap}{Integer. Gap to consider between each vintages. Default is 1 +\item{gap}{Integer. Gap to consider between each vintages. Default is 1 which means that revisions are calculated and tested for each vintages consecutively.} -\item{na.zero}{Boolean whether missing values should be considered as 0 or +\item{na.zero}{Boolean whether missing values should be considered as 0 or rather as data not (yet) available (the default).} } \description{ @@ -26,7 +26,7 @@ period_range<-seq(as.Date('2011-01-01'),as.Date('2020-10-01'),by='quarter') qtr<-(as.numeric(substr(period_range,6,7))+2)/3 time_period<-rep(paste0(format(period_range, "\%Y"), "Q", qtr),5) np<-length(period_range) -rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), rep("2022-12-31",np), rep("2023-06-30",np)) set.seed(1) xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) diff --git a/man/get_report.Rd b/man/get_report.Rd index 2851d32..7ad3d63 100644 --- a/man/get_report.Rd +++ b/man/get_report.Rd @@ -4,10 +4,10 @@ \alias{get_report} \title{Generate report on Revision Analysis} \usage{ -get_report(rslt, path.out = NULL, open.report = T) +get_report(rslt, path.out = NULL, open.report = TRUE) } \arguments{ -\item{rslt}{an object of class `"rjd3rev_vintages"` which is the output +\item{rslt}{an object of class `"rjd3rev_vintages"` which is the output of the function `revision_analysis()`} \item{path.out}{path of the output HTML file containing the report. Default @@ -26,7 +26,7 @@ period_range<-seq(as.Date('2011-01-01'),as.Date('2020-10-01'),by='quarter') qtr<-(as.numeric(substr(period_range,6,7))+2)/3 time_period<-rep(paste0(format(period_range, "\%Y"), "Q", qtr),5) np<-length(period_range) -rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), rep("2022-12-31",np), rep("2023-06-30",np)) set.seed(1) xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) diff --git a/man/orthogonallyModel1.Rd b/man/orthogonallyModel1.Rd index bc1169c..7edc074 100644 --- a/man/orthogonallyModel1.Rd +++ b/man/orthogonallyModel1.Rd @@ -4,15 +4,15 @@ \alias{orthogonallyModel1} \title{Orthogonally Model 1} \usage{ -orthogonallyModel1(revisions.view, nrevs = 1, na.zero = F) +orthogonallyModel1(revisions.view, nrevs = 1, na.zero = FALSE) } \arguments{ -\item{revisions.view}{mts object. Vertical or diagonal view of the +\item{revisions.view}{mts object. Vertical or diagonal view of the `get_revisions()` output} \item{nrevs}{Integer. Number of lags to consider.} -\item{na.zero}{Boolean whether missing values should be considered as 0 or +\item{na.zero}{Boolean whether missing values should be considered as 0 or rather as data not (yet) available (the default).} } \description{ @@ -24,7 +24,7 @@ period_range<-seq(as.Date('2011-01-01'),as.Date('2020-10-01'),by='quarter') qtr<-(as.numeric(substr(period_range,6,7))+2)/3 time_period<-rep(paste0(format(period_range, "\%Y"), "Q", qtr),5) np<-length(period_range) -rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), rep("2022-12-31",np), rep("2023-06-30",np)) set.seed(1) xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) diff --git a/man/orthogonallyModel2.Rd b/man/orthogonallyModel2.Rd index b1e5453..29498f8 100644 --- a/man/orthogonallyModel2.Rd +++ b/man/orthogonallyModel2.Rd @@ -4,15 +4,15 @@ \alias{orthogonallyModel2} \title{Orthogonally Model 2} \usage{ -orthogonallyModel2(revisions.view, reference = 1, na.zero = F) +orthogonallyModel2(revisions.view, reference = 1, na.zero = FALSE) } \arguments{ -\item{revisions.view}{mts object. Vertical or diagonal view of the +\item{revisions.view}{mts object. Vertical or diagonal view of the `get_revisions()` output} \item{reference}{Integer. Number of lags to consider.} -\item{na.zero}{Boolean whether missing values should be considered as 0 or +\item{na.zero}{Boolean whether missing values should be considered as 0 or rather as data not (yet) available (the default).} } \description{ @@ -24,7 +24,7 @@ period_range<-seq(as.Date('2011-01-01'),as.Date('2020-10-01'),by='quarter') qtr<-(as.numeric(substr(period_range,6,7))+2)/3 time_period<-rep(paste0(format(period_range, "\%Y"), "Q", qtr),5) np<-length(period_range) -rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), rep("2022-12-31",np), rep("2023-06-30",np)) set.seed(1) xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) diff --git a/man/revision_analysis.Rd b/man/revision_analysis.Rd index 17cf054..dff070f 100644 --- a/man/revision_analysis.Rd +++ b/man/revision_analysis.Rd @@ -10,52 +10,52 @@ revision_analysis( view = c("vertical", "diagonal"), n.releases = 3, transf.diff = c("auto", "forced", "none"), - transf.log = F, + transf.log = FALSE, descriptive.rounding = 3, nrevs = 1, ref = 1, - na.zero = F + na.zero = FALSE ) } \arguments{ -\item{vintages}{an object of class `"rjd3rev_vintages"` which is the output +\item{vintages}{an object of class `"rjd3rev_vintages"` which is the output of the function `create_vintages()`} -\item{gap}{Integer. Gap to consider between each vintages. Default is 1 +\item{gap}{Integer. Gap to consider between each vintages. Default is 1 which means that revisions are calculated and tested for each vintages consecutively.} \item{view}{Selected view. Can be "vertical" (the default) or "diagonal". -Vertical view shows the observed values at each time period by +Vertical view shows the observed values at each time period by the different vintages. Diagonal view shows subsequent releases -of a given time period, without regard for the date of -publication, which can be particularly informative when regular +of a given time period, without regard for the date of +publication, which can be particularly informative when regular estimation intervals exist. See `?create_vintages()` for more information about interests and drawbacks of each view.} -\item{n.releases}{only used when `view = "diagonal"`. Ignored otherwise. -Allow the user to limit the number of releases under +\item{n.releases}{only used when `view = "diagonal"`. Ignored otherwise. +Allow the user to limit the number of releases under investigation). When `view = "vertical"`, the user is invited to limit the number of vintages upstream through the parameter `vintage.selection` in `create_vintages()` whenever necessary.} -\item{transf.diff}{differentiation to apply to the data prior testing. Only +\item{transf.diff}{differentiation to apply to the data prior testing. Only used for regressions including vintage data as regressor -and/or regressand. Regression including revision data only -are never differentiated even if `transf.diff = "forced"`. +and/or regressand. Regression including revision data only +are never differentiated even if `transf.diff = "forced"`. Options are "automatic" (the default), "forced" and "none".} \item{transf.log}{Boolean whether a log-transformation should first be applied to the data. Default is FALSE.} -\item{descriptive.rounding}{Integer. Number of decimals to display for +\item{descriptive.rounding}{Integer. Number of decimals to display for descriptive statistics. Default is 3.} -\item{nrevs, ref}{Integer. Number of lags to consider for orthogonality tests +\item{nrevs, ref}{Integer. Number of lags to consider for orthogonality tests 1 and 2 respectively.} -\item{na.zero}{Boolean whether missing values should be considered as 0 or +\item{na.zero}{Boolean whether missing values should be considered as 0 or rather as data not yet available (the default).} } \value{ @@ -122,6 +122,6 @@ rslt3<-revision_analysis(vintages, gap=2, view = "vertical") } \seealso{ -`create_vintages()` to create the input object, +`create_vintages()` to create the input object, `get_report()` to get a summary and information the tests } diff --git a/man/signalnoise.Rd b/man/signalnoise.Rd index 54ab51b..74ebdce 100644 --- a/man/signalnoise.Rd +++ b/man/signalnoise.Rd @@ -4,22 +4,22 @@ \alias{signalnoise} \title{Signal VS Noise} \usage{ -signalnoise(vintages.view, gap = 1, na.zero = F) +signalnoise(vintages.view, gap = 1, na.zero = FALSE) } \arguments{ -\item{vintages.view}{mts object. Vertical or diagonal view of the +\item{vintages.view}{mts object. Vertical or diagonal view of the `create_vintages()` output} -\item{gap}{Integer. Gap to consider between each vintages. Default is 1 +\item{gap}{Integer. Gap to consider between each vintages. Default is 1 which means that revisions are calculated and tested for each vintages consecutively.} -\item{na.zero}{Boolean whether missing values should be considered as 0 or +\item{na.zero}{Boolean whether missing values should be considered as 0 or rather as data not (yet) available (the default).} } \description{ -Linear regression models to determine whether revisions are ‘news’ or ‘noise’. -For 'noise': R (revisions) on P (preliminary estimate). +Linear regression models to determine whether revisions are ‘news’ or ‘noise’. +For 'noise': R (revisions) on P (preliminary estimate). For 'news': R on L (latter estimate). } \examples{ @@ -28,7 +28,7 @@ period_range<-seq(as.Date('2011-01-01'),as.Date('2020-10-01'),by='quarter') qtr<-(as.numeric(substr(period_range,6,7))+2)/3 time_period<-rep(paste0(format(period_range, "\%Y"), "Q", qtr),5) np<-length(period_range) -rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), rep("2022-12-31",np), rep("2023-06-30",np)) set.seed(1) xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) diff --git a/man/slope_and_drift.Rd b/man/slope_and_drift.Rd index c49ebee..ee6af97 100644 --- a/man/slope_and_drift.Rd +++ b/man/slope_and_drift.Rd @@ -4,17 +4,17 @@ \alias{slope_and_drift} \title{Slope and Drift} \usage{ -slope_and_drift(vintages.view, gap = 1, na.zero = F) +slope_and_drift(vintages.view, gap = 1, na.zero = FALSE) } \arguments{ -\item{vintages.view}{mts object. Vertical or diagonal view of the +\item{vintages.view}{mts object. Vertical or diagonal view of the `create_vintages()` output} -\item{gap}{Integer. Gap to consider between each vintages. Default is 1 +\item{gap}{Integer. Gap to consider between each vintages. Default is 1 which means that revisions are calculated and tested for each vintages consecutively.} -\item{na.zero}{Boolean whether missing values should be considered as 0 or +\item{na.zero}{Boolean whether missing values should be considered as 0 or rather as data not (yet) available (the default).} } \description{ @@ -26,7 +26,7 @@ period_range<-seq(as.Date('2011-01-01'),as.Date('2020-10-01'),by='quarter') qtr<-(as.numeric(substr(period_range,6,7))+2)/3 time_period<-rep(paste0(format(period_range, "\%Y"), "Q", qtr),5) np<-length(period_range) -rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), rep("2022-12-31",np), rep("2023-06-30",np)) set.seed(1) xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) diff --git a/man/theil.Rd b/man/theil.Rd index 90aa566..ee43d5b 100644 --- a/man/theil.Rd +++ b/man/theil.Rd @@ -4,17 +4,17 @@ \alias{theil} \title{Theil's Inequality Coefficient U1} \usage{ -theil(vintages.view, gap = 1, na.zero = F) +theil(vintages.view, gap = 1, na.zero = FALSE) } \arguments{ -\item{vintages.view}{mts object. Vertical or diagonal view of the +\item{vintages.view}{mts object. Vertical or diagonal view of the `create_vintages()` output} -\item{gap}{Integer. Gap to consider between each vintages. Default is 1 +\item{gap}{Integer. Gap to consider between each vintages. Default is 1 which means that revisions are calculated and tested for each vintages consecutively.} -\item{na.zero}{Boolean whether missing values should be considered as 0 or +\item{na.zero}{Boolean whether missing values should be considered as 0 or rather as data not (yet) available (the default).} } \description{ @@ -26,7 +26,7 @@ period_range<-seq(as.Date('2011-01-01'),as.Date('2020-10-01'),by='quarter') qtr<-(as.numeric(substr(period_range,6,7))+2)/3 time_period<-rep(paste0(format(period_range, "\%Y"), "Q", qtr),5) np<-length(period_range) -rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), rep("2022-12-31",np), rep("2023-06-30",np)) set.seed(1) xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) diff --git a/man/theil2.Rd b/man/theil2.Rd index e9bd387..37b6ce4 100644 --- a/man/theil2.Rd +++ b/man/theil2.Rd @@ -4,17 +4,17 @@ \alias{theil2} \title{Theil's Inequality Coefficient U2} \usage{ -theil2(vintages.view, gap = 1, na.zero = F) +theil2(vintages.view, gap = 1, na.zero = FALSE) } \arguments{ -\item{vintages.view}{mts object. Vertical or diagonal view of the +\item{vintages.view}{mts object. Vertical or diagonal view of the `create_vintages()` output} -\item{gap}{Integer. Gap to consider between each vintages. Default is 1 +\item{gap}{Integer. Gap to consider between each vintages. Default is 1 which means that revisions are calculated and tested for each vintages consecutively..} -\item{na.zero}{Boolean whether missing values should be considered as 0 or +\item{na.zero}{Boolean whether missing values should be considered as 0 or rather as data not (yet) available (the default).} } \description{ @@ -26,7 +26,7 @@ period_range<-seq(as.Date('2011-01-01'),as.Date('2020-10-01'),by='quarter') qtr<-(as.numeric(substr(period_range,6,7))+2)/3 time_period<-rep(paste0(format(period_range, "\%Y"), "Q", qtr),5) np<-length(period_range) -rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), rep("2022-12-31",np), rep("2023-06-30",np)) set.seed(1) xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) @@ -37,7 +37,7 @@ for(i in 1:4){ obs_values<-c(obs_values,xt) } df<-data.frame(rev_date, time_period, obs_values) - + ## Create vintage and test vintages<-create_vintages(df, periodicity = 4) theil2(vintages$diagonal_view) diff --git a/man/unitroot.Rd b/man/unitroot.Rd index 43564a0..ec42a55 100644 --- a/man/unitroot.Rd +++ b/man/unitroot.Rd @@ -4,15 +4,15 @@ \alias{unitroot} \title{Unit root test} \usage{ -unitroot(vintages.view, adfk = 1, na.zero = F) +unitroot(vintages.view, adfk = 1, na.zero = FALSE) } \arguments{ -\item{vintages.view}{mts object. Vertical or diagonal view of the +\item{vintages.view}{mts object. Vertical or diagonal view of the `create_vintages()` output} \item{adfk}{Number of lags to consider for Augmented Dicky-Fuller (ADF) test} -\item{na.zero}{Boolean whether missing values should be considered as 0 or +\item{na.zero}{Boolean whether missing values should be considered as 0 or rather as data not (yet) available (the default).} } \description{ @@ -24,7 +24,7 @@ period_range<-seq(as.Date('2011-01-01'),as.Date('2020-10-01'),by='quarter') qtr<-(as.numeric(substr(period_range,6,7))+2)/3 time_period<-rep(paste0(format(period_range, "\%Y"), "Q", qtr),5) np<-length(period_range) -rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), rep("2022-12-31",np), rep("2023-06-30",np)) set.seed(1) xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) diff --git a/man/vecm.Rd b/man/vecm.Rd index b7f330c..44dbace 100644 --- a/man/vecm.Rd +++ b/man/vecm.Rd @@ -4,17 +4,22 @@ \alias{vecm} \title{Vector error correction model (VECM)} \usage{ -vecm(vintages.view, lag = 2, model = c("none", "cnt", "trend"), na.zero = F) +vecm( + vintages.view, + lag = 2, + model = c("none", "cnt", "trend"), + na.zero = FALSE +) } \arguments{ -\item{vintages.view}{mts object. Vertical or diagonal view of the +\item{vintages.view}{mts object. Vertical or diagonal view of the `create_vintages()` output} \item{lag}{Number of lags} \item{model}{Character. Must be "none" (the default), "cnt" or "trend".} -\item{na.zero}{Boolean whether missing values should be considered as 0 or +\item{na.zero}{Boolean whether missing values should be considered as 0 or rather as data not (yet) available (the default).} } \description{ @@ -27,7 +32,7 @@ period_range<-seq(as.Date('2011-01-01'),as.Date('2020-10-01'),by='quarter') qtr<-(as.numeric(substr(period_range,6,7))+2)/3 time_period<-rep(paste0(format(period_range, "\%Y"), "Q", qtr),5) np<-length(period_range) -rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), +rev_date<-c(rep("2021-06-30",np), rep("2021-12-31",np), rep("2022-06-30",np), rep("2022-12-31",np), rep("2023-06-30",np)) set.seed(1) xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) diff --git a/rjd3revisions.Rproj b/rjd3revisions.Rproj index 7e81b12..1fd1f6b 100644 --- a/rjd3revisions.Rproj +++ b/rjd3revisions.Rproj @@ -18,6 +18,6 @@ StripTrailingWhitespace: Yes BuildType: Package PackageUseDevtools: Yes PackageInstallArgs: --no-multiarch --with-keep.source -PackageRoxygenize: rd,collate,namespace +PackageRoxygenize: rd,collate,namespace,vignette UseNativePipeOperator: Yes From 0779d371e63b0ca22a83a544af8d2fbda45424bd Mon Sep 17 00:00:00 2001 From: Tanguy BARTHELEMY Date: Mon, 18 Mar 2024 10:22:26 +0100 Subject: [PATCH 17/56] quote linter --- R/output.R | 2 +- R/revision_analysis.R | 8 ++++---- R/revisions.R | 4 ++-- R/tests.R | 12 ++++++------ R/vintages.R | 4 ++-- 5 files changed, 15 insertions(+), 15 deletions(-) diff --git a/R/output.R b/R/output.R index f4c824a..f9bff63 100644 --- a/R/output.R +++ b/R/output.R @@ -23,7 +23,7 @@ summary.rjd3rev_revision_analysis<- function(x){ return(x$summary) }else{ format_font <- function(x){ - formattable::formatter('span', + formattable::formatter("span", style = x ~ formattable::style(color = ifelse(substr(x, 1, 1) == "G", "green", ifelse(substr(x, 1, 1) == "U", "orange", "red")), font.weight = ifelse(substr(x, 1, 1) == "S", "bold", "plain"))) diff --git a/R/revision_analysis.R b/R/revision_analysis.R index c70f4e4..2c80efc 100644 --- a/R/revision_analysis.R +++ b/R/revision_analysis.R @@ -453,8 +453,8 @@ get_rownames_diag <- function(vt, gap){ n<-ncol(vt) idx1<-rep(1:(n-gap), (n-gap):1) idx0<-sequence((n-gap):1)+rep(1:(n-gap), (n-gap):1) - w<-sapply(colnames(vt), function(s){paste0('[', s, ']')}) - rw<-mapply(function(a, b){paste(a, b, sep='_')}, w[idx1], w[idx0]) + w<-sapply(colnames(vt), function(s){paste0("[", s, "]")}) + rw<-mapply(function(a, b){paste(a, b, sep="_")}, w[idx1], w[idx0]) return(rw) } @@ -552,8 +552,8 @@ get_vd_rev <- function(vt, gap){ rev<-vt[, idx1, drop=FALSE]-vt[, idx0, drop=FALSE] - w<-sapply(colnames(vt), function(s){paste0('[', s, ']')}) - rw<-mapply(function(a, b){paste(a, b, sep='-')}, w[idx1], w[idx0]) + w<-sapply(colnames(vt), function(s){paste0("[", s, "]")}) + rw<-mapply(function(a, b){paste(a, b, sep="-")}, w[idx1], w[idx0]) rev<-`colnames<-`(rev, rw) return (rev) diff --git a/R/revisions.R b/R/revisions.R index 7a9c708..6e549ba 100644 --- a/R/revisions.R +++ b/R/revisions.R @@ -38,8 +38,8 @@ get_revisions<-function(vintages, gap=1){ rev<-vt[, idx1, drop=FALSE]-vt[, idx0, drop=FALSE] - w<-sapply(colnames(vt), function(s){paste0('[', s, ']')}) - rw<-mapply(function(a, b){paste(a, b, sep='-')}, w[idx1], w[idx0]) + w<-sapply(colnames(vt), function(s){paste0("[", s, "]")}) + rw<-mapply(function(a, b){paste(a, b, sep="-")}, w[idx1], w[idx0]) rev<-`colnames<-`(rev, rw) return (rev) diff --git a/R/tests.R b/R/tests.R index d9dfaff..aad3e95 100644 --- a/R/tests.R +++ b/R/tests.R @@ -371,8 +371,8 @@ efficiencyModel1<-function(vintages.view, gap=1, na.zero= FALSE){ } colnames(efficiencyModel1)<-OlsNames n<-dim(q)[2] - w<-sapply(colnames(q), function(s){paste0('[', s, ']')}) - rw<-mapply(function(a, b){paste(a, b, sep='-')}, w[(gap+1):n], w[1:(n-gap)]) + w<-sapply(colnames(q), function(s){paste0("[", s, "]")}) + rw<-mapply(function(a, b){paste(a, b, sep="-")}, w[(gap+1):n], w[1:(n-gap)]) rownames(efficiencyModel1)<-rw return (efficiencyModel1) } @@ -435,8 +435,8 @@ efficiencyModel2<-function(vintages.view, gap=1, na.zero= FALSE){ } colnames(efficiencyModel2)<-OlsNames n<-dim(q)[2] - w<-sapply(colnames(q), function(s){paste0('[', s, ']')}) - rw<-mapply(function(a, b){paste(a, b, sep='-')}, w[(gap+1):n], w[1:(n-gap)]) + w<-sapply(colnames(q), function(s){paste0("[", s, "]")}) + rw<-mapply(function(a, b){paste(a, b, sep="-")}, w[(gap+1):n], w[1:(n-gap)]) rownames(efficiencyModel2)<-rw[-1] return (efficiencyModel2) } @@ -617,8 +617,8 @@ signalnoise<-function(vintages.view, gap=1, na.zero= FALSE){ } colnames(sn)<-snNames n<-dim(q)[2] - w<-sapply(colnames(q), function(s){paste0('[', s, ']')}) - rw<-mapply(function(a, b){paste(a, b, sep='-')}, w[(gap+1):n], w[1:(n-gap)]) + w<-sapply(colnames(q), function(s){paste0("[", s, "]")}) + rw<-mapply(function(a, b){paste(a, b, sep="-")}, w[(gap+1):n], w[1:(n-gap)]) rownames(sn)<-rw return (sn) } diff --git a/R/vintages.R b/R/vintages.R index 36e5091..d373080 100644 --- a/R/vintages.R +++ b/R/vintages.R @@ -262,11 +262,11 @@ yp<-function(s){ return (ymd(y, 1)) }else{ p <- substr(s, 5, 5) - if (all(p == 'Q') | all(p == 'q')){ + if (all(p == "Q") | all(p == "q")){ q<-as.integer(substr(s, 6, 6)) return (yq(y, q)) } - if (all(p == 'M') | all(p == 'm')){ + if (all(p == "M") | all(p == "m")){ m<-as.integer(substr(s, 6, length(s))) return (ymd(y, m)) } From 3821a8f55cf40720d1a0fde5fd26398d533a336c Mon Sep 17 00:00:00 2001 From: Tanguy BARTHELEMY Date: Mon, 18 Mar 2024 10:25:55 +0100 Subject: [PATCH 18/56] =?UTF-8?q?logical=20&&=20and=20||=20in=20if=C3=83?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- R/revision_analysis.R | 8 ++++---- R/vintages.R | 4 ++-- 2 files changed, 6 insertions(+), 6 deletions(-) diff --git a/R/revision_analysis.R b/R/revision_analysis.R index 2c80efc..d2f65ad 100644 --- a/R/revision_analysis.R +++ b/R/revision_analysis.R @@ -196,7 +196,7 @@ revision_analysis<-function(vintages, is_stationary<-is_cointegrated<-FALSE }else if(transf.diff == "none"){ vts<-vtc<-vt - if(!is_stationary | !is_cointegrated){ + if(!is_stationary || !is_cointegrated){ warning("No differentiation considered even though stationarity and/or cointegration might not be present. This can lead to spurious regression.", call.=FALSE) } is_stationary<-is_cointegrated<-TRUE @@ -344,19 +344,19 @@ revision_analysis<-function(vintages, lb_test<-try(apply(diff(rv), 2, function(x) seasonality_qs(x, freq)), silent=TRUE) # Ljung-Box fd_test<-try(apply(diff(rv), 2, function(x) seasonality_friedman(x, freq)), silent=TRUE) # Friedman non-parametric test - if(!"try-error" %in% class(lb_test) & !"try-error" %in% class(fd_test) & freq>1){ + if(!"try-error" %in% class(lb_test) && !"try-error" %in% class(fd_test) && freq>1){ seas_rslt<-list(info_transformation=seas_trf_str, estimates_ljungbox=matrix(unlist(lb_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value", "p.value"))), estimates_friedman=matrix(unlist(fd_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value", "p.value")))) seas_lb_q<-eval_pvals(seas_rslt$estimates_ljungbox[, "p.value"], h0_good=TRUE) seas_fd_q<-eval_pvals(seas_rslt$estimates_friedman[, "p.value"], h0_good=TRUE) - }else if(!"try-error" %in% class(lb_test) & freq>1){ + }else if(!"try-error" %in% class(lb_test) && freq>1){ seas_rslt<-list(info_transformation=seas_trf_str, estimates_ljungbox=matrix(unlist(lb_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value", "p.value"))), estimates_friedman=NULL) seas_lb_q<-eval_pvals(seas_rslt$estimates_ljungbox[, "p.value"], h0_good=TRUE) seas_fd_q<-rep(NA, length(colnames(rv))) - }else if(!"try-error" %in% class(fd_test) & freq>1){ + }else if(!"try-error" %in% class(fd_test) && freq>1){ seas_rslt<-list(info_transformation=seas_trf_str, estimates_ljungbox=NULL, estimates_friedman=matrix(unlist(fd_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value", "p.value")))) diff --git a/R/vintages.R b/R/vintages.R index d373080..024a43d 100644 --- a/R/vintages.R +++ b/R/vintages.R @@ -262,11 +262,11 @@ yp<-function(s){ return (ymd(y, 1)) }else{ p <- substr(s, 5, 5) - if (all(p == "Q") | all(p == "q")){ + if (all(p == "Q") || all(p == "q")){ q<-as.integer(substr(s, 6, 6)) return (yq(y, q)) } - if (all(p == "M") | all(p == "m")){ + if (all(p == "M") || all(p == "m")){ m<-as.integer(substr(s, 6, length(s))) return (ymd(y, m)) } From 83a85f71d8bd3877e8cc41ce67627fadf193583c Mon Sep 17 00:00:00 2001 From: Tanguy BARTHELEMY Date: Mon, 18 Mar 2024 11:06:32 +0100 Subject: [PATCH 19/56] lintr brace --- R/jd3_rslts.R | 54 +++++++------- R/jd3_ts.R | 18 ++--- R/output.R | 12 +-- R/report.R | 4 +- R/revision_analysis.R | 152 +++++++++++++++++++------------------- R/revisions.R | 10 +-- R/tests.R | 118 ++++++++++++++--------------- R/vintages.R | 48 ++++++------ inst/templates/report.Rmd | 6 +- 9 files changed, 212 insertions(+), 210 deletions(-) diff --git a/R/jd3_rslts.R b/R/jd3_rslts.R index 1e73004..71aace3 100644 --- a/R/jd3_rslts.R +++ b/R/jd3_rslts.R @@ -1,6 +1,6 @@ #' @include jd3_ts.R -proc_numeric<-function(rslt, name){ +proc_numeric<-function(rslt, name) { s<-.jcall(rslt, "Ljava/lang/Object;", "getData", name, jd_clobj) if (!is.jnull(s)) .jcall(s, "D", "doubleValue") @@ -8,28 +8,28 @@ proc_numeric<-function(rslt, name){ return (NaN) } -proc_vector<-function(rslt, name){ +proc_vector<-function(rslt, name) { s<-.jcall(rslt, "Ljava/lang/Object;", "getData", name, jd_clobj) if (is.jnull(s)) return(NULL) .jevalArray(s) } -proc_int<-function(rslt, name){ +proc_int<-function(rslt, name) { s<-.jcall(rslt, "Ljava/lang/Object;", "getData", name, jd_clobj) if (is.jnull(s)) return(-1) .jcall(s, "I", "intValue") } -proc_bool<-function(rslt, name){ +proc_bool<-function(rslt, name) { s<-.jcall(rslt, "Ljava/lang/Object;", "getData", name, jd_clobj) if (is.jnull(s)) return(FALSE) .jcall(s, "Z", "booleanValue") } -proc_ts<-function(rslt, name){ +proc_ts<-function(rslt, name) { s<-.jcall(rslt, "Ljava/lang/Object;", "getData", name, jd_clobj) if (is.jnull(s)) return (NULL) @@ -39,21 +39,21 @@ proc_ts<-function(rslt, name){ return (NULL) } -proc_str<-function(rslt, name){ +proc_str<-function(rslt, name) { s<-.jcall(rslt, "Ljava/lang/Object;", "getData", name, jd_clobj) if (is.jnull(s)) return(NULL) .jcall(s, "S", "toString") } -proc_desc<-function(rslt, name){ +proc_desc<-function(rslt, name) { s<-.jcall(rslt, "Ljava/lang/Object;", "getData", name, jd_clobj) if (is.jnull(s)) return(NULL) .jevalArray(s) } -proc_test<-function(rslt, name){ +proc_test<-function(rslt, name) { s<-.jcall(rslt, "Ljava/lang/Object;", "getData", name, jd_clobj) if (is.jnull(s)) return(NULL) @@ -65,7 +65,7 @@ proc_test<-function(rslt, name){ all } -proc_parameter<-function(rslt, name){ +proc_parameter<-function(rslt, name) { s<-.jcall(rslt, "Ljava/lang/Object;", "getData", name, jd_clobj) if (is.jnull(s)) return(NULL) @@ -73,56 +73,56 @@ proc_parameter<-function(rslt, name){ return (val) } -proc_parameters<-function(rslt, name){ +proc_parameters<-function(rslt, name) { jd_p<-.jcall(rslt, "Ljava/lang/Object;", "getData", name, jd_clobj) if (is.jnull(jd_p)) return(NULL) p<-.jcastToArray(jd_p) len<-length(p) all<-array(0, dim=c(len)) - for (i in 1:len){ + for (i in 1:len) { all[i]<-.jcall(p[[i]], "D", "getValue") } all } -proc_matrix<-function(rslt, name){ +proc_matrix<-function(rslt, name) { s<-.jcall(rslt, "Ljava/lang/Object;", "getData", name, jd_clobj) if (is.jnull(s)) return(NULL) return (matrix_jd2r(s)) } -proc_data<-function(rslt, name){ +proc_data<-function(rslt, name) { s<-.jcall(rslt, "Ljava/lang/Object;", "getData", name, jd_clobj) if (is.jnull(s)) return (NULL) - if (.jinstanceof(s, "demetra/timeseries/TsData")) + if (.jinstanceof(s, "demetra/timeseries/TsData")) { return(ts_jd2r(.jcast(s, "demetra/timeseries/TsData"))) - else if (.jinstanceof(s, "java/lang/Number")) + + } else if (.jinstanceof(s, "java/lang/Number")) { return (.jcall(s, "D", "doubleValue")) - else if (.jinstanceof(s, "demetra/math/matrices/MatrixType")) + } else if (.jinstanceof(s, "demetra/math/matrices/MatrixType")) { return(matrix_jd2r(.jcast(s, "demetra/math/matrices/MatrixType"))) - else if (.jinstanceof(s, "demetra/data/Parameter")){ + } else if (.jinstanceof(s, "demetra/data/Parameter")) { val<-.jcall(s, "D", "getValue") - return (c(val)) - } - else if (.jinstanceof(s, "[Ldemetra/data/Parameter;")){ + return (c(val)) + } else if (.jinstanceof(s, "[Ldemetra/data/Parameter;")) { p<-.jcastToArray(s) len<-length(p) all<-array(0, dim=c(len)) - for (i in 1:len){ + for (i in 1:len) { all[i]<-.jcall(p[[i]], "D", "getValue") } return (all) - } - else if (.jcall(.jcall(s, "Ljava/lang/Class;", "getClass"), "Z", "isArray")) + } else if (.jcall(.jcall(s, "Ljava/lang/Class;", "getClass"), "Z", "isArray")) { return (.jevalArray(s, silent=TRUE)) - else + } else { return (.jcall(s, "S", "toString")) + } } -proc_dictionary<-function(name){ +proc_dictionary<-function(name) { jmapping<-.jcall(name, "Ldemetra/information/InformationMapping;", "getMapping") jmap<-.jnew("java/util/LinkedHashMap") .jcall(jmapping, "V", "fillDictionary", .jnull("java/lang/String"), .jcast(jmap, "java/util/Map"), TRUE) @@ -130,13 +130,13 @@ proc_dictionary<-function(name){ size<-.jcall(jkeys, "I", "size") keys<-array(dim=size) jiter<-.jcall(jkeys, "Ljava/util/Iterator;", "iterator") - for (i in 1:size){ + for (i in 1:size) { keys[i] <- .jcall(.jcall(jiter, "Ljava/lang/Object;", "next"), "Ljava/lang/String;", "toString") } return (keys) } -proc_likelihood<-function(jrslt, prefix){ +proc_likelihood<-function(jrslt, prefix) { return (list( ll=proc_numeric(jrslt, paste(prefix, "ll", sep="")), ssq=proc_numeric(jrslt, paste(prefix, "ssq", sep="")), diff --git a/R/jd3_ts.R b/R/jd3_ts.R index acf59f9..0ea415e 100644 --- a/R/jd3_ts.R +++ b/R/jd3_ts.R @@ -1,5 +1,5 @@ -ts_r2jd<-function(s){ - if (is.null(s)){ +ts_r2jd<-function(s) { + if (is.null(s)) { return (NULL) } freq<-frequency(s) @@ -8,14 +8,14 @@ ts_r2jd<-function(s){ as.integer(freq), as.integer(start[1]), as.integer(start[2]), as.double(s)) } -tsdomain_r2jd<-function(period, startYear, startPeriod, length){ +tsdomain_r2jd<-function(period, startYear, startPeriod, length) { .jcall("jdplus/toolkit/base/r/timeseries/TsUtility", "Ljdplus/toolkit/base/r/timeseries/TsDomain;", "of", as.integer(period), as.integer(startYear), as.integer(startPeriod), as.integer(length)) } -ts_jd2r<-function(s){ - if (is.null(s)){ +ts_jd2r<-function(s) { + if (is.null(s)) { return (NULL) } pstart<-.jcall("jdplus/toolkit/base/r/timeseries/TsUtility", "[I", "startPeriod", s) @@ -24,8 +24,8 @@ ts_jd2r<-function(s){ ts(x, start=pstart[2:3], frequency=pstart[1]) } -matrix_jd2r<-function(s){ - if (is.jnull(s)){ +matrix_jd2r<-function(s) { + if (is.jnull(s)) { return (NULL) } nr<-.jcall(s, "I", "getRowsCount") @@ -34,10 +34,10 @@ matrix_jd2r<-function(s){ return (array(d, dim=c(nr, nc))) } -matrix_r2jd<-function(s){ +matrix_r2jd<-function(s) { if (is.null(s)) return (.jnull("jdplus/toolkit/base/api/math/matrices/Matrix")) - if (!is.matrix(s)){ + if (!is.matrix(s)) { s<-matrix(s, nrow=length(s), ncol=1) } sdim<-dim(s) diff --git a/R/output.R b/R/output.R index f9bff63..6f10c53 100644 --- a/R/output.R +++ b/R/output.R @@ -4,7 +4,7 @@ #' @param \dots further arguments passed to or from other methods. #' @export #' -print.rjd3rev_revision_analysis <- function(x, ...){ +print.rjd3rev_revision_analysis <- function(x, ...) { print(list(call=x$call, descriptive_statistics=x$descriptive.statistics, @@ -16,13 +16,13 @@ print.rjd3rev_revision_analysis <- function(x, ...){ #' @param x an object of class "rjd3rev_revision_analysis" #' @export #' -summary.rjd3rev_revision_analysis<- function(x){ +summary.rjd3rev_revision_analysis<- function(x) { if (! requireNamespace("formattable", quietly = TRUE)) { warning("Please install 'formattable': install.packages('formattable') to get more visual output") return(x$summary) - }else{ - format_font <- function(x){ + } else { + format_font <- function(x) { formattable::formatter("span", style = x ~ formattable::style(color = ifelse(substr(x, 1, 1) == "G", "green", ifelse(substr(x, 1, 1) == "U", "orange", "red")), @@ -39,10 +39,10 @@ summary.rjd3rev_revision_analysis<- function(x){ #' @param \dots further arguments passed to or from other methods. #' @export #' -plot.rjd3rev_revision_analysis <- function(x, ...){ +plot.rjd3rev_revision_analysis <- function(x, ...) { rev<-x$revisions nc<-ncol(rev) - if(nc>4){ + if(nc>4) { rev<-rev[, 1:4] nc<-4 } diff --git a/R/report.R b/R/report.R index b858956..d6a9783 100644 --- a/R/report.R +++ b/R/report.R @@ -43,9 +43,9 @@ get_report <- function(rslt, #template_file<-"report.Rmd" template_file<-system.file("templates/report.Rmd", package = "rjd3revisions") - if(is.null(path.out)){ + if (is.null(path.out)) { path.out<-paste0(getwd(), "/", "revisions_report.html") - }else{ + } else { path.out<-ifelse(substr(path.out, length(path.out)-5, length(path.out)) != ".html", paste0(path.out, ".html"), path.out) diff --git a/R/revision_analysis.R b/R/revision_analysis.R index d2f65ad..9c08323 100644 --- a/R/revision_analysis.R +++ b/R/revision_analysis.R @@ -70,7 +70,7 @@ #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) #' rev<-rnorm(np*4,0,.1) #' obs_values<-xt -#' for(i in 1:4){ +#' for(i in 1:4) { #' xt<-xt+rev[(1+(i-1)*np):(i*np)] #' obs_values<-c(obs_values,xt) #' } @@ -108,7 +108,7 @@ revision_analysis<-function(vintages, descriptive.rounding = 3, nrevs = 1, ref = 1, - na.zero=FALSE){ + na.zero=FALSE) { options(scipen = 999) @@ -126,9 +126,9 @@ revision_analysis<-function(vintages, # Input selection ## Select vintage view - if(view == "vertical"){ + if(view == "vertical") { vt<-vintages$vertical_view - }else if (view == "diagonal"){ + }else if (view == "diagonal") { vt<-vintages$diagonal_view[, 1:n.releases] } @@ -137,42 +137,42 @@ revision_analysis<-function(vintages, freq<-frequency(vt) ### Log transformation - if(transf.log){ - if(length(vt[vt[!is.na(vt)] < 0])>0){ + if(transf.log) { + if(length(vt[vt[!is.na(vt)] < 0])>0) { warning("Logarithm transformation incompatible with negative data. No transformation considered.", call.=FALSE) rv<-rv_notrf is_log<-FALSE - }else{ + } else { vt<-log(vt) rv<-get_vd_rev(vt, gap) is_log<-TRUE } - }else{ + } else { rv<-rv_notrf is_log<-FALSE } ### Differentiation ur<-unitroot(vt, adfk=1, na.zero) # H0: non-stationary - if(!is.null(ur)){ + if(!is.null(ur)) { ur_rslt<-t(round(ur, 3)) ur_ADFpvals<-ur[, "ADF.pvalue"] pc_signif_ur<-length(ur_ADFpvals[ur_ADFpvals<.05])/length(ur_ADFpvals) is_stationary<-ifelse(pc_signif_ur>.8, TRUE, FALSE) - }else{ + } else { ur_rslt<-NULL is_stationary<-TRUE } coint<-cointegration(vt, adfk=1, na.zero) # H0: no-cointegration - if(is_stationary){ + if(is_stationary) { is_cointegrated<-TRUE - }else{ - if(!is.null(coint)){ + } else { + if(!is.null(coint)) { coint_pvals<-coint[, "pvalue"] pc_signif_coint<-length(coint_pvals[coint_pvals<.05])/length(coint_pvals) is_cointegrated<-ifelse(pc_signif_coint>.8, TRUE, FALSE) - }else{ + } else { is_cointegrated<-FALSE } } @@ -180,7 +180,7 @@ revision_analysis<-function(vintages, seasonality<-apply(vt, 2, check_seasonality) nt<-sum(seasonality) is_seasonal<-ifelse(nt/ncol(vt)>.8, TRUE, FALSE) - if(is_seasonal){ + if(is_seasonal) { vt_diff<-diff(vt, freq) delta_diff<-freq } else { @@ -188,15 +188,15 @@ revision_analysis<-function(vintages, delta_diff<-1 } - if(transf.diff == "auto"){ + if(transf.diff == "auto") { vts<-if(is_stationary) vt else vt_diff vtc<-if(is_cointegrated) vt else vt_diff - }else if(transf.diff == "forced"){ + }else if(transf.diff == "forced") { vts<-vtc<-vt_diff is_stationary<-is_cointegrated<-FALSE - }else if(transf.diff == "none"){ + }else if(transf.diff == "none") { vts<-vtc<-vt - if(!is_stationary || !is_cointegrated){ + if(!is_stationary || !is_cointegrated) { warning("No differentiation considered even though stationarity and/or cointegration might not be present. This can lead to spurious regression.", call.=FALSE) } is_stationary<-is_cointegrated<-TRUE @@ -215,19 +215,19 @@ revision_analysis<-function(vintages, theil_trf<-"None" U1<-theil(vt, gap, na.zero) U2<-theil2(vt, gap, na.zero) - if(!is.null(U1)){ + if(!is.null(U1)) { theil_rslt<-round(rbind(N, U1), 3) - if(!is.null(U2) && !all(is.nan(U2))==TRUE){ + if(!is.null(U2) && !all(is.nan(U2))==TRUE) { theil_rslt<-rbind(theil_rslt, U2=round(U2, 3)) theil_q<-eval_U(U2) U_det<-"U2" - }else{ + } else { theil_rslt<-rbind(theil_rslt, U2=rep(NA, length(U1))) theil_q<-eval_U(U1, U2=FALSE) U_det<-"U1" warning("Theil U2 could not be calculated. Theil U1 is considered instead in summary().", call.=FALSE) } - }else{ + } else { theil_rslt<-NULL theil_q<-rep(NA, length(colnames(rv))) } @@ -237,11 +237,11 @@ revision_analysis<-function(vintages, ### II.1_2. T-test and Augmented T-test ta_trf<-ifelse(is_log, "Log", "None") ta<-bias(rv, na.zero) - if(!is.null(ta)){ + if(!is.null(ta)) { ta_rslt<-t(round(ta, 3)) t_q<-eval_pvals(ta[, "pvalue"], h0_good=TRUE) ta_q<-eval_pvals(ta[, "pvalue.adjusted"], h0_good=TRUE) - }else{ + } else { ta_rslt<-NULL t_q<-ta_q<-rep(NA, length(colnames(rv))) } @@ -252,12 +252,12 @@ revision_analysis<-function(vintages, if (!is_cointegrated && !is_log) paste("Delta", delta_diff) else paste("Delta-Log", delta_diff) sd<-slope_and_drift(vtc, gap, na.zero) - if(!is.null(sd)){ + if(!is.null(sd)) { sd_rslt<-format_reg_output(sd, is_log, !is_cointegrated) sd_m_q<-eval_pvals(sd[, "intercept.pvalue"], h0_good=TRUE) sd_r_q<-eval_pvals(sd[, "slope.pvalue"], h0_good=TRUE) sd_diagnostics<-regression_diagnostics(sd) - }else{ + } else { sd_rslt<-sd_diagnostics<-NULL sd_m_q<-sd_r_q<-rep(NA, length(colnames(vtc)[-c(1:gap)])) } @@ -270,12 +270,12 @@ revision_analysis<-function(vintages, if (!is_stationary && !is_log) paste("Delta", delta_diff) else paste("Delta-Log", delta_diff) eff1<-efficiencyModel1(vts, gap, na.zero) - if(!is.null(eff1)){ + if(!is.null(eff1)) { eff1_rslt<-format_reg_output(eff1, is_log, !is_stationary) eff1_m_q<-eval_pvals(eff1[, "intercept.pvalue"], h0_good=TRUE) eff1_r_q<-eval_pvals(eff1[, "slope.pvalue"], h0_good=TRUE) eff1_diagnostics<-regression_diagnostics(eff1) - }else{ + } else { eff1_rslt<-eff1_diagnostics<-NULL eff1_m_q<-eff1_r_q<-rep(NA, length(colnames(rv))) } @@ -283,12 +283,12 @@ revision_analysis<-function(vintages, ### III.2. Regression of latter revisions (Rv) on previous revisions (Rv_1) eff2_trf<-ifelse(is_log, "Log", "None") eff2<-efficiencyModel2(vt, gap, na.zero) - if(!is.null(eff2)){ + if(!is.null(eff2)) { eff2_rslt<-format_reg_output(eff2, is_log, FALSE) eff2_m_q<-c("", eval_pvals(eff2[, "intercept.pvalue"], h0_good=TRUE)) eff2_r_q<-c("", eval_pvals(eff2[, "slope.pvalue"], h0_good=TRUE)) eff2_diagnostics<-regression_diagnostics(eff2) - }else{ + } else { eff2_rslt<-eff2_diagnostics<-NULL eff2_m_q<-eff2_r_q<-c("", rep(NA, length(colnames(rv)[-1]))) } @@ -298,12 +298,12 @@ revision_analysis<-function(vintages, ### IV.1. Regression of latter revisions (Rv) on previous revisions (Rv_1, Rv_2,...Rv_p) orth1_trf<-ifelse(is_log, "Log", "None") orth1<-orthogonallyModel1(rv, nrevs, na.zero) - if(!is.null(orth1)){ + if(!is.null(orth1)) { orth1_rslt<-format_reg_output(orth1, is_log, FALSE) orth1_m_q<-c(rep("", nrevs), eval_pvals(orth1[, "intercept.pvalue"], h0_good=TRUE)) orth1_r_q<-c(rep("", nrevs), eval_pvals(pf(orth1[, "F"], nrevs, orth1[, "N"]-nrevs-1), h0_good=TRUE)) orth1_diagnostics<-regression_diagnostics(orth1) - }else{ + } else { orth1_rslt<-orth1_diagnostics<-NULL if(ncol(rv)>nrevs) orth1_m_q<-orth1_r_q<-c(rep("", nrevs), rep(NA, length(colnames(rv)[-c(1:nrevs)]))) else orth1_m_q<-orth1_r_q<-rep("", nrevs) @@ -312,12 +312,12 @@ revision_analysis<-function(vintages, ### IV.2. Regression model of latter revisions (Rv) on previous revisions at a specific version (Rv_k) orth2_trf<-ifelse(is_log, "Log", "None") orth2<-orthogonallyModel2(rv, ref, na.zero) - if(!is.null(orth2)){ + if(!is.null(orth2)) { orth2_rslt<-format_reg_output(orth2, is_log, FALSE) orth2_m_q<-c(rep("", ref), eval_pvals(orth2[, "intercept.pvalue"], h0_good=TRUE)) orth2_r_q<-c(rep("", ref), eval_pvals(orth2[, "slope.pvalue"], h0_good=TRUE)) orth2_diagnostics<-regression_diagnostics(orth2) - }else{ + } else { orth2_rslt<-orth2_diagnostics<-NULL if(ncol(rv)>ref) orth2_m_q<-orth2_r_q<-c(rep("", ref), rep(NA, length(colnames(rv)[-c(1:ref)]))) else orth2_m_q<-orth2_r_q<-rep("", ref) @@ -328,12 +328,12 @@ revision_analysis<-function(vintages, ac_trf_str<-ifelse(ac_trf == "Log", get_info_transformation(TRUE, FALSE), get_info_transformation(FALSE, FALSE)) pm_test<-try(apply(rv, 2, function(x) ljungbox(x[!is.na(x)], k=2)), silent=TRUE) # Ljung-Box up to k - if(!"try-error" %in% class(pm_test)){ + if(!"try-error" %in% class(pm_test)) { pm_test_mat<-matrix(unlist(pm_test), ncol=2, byrow=TRUE)[, , drop=FALSE] dimnames(pm_test_mat)<-list(colnames(rv), c("value", "p.value")) ac_rslt<-list(info_transformation=ac_trf_str, estimates_ljungbox=pm_test_mat) ac_q<-eval_pvals(ac_rslt$estimates_ljungbox[, "p.value"], h0_good=TRUE) - }else{ + } else { ac_rslt<-NULL ac_q<-rep(NA, length(colnames(rv))) } @@ -344,25 +344,25 @@ revision_analysis<-function(vintages, lb_test<-try(apply(diff(rv), 2, function(x) seasonality_qs(x, freq)), silent=TRUE) # Ljung-Box fd_test<-try(apply(diff(rv), 2, function(x) seasonality_friedman(x, freq)), silent=TRUE) # Friedman non-parametric test - if(!"try-error" %in% class(lb_test) && !"try-error" %in% class(fd_test) && freq>1){ + if(!"try-error" %in% class(lb_test) && !"try-error" %in% class(fd_test) && freq>1) { seas_rslt<-list(info_transformation=seas_trf_str, estimates_ljungbox=matrix(unlist(lb_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value", "p.value"))), estimates_friedman=matrix(unlist(fd_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value", "p.value")))) seas_lb_q<-eval_pvals(seas_rslt$estimates_ljungbox[, "p.value"], h0_good=TRUE) seas_fd_q<-eval_pvals(seas_rslt$estimates_friedman[, "p.value"], h0_good=TRUE) - }else if(!"try-error" %in% class(lb_test) && freq>1){ + }else if(!"try-error" %in% class(lb_test) && freq>1) { seas_rslt<-list(info_transformation=seas_trf_str, estimates_ljungbox=matrix(unlist(lb_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value", "p.value"))), estimates_friedman=NULL) seas_lb_q<-eval_pvals(seas_rslt$estimates_ljungbox[, "p.value"], h0_good=TRUE) seas_fd_q<-rep(NA, length(colnames(rv))) - }else if(!"try-error" %in% class(fd_test) && freq>1){ + }else if(!"try-error" %in% class(fd_test) && freq>1) { seas_rslt<-list(info_transformation=seas_trf_str, estimates_ljungbox=NULL, estimates_friedman=matrix(unlist(fd_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value", "p.value")))) seas_lb_q<-rep(NA, length(colnames(rv))) seas_fd_q<-eval_pvals(seas_rslt$estimates_friedman[, "p.value"], h0_good=TRUE) - }else{ + } else { seas_rslt<-NULL seas_lb_q<-seas_fd_q<-rep(NA, length(colnames(rv))) } @@ -373,12 +373,12 @@ revision_analysis<-function(vintages, if(!is_stationary && !is_log) paste("Delta", delta_diff) else paste("Delta-Log", delta_diff) sn<-signalnoise(vts, gap, na.zero) - if(!is.null(sn)){ + if(!is.null(sn)) { sn_rslt<-list(info_transformation=get_info_transformation(is_log, !is_stationary), estimates=t(round(sn, 3))) sn_noise_q<-eval_pvals(sn[, "Noise.pvalue"], h0_good=TRUE) sn_news_q<-eval_pvals(sn[, "News.pvalue"], h0_good=FALSE) - }else{ + } else { sn_rslt<-NULL sn_noise_q<-sn_news_q<-rep(NA, colnames(rv)) } @@ -394,9 +394,9 @@ revision_analysis<-function(vintages, ## 3. VECM errcorr<-vecm(vt, lag=2, model="none", na.zero) - if(!is.null(errcorr)){ + if(!is.null(errcorr)) { vecm_rslt<-round(errcorr, 3) - }else{ + } else { vecm_rslt<-NULL } @@ -448,33 +448,33 @@ revision_analysis<-function(vintages, -get_rownames_diag <- function(vt, gap){ +get_rownames_diag <- function(vt, gap) { # Example for n=4: v1_v2, v1_v3, v1_v4, v2_v3, v2_v4, v3_v4 n<-ncol(vt) idx1<-rep(1:(n-gap), (n-gap):1) idx0<-sequence((n-gap):1)+rep(1:(n-gap), (n-gap):1) - w<-sapply(colnames(vt), function(s){paste0("[", s, "]")}) - rw<-mapply(function(a, b){paste(a, b, sep="_")}, w[idx1], w[idx0]) + w<-sapply(colnames(vt), function(s) paste0("[", s, "]")) + rw<-mapply(function(a, b) paste(a, b, sep="_"), w[idx1], w[idx0]) return(rw) } -eval_pvals<-function(pval, h0_good = TRUE, residuals = FALSE){ +eval_pvals<-function(pval, h0_good = TRUE, residuals = FALSE) { pval<-as.numeric(pval) - if(! residuals){ - if(h0_good){ + if(! residuals) { + if(h0_good) { quality<-ifelse(pval>.05, "Good", ifelse(pval>.01, "Uncertain", ifelse(pval>.001, "Bad", "Severe"))) - }else{ + } else { quality<-ifelse(pval<.05, "Good", "Uncertain") } - }else{ - if(h0_good){ + } else { + if(h0_good) { quality<-ifelse(pval>.1, "Good", ifelse(pval>.01, "Uncertain", "Bad")) - }else{ + } else { quality<-ifelse(pval<.05, "Good", "Uncertain") } } @@ -483,14 +483,14 @@ eval_pvals<-function(pval, h0_good = TRUE, residuals = FALSE){ return(paste0(quality, " (", trimws(format(round(pval, 3), nsmall=3)), ")")) } -eval_U<-function(U, U2=TRUE){ +eval_U<-function(U, U2=TRUE) { U<-as.numeric(U) - if(U2){ + if(U2) { quality<-ifelse(U>=1, "Severe", ifelse(U>.9, "Bad", ifelse(U>.8, "Uncertain", "Good"))) - }else{ + } else { quality<-ifelse(U>.99, "Severe", ifelse(U>.9, "Bad", ifelse(U>.8, "Uncertain", "Good"))) @@ -500,7 +500,7 @@ eval_U<-function(U, U2=TRUE){ return(paste0(quality, " (", trimws(format(round(U, 3), nsmall=3)), ")")) } -format_reg_output<-function(x, is_log, is_diff){ +format_reg_output<-function(x, is_log, is_diff) { info_transformation<-get_info_transformation(is_log, is_diff) x_df<-as.data.frame(t(round(x, 3))) @@ -514,21 +514,21 @@ format_reg_output<-function(x, is_log, is_diff){ return(list(info_transformation=info_transformation, estimates=estim, residuals=tests)) } -get_info_transformation<-function(is_log, is_diff){ - if(is_log){ +get_info_transformation<-function(is_log, is_diff) { + if(is_log) { info_transformation<-"Series have been log-transformed" if(is_diff) info_transformation<-paste(info_transformation, "and differentiated") - }else{ - if(is_diff){ + } else { + if(is_diff) { info_transformation<-"Series have been differentiated" - }else{ + } else { info_transformation<-"No transformation" } } return(info_transformation) } -regression_diagnostics<-function(reg_output){ +regression_diagnostics<-function(reg_output) { jb<-eval_pvals(reg_output[, "JarqueBera.pvalue"], residuals=TRUE) bp<-eval_pvals(reg_output[, "BreuschPagan.pvalue"], residuals=TRUE) @@ -544,7 +544,7 @@ regression_diagnostics<-function(reg_output){ return(rslt) } -get_vd_rev <- function(vt, gap){ +get_vd_rev <- function(vt, gap) { n<-dim(vt)[2] idx1<-(gap+1):n @@ -552,34 +552,34 @@ get_vd_rev <- function(vt, gap){ rev<-vt[, idx1, drop=FALSE]-vt[, idx0, drop=FALSE] - w<-sapply(colnames(vt), function(s){paste0("[", s, "]")}) - rw<-mapply(function(a, b){paste(a, b, sep="-")}, w[idx1], w[idx0]) + w<-sapply(colnames(vt), function(s) paste0("[", s, "]")) + rw<-mapply(function(a, b) paste(a, b, sep="-"), w[idx1], w[idx0]) rev<-`colnames<-`(rev, rw) return (rev) } -check_seasonality <- function(x){ +check_seasonality <- function(x) { - if(frequency(x)>1){ + if(frequency(x)>1) { x_diff<-diff(x) lb_pval<-try(seasonality_qs(x_diff, frequency(x))$pvalue, silent=TRUE) # Ljung-Box fd_pval<-try(seasonality_friedman(x_diff, frequency(x))$pvalue, silent=TRUE) # Friedman non-parametric test test_succeeded<-c(!"try-error" %in% class(lb_pval), !"try-error" %in% class(fd_pval)) - if(all(test_succeeded)){ + if(all(test_succeeded)) { pvals<-c(lb_pval, fd_pval) seasonality<-ifelse(length(pvals[which(pvals<.05)])==2, TRUE, FALSE) - }else if(any(test_succeeded)){ - if(test_succeeded[1]){ + }else if(any(test_succeeded)) { + if(test_succeeded[1]) { seasonality<-ifelse(lb_pval<.01, TRUE, FALSE) - }else if(test_succeeded[2]){ + }else if(test_succeeded[2]) { seasonality<-ifelse(fd_pval<.01, TRUE, FALSE) } - }else{ + } else { seasonality<-FALSE } - }else{ + } else { seasonality<-FALSE } return(seasonality) diff --git a/R/revisions.R b/R/revisions.R index 6e549ba..3c49688 100644 --- a/R/revisions.R +++ b/R/revisions.R @@ -24,13 +24,13 @@ #' vintages<-create_vintages(df, periodicity = 4) #' revisions<-get_revisions(vintages, gap=1) #' -get_revisions<-function(vintages, gap=1){ - if(!class(vintages)=="rjd3rev_vintages"){ +get_revisions<-function(vintages, gap=1) { + if(!class(vintages)=="rjd3rev_vintages") { warning("Wrong input. vintages must be an object of class 'rjd3rev_vintages'.") return(NULL) } - get_vd_rev <- function(vt, gap){ + get_vd_rev <- function(vt, gap) { n<-dim(vt)[2] idx1<-(gap+1):n @@ -38,8 +38,8 @@ get_revisions<-function(vintages, gap=1){ rev<-vt[, idx1, drop=FALSE]-vt[, idx0, drop=FALSE] - w<-sapply(colnames(vt), function(s){paste0("[", s, "]")}) - rw<-mapply(function(a, b){paste(a, b, sep="-")}, w[idx1], w[idx0]) + w<-sapply(colnames(vt), function(s) paste0("[", s, "]")) + rw<-mapply(FUN = function(a, b) paste(a, b, sep = "-"), w[idx1], w[idx0]) rev<-`colnames<-`(rev, rw) return (rev) diff --git a/R/tests.R b/R/tests.R index aad3e95..a837c93 100644 --- a/R/tests.R +++ b/R/tests.R @@ -29,22 +29,22 @@ egNames<-c("value", "stderr", "statistic", "pvalue") snNames<-c("News.R2", "News.F", "News.pvalue", "Noise.R2", "Noise.F", "Noise.pvalue") -OlsCNames<-function(nregs){ +OlsCNames<-function(nregs) { n<-c("intercept.estimate", "intercept.stderr", "intercept.pvalue") - for (i in 1:nregs){ + for (i in 1:nregs) { cur<-paste0("x(", i, ")") n<-c(n, paste0(cur, ".estimate"), paste0(cur, ".stderr"), paste0(cur, ".pvalue")) } return (n) } -OlsAllNames<-function(nregs){ +OlsAllNames<-function(nregs) { return (c(OlsAdjNames, OlsCNames(nregs), OlsTestNames)) } -vecmAllNames<-function(lag){ +vecmAllNames<-function(lag) { t<-m<-c() - for (i in lag:1){ + for (i in lag:1) { t<-c(t, paste0("trace(", i, ")")) m<-c(m, paste0("max(", i, ")")) } @@ -70,7 +70,7 @@ vecmAllNames<-function(lag){ #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) #' rev<-rnorm(np*4,0,.1) #' obs_values<-xt -#' for(i in 1:4){ +#' for(i in 1:4) { #' xt<-xt+rev[(1+(i-1)*np):(i*np)] #' obs_values<-c(obs_values,xt) #' } @@ -81,9 +81,9 @@ vecmAllNames<-function(lag){ #' revisions<-get_revisions(vintages, gap=1) #' descriptive_statistics(revisions$diagonal_view, rounding=1) #' -descriptive_statistics<-function(revisions.view, rounding=3){ +descriptive_statistics<-function(revisions.view, rounding=3) { - descriptive_statistics_one<-function(r){ + descriptive_statistics_one<-function(r) { rc<-as.numeric(r[!is.na(r)]) n<-length(rc) @@ -134,7 +134,7 @@ descriptive_statistics<-function(revisions.view, rounding=3){ #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) #' rev<-rnorm(np*4,0,.1) #' obs_values<-xt -#' for(i in 1:4){ +#' for(i in 1:4) { #' xt<-xt+rev[(1+(i-1)*np):(i*np)] #' obs_values<-c(obs_values,xt) #' } @@ -144,12 +144,12 @@ descriptive_statistics<-function(revisions.view, rounding=3){ #' vintages<-create_vintages(df, periodicity = 4) #' theil(vintages$diagonal_view) #' -theil<-function(vintages.view, gap=1, na.zero= FALSE){ +theil<-function(vintages.view, gap=1, na.zero= FALSE) { q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) theil<-try(.jcall("jdplus/revisions/base/r/Utility", "[D", "theil", jq, as.integer(gap)), silent= TRUE) - if("try-error" %in% class(theil)){ + if("try-error" %in% class(theil)) { warning("theil could not be performed", call.= FALSE) return(NULL) } @@ -181,7 +181,7 @@ theil<-function(vintages.view, gap=1, na.zero= FALSE){ #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) #' rev<-rnorm(np*4,0,.1) #' obs_values<-xt -#' for(i in 1:4){ +#' for(i in 1:4) { #' xt<-xt+rev[(1+(i-1)*np):(i*np)] #' obs_values<-c(obs_values,xt) #' } @@ -191,12 +191,12 @@ theil<-function(vintages.view, gap=1, na.zero= FALSE){ #' vintages<-create_vintages(df, periodicity = 4) #' theil2(vintages$diagonal_view) #' -theil2<-function(vintages.view, gap=1, na.zero= FALSE){ +theil2<-function(vintages.view, gap=1, na.zero= FALSE) { q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) theil2<-try(.jcall("jdplus/revisions/base/r/Utility", "[D", "theil2", jq, as.integer(gap)), silent= TRUE) - if("try-error" %in% class(theil2)){ + if("try-error" %in% class(theil2)) { warning("theil2 could not be performed", call.= FALSE) return(NULL) } @@ -225,7 +225,7 @@ theil2<-function(vintages.view, gap=1, na.zero= FALSE){ #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) #' rev<-rnorm(np*4,0,.1) #' obs_values<-xt -#' for(i in 1:4){ +#' for(i in 1:4) { #' xt<-xt+rev[(1+(i-1)*np):(i*np)] #' obs_values<-c(obs_values,xt) #' } @@ -236,18 +236,18 @@ theil2<-function(vintages.view, gap=1, na.zero= FALSE){ #' revisions<-get_revisions(vintages, gap=1) #' bias(revisions$diagonal_view) #' -bias<-function(revisions.view, na.zero= FALSE){ +bias<-function(revisions.view, na.zero= FALSE) { r<-revisions.view if(na.zero) r[is.na(r)]<-0 jrevs<-matrix_r2jd(r) jbias<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "bias", jrevs), silent= TRUE) - if("try-error" %in% class(bias)){ + if("try-error" %in% class(bias)) { warning("bias could not be performed", call.= FALSE) return(NULL) } bias <- matrix_jd2r(jbias) bias[rowSums(bias[])==0, ]<-NaN # fix non-calculable cases - if(all(is.nan(bias))){ + if(all(is.nan(bias))) { warning("bias could not be performed", call.= FALSE) return(NULL) } @@ -285,7 +285,7 @@ bias<-function(revisions.view, na.zero= FALSE){ #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) #' rev<-rnorm(np*4,0,.1) #' obs_values<-xt -#' for(i in 1:4){ +#' for(i in 1:4) { #' xt<-xt+rev[(1+(i-1)*np):(i*np)] #' obs_values<-c(obs_values,xt) #' } @@ -295,18 +295,18 @@ bias<-function(revisions.view, na.zero= FALSE){ #' vintages<-create_vintages(df, periodicity = 4) #' slope_and_drift(vintages$diagonal_view) #' -slope_and_drift<-function(vintages.view, gap=1, na.zero= FALSE){ +slope_and_drift<-function(vintages.view, gap=1, na.zero= FALSE) { q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "slopeAndDrift", jq, as.integer(gap)), silent= TRUE) - if("try-error" %in% class(jsd)){ + if("try-error" %in% class(jsd)) { warning("Slope and drift could not be performed", call.= FALSE) return(NULL) } slope_and_drift <- matrix_jd2r(jsd) slope_and_drift[rowSums(slope_and_drift[])==0, ]<-NaN # fix non-calculable cases - if(all(is.nan(slope_and_drift))){ + if(all(is.nan(slope_and_drift))) { warning("slope_and_drift could not be performed", call.= FALSE) return(NULL) } @@ -344,7 +344,7 @@ slope_and_drift<-function(vintages.view, gap=1, na.zero= FALSE){ #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) #' rev<-rnorm(np*4,0,.1) #' obs_values<-xt -#' for(i in 1:4){ +#' for(i in 1:4) { #' xt<-xt+rev[(1+(i-1)*np):(i*np)] #' obs_values<-c(obs_values,xt) #' } @@ -354,25 +354,25 @@ slope_and_drift<-function(vintages.view, gap=1, na.zero= FALSE){ #' vintages<-create_vintages(df, periodicity = 4) #' efficiencyModel1(vintages$diagonal_view) #' -efficiencyModel1<-function(vintages.view, gap=1, na.zero= FALSE){ +efficiencyModel1<-function(vintages.view, gap=1, na.zero= FALSE) { q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) jef1<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "efficiencyModel1", jq, as.integer(gap)), silent= TRUE) - if("try-error" %in% class(jef1)){ + if("try-error" %in% class(jef1)) { warning("efficiencyModel1 could not be performed", call.= FALSE) return(NULL) } efficiencyModel1 <- matrix_jd2r(jef1) efficiencyModel1[rowSums(efficiencyModel1[])==0, ]<-NaN # fix non-calculable cases - if(all(is.nan(efficiencyModel1))){ + if(all(is.nan(efficiencyModel1))) { warning("efficiencyModel1 could not be performed", call.= FALSE) return(NULL) } colnames(efficiencyModel1)<-OlsNames n<-dim(q)[2] - w<-sapply(colnames(q), function(s){paste0("[", s, "]")}) - rw<-mapply(function(a, b){paste(a, b, sep="-")}, w[(gap+1):n], w[1:(n-gap)]) + w<-sapply(colnames(q), function(s) paste0("[", s, "]")) + rw<-mapply(function(a, b) paste(a, b, sep="-"), w[(gap+1):n], w[1:(n-gap)]) rownames(efficiencyModel1)<-rw return (efficiencyModel1) } @@ -404,7 +404,7 @@ efficiencyModel1<-function(vintages.view, gap=1, na.zero= FALSE){ #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) #' rev<-rnorm(np*4,0,.1) #' obs_values<-xt -#' for(i in 1:4){ +#' for(i in 1:4) { #' xt<-xt+rev[(1+(i-1)*np):(i*np)] #' obs_values<-c(obs_values,xt) #' } @@ -414,12 +414,12 @@ efficiencyModel1<-function(vintages.view, gap=1, na.zero= FALSE){ #' vintages<-create_vintages(df, periodicity = 4) #' efficiencyModel2(vintages$diagonal_view) #' -efficiencyModel2<-function(vintages.view, gap=1, na.zero= FALSE){ +efficiencyModel2<-function(vintages.view, gap=1, na.zero= FALSE) { q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) jef2<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "efficiencyModel2", jq, as.integer(gap)), silent= TRUE) - if("try-error" %in% class(jef2)){ + if("try-error" %in% class(jef2)) { warning("efficiencyModel2 could not be performed", call.= FALSE) return(NULL) } @@ -429,14 +429,14 @@ efficiencyModel2<-function(vintages.view, gap=1, na.zero= FALSE){ return(NULL) } efficiencyModel2[rowSums(efficiencyModel2[])==0, ]<-NaN # fix non-calculable cases - if(all(is.nan(efficiencyModel2))){ + if(all(is.nan(efficiencyModel2))) { warning("efficiencyModel2 could not be performed", call.= FALSE) return(NULL) } colnames(efficiencyModel2)<-OlsNames n<-dim(q)[2] - w<-sapply(colnames(q), function(s){paste0("[", s, "]")}) - rw<-mapply(function(a, b){paste(a, b, sep="-")}, w[(gap+1):n], w[1:(n-gap)]) + w<-sapply(colnames(q), function(s) paste0("[", s, "]")) + rw<-mapply(function(a, b) paste(a, b, sep="-"), w[(gap+1):n], w[1:(n-gap)]) rownames(efficiencyModel2)<-rw[-1] return (efficiencyModel2) } @@ -466,7 +466,7 @@ efficiencyModel2<-function(vintages.view, gap=1, na.zero= FALSE){ #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) #' rev<-rnorm(np*4,0,.1) #' obs_values<-xt -#' for(i in 1:4){ +#' for(i in 1:4) { #' xt<-xt+rev[(1+(i-1)*np):(i*np)] #' obs_values<-c(obs_values,xt) #' } @@ -477,12 +477,12 @@ efficiencyModel2<-function(vintages.view, gap=1, na.zero= FALSE){ #' revisions<-get_revisions(vintages, gap=1) #' orthogonallyModel1(revisions$diagonal_view) #' -orthogonallyModel1<-function(revisions.view, nrevs=1, na.zero= FALSE){ +orthogonallyModel1<-function(revisions.view, nrevs=1, na.zero= FALSE) { r<-revisions.view if(na.zero) r[is.na(r)]<-0 jr<-matrix_r2jd(as.matrix(r)) jom<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "orthogonallyModel1", jr, as.integer(nrevs)), silent= TRUE) - if("try-error" %in% class(jom)){ + if("try-error" %in% class(jom)) { warning("orthogonallyModel1 could not be performed", call.= FALSE) return(NULL) } @@ -492,7 +492,7 @@ orthogonallyModel1<-function(revisions.view, nrevs=1, na.zero= FALSE){ return(NULL) } om[rowSums(om[])==0, ]<-NaN # fix non-calculable cases - if(all(is.nan(om))){ + if(all(is.nan(om))) { warning("orthogonallyModel1 could not be performed", call.= FALSE) return(NULL) } @@ -526,7 +526,7 @@ orthogonallyModel1<-function(revisions.view, nrevs=1, na.zero= FALSE){ #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) #' rev<-rnorm(np*4,0,.1) #' obs_values<-xt -#' for(i in 1:4){ +#' for(i in 1:4) { #' xt<-xt+rev[(1+(i-1)*np):(i*np)] #' obs_values<-c(obs_values,xt) #' } @@ -537,12 +537,12 @@ orthogonallyModel1<-function(revisions.view, nrevs=1, na.zero= FALSE){ #' revisions<-get_revisions(vintages, gap=1) #' orthogonallyModel2(revisions$diagonal_view) #' -orthogonallyModel2<-function(revisions.view, reference=1, na.zero= FALSE){ +orthogonallyModel2<-function(revisions.view, reference=1, na.zero= FALSE) { r<-revisions.view if(na.zero) r[is.na(r)]<-0 jr<-matrix_r2jd(as.matrix(r)) jom<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "orthogonallyModel2", jr, as.integer(reference)), silent= TRUE) - if("try-error" %in% class(jom)){ + if("try-error" %in% class(jom)) { warning("orthogonallyModel2 could not be performed", call.= FALSE) return(NULL) } @@ -552,7 +552,7 @@ orthogonallyModel2<-function(revisions.view, reference=1, na.zero= FALSE){ return(NULL) } om[rowSums(om[])==0, ]<-NaN # fix non-calculable cases - if(all(is.nan(om))){ + if(all(is.nan(om))) { warning("orthogonallyModel2 could not be performed", call.= FALSE) return(NULL) } @@ -590,7 +590,7 @@ orthogonallyModel2<-function(revisions.view, reference=1, na.zero= FALSE){ #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) #' rev<-rnorm(np*4,0,.1) #' obs_values<-xt -#' for(i in 1:4){ +#' for(i in 1:4) { #' xt<-xt+rev[(1+(i-1)*np):(i*np)] #' obs_values<-c(obs_values,xt) #' } @@ -600,25 +600,25 @@ orthogonallyModel2<-function(revisions.view, reference=1, na.zero= FALSE){ #' vintages<-create_vintages(df, periodicity = 4) #' signalnoise(vintages$diagonal_view) #' -signalnoise<-function(vintages.view, gap=1, na.zero= FALSE){ +signalnoise<-function(vintages.view, gap=1, na.zero= FALSE) { q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "signalNoise", jq, as.integer(gap)), silent= TRUE) - if("try-error" %in% class(jsd)){ + if("try-error" %in% class(jsd)) { warning("signalnoise could not be performed", call.= FALSE) return(NULL) } sn<-matrix_jd2r(jsd) sn[rowSums(sn[])==0, ]<-NaN # fix non-calculable cases - if(all(is.nan(sn))){ + if(all(is.nan(sn))) { warning("SignalNoise could not be performed", call.= FALSE) return(NULL) } colnames(sn)<-snNames n<-dim(q)[2] - w<-sapply(colnames(q), function(s){paste0("[", s, "]")}) - rw<-mapply(function(a, b){paste(a, b, sep="-")}, w[(gap+1):n], w[1:(n-gap)]) + w<-sapply(colnames(q), function(s) paste0("[", s, "]")) + rw<-mapply(function(a, b) paste(a, b, sep="-"), w[(gap+1):n], w[1:(n-gap)]) rownames(sn)<-rw return (sn) } @@ -646,7 +646,7 @@ signalnoise<-function(vintages.view, gap=1, na.zero= FALSE){ #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) #' rev<-rnorm(np*4,0,.1) #' obs_values<-xt -#' for(i in 1:4){ +#' for(i in 1:4) { #' xt<-xt+rev[(1+(i-1)*np):(i*np)] #' obs_values<-c(obs_values,xt) #' } @@ -656,12 +656,12 @@ signalnoise<-function(vintages.view, gap=1, na.zero= FALSE){ #' vintages<-create_vintages(df, periodicity = 4) #' unitroot(vintages$diagonal_view) #' -unitroot<-function(vintages.view, adfk=1, na.zero= FALSE){ +unitroot<-function(vintages.view, adfk=1, na.zero= FALSE) { q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "unitroot", jq, as.integer(adfk)), silent= TRUE) - if("try-error" %in% class(jsd)){ + if("try-error" %in% class(jsd)) { warning("unit root test could not be performed", call.= FALSE) return(NULL) } @@ -694,7 +694,7 @@ unitroot<-function(vintages.view, adfk=1, na.zero= FALSE){ #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) #' rev<-rnorm(np*4,0,.1) #' obs_values<-xt -#' for(i in 1:4){ +#' for(i in 1:4) { #' xt<-xt+rev[(1+(i-1)*np):(i*np)] #' obs_values<-c(obs_values,xt) #' } @@ -704,12 +704,12 @@ unitroot<-function(vintages.view, adfk=1, na.zero= FALSE){ #' vintages<-create_vintages(df, periodicity = 4) #' cointegration(vintages$diagonal_view) #' -cointegration<-function(vintages.view, adfk=1, na.zero= FALSE){ +cointegration<-function(vintages.view, adfk=1, na.zero= FALSE) { q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "cointegration", jq, as.integer(adfk)), silent= TRUE) - if("try-error" %in% class(jsd)){ + if("try-error" %in% class(jsd)) { warning("cointegration test could not be performed", call.= FALSE) return(NULL) } @@ -744,7 +744,7 @@ cointegration<-function(vintages.view, adfk=1, na.zero= FALSE){ #' xt<-cumsum(sample(rnorm(1000,0,1), np, TRUE)) #' rev<-rnorm(np*4,0,.1) #' obs_values<-xt -#' for(i in 1:4){ +#' for(i in 1:4) { #' xt<-xt+rev[(1+(i-1)*np):(i*np)] #' obs_values<-c(obs_values,xt) #' } @@ -754,13 +754,13 @@ cointegration<-function(vintages.view, adfk=1, na.zero= FALSE){ #' vintages<-create_vintages(df, periodicity = 4) #' vecm(vintages$diagonal_view) #' -vecm<-function(vintages.view, lag=2, model = c("none", "cnt", "trend"), na.zero= FALSE){ +vecm<-function(vintages.view, lag=2, model = c("none", "cnt", "trend"), na.zero= FALSE) { model<-match.arg(model) q<-vintages.view if(na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "vecm", jq, as.integer(lag), model), silent= TRUE) - if("try-error" %in% class(jsd)){ + if("try-error" %in% class(jsd)) { warning("vecm could not be performed", call.= FALSE) return(NULL) } @@ -772,13 +772,13 @@ vecm<-function(vintages.view, lag=2, model = c("none", "cnt", "trend"), na.zero= # Auto-correlation tests on OLS residuals # -# auto_correlation<-function(vintages.view, nbreuschgodfrey=1, nljungbox=1, na.zero= FALSE){ +# auto_correlation<-function(vintages.view, nbreuschgodfrey=1, nljungbox=1, na.zero= FALSE) { # q<-vintages.view # if(na.zero) q[is.na(q)]<-0 # jq<-matrix_r2jd(q) # jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "autoCorrelation", jq # , as.integer(nbreuschgodfrey), as.integer(nljungbox)), silent= TRUE) -# if("try-error" %in% class(jsd)){ +# if("try-error" %in% class(jsd)) { # warning("auto_correlation test on OLS residuals could not be performed", call.= FALSE) # return(NULL) # } diff --git a/R/vintages.R b/R/vintages.R index 024a43d..9a539d4 100644 --- a/R/vintages.R +++ b/R/vintages.R @@ -77,7 +77,7 @@ create_vintages<- function(df, periodicity, vintage.selection = NULL, revdate.fo jfac<-.jnew("jdplus/revisions/base/r/VintagesFactory", as.integer(periodicity)) # check input - if(! is.data.frame(df)){ + if(! is.data.frame(df)) { warning("Wrong input type. Must be a data.frame.") return(NULL) } @@ -89,30 +89,30 @@ create_vintages<- function(df, periodicity, vintage.selection = NULL, revdate.fo colnames(df)<-c("revdate", "time", "obs_value") df$revdate<-as.Date(as.character(df$revdate), revdate.format) - if (any(is.na(df$revdate))){ + if (any(is.na(df$revdate))) { warning("Wrong input in first column. Revision dates not in a correct format. The parameter revdate.format might be mispecified.") return(NULL) } - if(is.null(yp(df$time))){ + if(is.null(yp(df$time))) { warning("Wrong input in second column. Time periods not in a correct format. Examples of correct formats are 2023M01, 2023Q1 or 2023.") return(NULL) - }else{ + } else { df$time<-yp(df$time) } - if(! is.numeric(df$obs_value)){ + if(! is.numeric(df$obs_value)) { warning("Wrong input in third column. Obsevation values must be numeric.") return(NULL) } # Vintages selection - if(!is.null(vintage.selection)){ + if(!is.null(vintage.selection)) { df<-subset(df, revdate >= as.Date(vintage.selection[[1]]) & revdate <= as.Date(vintage.selection[[2]])) - if(nrow(df) == 0){ + if(nrow(df) == 0) { warning("Vintage selection out of range!") return(NULL) } } - if(length(unique(df$revdate))<2){ + if(length(unique(df$revdate))<2) { warning("Too few number of vintages. Number of unique revision dates must be >= 2.") return(NULL) } @@ -181,7 +181,7 @@ create_vintages<- function(df, periodicity, vintage.selection = NULL, revdate.fo #' vintage.selection=NULL, #' revdate.format="%Y-%m-%d") #' } -create_vintages_from_csv<-function(file, periodicity, separator = ",", vintage.selection=NULL, revdate.format="%Y.%m.%d"){ +create_vintages_from_csv<-function(file, periodicity, separator = ",", vintage.selection=NULL, revdate.format="%Y.%m.%d") { df<-as.data.frame(read.csv(file, sep = separator, stringsAsFactors = FALSE)) @@ -221,9 +221,11 @@ create_vintages_from_csv<-function(file, periodicity, separator = ",", vintage.s #' vintage.selection=NULL, #' revdate.format="%d/%m/%Y")) #' } -create_vintages_from_xlsx<-function(file, sheetname, periodicity, vintage.selection = NULL, revdate.format= "%Y.%m.%d"){ +create_vintages_from_xlsx<-function(file, sheetname, periodicity, vintage.selection = NULL, revdate.format= "%Y.%m.%d") { - if(! require(readxl)){stop("package 'readxl' must be installed to run the function 'create_vintages_from_xlsx'")} + if(! require(readxl)) { + stop("package 'readxl' must be installed to run the function 'create_vintages_from_xlsx'") + } df<-as.data.frame(read_excel(file, sheet = sheetname)) @@ -232,7 +234,7 @@ create_vintages_from_xlsx<-function(file, sheetname, periodicity, vintage.select -vintageTableFromFactory<-function(jfac){ +vintageTableFromFactory<-function(jfac) { jvn<-.jcall(jfac, "Ljdplus/revisions/base/r/Vintages;", "build") jmat<-.jcall(jvn, "Ljdplus/revisions/base/api/timeseries/TsMatrix;", "vtable") @@ -248,25 +250,25 @@ vintageTableFromFactory<-function(jfac){ } -ymd<-function(y, m, d=1){ +ymd<-function(y, m, d=1) { return (as.Date(sprintf("%04i-%02i-%02i", y, m, d))) } -yq<-function(y, q){ +yq<-function(y, q) { return (as.Date(sprintf("%04i-%02i-%02i", y, q*3-2, 1))) } -yp<-function(s){ +yp<-function(s) { y<-as.integer(substr(s, 1, 4)) - if(nchar(as.character(s))[1] == 4){ + if(nchar(as.character(s))[1] == 4) { return (ymd(y, 1)) - }else{ + } else { p <- substr(s, 5, 5) - if (all(p == "Q") || all(p == "q")){ + if (all(p == "Q") || all(p == "q")) { q<-as.integer(substr(s, 6, 6)) return (yq(y, q)) } - if (all(p == "M") || all(p == "m")){ + if (all(p == "M") || all(p == "m")) { m<-as.integer(substr(s, 6, length(s))) return (ymd(y, m)) } @@ -274,15 +276,15 @@ yp<-function(s){ return (NULL) } -d2t<-function(d, periodicity){ +d2t<-function(d, periodicity) { y<-floor(d) frac<-d%%1 date<-ymd(y, 1, 1)+(ymd(y+1, 1, 1)-ymd(y, 1, 1))*frac - if (periodicity == 12){ + if (periodicity == 12) { return (paste0(y, "M", format(date, "%m"))) - }else if (periodicity == 4){ + }else if (periodicity == 4) { return (paste0(y, "Q", (as.numeric(format(date, "%m"))+2)/3)) - }else if (periodicity == 1){ + }else if (periodicity == 1) { return (y) } return(NULL) diff --git a/inst/templates/report.Rmd b/inst/templates/report.Rmd index db497bc..a761051 100644 --- a/inst/templates/report.Rmd +++ b/inst/templates/report.Rmd @@ -30,7 +30,7 @@ selection<-c("N", "mean revision", "st.dev.", "% positive", "% zero", "% negativ if (! requireNamespace("kableExtra", quietly=TRUE)) { knitr::kable(descriptive_statistics[selection, , drop=FALSE], format="html") warning("Please install kableExtra: install.packages('kableExtra') to get more visual table output") -}else{ +} else { kableExtra::kable_minimal(knitr::kable(descriptive_statistics[selection, , drop=FALSE], format="html")) } ``` @@ -39,8 +39,8 @@ if (! requireNamespace("kableExtra", quietly=TRUE)) { ```{r summarytable, echo = FALSE} if (! requireNamespace("kableExtra", quietly=TRUE)) { knitr::kable(main_results, format="html") -}else{ - format_font <- function(x){ +} else { + format_font <- function(x) { kableExtra::cell_spec(x, color = ifelse(is.na(x), "black", ifelse(substr(x, 1, 1) == "G", "green", From 3baddfdc972f4fadb611f2acfe58ead0e81a3ff5 Mon Sep 17 00:00:00 2001 From: Tanguy BARTHELEMY Date: Mon, 18 Mar 2024 11:08:16 +0100 Subject: [PATCH 20/56] remove space return ( --- R/jd3_rslts.R | 26 +++++++++++++------------- R/jd3_ts.R | 12 ++++++------ R/revision_analysis.R | 2 +- R/revisions.R | 4 ++-- R/tests.R | 28 ++++++++++++++-------------- R/vintages.R | 24 ++++++++++++------------ 6 files changed, 48 insertions(+), 48 deletions(-) diff --git a/R/jd3_rslts.R b/R/jd3_rslts.R index 71aace3..5f5f432 100644 --- a/R/jd3_rslts.R +++ b/R/jd3_rslts.R @@ -5,7 +5,7 @@ proc_numeric<-function(rslt, name) { if (!is.jnull(s)) .jcall(s, "D", "doubleValue") else - return (NaN) + return(NaN) } proc_vector<-function(rslt, name) { @@ -32,11 +32,11 @@ proc_bool<-function(rslt, name) { proc_ts<-function(rslt, name) { s<-.jcall(rslt, "Ljava/lang/Object;", "getData", name, jd_clobj) if (is.jnull(s)) - return (NULL) + return(NULL) if (.jinstanceof(s, "demetra/timeseries/TsData")) return(ts_jd2r(.jcast(s, "demetra/timeseries/TsData"))) else - return (NULL) + return(NULL) } proc_str<-function(rslt, name) { @@ -70,7 +70,7 @@ proc_parameter<-function(rslt, name) { if (is.jnull(s)) return(NULL) val<-.jcall(s, "D", "getValue") - return (val) + return(val) } proc_parameters<-function(rslt, name) { @@ -90,23 +90,23 @@ proc_matrix<-function(rslt, name) { s<-.jcall(rslt, "Ljava/lang/Object;", "getData", name, jd_clobj) if (is.jnull(s)) return(NULL) - return (matrix_jd2r(s)) + return(matrix_jd2r(s)) } proc_data<-function(rslt, name) { s<-.jcall(rslt, "Ljava/lang/Object;", "getData", name, jd_clobj) if (is.jnull(s)) - return (NULL) + return(NULL) if (.jinstanceof(s, "demetra/timeseries/TsData")) { return(ts_jd2r(.jcast(s, "demetra/timeseries/TsData"))) } else if (.jinstanceof(s, "java/lang/Number")) { - return (.jcall(s, "D", "doubleValue")) + return(.jcall(s, "D", "doubleValue")) } else if (.jinstanceof(s, "demetra/math/matrices/MatrixType")) { return(matrix_jd2r(.jcast(s, "demetra/math/matrices/MatrixType"))) } else if (.jinstanceof(s, "demetra/data/Parameter")) { val<-.jcall(s, "D", "getValue") - return (c(val)) + return(c(val)) } else if (.jinstanceof(s, "[Ldemetra/data/Parameter;")) { p<-.jcastToArray(s) len<-length(p) @@ -114,11 +114,11 @@ proc_data<-function(rslt, name) { for (i in 1:len) { all[i]<-.jcall(p[[i]], "D", "getValue") } - return (all) + return(all) } else if (.jcall(.jcall(s, "Ljava/lang/Class;", "getClass"), "Z", "isArray")) { - return (.jevalArray(s, silent=TRUE)) + return(.jevalArray(s, silent=TRUE)) } else { - return (.jcall(s, "S", "toString")) + return(.jcall(s, "S", "toString")) } } @@ -133,11 +133,11 @@ proc_dictionary<-function(name) { for (i in 1:size) { keys[i] <- .jcall(.jcall(jiter, "Ljava/lang/Object;", "next"), "Ljava/lang/String;", "toString") } - return (keys) + return(keys) } proc_likelihood<-function(jrslt, prefix) { - return (list( + return(list( ll=proc_numeric(jrslt, paste(prefix, "ll", sep="")), ssq=proc_numeric(jrslt, paste(prefix, "ssq", sep="")), ser=proc_numeric(jrslt, paste(prefix, "ser", sep="")), diff --git a/R/jd3_ts.R b/R/jd3_ts.R index 0ea415e..a14cabe 100644 --- a/R/jd3_ts.R +++ b/R/jd3_ts.R @@ -1,6 +1,6 @@ ts_r2jd<-function(s) { if (is.null(s)) { - return (NULL) + return(NULL) } freq<-frequency(s) start<-start(s) @@ -16,7 +16,7 @@ tsdomain_r2jd<-function(period, startYear, startPeriod, length) { ts_jd2r<-function(s) { if (is.null(s)) { - return (NULL) + return(NULL) } pstart<-.jcall("jdplus/toolkit/base/r/timeseries/TsUtility", "[I", "startPeriod", s) jx<-.jcall(s, "Ljdplus/toolkit/base/api/data/DoubleSeq;", "getValues") @@ -26,20 +26,20 @@ ts_jd2r<-function(s) { matrix_jd2r<-function(s) { if (is.jnull(s)) { - return (NULL) + return(NULL) } nr<-.jcall(s, "I", "getRowsCount") nc<-.jcall(s, "I", "getColumnsCount") d<-.jcall(s, "[D", "toArray") - return (array(d, dim=c(nr, nc))) + return(array(d, dim=c(nr, nc))) } matrix_r2jd<-function(s) { if (is.null(s)) - return (.jnull("jdplus/toolkit/base/api/math/matrices/Matrix")) + return(.jnull("jdplus/toolkit/base/api/math/matrices/Matrix")) if (!is.matrix(s)) { s<-matrix(s, nrow=length(s), ncol=1) } sdim<-dim(s) - return (.jcall("jdplus/toolkit/base/api/math/matrices/Matrix", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "of", as.double(s), as.integer(sdim[1]), as.integer(sdim[2]))) + return(.jcall("jdplus/toolkit/base/api/math/matrices/Matrix", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "of", as.double(s), as.integer(sdim[1]), as.integer(sdim[2]))) } diff --git a/R/revision_analysis.R b/R/revision_analysis.R index 9c08323..50ad91c 100644 --- a/R/revision_analysis.R +++ b/R/revision_analysis.R @@ -556,7 +556,7 @@ get_vd_rev <- function(vt, gap) { rw<-mapply(function(a, b) paste(a, b, sep="-"), w[idx1], w[idx0]) rev<-`colnames<-`(rev, rw) - return (rev) + return(rev) } check_seasonality <- function(x) { diff --git a/R/revisions.R b/R/revisions.R index 3c49688..45a5e05 100644 --- a/R/revisions.R +++ b/R/revisions.R @@ -42,12 +42,12 @@ get_revisions<-function(vintages, gap=1) { rw<-mapply(FUN = function(a, b) paste(a, b, sep = "-"), w[idx1], w[idx0]) rev<-`colnames<-`(rev, rw) - return (rev) + return(rev) } vr<-get_vd_rev(vintages$vertical_view, gap) hr<-`colnames<-`(t(vr), colnames(vintages$horizontal_view)) dr<-get_vd_rev(vintages$diagonal_view, gap) - return (list(vertical_view=vr, horizontal_view=hr, diagonal_view=dr)) + return(list(vertical_view=vr, horizontal_view=hr, diagonal_view=dr)) } diff --git a/R/tests.R b/R/tests.R index a837c93..51701ef 100644 --- a/R/tests.R +++ b/R/tests.R @@ -35,11 +35,11 @@ OlsCNames<-function(nregs) { cur<-paste0("x(", i, ")") n<-c(n, paste0(cur, ".estimate"), paste0(cur, ".stderr"), paste0(cur, ".pvalue")) } - return (n) + return(n) } OlsAllNames<-function(nregs) { - return (c(OlsAdjNames, OlsCNames(nregs), OlsTestNames)) + return(c(OlsAdjNames, OlsCNames(nregs), OlsTestNames)) } vecmAllNames<-function(lag) { @@ -105,7 +105,7 @@ descriptive_statistics<-function(revisions.view, rounding=3) { ds<-apply(revisions.view, 2, descriptive_statistics_one) - return (`rownames<-`(round(ds, rounding), descriptiveStatNames)) + return(`rownames<-`(round(ds, rounding), descriptiveStatNames)) } #' Theil's Inequality Coefficient U1 @@ -153,7 +153,7 @@ theil<-function(vintages.view, gap=1, na.zero= FALSE) { warning("theil could not be performed", call.= FALSE) return(NULL) } - return (theil) + return(theil) } #' Theil's Inequality Coefficient U2 @@ -200,7 +200,7 @@ theil2<-function(vintages.view, gap=1, na.zero= FALSE) { warning("theil2 could not be performed", call.= FALSE) return(NULL) } - return (theil2) + return(theil2) } #' Estimate bias using t-test and augmented t-test @@ -312,7 +312,7 @@ slope_and_drift<-function(vintages.view, gap=1, na.zero= FALSE) { } colnames(slope_and_drift)<-OlsNames rownames(slope_and_drift)<-colnames(q)[-(1:gap)] - return (slope_and_drift) + return(slope_and_drift) } @@ -374,7 +374,7 @@ efficiencyModel1<-function(vintages.view, gap=1, na.zero= FALSE) { w<-sapply(colnames(q), function(s) paste0("[", s, "]")) rw<-mapply(function(a, b) paste(a, b, sep="-"), w[(gap+1):n], w[1:(n-gap)]) rownames(efficiencyModel1)<-rw - return (efficiencyModel1) + return(efficiencyModel1) } #' Efficiency Model 2 @@ -438,7 +438,7 @@ efficiencyModel2<-function(vintages.view, gap=1, na.zero= FALSE) { w<-sapply(colnames(q), function(s) paste0("[", s, "]")) rw<-mapply(function(a, b) paste(a, b, sep="-"), w[(gap+1):n], w[1:(n-gap)]) rownames(efficiencyModel2)<-rw[-1] - return (efficiencyModel2) + return(efficiencyModel2) } #' Orthogonally Model 1 @@ -498,7 +498,7 @@ orthogonallyModel1<-function(revisions.view, nrevs=1, na.zero= FALSE) { } colnames(om)<-OlsAllNames(nrevs) rownames(om)<-colnames(r[-c(1:nrevs)]) - return (om) + return(om) } #' Orthogonally Model 2 @@ -558,7 +558,7 @@ orthogonallyModel2<-function(revisions.view, reference=1, na.zero= FALSE) { } colnames(om)<-OlsNames rownames(om)<-colnames(r)[-c(1:reference)] - return (om) + return(om) } #' Signal VS Noise @@ -620,7 +620,7 @@ signalnoise<-function(vintages.view, gap=1, na.zero= FALSE) { w<-sapply(colnames(q), function(s) paste0("[", s, "]")) rw<-mapply(function(a, b) paste(a, b, sep="-"), w[(gap+1):n], w[1:(n-gap)]) rownames(sn)<-rw - return (sn) + return(sn) } #' Unit root test @@ -716,7 +716,7 @@ cointegration<-function(vintages.view, adfk=1, na.zero= FALSE) { eg<-matrix_jd2r(jsd) colnames(eg)<-egNames rownames(eg)<-get_rownames_diag(q, adfk) - return (eg) + return(eg) } #' Vector error correction model (VECM) @@ -767,7 +767,7 @@ vecm<-function(vintages.view, lag=2, model = c("none", "cnt", "trend"), na.zero= vecm<-matrix_jd2r(jsd) colnames(vecm)<-vecmAllNames(lag) rownames(vecm)<-get_rownames_diag(q, 1) - return (vecm) + return(vecm) } # Auto-correlation tests on OLS residuals @@ -785,5 +785,5 @@ vecm<-function(vintages.view, lag=2, model = c("none", "cnt", "trend"), na.zero= # ac<-matrix_jd2r(jsd) # colnames(ac)<-acNames # rownames(ac)<-get_rownames_diag(q, 1) -# return (ac) +# return(ac) # } diff --git a/R/vintages.R b/R/vintages.R index 9a539d4..62128af 100644 --- a/R/vintages.R +++ b/R/vintages.R @@ -125,7 +125,7 @@ create_vintages<- function(df, periodicity, vintage.selection = NULL, revdate.fo timedate<-x[[2]] val<-x[[3]] .jcall(jfac, "V", "add", as.character(timedate), as.character(revdate), val) - return (NULL) + return(NULL) } lapply(input, FUN=add_to_JD3revisions) @@ -145,7 +145,7 @@ create_vintages<- function(df, periodicity, vintage.selection = NULL, revdate.fo vintages <- list(vertical_view = vv, horizontal_view = vh, diagonal_view = vd) class(vintages) <- "rjd3rev_vintages" - return (vintages) + return(vintages) } #' Create vintages table from CSV or TXT files @@ -246,34 +246,34 @@ vintageTableFromFactory<-function(jfac) { data[is.nan(data)]<-NA tsm<-ts(data, frequency = pstart[1], start = pstart[-1]) tsm<-`colnames<-`(tsm, cols) - return (tsm) + return(tsm) } ymd<-function(y, m, d=1) { - return (as.Date(sprintf("%04i-%02i-%02i", y, m, d))) + return(as.Date(sprintf("%04i-%02i-%02i", y, m, d))) } yq<-function(y, q) { - return (as.Date(sprintf("%04i-%02i-%02i", y, q*3-2, 1))) + return(as.Date(sprintf("%04i-%02i-%02i", y, q*3-2, 1))) } yp<-function(s) { y<-as.integer(substr(s, 1, 4)) if(nchar(as.character(s))[1] == 4) { - return (ymd(y, 1)) + return(ymd(y, 1)) } else { p <- substr(s, 5, 5) if (all(p == "Q") || all(p == "q")) { q<-as.integer(substr(s, 6, 6)) - return (yq(y, q)) + return(yq(y, q)) } if (all(p == "M") || all(p == "m")) { m<-as.integer(substr(s, 6, length(s))) - return (ymd(y, m)) + return(ymd(y, m)) } } - return (NULL) + return(NULL) } d2t<-function(d, periodicity) { @@ -281,11 +281,11 @@ d2t<-function(d, periodicity) { frac<-d%%1 date<-ymd(y, 1, 1)+(ymd(y+1, 1, 1)-ymd(y, 1, 1))*frac if (periodicity == 12) { - return (paste0(y, "M", format(date, "%m"))) + return(paste0(y, "M", format(date, "%m"))) }else if (periodicity == 4) { - return (paste0(y, "Q", (as.numeric(format(date, "%m"))+2)/3)) + return(paste0(y, "Q", (as.numeric(format(date, "%m"))+2)/3)) }else if (periodicity == 1) { - return (y) + return(y) } return(NULL) } From f02f03b5ba52e8bacf596306b85c605f97cbe8e0 Mon Sep 17 00:00:00 2001 From: Tanguy BARTHELEMY Date: Mon, 18 Mar 2024 11:44:29 +0100 Subject: [PATCH 21/56] add space after if --- R/output.R | 2 +- R/report.R | 2 +- R/revision_analysis.R | 96 +++++++++++++++++++++---------------------- R/revisions.R | 4 +- R/tests.R | 68 +++++++++++++++--------------- R/vintages.R | 18 ++++---- 6 files changed, 95 insertions(+), 95 deletions(-) diff --git a/R/output.R b/R/output.R index 6f10c53..6f301bb 100644 --- a/R/output.R +++ b/R/output.R @@ -42,7 +42,7 @@ summary.rjd3rev_revision_analysis<- function(x) { plot.rjd3rev_revision_analysis <- function(x, ...) { rev<-x$revisions nc<-ncol(rev) - if(nc>4) { + if (nc>4) { rev<-rev[, 1:4] nc<-4 } diff --git a/R/report.R b/R/report.R index d6a9783..6a8e0c7 100644 --- a/R/report.R +++ b/R/report.R @@ -60,5 +60,5 @@ get_report <- function(rslt, output_options = list(self_contained = FALSE, mathjax = "local"), envir = e) - if(open.report) utils::browseURL(path.out) + if (open.report) utils::browseURL(path.out) } diff --git a/R/revision_analysis.R b/R/revision_analysis.R index 50ad91c..3df1298 100644 --- a/R/revision_analysis.R +++ b/R/revision_analysis.R @@ -120,13 +120,13 @@ revision_analysis<-function(vintages, view<-match.arg(view) transf.diff<-match.arg(transf.diff) - if(is.null(vintages)) stop("No vintage found!") - if(n.releases<(1+gap)) stop("'n.releases' must be >= (1+gap)") + if (is.null(vintages)) stop("No vintage found!") + if (n.releases<1+gap) stop("'n.releases' must be >= (1+gap)") # Input selection ## Select vintage view - if(view == "vertical") { + if (view == "vertical") { vt<-vintages$vertical_view }else if (view == "diagonal") { vt<-vintages$diagonal_view[, 1:n.releases] @@ -137,8 +137,8 @@ revision_analysis<-function(vintages, freq<-frequency(vt) ### Log transformation - if(transf.log) { - if(length(vt[vt[!is.na(vt)] < 0])>0) { + if (transf.log) { + if (length(vt[vt[!is.na(vt)] < 0])>0) { warning("Logarithm transformation incompatible with negative data. No transformation considered.", call.=FALSE) rv<-rv_notrf is_log<-FALSE @@ -154,7 +154,7 @@ revision_analysis<-function(vintages, ### Differentiation ur<-unitroot(vt, adfk=1, na.zero) # H0: non-stationary - if(!is.null(ur)) { + if (!is.null(ur)) { ur_rslt<-t(round(ur, 3)) ur_ADFpvals<-ur[, "ADF.pvalue"] pc_signif_ur<-length(ur_ADFpvals[ur_ADFpvals<.05])/length(ur_ADFpvals) @@ -165,10 +165,10 @@ revision_analysis<-function(vintages, } coint<-cointegration(vt, adfk=1, na.zero) # H0: no-cointegration - if(is_stationary) { + if (is_stationary) { is_cointegrated<-TRUE } else { - if(!is.null(coint)) { + if (!is.null(coint)) { coint_pvals<-coint[, "pvalue"] pc_signif_coint<-length(coint_pvals[coint_pvals<.05])/length(coint_pvals) is_cointegrated<-ifelse(pc_signif_coint>.8, TRUE, FALSE) @@ -180,7 +180,7 @@ revision_analysis<-function(vintages, seasonality<-apply(vt, 2, check_seasonality) nt<-sum(seasonality) is_seasonal<-ifelse(nt/ncol(vt)>.8, TRUE, FALSE) - if(is_seasonal) { + if (is_seasonal) { vt_diff<-diff(vt, freq) delta_diff<-freq } else { @@ -188,15 +188,15 @@ revision_analysis<-function(vintages, delta_diff<-1 } - if(transf.diff == "auto") { - vts<-if(is_stationary) vt else vt_diff - vtc<-if(is_cointegrated) vt else vt_diff - }else if(transf.diff == "forced") { + if (transf.diff == "auto") { + vts<-if (is_stationary) vt else vt_diff + vtc<-if (is_cointegrated) vt else vt_diff + }else if (transf.diff == "forced") { vts<-vtc<-vt_diff is_stationary<-is_cointegrated<-FALSE - }else if(transf.diff == "none") { + }else if (transf.diff == "none") { vts<-vtc<-vt - if(!is_stationary || !is_cointegrated) { + if (!is_stationary || !is_cointegrated) { warning("No differentiation considered even though stationarity and/or cointegration might not be present. This can lead to spurious regression.", call.=FALSE) } is_stationary<-is_cointegrated<-TRUE @@ -215,9 +215,9 @@ revision_analysis<-function(vintages, theil_trf<-"None" U1<-theil(vt, gap, na.zero) U2<-theil2(vt, gap, na.zero) - if(!is.null(U1)) { + if (!is.null(U1)) { theil_rslt<-round(rbind(N, U1), 3) - if(!is.null(U2) && !all(is.nan(U2))==TRUE) { + if (!is.null(U2) && !all(is.nan(U2))==TRUE) { theil_rslt<-rbind(theil_rslt, U2=round(U2, 3)) theil_q<-eval_U(U2) U_det<-"U2" @@ -237,7 +237,7 @@ revision_analysis<-function(vintages, ### II.1_2. T-test and Augmented T-test ta_trf<-ifelse(is_log, "Log", "None") ta<-bias(rv, na.zero) - if(!is.null(ta)) { + if (!is.null(ta)) { ta_rslt<-t(round(ta, 3)) t_q<-eval_pvals(ta[, "pvalue"], h0_good=TRUE) ta_q<-eval_pvals(ta[, "pvalue.adjusted"], h0_good=TRUE) @@ -252,7 +252,7 @@ revision_analysis<-function(vintages, if (!is_cointegrated && !is_log) paste("Delta", delta_diff) else paste("Delta-Log", delta_diff) sd<-slope_and_drift(vtc, gap, na.zero) - if(!is.null(sd)) { + if (!is.null(sd)) { sd_rslt<-format_reg_output(sd, is_log, !is_cointegrated) sd_m_q<-eval_pvals(sd[, "intercept.pvalue"], h0_good=TRUE) sd_r_q<-eval_pvals(sd[, "slope.pvalue"], h0_good=TRUE) @@ -270,7 +270,7 @@ revision_analysis<-function(vintages, if (!is_stationary && !is_log) paste("Delta", delta_diff) else paste("Delta-Log", delta_diff) eff1<-efficiencyModel1(vts, gap, na.zero) - if(!is.null(eff1)) { + if (!is.null(eff1)) { eff1_rslt<-format_reg_output(eff1, is_log, !is_stationary) eff1_m_q<-eval_pvals(eff1[, "intercept.pvalue"], h0_good=TRUE) eff1_r_q<-eval_pvals(eff1[, "slope.pvalue"], h0_good=TRUE) @@ -283,7 +283,7 @@ revision_analysis<-function(vintages, ### III.2. Regression of latter revisions (Rv) on previous revisions (Rv_1) eff2_trf<-ifelse(is_log, "Log", "None") eff2<-efficiencyModel2(vt, gap, na.zero) - if(!is.null(eff2)) { + if (!is.null(eff2)) { eff2_rslt<-format_reg_output(eff2, is_log, FALSE) eff2_m_q<-c("", eval_pvals(eff2[, "intercept.pvalue"], h0_good=TRUE)) eff2_r_q<-c("", eval_pvals(eff2[, "slope.pvalue"], h0_good=TRUE)) @@ -298,28 +298,28 @@ revision_analysis<-function(vintages, ### IV.1. Regression of latter revisions (Rv) on previous revisions (Rv_1, Rv_2,...Rv_p) orth1_trf<-ifelse(is_log, "Log", "None") orth1<-orthogonallyModel1(rv, nrevs, na.zero) - if(!is.null(orth1)) { + if (!is.null(orth1)) { orth1_rslt<-format_reg_output(orth1, is_log, FALSE) orth1_m_q<-c(rep("", nrevs), eval_pvals(orth1[, "intercept.pvalue"], h0_good=TRUE)) orth1_r_q<-c(rep("", nrevs), eval_pvals(pf(orth1[, "F"], nrevs, orth1[, "N"]-nrevs-1), h0_good=TRUE)) orth1_diagnostics<-regression_diagnostics(orth1) } else { orth1_rslt<-orth1_diagnostics<-NULL - if(ncol(rv)>nrevs) orth1_m_q<-orth1_r_q<-c(rep("", nrevs), rep(NA, length(colnames(rv)[-c(1:nrevs)]))) + if (ncol(rv)>nrevs) orth1_m_q<-orth1_r_q<-c(rep("", nrevs), rep(NA, length(colnames(rv)[-c(1:nrevs)]))) else orth1_m_q<-orth1_r_q<-rep("", nrevs) } ### IV.2. Regression model of latter revisions (Rv) on previous revisions at a specific version (Rv_k) orth2_trf<-ifelse(is_log, "Log", "None") orth2<-orthogonallyModel2(rv, ref, na.zero) - if(!is.null(orth2)) { + if (!is.null(orth2)) { orth2_rslt<-format_reg_output(orth2, is_log, FALSE) orth2_m_q<-c(rep("", ref), eval_pvals(orth2[, "intercept.pvalue"], h0_good=TRUE)) orth2_r_q<-c(rep("", ref), eval_pvals(orth2[, "slope.pvalue"], h0_good=TRUE)) orth2_diagnostics<-regression_diagnostics(orth2) } else { orth2_rslt<-orth2_diagnostics<-NULL - if(ncol(rv)>ref) orth2_m_q<-orth2_r_q<-c(rep("", ref), rep(NA, length(colnames(rv)[-c(1:ref)]))) + if (ncol(rv)>ref) orth2_m_q<-orth2_r_q<-c(rep("", ref), rep(NA, length(colnames(rv)[-c(1:ref)]))) else orth2_m_q<-orth2_r_q<-rep("", ref) } @@ -328,7 +328,7 @@ revision_analysis<-function(vintages, ac_trf_str<-ifelse(ac_trf == "Log", get_info_transformation(TRUE, FALSE), get_info_transformation(FALSE, FALSE)) pm_test<-try(apply(rv, 2, function(x) ljungbox(x[!is.na(x)], k=2)), silent=TRUE) # Ljung-Box up to k - if(!"try-error" %in% class(pm_test)) { + if (!"try-error" %in% class(pm_test)) { pm_test_mat<-matrix(unlist(pm_test), ncol=2, byrow=TRUE)[, , drop=FALSE] dimnames(pm_test_mat)<-list(colnames(rv), c("value", "p.value")) ac_rslt<-list(info_transformation=ac_trf_str, estimates_ljungbox=pm_test_mat) @@ -344,19 +344,19 @@ revision_analysis<-function(vintages, lb_test<-try(apply(diff(rv), 2, function(x) seasonality_qs(x, freq)), silent=TRUE) # Ljung-Box fd_test<-try(apply(diff(rv), 2, function(x) seasonality_friedman(x, freq)), silent=TRUE) # Friedman non-parametric test - if(!"try-error" %in% class(lb_test) && !"try-error" %in% class(fd_test) && freq>1) { + if (!"try-error" %in% class(lb_test) && !"try-error" %in% class(fd_test) && freq>1) { seas_rslt<-list(info_transformation=seas_trf_str, estimates_ljungbox=matrix(unlist(lb_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value", "p.value"))), estimates_friedman=matrix(unlist(fd_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value", "p.value")))) seas_lb_q<-eval_pvals(seas_rslt$estimates_ljungbox[, "p.value"], h0_good=TRUE) seas_fd_q<-eval_pvals(seas_rslt$estimates_friedman[, "p.value"], h0_good=TRUE) - }else if(!"try-error" %in% class(lb_test) && freq>1) { + }else if (!"try-error" %in% class(lb_test) && freq>1) { seas_rslt<-list(info_transformation=seas_trf_str, estimates_ljungbox=matrix(unlist(lb_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value", "p.value"))), estimates_friedman=NULL) seas_lb_q<-eval_pvals(seas_rslt$estimates_ljungbox[, "p.value"], h0_good=TRUE) seas_fd_q<-rep(NA, length(colnames(rv))) - }else if(!"try-error" %in% class(fd_test) && freq>1) { + }else if (!"try-error" %in% class(fd_test) && freq>1) { seas_rslt<-list(info_transformation=seas_trf_str, estimates_ljungbox=NULL, estimates_friedman=matrix(unlist(fd_test), ncol=2, byrow = TRUE, dimnames = list(colnames(rv), c("value", "p.value")))) @@ -368,12 +368,12 @@ revision_analysis<-function(vintages, } ## V. Signal vs Noise - sn_trf<-if(is_stationary && !is_log) "None" else - if(is_stationary && is_log) "Log" else - if(!is_stationary && !is_log) paste("Delta", delta_diff) else + sn_trf<-if (is_stationary && !is_log) "None" else + if (is_stationary && is_log) "Log" else + if (!is_stationary && !is_log) paste("Delta", delta_diff) else paste("Delta-Log", delta_diff) sn<-signalnoise(vts, gap, na.zero) - if(!is.null(sn)) { + if (!is.null(sn)) { sn_rslt<-list(info_transformation=get_info_transformation(is_log, !is_stationary), estimates=t(round(sn, 3))) sn_noise_q<-eval_pvals(sn[, "Noise.pvalue"], h0_good=TRUE) @@ -390,11 +390,11 @@ revision_analysis<-function(vintages, ## see before ## 2. Cointegration test - if(!is.null(coint)) coint_rslt<-round(coint, 3) + if (!is.null(coint)) coint_rslt<-round(coint, 3) ## 3. VECM errcorr<-vecm(vt, lag=2, model="none", na.zero) - if(!is.null(errcorr)) { + if (!is.null(errcorr)) { vecm_rslt<-round(errcorr, 3) } else { vecm_rslt<-NULL @@ -462,8 +462,8 @@ get_rownames_diag <- function(vt, gap) { eval_pvals<-function(pval, h0_good = TRUE, residuals = FALSE) { pval<-as.numeric(pval) - if(! residuals) { - if(h0_good) { + if (! residuals) { + if (h0_good) { quality<-ifelse(pval>.05, "Good", ifelse(pval>.01, "Uncertain", ifelse(pval>.001, "Bad", "Severe"))) @@ -471,7 +471,7 @@ eval_pvals<-function(pval, h0_good = TRUE, residuals = FALSE) { quality<-ifelse(pval<.05, "Good", "Uncertain") } } else { - if(h0_good) { + if (h0_good) { quality<-ifelse(pval>.1, "Good", ifelse(pval>.01, "Uncertain", "Bad")) } else { @@ -486,7 +486,7 @@ eval_pvals<-function(pval, h0_good = TRUE, residuals = FALSE) { eval_U<-function(U, U2=TRUE) { U<-as.numeric(U) - if(U2) { + if (U2) { quality<-ifelse(U>=1, "Severe", ifelse(U>.9, "Bad", ifelse(U>.8, "Uncertain", "Good"))) @@ -515,11 +515,11 @@ format_reg_output<-function(x, is_log, is_diff) { } get_info_transformation<-function(is_log, is_diff) { - if(is_log) { + if (is_log) { info_transformation<-"Series have been log-transformed" - if(is_diff) info_transformation<-paste(info_transformation, "and differentiated") + if (is_diff) info_transformation<-paste(info_transformation, "and differentiated") } else { - if(is_diff) { + if (is_diff) { info_transformation<-"Series have been differentiated" } else { info_transformation<-"No transformation" @@ -547,7 +547,7 @@ regression_diagnostics<-function(reg_output) { get_vd_rev <- function(vt, gap) { n<-dim(vt)[2] - idx1<-(gap+1):n + idx1<- (gap+1):n idx0<-1:(n-gap) rev<-vt[, idx1, drop=FALSE]-vt[, idx0, drop=FALSE] @@ -561,19 +561,19 @@ get_vd_rev <- function(vt, gap) { check_seasonality <- function(x) { - if(frequency(x)>1) { + if (frequency(x)>1) { x_diff<-diff(x) lb_pval<-try(seasonality_qs(x_diff, frequency(x))$pvalue, silent=TRUE) # Ljung-Box fd_pval<-try(seasonality_friedman(x_diff, frequency(x))$pvalue, silent=TRUE) # Friedman non-parametric test test_succeeded<-c(!"try-error" %in% class(lb_pval), !"try-error" %in% class(fd_pval)) - if(all(test_succeeded)) { + if (all(test_succeeded)) { pvals<-c(lb_pval, fd_pval) seasonality<-ifelse(length(pvals[which(pvals<.05)])==2, TRUE, FALSE) - }else if(any(test_succeeded)) { - if(test_succeeded[1]) { + }else if (any(test_succeeded)) { + if (test_succeeded[1]) { seasonality<-ifelse(lb_pval<.01, TRUE, FALSE) - }else if(test_succeeded[2]) { + }else if (test_succeeded[2]) { seasonality<-ifelse(fd_pval<.01, TRUE, FALSE) } } else { diff --git a/R/revisions.R b/R/revisions.R index 45a5e05..525a8bb 100644 --- a/R/revisions.R +++ b/R/revisions.R @@ -25,7 +25,7 @@ #' revisions<-get_revisions(vintages, gap=1) #' get_revisions<-function(vintages, gap=1) { - if(!class(vintages)=="rjd3rev_vintages") { + if (!class(vintages)=="rjd3rev_vintages") { warning("Wrong input. vintages must be an object of class 'rjd3rev_vintages'.") return(NULL) } @@ -33,7 +33,7 @@ get_revisions<-function(vintages, gap=1) { get_vd_rev <- function(vt, gap) { n<-dim(vt)[2] - idx1<-(gap+1):n + idx1<- (gap+1):n idx0<-1:(n-gap) rev<-vt[, idx1, drop=FALSE]-vt[, idx0, drop=FALSE] diff --git a/R/tests.R b/R/tests.R index 51701ef..4308b29 100644 --- a/R/tests.R +++ b/R/tests.R @@ -146,10 +146,10 @@ descriptive_statistics<-function(revisions.view, rounding=3) { #' theil<-function(vintages.view, gap=1, na.zero= FALSE) { q<-vintages.view - if(na.zero) q[is.na(q)]<-0 + if (na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) theil<-try(.jcall("jdplus/revisions/base/r/Utility", "[D", "theil", jq, as.integer(gap)), silent= TRUE) - if("try-error" %in% class(theil)) { + if ("try-error" %in% class(theil)) { warning("theil could not be performed", call.= FALSE) return(NULL) } @@ -193,10 +193,10 @@ theil<-function(vintages.view, gap=1, na.zero= FALSE) { #' theil2<-function(vintages.view, gap=1, na.zero= FALSE) { q<-vintages.view - if(na.zero) q[is.na(q)]<-0 + if (na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) theil2<-try(.jcall("jdplus/revisions/base/r/Utility", "[D", "theil2", jq, as.integer(gap)), silent= TRUE) - if("try-error" %in% class(theil2)) { + if ("try-error" %in% class(theil2)) { warning("theil2 could not be performed", call.= FALSE) return(NULL) } @@ -238,16 +238,16 @@ theil2<-function(vintages.view, gap=1, na.zero= FALSE) { #' bias<-function(revisions.view, na.zero= FALSE) { r<-revisions.view - if(na.zero) r[is.na(r)]<-0 + if (na.zero) r[is.na(r)]<-0 jrevs<-matrix_r2jd(r) jbias<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "bias", jrevs), silent= TRUE) - if("try-error" %in% class(bias)) { + if ("try-error" %in% class(bias)) { warning("bias could not be performed", call.= FALSE) return(NULL) } bias <- matrix_jd2r(jbias) bias[rowSums(bias[])==0, ]<-NaN # fix non-calculable cases - if(all(is.nan(bias))) { + if (all(is.nan(bias))) { warning("bias could not be performed", call.= FALSE) return(NULL) } @@ -297,16 +297,16 @@ bias<-function(revisions.view, na.zero= FALSE) { #' slope_and_drift<-function(vintages.view, gap=1, na.zero= FALSE) { q<-vintages.view - if(na.zero) q[is.na(q)]<-0 + if (na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "slopeAndDrift", jq, as.integer(gap)), silent= TRUE) - if("try-error" %in% class(jsd)) { + if ("try-error" %in% class(jsd)) { warning("Slope and drift could not be performed", call.= FALSE) return(NULL) } slope_and_drift <- matrix_jd2r(jsd) slope_and_drift[rowSums(slope_and_drift[])==0, ]<-NaN # fix non-calculable cases - if(all(is.nan(slope_and_drift))) { + if (all(is.nan(slope_and_drift))) { warning("slope_and_drift could not be performed", call.= FALSE) return(NULL) } @@ -356,16 +356,16 @@ slope_and_drift<-function(vintages.view, gap=1, na.zero= FALSE) { #' efficiencyModel1<-function(vintages.view, gap=1, na.zero= FALSE) { q<-vintages.view - if(na.zero) q[is.na(q)]<-0 + if (na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) jef1<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "efficiencyModel1", jq, as.integer(gap)), silent= TRUE) - if("try-error" %in% class(jef1)) { + if ("try-error" %in% class(jef1)) { warning("efficiencyModel1 could not be performed", call.= FALSE) return(NULL) } efficiencyModel1 <- matrix_jd2r(jef1) efficiencyModel1[rowSums(efficiencyModel1[])==0, ]<-NaN # fix non-calculable cases - if(all(is.nan(efficiencyModel1))) { + if (all(is.nan(efficiencyModel1))) { warning("efficiencyModel1 could not be performed", call.= FALSE) return(NULL) } @@ -416,20 +416,20 @@ efficiencyModel1<-function(vintages.view, gap=1, na.zero= FALSE) { #' efficiencyModel2<-function(vintages.view, gap=1, na.zero= FALSE) { q<-vintages.view - if(na.zero) q[is.na(q)]<-0 + if (na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) jef2<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "efficiencyModel2", jq, as.integer(gap)), silent= TRUE) - if("try-error" %in% class(jef2)) { + if ("try-error" %in% class(jef2)) { warning("efficiencyModel2 could not be performed", call.= FALSE) return(NULL) } efficiencyModel2 <- matrix_jd2r(jef2) - if(length(efficiencyModel2)==0) { + if (length(efficiencyModel2)==0) { warning("efficiencyModel2 could not be performed: Too few number of vintages", call.= FALSE) return(NULL) } efficiencyModel2[rowSums(efficiencyModel2[])==0, ]<-NaN # fix non-calculable cases - if(all(is.nan(efficiencyModel2))) { + if (all(is.nan(efficiencyModel2))) { warning("efficiencyModel2 could not be performed", call.= FALSE) return(NULL) } @@ -479,10 +479,10 @@ efficiencyModel2<-function(vintages.view, gap=1, na.zero= FALSE) { #' orthogonallyModel1<-function(revisions.view, nrevs=1, na.zero= FALSE) { r<-revisions.view - if(na.zero) r[is.na(r)]<-0 + if (na.zero) r[is.na(r)]<-0 jr<-matrix_r2jd(as.matrix(r)) jom<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "orthogonallyModel1", jr, as.integer(nrevs)), silent= TRUE) - if("try-error" %in% class(jom)) { + if ("try-error" %in% class(jom)) { warning("orthogonallyModel1 could not be performed", call.= FALSE) return(NULL) } @@ -492,7 +492,7 @@ orthogonallyModel1<-function(revisions.view, nrevs=1, na.zero= FALSE) { return(NULL) } om[rowSums(om[])==0, ]<-NaN # fix non-calculable cases - if(all(is.nan(om))) { + if (all(is.nan(om))) { warning("orthogonallyModel1 could not be performed", call.= FALSE) return(NULL) } @@ -539,10 +539,10 @@ orthogonallyModel1<-function(revisions.view, nrevs=1, na.zero= FALSE) { #' orthogonallyModel2<-function(revisions.view, reference=1, na.zero= FALSE) { r<-revisions.view - if(na.zero) r[is.na(r)]<-0 + if (na.zero) r[is.na(r)]<-0 jr<-matrix_r2jd(as.matrix(r)) jom<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "orthogonallyModel2", jr, as.integer(reference)), silent= TRUE) - if("try-error" %in% class(jom)) { + if ("try-error" %in% class(jom)) { warning("orthogonallyModel2 could not be performed", call.= FALSE) return(NULL) } @@ -552,7 +552,7 @@ orthogonallyModel2<-function(revisions.view, reference=1, na.zero= FALSE) { return(NULL) } om[rowSums(om[])==0, ]<-NaN # fix non-calculable cases - if(all(is.nan(om))) { + if (all(is.nan(om))) { warning("orthogonallyModel2 could not be performed", call.= FALSE) return(NULL) } @@ -602,16 +602,16 @@ orthogonallyModel2<-function(revisions.view, reference=1, na.zero= FALSE) { #' signalnoise<-function(vintages.view, gap=1, na.zero= FALSE) { q<-vintages.view - if(na.zero) q[is.na(q)]<-0 + if (na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "signalNoise", jq, as.integer(gap)), silent= TRUE) - if("try-error" %in% class(jsd)) { + if ("try-error" %in% class(jsd)) { warning("signalnoise could not be performed", call.= FALSE) return(NULL) } sn<-matrix_jd2r(jsd) sn[rowSums(sn[])==0, ]<-NaN # fix non-calculable cases - if(all(is.nan(sn))) { + if (all(is.nan(sn))) { warning("SignalNoise could not be performed", call.= FALSE) return(NULL) } @@ -658,10 +658,10 @@ signalnoise<-function(vintages.view, gap=1, na.zero= FALSE) { #' unitroot<-function(vintages.view, adfk=1, na.zero= FALSE) { q<-vintages.view - if(na.zero) q[is.na(q)]<-0 + if (na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "unitroot", jq, as.integer(adfk)), silent= TRUE) - if("try-error" %in% class(jsd)) { + if ("try-error" %in% class(jsd)) { warning("unit root test could not be performed", call.= FALSE) return(NULL) } @@ -706,10 +706,10 @@ unitroot<-function(vintages.view, adfk=1, na.zero= FALSE) { #' cointegration<-function(vintages.view, adfk=1, na.zero= FALSE) { q<-vintages.view - if(na.zero) q[is.na(q)]<-0 + if (na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "cointegration", jq, as.integer(adfk)), silent= TRUE) - if("try-error" %in% class(jsd)) { + if ("try-error" %in% class(jsd)) { warning("cointegration test could not be performed", call.= FALSE) return(NULL) } @@ -757,10 +757,10 @@ cointegration<-function(vintages.view, adfk=1, na.zero= FALSE) { vecm<-function(vintages.view, lag=2, model = c("none", "cnt", "trend"), na.zero= FALSE) { model<-match.arg(model) q<-vintages.view - if(na.zero) q[is.na(q)]<-0 + if (na.zero) q[is.na(q)]<-0 jq<-matrix_r2jd(q) jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "vecm", jq, as.integer(lag), model), silent= TRUE) - if("try-error" %in% class(jsd)) { + if ("try-error" %in% class(jsd)) { warning("vecm could not be performed", call.= FALSE) return(NULL) } @@ -774,11 +774,11 @@ vecm<-function(vintages.view, lag=2, model = c("none", "cnt", "trend"), na.zero= # # auto_correlation<-function(vintages.view, nbreuschgodfrey=1, nljungbox=1, na.zero= FALSE) { # q<-vintages.view -# if(na.zero) q[is.na(q)]<-0 +# if (na.zero) q[is.na(q)]<-0 # jq<-matrix_r2jd(q) # jsd<-try(.jcall("jdplus/revisions/base/r/Utility", "Ljdplus/toolkit/base/api/math/matrices/Matrix;", "autoCorrelation", jq # , as.integer(nbreuschgodfrey), as.integer(nljungbox)), silent= TRUE) -# if("try-error" %in% class(jsd)) { +# if ("try-error" %in% class(jsd)) { # warning("auto_correlation test on OLS residuals could not be performed", call.= FALSE) # return(NULL) # } diff --git a/R/vintages.R b/R/vintages.R index 62128af..7435bd1 100644 --- a/R/vintages.R +++ b/R/vintages.R @@ -77,7 +77,7 @@ create_vintages<- function(df, periodicity, vintage.selection = NULL, revdate.fo jfac<-.jnew("jdplus/revisions/base/r/VintagesFactory", as.integer(periodicity)) # check input - if(! is.data.frame(df)) { + if (! is.data.frame(df)) { warning("Wrong input type. Must be a data.frame.") return(NULL) } @@ -93,26 +93,26 @@ create_vintages<- function(df, periodicity, vintage.selection = NULL, revdate.fo warning("Wrong input in first column. Revision dates not in a correct format. The parameter revdate.format might be mispecified.") return(NULL) } - if(is.null(yp(df$time))) { + if (is.null(yp(df$time))) { warning("Wrong input in second column. Time periods not in a correct format. Examples of correct formats are 2023M01, 2023Q1 or 2023.") return(NULL) } else { df$time<-yp(df$time) } - if(! is.numeric(df$obs_value)) { + if (! is.numeric(df$obs_value)) { warning("Wrong input in third column. Obsevation values must be numeric.") return(NULL) } # Vintages selection - if(!is.null(vintage.selection)) { + if (!is.null(vintage.selection)) { df<-subset(df, revdate >= as.Date(vintage.selection[[1]]) & revdate <= as.Date(vintage.selection[[2]])) - if(nrow(df) == 0) { + if (nrow(df) == 0) { warning("Vintage selection out of range!") return(NULL) } } - if(length(unique(df$revdate))<2) { + if (length(unique(df$revdate))<2) { warning("Too few number of vintages. Number of unique revision dates must be >= 2.") return(NULL) } @@ -223,7 +223,7 @@ create_vintages_from_csv<-function(file, periodicity, separator = ",", vintage.s #' } create_vintages_from_xlsx<-function(file, sheetname, periodicity, vintage.selection = NULL, revdate.format= "%Y.%m.%d") { - if(! require(readxl)) { + if (! require(readxl)) { stop("package 'readxl' must be installed to run the function 'create_vintages_from_xlsx'") } @@ -260,7 +260,7 @@ yq<-function(y, q) { yp<-function(s) { y<-as.integer(substr(s, 1, 4)) - if(nchar(as.character(s))[1] == 4) { + if (nchar(as.character(s))[1] == 4) { return(ymd(y, 1)) } else { p <- substr(s, 5, 5) @@ -279,7 +279,7 @@ yp<-function(s) { d2t<-function(d, periodicity) { y<-floor(d) frac<-d%%1 - date<-ymd(y, 1, 1)+(ymd(y+1, 1, 1)-ymd(y, 1, 1))*frac + date<-ymd(y, 1, 1)+ (ymd(y+1, 1, 1)-ymd(y, 1, 1))*frac if (periodicity == 12) { return(paste0(y, "M", format(date, "%m"))) }else if (periodicity == 4) { From 5b376ebfda3e8855900ffe0a56ca3f06c7556926 Mon Sep 17 00:00:00 2001 From: Lemasson Corentin Date: Mon, 18 Mar 2024 17:38:19 +0100 Subject: [PATCH 22/56] add gh pages --- .Rbuildignore | 4 +++ .github/.gitignore | 1 + .github/workflows/pkgdown.yaml | 57 ++++++++++++++++++++++++++++++++++ .gitignore | 1 + DESCRIPTION | 1 + _pkgdown.yml | 4 +++ 6 files changed, 68 insertions(+) create mode 100644 .github/.gitignore create mode 100644 .github/workflows/pkgdown.yaml create mode 100644 _pkgdown.yml diff --git a/.Rbuildignore b/.Rbuildignore index 60b8d9d..b546a3f 100644 --- a/.Rbuildignore +++ b/.Rbuildignore @@ -2,3 +2,7 @@ ^\.Rproj\.user$ ^doc$ ^Meta$ +^_pkgdown\.yml$ +^docs$ +^pkgdown$ +^\.github$ diff --git a/.github/.gitignore b/.github/.gitignore new file mode 100644 index 0000000..2d19fc7 --- /dev/null +++ b/.github/.gitignore @@ -0,0 +1 @@ +*.html diff --git a/.github/workflows/pkgdown.yaml b/.github/workflows/pkgdown.yaml new file mode 100644 index 0000000..37245eb --- /dev/null +++ b/.github/workflows/pkgdown.yaml @@ -0,0 +1,57 @@ +# Workflow derived from https://github.com/r-lib/actions/tree/v2/examples +# Need help debugging build failures? Start at https://github.com/r-lib/actions#where-to-find-help +on: + push: + branches: [main, master, develop] + pull_request: + branches: [main, master, develop] + release: + types: [published] + workflow_dispatch: + +name: pkgdown + +jobs: + pkgdown: + runs-on: ubuntu-latest + # Only restrict concurrency for non-PR jobs + concurrency: + group: pkgdown-${{ github.event_name != 'pull_request' || github.run_id }} + env: + GITHUB_PAT: ${{ secrets.GITHUB_TOKEN }} + permissions: + contents: write + steps: + - uses: actions/checkout@v4 + + - uses: actions/setup-java@v3 + with: + distribution: 'zulu' # See 'Supported distributions' for available options + java-version: '17' + + - uses: r-lib/actions/setup-pandoc@v2 + + - uses: r-lib/actions/setup-r@v2 + with: + use-public-rspm: true + + # - name: Set up for RProtoBuf + # run: sudo apt-get update -y && sudo apt-get install protobuf-compiler libprotobuf-dev libprotoc-dev + + + - uses: r-lib/actions/setup-r-dependencies@v2 + with: + extra-packages: any::pkgdown, local::. + needs: website + + - name: Build site + run: pkgdown::build_site_github_pages(new_process = FALSE, install = FALSE) + shell: Rscript {0} + + - name: Deploy to GitHub pages 🚀 + if: github.event_name != 'pull_request' + uses: JamesIves/github-pages-deploy-action@v4.4.1 + with: + clean: false + branch: gh-pages + folder: docs diff --git a/.gitignore b/.gitignore index 99ac7be..c62e3c8 100644 --- a/.gitignore +++ b/.gitignore @@ -6,3 +6,4 @@ inst/doc /doc/ /Meta/ +docs diff --git a/DESCRIPTION b/DESCRIPTION index 3dc055e..8c3ceca 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -41,3 +41,4 @@ Collate: 'zzz.R' RoxygenNote: 7.3.1 VignetteBuilder: knitr +URL: https://rjdemetra.github.io/rjd3revisions/ diff --git a/_pkgdown.yml b/_pkgdown.yml new file mode 100644 index 0000000..fd69446 --- /dev/null +++ b/_pkgdown.yml @@ -0,0 +1,4 @@ +url: https://rjdemetra.github.io/rjd3revisions/ +template: + bootstrap: 5 + From e4f6783132667b7e7067771faf34cb93b8cb6bb7 Mon Sep 17 00:00:00 2001 From: Lemasson Corentin Date: Tue, 19 Mar 2024 10:06:11 +0100 Subject: [PATCH 23/56] update dependency --- .github/workflows/pkgdown.yaml | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/.github/workflows/pkgdown.yaml b/.github/workflows/pkgdown.yaml index 37245eb..a8cf7e5 100644 --- a/.github/workflows/pkgdown.yaml +++ b/.github/workflows/pkgdown.yaml @@ -35,8 +35,8 @@ jobs: with: use-public-rspm: true - # - name: Set up for RProtoBuf - # run: sudo apt-get update -y && sudo apt-get install protobuf-compiler libprotobuf-dev libprotoc-dev + - name: Set up for RProtoBuf + run: sudo apt-get update -y && sudo apt-get install protobuf-compiler libprotobuf-dev libprotoc-dev - uses: r-lib/actions/setup-r-dependencies@v2 From 8a57a9c85f25b3bbb23cfe22ab323e4db9d084d8 Mon Sep 17 00:00:00 2001 From: Tanguy BARTHELEMY Date: Thu, 21 Mar 2024 19:17:43 +0100 Subject: [PATCH 24/56] add LICENSE file --- .Rbuildignore | 1 + DESCRIPTION | 2 +- LICENSE | 185 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European Union 2007, 2016 + +This European Union Public Licence (the ‘EUPL’) applies to the Work (as defined below) which is provided under the terms of this Licence. Any use of the Work, other than as authorised under this Licence is prohibited (to the extent such use is covered by a right of the copyright holder of the Work). + +The Work is provided under the terms of this Licence when the Licensor (as defined below) has placed the following notice immediately following the copyright notice for the Work: + +Licensed under the EUPL + +or has expressed by any other means his willingness to license under the EUPL. + + +1. Definitions + +In this Licence, the following terms have the following meaning: + +— ‘The Licence’: this Licence. + +— ‘The Original Work’: the work or software distributed or communicated by the Licensor under this Licence, available as Source Code and also as Executable Code as the case may be. + +— ‘Derivative Works’: the works or software that could be created by the Licensee, based upon the Original Work or modifications thereof. This Licence does not define the extent of modification or dependence on the Original Work required in order to classify a work as a Derivative Work; this extent is determined by copyright law applicable in the country mentioned in Article 15. + +— ‘The Work’: the Original Work or its Derivative Works. + +— ‘The Source Code’: the human-readable form of the Work which is the most convenient for people to study and modify. + +— ‘The Executable Code’: any code which has generally been compiled and which is meant to be interpreted by a computer as a program. + +— ‘The Licensor’: the natural or legal person that distributes or communicates the Work under the Licence. + +— ‘Contributor(s)’: any natural or legal person who modifies the Work under the Licence, or otherwise contributes to the creation of a Derivative Work. + +— ‘The Licensee’ or ‘You’: any natural or legal person who makes any usage of the Work under the terms of the Licence. + +— ‘Distribution’ or ‘Communication’: any act of selling, giving, lending, renting, distributing, communicating, transmitting, or otherwise making available, online or offline, copies of the Work or providing access to its essential functionalities at the disposal of any other natural or legal person. + + +2. 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Clicking on that icon indicates your clear and irrevocable acceptance of this Licence and all of its terms and conditions. + +Similarly, you irrevocably accept this Licence and all of its terms and conditions by exercising any rights granted to You by Article 2 of this Licence, such as the use of the Work, the creation by You of a Derivative Work or the Distribution or Communication by You of the Work or copies thereof. + + +11. Information to the public + +In case of any Distribution or Communication of the Work by means of electronic communication by You (for example, by offering to download the Work from a remote location) the distribution channel or media (for example, a website) must at least provide to the public the information requested by the applicable law regarding the Licensor, the Licence and the way it may be accessible, concluded, stored and reproduced by the Licensee. + + +12. Termination of the Licence + +The Licence and the rights granted hereunder will terminate automatically upon any breach by the Licensee of the terms of the Licence. + +Such a termination will not terminate the licences of any person who has received the Work from the Licensee under the Licence, provided such persons remain in full compliance with the Licence. + + +13. Miscellaneous + +Without prejudice of Article 9 above, the Licence represents the complete agreement between the Parties as to the Work. + +If any provision of the Licence is invalid or unenforceable under applicable law, this will not affect the validity or enforceability of the Licence as a whole. Such provision will be construed or reformed so as necessary to make it valid and enforceable. + +The European Commission may publish other linguistic versions or new versions of this Licence or updated versions of the Appendix, so far this is required and reasonable, without reducing the scope of the rights granted by the Licence. New versions of the Licence will be published with a unique version number. + +All linguistic versions of this Licence, approved by the European Commission, have identical value. Parties can take advantage of the linguistic version of their choice. + + +14. Jurisdiction + +Without prejudice to specific agreement between parties, + +— any litigation resulting from the interpretation of this License, arising between the European Union institutions, bodies, offices or agencies, as a Licensor, and any Licensee, will be subject to the jurisdiction of the Court of Justice of the European Union, as laid down in article 272 of the Treaty on the Functioning of the European Union, + +— any litigation arising between other parties and resulting from the interpretation of this License, will be subject to the exclusive jurisdiction of the competent court where the Licensor resides or conducts its primary business. + + +15. Applicable Law + +Without prejudice to specific agreement between parties, + +— this Licence shall be governed by the law of the European Union Member State where the Licensor has his seat, resides or has his registered office, + +— this licence shall be governed by Belgian law if the Licensor has no seat, residence or registered office inside a European Union Member State. +Appendix + +‘Compatible Licences’ according to Article 5 EUPL are: + +— GNU General Public License (GPL) v. 2, v. 3 + +— GNU Affero General Public License (AGPL) v. 3 + +— Open Software License (OSL) v. 2.1, v. 3.0 + +— Eclipse Public License (EPL) v. 1.0 + +— CeCILL v. 2.0, v. 2.1 + +— Mozilla Public Licence (MPL) v. 2 + +— GNU Lesser General Public Licence (LGPL) v. 2.1, v. 3 + +— Creative Commons Attribution-ShareAlike v. 3.0 Unported (CC BY-SA 3.0) for works other than software + +— European Union Public Licence (EUPL) v. 1.1, v. 1.2 + +— Québec Free and Open-Source Licence — Reciprocity (LiLiQ-R) or Strong Reciprocity (LiLiQ-R+) + +The European Commission may update this Appendix to later versions of the above licences without producing a new version of the EUPL, as long as they provide the rights granted in Article 2 of this Licence and protect the covered Source Code from exclusive appropriation. + +All other changes or additions to this Appendix require the production of a new EUPL version. diff --git a/NEWS.md b/NEWS.md new file mode 100644 index 0000000..7460369 --- /dev/null +++ b/NEWS.md @@ -0,0 +1,3 @@ +# rjd3revisions 1.1.0 + +* Initial CRAN submission. diff --git a/revisions_report_files/mathjax-27/config/AM_CHTML-full.js b/revisions_report_files/mathjax-27/config/AM_CHTML-full.js new file mode 100644 index 0000000..20db1ec --- /dev/null +++ b/revisions_report_files/mathjax-27/config/AM_CHTML-full.js @@ -0,0 +1,53 @@ +/* + * /MathJax/config/AM_CHTML-full.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/AsciiMath/config.js", + "[MathJax]/jax/output/CommonHTML/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/asciimath2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/jax/input/AsciiMath/jax.js", + "[MathJax]/jax/output/CommonHTML/jax.js", + "[MathJax]/jax/output/CommonHTML/autoload/mtable.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); 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+MathJax.Extension.asciimath2jax={version:"2.7.6",config:{delimiters:[["`","`"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"asciimath2jax_ignore",processClass:"asciimath2jax_process",preview:"AsciiMath"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("asciimath2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],c,a,b=this.config;this.match={};if(b.delimiters.length===0){return false}for(c=0,a=b.delimiters.length;c0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin 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t}},handleText:function(u,x,t,w){if(u.childNodes.length===0){a.addElement(u,"mjx-char");w=a.BBOX.empty(w)}if(typeof(t)==="string"){t=this.FONTDATA.VARIANT[t]}if(!t){t=this.FONTDATA.VARIANT[d.VARIANT.NORMAL]}var s={text:x,i:0,length:x.length},v=[];if(t.style&&s.length){v.push(this.styledText(t,x))}else{while(s.i-w.b){u.firstChild.style.paddingBottom=this.EmRounded(w.d+w.b)}return w},createDelimiter:function(x,s,u,A,v){if(!s){var B=this.BBOX.zero();B.w=B.r=this.TEX.nulldelimiterspace;a.addElement(x,"mjx-box",{style:{width:B.w}});return B}if(!(u instanceof Array)){u=[u,u]}var z=u[1];u=u[0];var t={alias:s};while(t.alias){s=t.alias;t=this.FONTDATA.DELIMITERS[s];if(!t){t={HW:[0,this.FONTDATA.VARIANT[d.VARIANT.NORMAL]]}}}if(t.load){f.RestartAfter(o.Require(this.fontDir+"/TeX/fontdata-"+t.load+".js"))}for(var 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this.data[s].CHTML}return a.BBOX.zero()},CHTMLdrawBBox:function(t,u){if(!u){u=this.CHTML}var s=a.Element("mjx-box",{style:{opacity:0.25,"margin-left":a.Em(-(u.w+(u.R||0)))}},[["mjx-box",{style:{height:a.Em(u.h),width:a.Em(u.w),"background-color":"red"}}],["mjx-box",{style:{height:a.Em(u.d),width:a.Em(u.w),"margin-left":a.Em(-u.w),"vertical-align":a.Em(-u.d),"background-color":"green"}}]]);if(t.nextSibling){t.parentNode.insertBefore(s,t.nextSibling)}else{t.parentNode.appendChild(s)}},CHTMLnotEmpty:function(s){while(s&&s.data.length<2&&(s.type==="mrow"||s.type==="texatom")){s=s.data[0]}return !!s}},{CHTMLautoload:function(){this.constructor.Augment({toCommonHTML:d.mbase.CHTMLautoloadFail});var s=a.autoloadDir+"/"+this.type+".js";f.RestartAfter(o.Require(s))},CHTMLautoloadFail:function(){throw Error("CommonHTML can't autoload '"+this.type+"'")},CHTMLautoloadList:{},CHTMLautoloadFile:function(s){if(d.mbase.CHTMLautoloadList.hasOwnProperty(s)){throw Error("CommonHTML can't autoload file 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v=this.Get("alttext");if(v&&!x.getAttribute("aria-label")){x.setAttribute("aria-label",v)}if(this.CHTML.pwidth){x.parentNode.style.minWidth=this.CHTML.mwidth||a.Em(this.CHTML.w);x.parentNode.className="mjx-full-width "+x.parentNode.className;x.style.width=this.CHTML.pwidth}else{if(!this.isMultiline&&this.Get("display")==="block"){var u=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(u.indentalignfirst!==d.INDENTALIGN.INDENTALIGN){u.indentalign=u.indentalignfirst}if(u.indentalign===d.INDENTALIGN.AUTO){u.indentalign=r.displayAlign}if(u.indentshiftfirst!==d.INDENTSHIFT.INDENTSHIFT){u.indentshift=u.indentshiftfirst}if(u.indentshift==="auto"){u.indentshift="0"}var t=this.CHTMLlength2em(u.indentshift,a.cwidth);if(r.displayIndent!=="0"){var s=this.CHTMLlength2em(r.displayIndent,a.cwidth);t+=(u.indentalign===d.INDENTALIGN.RIGHT?-s:s)}var w=x.parentNode.parentNode.style;x.parentNode.style.textAlign=w.textAlign=u.indentalign;if(t){t*=a.em/a.outerEm;f.Insert(w,({left:{marginLeft:a.Em(t)},right:{marginRight:a.Em(-t)},center:{marginLeft:a.Em(t),marginRight:a.Em(-t)}})[u.indentalign])}}}return x}});d.mi.Augment({toCommonHTML:function(s){s=this.CHTMLdefaultNode(s);var u=this.CHTML,t=this.data.join("");if(u.skew!=null&&!a.isChar(t)){delete u.skew}if(u.r>u.w&&a.isChar(t)&&!this.CHTMLvariant.noIC){u.ic=u.r-u.w;u.w=u.r;s.lastChild.style.paddingRight=a.Em(u.ic)}return s}});d.mn.Augment({CHTMLremapMinus:function(s){return s.replace(/^-/,"\u2212")},toCommonHTML:function(s){s=this.CHTMLdefaultNode(s,{childOptions:{remap:this.CHTMLremapMinus}});var u=this.CHTML,t=this.data.join("");if(u.skew!=null&&!a.isChar(t)){delete u.skew}if(u.r>u.w&&a.isChar(t)&&!this.CHTMLvariant.noIC){u.ic=u.r-u.w;u.w=u.r;s.lastChild.style.paddingRight=a.Em(u.ic)}return s}});d.mo.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLgetVariant();this.CHTMLhandleScale(v);a.BBOX.empty(this.CHTML);var t=this.getValues("displaystyle","largeop");t.variant=this.CHTMLvariant;t.text=this.data.join("");if(t.text==""){if(this.fence){v.style.width=a.Em(a.TEX.nulldelimiterspace)}}else{this.CHTMLadjustAccent(t);this.CHTMLadjustVariant(t);for(var u=0,s=this.data.length;u0){if(!this.hasValue("lspace")){t.lspace=0.15}if(!this.hasValue("rspace")){t.rspace=0.15}}var s=this,u=this.Parent();while(u&&u.isEmbellished()&&u.Core()===s){s=u;u=u.Parent();v=s.CHTMLnodeElement()}if(t.lspace){v.style.paddingLeft=a.Em(t.lspace)}if(t.rspace){v.style.paddingRight=a.Em(t.rspace)}this.CHTML.L=t.lspace;this.CHTML.R=t.rspace}else{this.SUPER(arguments).CHTMLhandleSpace.apply(this,arguments)}},CHTMLadjustAccent:function(u){var t=this.CoreParent();u.parent=t;if(a.isChar(u.text)&&t&&t.isa(d.munderover)){var v=t.data[t.over],s=t.data[t.under];if(v&&this===v.CoreMO()&&t.Get("accent")){u.remapchars=a.FONTDATA.REMAPACCENT}else{if(s&&this===s.CoreMO()&&t.Get("accentunder")){u.remapchars=a.FONTDATA.REMAPACCENTUNDER}}}},CHTMLadjustVariant:function(t){var s=t.parent,u=(s&&s.isa(d.msubsup)&&this!==s.data[s.base]);if(t.largeop){t.mathvariant=(t.displaystyle?"-largeOp":"-smallOp")}if(u){t.remapchars=this.remapChars;if(t.text.match(/['`"\u00B4\u2032-\u2037\u2057]/)){t.mathvariant="-TeX-variant"}}},CHTMLfixCombiningChar:function(s){s=s.firstChild;var t=a.Element("mjx-box",{style:{width:".25em","margin-left":"-.25em"}});s.insertBefore(t,s.firstChild)},CHTMLcenterOp:function(s){var u=this.CHTML;var t=(u.h-u.d)/2-a.TEX.axis_height;if(Math.abs(t)>0.001){s.style.verticalAlign=a.Em(-t)}u.h-=t;u.d+=t;if(u.r>u.w){u.ic=u.r-u.w;u.w=u.r;s.style.paddingRight=a.Em(u.ic)}},CHTMLcanStretch:function(w,u,v){if(!this.Get("stretchy")){return false}var x=this.data.join("");if(!a.isChar(x)){return false}var t={text:x};this.CHTMLadjustAccent(t);if(t.remapchars){x=t.remapchars[x]||x}x=a.FONTDATA.DELIMITERS[x.charCodeAt(0)];var s=(x&&x.dir===w.substr(0,1));if(s){s=(this.CHTML.h!==u||this.CHTML.d!==v||!!this.Get("minsize",true)||!!this.Get("maxsize",true));if(s){this.CHTML.stretch=true}}return s},CHTMLstretchV:function(v,y){var w=this.CHTMLnodeElement(),x=this.CHTML;var t=this.getValues("symmetric","maxsize","minsize");var u,s=a.TEX.axis_height;if(t.symmetric){u=2*Math.max(v-s,y+s)}else{u=v+y}t.maxsize=this.CHTMLlength2em(t.maxsize,x.h+x.d);t.minsize=this.CHTMLlength2em(t.minsize,x.h+x.d);u=Math.max(t.minsize,Math.min(t.maxsize,u));if(u!==x.sH){if(u!=t.minsize){u=[Math.max(u*a.TEX.delimiterfactor/1000,u-a.TEX.delimitershortfall),u]}while(w.firstChild){w.removeChild(w.firstChild)}this.CHTML=x=a.createDelimiter(w,this.data.join("").charCodeAt(0),u,x);x.sH=(u instanceof Array?u[1]:u);if(t.symmetric){u=(x.h+x.d)/2+s}else{u=(x.h+x.d)*v/(v+y)}u-=x.h;if(Math.abs(u)>0.05){w.style.verticalAlign=a.Em(u);x.h+=u;x.d-=u;x.t+=u;x.b-=u}}return this.CHTML},CHTMLstretchH:function(u,s){var v=this.CHTML;var t=this.getValues("maxsize","minsize","mathvariant","fontweight");if((t.fontweight==="bold"||(this.removedStyles||{}).fontWeight==="bold"||parseInt(t.fontweight)>=600)&&!this.Get("mathvariant",true)){t.mathvariant=d.VARIANT.BOLD}t.maxsize=this.CHTMLlength2em(t.maxsize,v.w);t.minsize=this.CHTMLlength2em(t.minsize,v.w);s=Math.max(t.minsize,Math.min(t.maxsize,s));if(s!==v.sW){while(u.firstChild){u.removeChild(u.firstChild)}this.CHTML=v=a.createDelimiter(u,this.data.join("").charCodeAt(0),s,v,t.mathvariant);v.sW=s}return this.CHTML}});d.mtext.Augment({CHTMLgetVariant:function(){if(a.config.mtextFontInherit||this.Parent().type==="merror"){var u=(a.config.scale/100)/a.scale;var t={cache:{},fonts:[],className:"MJXc-font-inherit",rscale:u,style:{"font-size":a.Percent(u)}};var s=this.Get("mathvariant");if(s.match(/bold/)){t.style["font-weight"]="bold"}if(s.match(/italic|-tex-mathit/)){t.style["font-style"]="italic"}if(s==="monospace"){t.className+=" MJXc-monospace-font"}if(s==="double-struck"){t.className+=" MJXc-double-struck-font"}if(s.match(/fraktur/)){t.className+=" MJXc-fraktur-font"}if(s.match(/sans-serif/)){t.className+=" MJXc-sans-serif-font"}if(s.match(/script/)){t.className+=" MJXc-script-font"}this.CHTMLvariant=t}else{this.SUPER(arguments).CHTMLgetVariant.call(this)}}});d.merror.Augment({toCommonHTML:function(s){s=this.CHTMLdefaultNode(s);var t=this.CHTML;t.rescale(0.9);t.h+=3/a.em;if(t.h>t.t){t.t=t.h}t.d+=3/a.em;if(t.d>t.b){t.b=t.d}t.w+=8/a.em;t.r=t.w;t.l=0;return s}});d.mspace.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLhandleScale(v);var t=this.getValues("height","depth","width");var s=this.CHTMLlength2em(t.width),u=this.CHTMLlength2em(t.height),y=this.CHTMLlength2em(t.depth);var x=this.CHTML;x.w=x.r=s;x.h=x.t=u;x.d=x.b=y;x.l=0;if(s<0){v.style.marginRight=a.Em(s);s=0}v.style.width=a.Em(s);v.style.height=a.Em(Math.max(0,u+y));if(y){v.style.verticalAlign=a.Em(-y)}this.CHTMLhandleBBox(v);this.CHTMLhandleColor(v);return v}});d.mpadded.Augment({toCommonHTML:function(t,F){var s;if(F&&F.stretch){t=t.firstChild;s=t.firstChild}else{t=this.CHTMLdefaultNode(t,{childNodes:"mjx-box",forceChild:true});s=t.firstChild;t=a.addElement(t,"mjx-block");t.appendChild(s);a.addElement(t,"mjx-strut")}var z=this.CHTMLbboxFor(0);var D=this.getValues("width","height","depth","lspace","voffset");var B=0,A=0,C=z.w,u=z.h,v=z.d;s.style.width=0;s.style.margin=a.Em(-u)+" 0 "+a.Em(-v);if(D.width!==""){C=this.CHTMLdimen(D.width,"w",C,0)}if(D.height!==""){u=this.CHTMLdimen(D.height,"h",u,0)}if(D.depth!==""){v=this.CHTMLdimen(D.depth,"d",v,0)}if(D.voffset!==""){A=this.CHTMLdimen(D.voffset);if(A){s.style.position="relative";s.style.top=a.Em(-A)}}if(D.lspace!==""){B=this.CHTMLdimen(D.lspace);if(B){s.style.position="relative";s.style.left=a.Em(B)}}t.style.width=0;t.style.marginTop=a.Em(u-k);t.style.padding="0 "+a.Em(C)+" "+a.Em(v)+" 0";var E=a.BBOX({w:C,h:u,d:v,l:0,r:C,t:u,b:v,scale:this.CHTML.scale,rscale:this.CHTML.rscale});E.combine(z,B,A);E.w=C;E.h=u;E.d=v;this.CHTML=E;return t.parentNode},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLdimen:function(w,y,x,s){if(s==null){s=-i}w=String(w);var t=w.match(/width|height|depth/);var u=(t?this.CHTML[t[0].charAt(0)]:(y?this.CHTML[y]:0));var v=(this.CHTMLlength2em(w,u)||0);if(w.match(/^[-+]/)&&x!=null){v+=x}if(s!=null){v=Math.max(s,v)}return v}});d.munderover.Augment({toCommonHTML:function(w,G){var E=this.getValues("displaystyle","accent","accentunder","align");var u=this.data[this.base];if(!E.displaystyle&&u!=null&&(u.movablelimits||u.CoreMO().Get("movablelimits"))){return d.msubsup.prototype.toCommonHTML.call(this,w,t)}var B,z,s=[],t=false;if(G&&G.stretch){if(this.data[this.base]){u=a.getNode(w,"mjx-op")}if(this.data[this.under]){B=a.getNode(w,"mjx-under")}if(this.data[this.over]){z=a.getNode(w,"mjx-over")}s[0]=u;s[1]=B||z;s[2]=z;t=true}else{var y=["mjx-op","mjx-under","mjx-over"];if(this.over===1){y[1]=y[2]}w=this.CHTMLdefaultNode(w,{childNodes:y,noBBox:true,forceChild:true,minChildren:2});s[0]=u=w.removeChild(w.firstChild);s[1]=B=z=w.removeChild(w.firstChild);if(w.firstChild){s[2]=z=w.removeChild(w.firstChild)}}var x=[],v=this.CHTMLgetBBoxes(x,s,E);var F=x[this.base],C=this.CHTML;C.w=v;C.h=F.h;C.d=F.d;if(F.h<0.35){u.style.marginTop=a.Em(F.h-0.35)}if(E.accent&&F.hu){u=s}}if(u===-i){u=s}for(y=0;yD.w){D.skew+=(D.w-(A.x+u*A.w))/2}}}else{y=a.TEX.big_op_spacing1;x=a.TEX.big_op_spacing3;v=Math.max(y,x-Math.max(0,u*A.d))}A.x+=E/2;A.y=D.h+v+w+u*A.d;if(v){B.style.paddingBottom=a.Em(v/u)}if(w){B.style.paddingTop=a.Em(w/u)}return C},CHTMLaddUnderscript:function(B,z,E,D,t,A,s){var C=this.CHTML;var y,x,w=a.TEX.big_op_spacing5,v;var F=z[this.under],u=F.rscale;if(!s){a.addElement(t,"mjx-itable",{},[["mjx-row",{},[["mjx-cell"]]],["mjx-row"]]);t.firstChild.firstChild.firstChild.appendChild(A);t.firstChild.lastChild.appendChild(B)}if(F.D){F.d=F.D}if(F.d<0){B.firstChild.style.verticalAlign="top";t.firstChild.style.marginBottom=a.Em(F.d)}if(E.accentunder){v=2*a.TEX.rule_thickness;w=0}else{y=a.TEX.big_op_spacing2;x=a.TEX.big_op_spacing4;v=Math.max(y,x-u*F.h)}F.x=-D/2;F.y=-(C.d+v+w+u*F.h);if(v){B.style.paddingTop=a.Em(v/u)}if(w){B.style.paddingBottom=a.Em(w/u)}},CHTMLplaceBoxes:function(s,B,A,E,z){var t=this.CHTML.w,y,v=z.length,x;var D=a.BBOX.zero();D.scale=this.CHTML.scale;D.rscale=this.CHTML.rscale;z[this.base].x=z[this.base].y=0;var F=i;for(y=0;y0){L+=Q;J-=Q}}L=Math.max(L,A.superscriptshift);J=Math.max(J,A.subscriptshift);H.style.paddingRight=a.Em(N/B);z.style.paddingBottom=a.Em(L/w+J/B-W.d-P.h/B*w);z.style.paddingLeft=a.Em(Y/w);z.style.paddingRight=a.Em(N/w);E.style.verticalAlign=a.Em(-J);G.combine(W,I+Y,L);G.combine(P,I,-J)}}G.clean();return S},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLchildNode:function(u,t){var s=["mjx-base","mjx-sub","mjx-sup"];if(this.over===1){s[1]=s[2]}return a.getNode(u,s[t])}});d.mfrac.Augment({toCommonHTML:function(N){N=this.CHTMLdefaultNode(N,{childNodes:["mjx-numerator","mjx-denominator"],childOptions:{autowidth:true},forceChild:true,noBBox:true,minChildren:2});var x=this.getValues("linethickness","displaystyle","numalign","denomalign","bevelled");var O=x.displaystyle;var D=N.firstChild,w=N.lastChild;var 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n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return 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q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" 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i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible 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+ * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/AsciiMath/config.js", + "[MathJax]/jax/output/CommonHTML/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/asciimath2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/jax/input/AsciiMath/jax.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + 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q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return 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r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return 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MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" 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i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var 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Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/AsciiMath/config.js", + "[MathJax]/jax/output/SVG/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/asciimath2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/jax/input/AsciiMath/jax.js", + "[MathJax]/jax/output/SVG/jax.js", + "[MathJax]/jax/output/SVG/autoload/mtable.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + 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+MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.asciimath2jax={version:"2.7.6",config:{delimiters:[["`","`"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"asciimath2jax_ignore",processClass:"asciimath2jax_process",preview:"AsciiMath"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" 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s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var 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Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/AsciiMath/config.js", + "[MathJax]/jax/output/SVG/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/asciimath2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/jax/input/AsciiMath/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + 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MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/output/CommonHTML/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/output/CommonHTML/jax.js", + "[MathJax]/jax/output/CommonHTML/autoload/mtable.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + 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s}});d.mo.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLgetVariant();this.CHTMLhandleScale(v);a.BBOX.empty(this.CHTML);var t=this.getValues("displaystyle","largeop");t.variant=this.CHTMLvariant;t.text=this.data.join("");if(t.text==""){if(this.fence){v.style.width=a.Em(a.TEX.nulldelimiterspace)}}else{this.CHTMLadjustAccent(t);this.CHTMLadjustVariant(t);for(var u=0,s=this.data.length;u0){if(!this.hasValue("lspace")){t.lspace=0.15}if(!this.hasValue("rspace")){t.rspace=0.15}}var s=this,u=this.Parent();while(u&&u.isEmbellished()&&u.Core()===s){s=u;u=u.Parent();v=s.CHTMLnodeElement()}if(t.lspace){v.style.paddingLeft=a.Em(t.lspace)}if(t.rspace){v.style.paddingRight=a.Em(t.rspace)}this.CHTML.L=t.lspace;this.CHTML.R=t.rspace}else{this.SUPER(arguments).CHTMLhandleSpace.apply(this,arguments)}},CHTMLadjustAccent:function(u){var t=this.CoreParent();u.parent=t;if(a.isChar(u.text)&&t&&t.isa(d.munderover)){var v=t.data[t.over],s=t.data[t.under];if(v&&this===v.CoreMO()&&t.Get("accent")){u.remapchars=a.FONTDATA.REMAPACCENT}else{if(s&&this===s.CoreMO()&&t.Get("accentunder")){u.remapchars=a.FONTDATA.REMAPACCENTUNDER}}}},CHTMLadjustVariant:function(t){var s=t.parent,u=(s&&s.isa(d.msubsup)&&this!==s.data[s.base]);if(t.largeop){t.mathvariant=(t.displaystyle?"-largeOp":"-smallOp")}if(u){t.remapchars=this.remapChars;if(t.text.match(/['`"\u00B4\u2032-\u2037\u2057]/)){t.mathvariant="-TeX-variant"}}},CHTMLfixCombiningChar:function(s){s=s.firstChild;var t=a.Element("mjx-box",{style:{width:".25em","margin-left":"-.25em"}});s.insertBefore(t,s.firstChild)},CHTMLcenterOp:function(s){var u=this.CHTML;var t=(u.h-u.d)/2-a.TEX.axis_height;if(Math.abs(t)>0.001){s.style.verticalAlign=a.Em(-t)}u.h-=t;u.d+=t;if(u.r>u.w){u.ic=u.r-u.w;u.w=u.r;s.style.paddingRight=a.Em(u.ic)}},CHTMLcanStretch:function(w,u,v){if(!this.Get("stretchy")){return false}var x=this.data.join("");if(!a.isChar(x)){return false}var t={text:x};this.CHTMLadjustAccent(t);if(t.remapchars){x=t.remapchars[x]||x}x=a.FONTDATA.DELIMITERS[x.charCodeAt(0)];var s=(x&&x.dir===w.substr(0,1));if(s){s=(this.CHTML.h!==u||this.CHTML.d!==v||!!this.Get("minsize",true)||!!this.Get("maxsize",true));if(s){this.CHTML.stretch=true}}return s},CHTMLstretchV:function(v,y){var w=this.CHTMLnodeElement(),x=this.CHTML;var t=this.getValues("symmetric","maxsize","minsize");var u,s=a.TEX.axis_height;if(t.symmetric){u=2*Math.max(v-s,y+s)}else{u=v+y}t.maxsize=this.CHTMLlength2em(t.maxsize,x.h+x.d);t.minsize=this.CHTMLlength2em(t.minsize,x.h+x.d);u=Math.max(t.minsize,Math.min(t.maxsize,u));if(u!==x.sH){if(u!=t.minsize){u=[Math.max(u*a.TEX.delimiterfactor/1000,u-a.TEX.delimitershortfall),u]}while(w.firstChild){w.removeChild(w.firstChild)}this.CHTML=x=a.createDelimiter(w,this.data.join("").charCodeAt(0),u,x);x.sH=(u instanceof Array?u[1]:u);if(t.symmetric){u=(x.h+x.d)/2+s}else{u=(x.h+x.d)*v/(v+y)}u-=x.h;if(Math.abs(u)>0.05){w.style.verticalAlign=a.Em(u);x.h+=u;x.d-=u;x.t+=u;x.b-=u}}return this.CHTML},CHTMLstretchH:function(u,s){var v=this.CHTML;var t=this.getValues("maxsize","minsize","mathvariant","fontweight");if((t.fontweight==="bold"||(this.removedStyles||{}).fontWeight==="bold"||parseInt(t.fontweight)>=600)&&!this.Get("mathvariant",true)){t.mathvariant=d.VARIANT.BOLD}t.maxsize=this.CHTMLlength2em(t.maxsize,v.w);t.minsize=this.CHTMLlength2em(t.minsize,v.w);s=Math.max(t.minsize,Math.min(t.maxsize,s));if(s!==v.sW){while(u.firstChild){u.removeChild(u.firstChild)}this.CHTML=v=a.createDelimiter(u,this.data.join("").charCodeAt(0),s,v,t.mathvariant);v.sW=s}return this.CHTML}});d.mtext.Augment({CHTMLgetVariant:function(){if(a.config.mtextFontInherit||this.Parent().type==="merror"){var u=(a.config.scale/100)/a.scale;var t={cache:{},fonts:[],className:"MJXc-font-inherit",rscale:u,style:{"font-size":a.Percent(u)}};var s=this.Get("mathvariant");if(s.match(/bold/)){t.style["font-weight"]="bold"}if(s.match(/italic|-tex-mathit/)){t.style["font-style"]="italic"}if(s==="monospace"){t.className+=" MJXc-monospace-font"}if(s==="double-struck"){t.className+=" MJXc-double-struck-font"}if(s.match(/fraktur/)){t.className+=" MJXc-fraktur-font"}if(s.match(/sans-serif/)){t.className+=" MJXc-sans-serif-font"}if(s.match(/script/)){t.className+=" MJXc-script-font"}this.CHTMLvariant=t}else{this.SUPER(arguments).CHTMLgetVariant.call(this)}}});d.merror.Augment({toCommonHTML:function(s){s=this.CHTMLdefaultNode(s);var t=this.CHTML;t.rescale(0.9);t.h+=3/a.em;if(t.h>t.t){t.t=t.h}t.d+=3/a.em;if(t.d>t.b){t.b=t.d}t.w+=8/a.em;t.r=t.w;t.l=0;return s}});d.mspace.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLhandleScale(v);var t=this.getValues("height","depth","width");var s=this.CHTMLlength2em(t.width),u=this.CHTMLlength2em(t.height),y=this.CHTMLlength2em(t.depth);var x=this.CHTML;x.w=x.r=s;x.h=x.t=u;x.d=x.b=y;x.l=0;if(s<0){v.style.marginRight=a.Em(s);s=0}v.style.width=a.Em(s);v.style.height=a.Em(Math.max(0,u+y));if(y){v.style.verticalAlign=a.Em(-y)}this.CHTMLhandleBBox(v);this.CHTMLhandleColor(v);return v}});d.mpadded.Augment({toCommonHTML:function(t,F){var s;if(F&&F.stretch){t=t.firstChild;s=t.firstChild}else{t=this.CHTMLdefaultNode(t,{childNodes:"mjx-box",forceChild:true});s=t.firstChild;t=a.addElement(t,"mjx-block");t.appendChild(s);a.addElement(t,"mjx-strut")}var z=this.CHTMLbboxFor(0);var D=this.getValues("width","height","depth","lspace","voffset");var B=0,A=0,C=z.w,u=z.h,v=z.d;s.style.width=0;s.style.margin=a.Em(-u)+" 0 "+a.Em(-v);if(D.width!==""){C=this.CHTMLdimen(D.width,"w",C,0)}if(D.height!==""){u=this.CHTMLdimen(D.height,"h",u,0)}if(D.depth!==""){v=this.CHTMLdimen(D.depth,"d",v,0)}if(D.voffset!==""){A=this.CHTMLdimen(D.voffset);if(A){s.style.position="relative";s.style.top=a.Em(-A)}}if(D.lspace!==""){B=this.CHTMLdimen(D.lspace);if(B){s.style.position="relative";s.style.left=a.Em(B)}}t.style.width=0;t.style.marginTop=a.Em(u-k);t.style.padding="0 "+a.Em(C)+" "+a.Em(v)+" 0";var E=a.BBOX({w:C,h:u,d:v,l:0,r:C,t:u,b:v,scale:this.CHTML.scale,rscale:this.CHTML.rscale});E.combine(z,B,A);E.w=C;E.h=u;E.d=v;this.CHTML=E;return t.parentNode},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLdimen:function(w,y,x,s){if(s==null){s=-i}w=String(w);var t=w.match(/width|height|depth/);var u=(t?this.CHTML[t[0].charAt(0)]:(y?this.CHTML[y]:0));var v=(this.CHTMLlength2em(w,u)||0);if(w.match(/^[-+]/)&&x!=null){v+=x}if(s!=null){v=Math.max(s,v)}return v}});d.munderover.Augment({toCommonHTML:function(w,G){var E=this.getValues("displaystyle","accent","accentunder","align");var u=this.data[this.base];if(!E.displaystyle&&u!=null&&(u.movablelimits||u.CoreMO().Get("movablelimits"))){return d.msubsup.prototype.toCommonHTML.call(this,w,t)}var B,z,s=[],t=false;if(G&&G.stretch){if(this.data[this.base]){u=a.getNode(w,"mjx-op")}if(this.data[this.under]){B=a.getNode(w,"mjx-under")}if(this.data[this.over]){z=a.getNode(w,"mjx-over")}s[0]=u;s[1]=B||z;s[2]=z;t=true}else{var y=["mjx-op","mjx-under","mjx-over"];if(this.over===1){y[1]=y[2]}w=this.CHTMLdefaultNode(w,{childNodes:y,noBBox:true,forceChild:true,minChildren:2});s[0]=u=w.removeChild(w.firstChild);s[1]=B=z=w.removeChild(w.firstChild);if(w.firstChild){s[2]=z=w.removeChild(w.firstChild)}}var x=[],v=this.CHTMLgetBBoxes(x,s,E);var F=x[this.base],C=this.CHTML;C.w=v;C.h=F.h;C.d=F.d;if(F.h<0.35){u.style.marginTop=a.Em(F.h-0.35)}if(E.accent&&F.hu){u=s}}if(u===-i){u=s}for(y=0;yD.w){D.skew+=(D.w-(A.x+u*A.w))/2}}}else{y=a.TEX.big_op_spacing1;x=a.TEX.big_op_spacing3;v=Math.max(y,x-Math.max(0,u*A.d))}A.x+=E/2;A.y=D.h+v+w+u*A.d;if(v){B.style.paddingBottom=a.Em(v/u)}if(w){B.style.paddingTop=a.Em(w/u)}return C},CHTMLaddUnderscript:function(B,z,E,D,t,A,s){var C=this.CHTML;var y,x,w=a.TEX.big_op_spacing5,v;var F=z[this.under],u=F.rscale;if(!s){a.addElement(t,"mjx-itable",{},[["mjx-row",{},[["mjx-cell"]]],["mjx-row"]]);t.firstChild.firstChild.firstChild.appendChild(A);t.firstChild.lastChild.appendChild(B)}if(F.D){F.d=F.D}if(F.d<0){B.firstChild.style.verticalAlign="top";t.firstChild.style.marginBottom=a.Em(F.d)}if(E.accentunder){v=2*a.TEX.rule_thickness;w=0}else{y=a.TEX.big_op_spacing2;x=a.TEX.big_op_spacing4;v=Math.max(y,x-u*F.h)}F.x=-D/2;F.y=-(C.d+v+w+u*F.h);if(v){B.style.paddingTop=a.Em(v/u)}if(w){B.style.paddingBottom=a.Em(w/u)}},CHTMLplaceBoxes:function(s,B,A,E,z){var t=this.CHTML.w,y,v=z.length,x;var D=a.BBOX.zero();D.scale=this.CHTML.scale;D.rscale=this.CHTML.rscale;z[this.base].x=z[this.base].y=0;var F=i;for(y=0;y0){L+=Q;J-=Q}}L=Math.max(L,A.superscriptshift);J=Math.max(J,A.subscriptshift);H.style.paddingRight=a.Em(N/B);z.style.paddingBottom=a.Em(L/w+J/B-W.d-P.h/B*w);z.style.paddingLeft=a.Em(Y/w);z.style.paddingRight=a.Em(N/w);E.style.verticalAlign=a.Em(-J);G.combine(W,I+Y,L);G.combine(P,I,-J)}}G.clean();return S},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLchildNode:function(u,t){var s=["mjx-base","mjx-sub","mjx-sup"];if(this.over===1){s[1]=s[2]}return a.getNode(u,s[t])}});d.mfrac.Augment({toCommonHTML:function(N){N=this.CHTMLdefaultNode(N,{childNodes:["mjx-numerator","mjx-denominator"],childOptions:{autowidth:true},forceChild:true,noBBox:true,minChildren:2});var x=this.getValues("linethickness","displaystyle","numalign","denomalign","bevelled");var O=x.displaystyle;var D=N.firstChild,w=N.lastChild;var y=a.addElement(N,"mjx-box");y.appendChild(D);y.appendChild(w);N.appendChild(y);if(x.numalign!=="center"){D.style.textAlign=x.numalign}if(x.denomalign!=="center"){w.style.textAlign=x.denomalign}var P=this.CHTMLbboxFor(0),B=this.CHTMLbboxFor(1),C=a.BBOX.empty(this.CHTML),F=P.rscale,z=B.rscale;x.linethickness=Math.max(0,a.thickness2em(x.linethickness||"0",C.scale));var M=a.TEX.min_rule_thickness/a.em,T=a.TEX.axis_height;var J=x.linethickness,L,K,I,G;if(x.bevelled){y.className+=" MJXc-bevelled";var S=(O?0.4:0.15);var E=Math.max(F*(P.h+P.d),z*(B.h+B.d))+2*S;var R=a.Element("mjx-bevel");y.insertBefore(R,w);var s=a.createDelimiter(R,47,E);I=F*(P.d-P.h)/2+T+S;G=z*(B.d-B.h)/2+T-S;if(I){D.style.verticalAlign=a.Em(I/F)}if(G){w.style.verticalAlign=a.Em(G/z)}R.style.marginLeft=R.style.marginRight=a.Em(-S/2);C.combine(P,0,I);C.combine(s,F*P.w-S/2,0);C.combine(B,F*P.w+s.w-S,G);C.clean()}else{y.className+=" MJXc-stacked";if(O){I=a.TEX.num1;G=a.TEX.denom1}else{I=(J===0?a.TEX.num3:a.TEX.num2);G=a.TEX.denom2}if(J===0){L=Math.max((O?7:3)*a.TEX.rule_thickness,2*M);K=(I-P.d*F)-(B.h*z-G);if(KD){s=((A.h+A.d)-(D-G))/2}D=F.h+s+G;var B=this.CHTMLaddRoot(w,A,A.h+A.d-D);v.style.paddingTop=a.Em(s);v.style.borderTop=a.Px(y*F.scale,1)+" solid";E.style.paddingTop=a.Em(2*G-y);F.h+=s+2*G;C.combine(A,B,D-A.h);C.combine(F,B+A.w,0);C.clean();return w},CHTMLaddRoot:function(){return 0},CHTMLhandleBBox:function(s){var t=this.CHTMLbboxFor(0);delete t.pwidth;this.SUPER(arguments).CHTMLhandleBBox.apply(this,arguments)}});d.mroot.Augment({toCommonHTML:d.msqrt.prototype.toCommonHTML,CHTMLhandleBBox:d.msqrt.prototype.CHTMLhandleBBox,CHTMLaddRoot:function(A,u,v){if(!this.data[1]){return}var z=this.CHTML,B=this.data[1].CHTML,x=A.firstChild;var s=B.rscale;var t=this.CHTMLrootHeight(B,u,s)-v;var y=Math.min(B.w,B.r);var C=Math.max(y,u.offset/s);if(t){x.style.verticalAlign=a.Em(t/s)}if(C>y){x.firstChild.style.paddingLeft=a.Em(C-y)}C-=u.offset/s;x.style.width=a.Em(C);z.combine(B,0,t);return C*s},CHTMLrootHeight:function(u,s,t){return 0.45*(s.h+s.d-0.9)+s.offset+Math.max(0,u.d-0.075)}});d.mfenced.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLhandleScale(v);this.CHTMLaddChild(v,"open",{});for(var u=0,s=this.data.length;ua.linebreakWidth)||this.hasNewline()},CHTMLstretchV:function(s,t){this.CHTMLstretchChildV(this.CoreIndex(),s,t);return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLstretchChildH(this.CoreIndex(),s,t);return this.CHTML}});d.TeXAtom.Augment({toCommonHTML:function(x,w){if(!w||!w.stretch){x=this.CHTMLdefaultNode(x)}if(this.texClass===d.TEXCLASS.VCENTER){var s=a.TEX.axis_height,u=this.CHTML;var t=s-(u.h+u.d)/2+u.d;if(Math.abs(t)>0.001){x.style.verticalAlign=a.Em(t);u.h+=t;u.t+=t;u.d-=t;u.b-=t}}return x},CHTMLstretchV:function(s,t){this.CHTMLupdateFrom(this.Core().CHTMLstretchV(s,t));this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,s));this.toCommonHTML(t,{stretch:true});return this.CHTML}});d.semantics.Augment({toCommonHTML:function(s){s=this.CHTMLcreateNode(s);if(this.data[0]){this.data[0].toCommonHTML(s);this.CHTMLupdateFrom(this.data[0].CHTML);this.CHTMLhandleBBox(s)}return s}});d.annotation.Augment({toCommonHTML:function(s){return this.CHTMLcreateNode(s)}});d["annotation-xml"].Augment({toCommonHTML:d.mbase.CHTMLautoload});d.ms.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mglyph.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.menclose.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.maction.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mmultiscripts.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mtable.Augment({toCommonHTML:d.mbase.CHTMLautoload});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(f.config.menuSettings.zoom!=="None"){o.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.CommonHTML); +MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var g="2.7.6";var b=MathJax.ElementJax.mml,a=MathJax.Hub.config,e=MathJax.OutputJax.CommonHTML,d=MathJax.Hub.SplitList;var c=-1,f=1000000;b.mtable.Augment({toCommonHTML:function(l){var m={rows:[],labels:[],labeled:false};l=this.CHTMLdefaultNode(l,{noBBox:true,childOptions:m});var k=e.Element("mjx-table");while(l.firstChild){k.appendChild(l.firstChild)}l.appendChild(k);var h=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width","side","minlabelspacing","useHeight");var j=e.TEX.min_rule_thickness/e.em;m.t=e.Px(j*this.CHTML.scale,1);this.CHTMLgetBoxSizes(h,m);this.CHTMLgetAttributes(h,m);this.CHTMLadjustCells(h,m);if(h.frame){k.style.border=m.t+" "+h.frame}this.CHTMLalignV(h,m,l);this.CHTMLcolumnWidths(h,m,l);this.CHTMLstretchCells(h,m);if(m.labeled){this.CHTMLaddLabels(h,m,l,k)}var i=this.CHTML;i.w=i.r=m.R;i.h=i.t=m.T-m.B;i.d=i.b=m.B;if(!h.frame&&!i.pwidth){l.style.padding="0 "+e.Em(1/6);i.L=i.R=1/6}this.CHTMLhandleSpace(l);this.CHTMLhandleBBox(l);this.CHTMLhandleColor(l);return l},CHTMLgetBoxSizes:function(z,k){var r=e.FONTDATA.lineH*z.useHeight,t=e.FONTDATA.lineD*z.useHeight;var y=[],h=[],l=[],w=-1,q,n;for(q=0,n=this.data.length;qw){w=p}}var u=B.data[p-A].CHTML;if(u.h>y[q]){y[q]=u.h}if(u.d>h[q]){h[q]=u.d}if(u.w>l[p]){l[p]=u.w}}}if(z.equalrows){k.HD=true;var x=Math.max.apply(Math,y);var o=Math.max.apply(Math,h);for(q=0,n=y.length;qt||m<=0){m=null}}else{w.align=this.defaults.align}var p=0,l=0,u=e.TEX.axis_height;if(w.fspace){p+=k.FSPACE[1]}if(w.frame){p+=2/e.em;l+=1/e.em}for(var q=0;q=m){l+=r+s+x[q]}}}if(!m){l=({top:p,bottom:0,center:p/2,baseline:p/2,axis:p/2-u})[w.align]}if(l){o.style.verticalAlign=e.Em(-l)}k.T=p;k.B=l},CHTMLcolumnWidths:function(l,r,A){var I=r.CWIDTH,K=r.CSPACE,u=r.J,F;var G=0,n=false,y=l.width.match(/%$/);var H,B,v;if(l.width!=="auto"&&!y){G=Math.max(0,this.CHTMLlength2em(l.width,r.R));n=true}if(l.equalcolumns){if(y){var z=e.Percent(1/(u+1));for(F=0;F<=u;F++){I[F]=z}}else{v=Math.max.apply(Math,r.W);if(l.width!=="auto"){var 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document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var 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n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var 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r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var 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r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 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MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible 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Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/output/CommonHTML/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + 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+MathJax.Extension.mml2jax={version:"2.7.6",config:{preview:"mathml"},MMLnamespace:"http://www.w3.org/1998/Math/MathML",PreProcess:function(e){if(!this.configured){this.config=MathJax.Hub.CombineConfig("mml2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.InitBrowser();this.configured=true}if(typeof(e)==="string"){e=document.getElementById(e)}if(!e){e=document.body}var h=[];this.PushMathElements(h,e,"math");this.PushMathElements(h,e,"math",this.MMLnamespace);var d,b;if(typeof(document.namespaces)!=="undefined"){try{for(d=0,b=document.namespaces.length;d/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/ /g," ")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c=""}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&").replace(//g,">").replace(/\"/g,""")},createPreview:function(g,f){var e=this.config.preview;if(e==="none"){return}var i=false;var c=MathJax.Hub.config.preRemoveClass;if((f.previousSibling||{}).className===c){return}if(e==="mathml"){i=true;if(this.MathTagBug){e="alttext"}else{e=g.cloneNode(true)}}if(e==="alttext"||e==="altimg"){i=true;var d=this.filterPreview(g.getAttribute("alttext"));if(e==="alttext"){if(d!=null){e=MathJax.HTML.TextNode(d)}else{e=null}}else{var a=g.getAttribute("altimg");if(a!=null){var b={width:g.getAttribute("altimg-width"),height:g.getAttribute("altimg-height")};e=MathJax.HTML.Element("img",{src:a,alt:d,style:b})}else{e=null}}}if(e){var h;if(i){h=MathJax.HTML.Element("span",{className:c});h.appendChild(e)}else{h=MathJax.HTML.Element("span",{className:c},e)}f.parentNode.insertBefore(h,f)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"x"});var 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F=(B.config.showMathMenu!=null?B:d).config.showMathMenu;if(!F||(k.context!=="MathJax"&&!w)){return}if(c.msieEventBug){t=window.event||t}n.ClearSelection();f.ClearHoverTimer();if(v.hover){if(v.hover.remove){clearTimeout(v.hover.remove);delete v.hover.remove}v.hover.nofade=true}var u=MathJax.Menu;var G,D;if(u){if(u.loadingDomain){return n.False(t)}G=m.loadDomain("MathMenu");if(!G){u.jax=v;var r=u.menu.Find("Show Math As").submenu;r.items[0].name=v.sourceMenuTitle;r.items[0].format=(v.sourceMenuFormat||"MathML");r.items[1].name=j[v.inputJax].sourceMenuTitle;r.items[5].disabled=!j[v.inputJax].annotationEncoding;var A=r.items[2];A.disabled=true;var q=A.submenu.items;annotationList=MathJax.Hub.Config.semanticsAnnotations;for(var z=0,y=q.length;z0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete 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s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var 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MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/output/SVG/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/output/SVG/jax.js", + "[MathJax]/jax/output/SVG/autoload/mtable.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + 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s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible 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+ * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/output/SVG/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + 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+MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.mml2jax={version:"2.7.6",config:{preview:"mathml"},MMLnamespace:"http://www.w3.org/1998/Math/MathML",PreProcess:function(e){if(!this.configured){this.config=MathJax.Hub.CombineConfig("mml2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.InitBrowser();this.configured=true}if(typeof(e)==="string"){e=document.getElementById(e)}if(!e){e=document.body}var h=[];this.PushMathElements(h,e,"math");this.PushMathElements(h,e,"math",this.MMLnamespace);var 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r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/MML_SVG.js"); diff --git a/revisions_report_files/mathjax-27/config/MMLorHTML.js b/revisions_report_files/mathjax-27/config/MMLorHTML.js new file mode 100644 index 0000000..727861e --- /dev/null +++ b/revisions_report_files/mathjax-27/config/MMLorHTML.js @@ -0,0 +1,19 @@ +/* + * /MathJax/config/MMLorHTML.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +(function(c,g){var f="2.7.0";var a=MathJax.Hub.CombineConfig("MMLorHTML",{prefer:{MSIE:"MML",Firefox:"HTML",Opera:"HTML",Chrome:"HTML",Safari:"HTML",other:"HTML"}});var e={Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4};var b=(g.version==="0.0"||g.versionAtLeast(e[g]||0));var d=(g.isFirefox&&g.versionAtLeast("1.5"))||(g.isMSIE&&g.hasMathPlayer)||(g.isSafari&&g.versionAtLeast("5.0"))||(g.isOpera&&g.versionAtLeast("9.52"));c.Register.StartupHook("End Config",function(){var h=(a.prefer&&typeof(a.prefer)==="object"?a.prefer[MathJax.Hub.Browser]||a.prefer.other||"HTML":a.prefer);if(b||d){if(d&&(h==="MML"||!b)){if(MathJax.OutputJax.NativeMML){MathJax.OutputJax.NativeMML.Register("jax/mml")}else{c.config.jax.unshift("output/NativeMML")}c.Startup.signal.Post("NativeMML output selected")}else{if(MathJax.OutputJax["HTML-CSS"]){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}else{c.config.jax.unshift("output/HTML-CSS")}c.Startup.signal.Post("HTML-CSS output selected")}}else{c.PreProcess.disabled=true;c.prepareScripts.disabled=true;MathJax.Message.Set(["MathJaxNotSupported","Your browser does not support MathJax"],null,4000);c.Startup.signal.Post("MathJax not supported")}})})(MathJax.Hub,MathJax.Hub.Browser);MathJax.Ajax.loadComplete("[MathJax]/config/MMLorHTML.js"); diff --git a/revisions_report_files/mathjax-27/config/Safe.js b/revisions_report_files/mathjax-27/config/Safe.js new file mode 100644 index 0000000..a76efe4 --- /dev/null +++ b/revisions_report_files/mathjax-27/config/Safe.js @@ -0,0 +1,19 @@ +/* + * /MathJax/config/Safe.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Hub.Register.StartupHook("End Config",function(){if(!MathJax.Hub.config.extensions){MathJax.Hub.config.extensions=[]}MathJax.Hub.config.extensions.push("Safe.js")});MathJax.Ajax.loadComplete("[MathJax]/config/Safe.js"); diff --git a/revisions_report_files/mathjax-27/config/TeX-AMS-MML_HTMLorMML.js b/revisions_report_files/mathjax-27/config/TeX-AMS-MML_HTMLorMML.js new file mode 100644 index 0000000..c8507f5 --- /dev/null +++ b/revisions_report_files/mathjax-27/config/TeX-AMS-MML_HTMLorMML.js @@ -0,0 +1,69 @@ +/* + * /MathJax/config/TeX-AMS-MML_HTMLorMML.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Hub.Config({delayJaxRegistration: true}); + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/TeX/config.js", + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/output/HTML-CSS/config.js", + "[MathJax]/jax/output/NativeMML/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/config/MMLorHTML.js", + "[MathJax]/extensions/tex2jax.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/extensions/TeX/noErrors.js", + "[MathJax]/extensions/TeX/noUndefined.js", + "[MathJax]/jax/input/TeX/jax.js", + "[MathJax]/extensions/TeX/AMSmath.js", + "[MathJax]/extensions/TeX/AMSsymbols.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.6",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); +MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.6",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); 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s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var 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w=l.TEXT(t*100/a.config.scale,B,{"font-family":u.defaultFamily||a.config.undefinedFamily,"font-style":(u.italic?"italic":""),"font-weight":(u.bold?"bold":"")});if(u.h!=null){w.h=u.h}if(u.d!=null){w.d=u.d}B=l.G();B.Add(w);x.Add(B,x.w,0);e.signal.Post(["SVG Jax - unknown char",q,u])}}}if(a.isChar(D)&&r.skew&&r.skew[q]){x.skew=r.skew[q]*1000}if(x.element.childNodes.length===1&&!x.element.firstChild.getAttribute("x")){x.element=x.element.firstChild;x.removeable=false;x.scale=t}return x},lookupChar:function(r,u){var q,o;if(!r.FONTS){var t=this.FONTDATA.FONTS;var s=(r.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(s instanceof Array)){s=[s]}if(r.fonts!=s){r.fonts=s}r.FONTS=[];for(q=0,o=s.length;q=55296&&p<56319)},findBlock:function(o,s){if(o.Ranges){for(var r=0,n=o.Ranges.length;r=0;p--){if(o.Ranges[p][2]==q){o.Ranges.splice(p,1)}}this.loadFont(o.directory+"/"+q+".js")}}}},loadFont:function(n){e.RestartAfter(j.Require(this.fontDir+"/"+n))},createDelimiter:function(n,p,s,q){if(!s){s=1}var u=l.G();if(!n){u.Clean();delete u.element;u.w=u.r=this.TeX.nulldelimiterspace*s;return u}if(!(p instanceof Array)){p=[p,p]}var v=p[1];p=p[0];var o={alias:n};while(o.alias){n=o.alias;o=this.FONTDATA.DELIMITERS[n];if(!o){o={HW:[0,this.FONTDATA.VARIANT[i.VARIANT.NORMAL]]}}}if(o.load){e.RestartAfter(j.Require(this.fontDir+"/fontdata-"+o.load+".js"))}for(var t=0,r=o.HW.length;t=p-10-a.config.blacker||(t==r-1&&!o.stretch)){if(o.HW[t][2]){s*=o.HW[t][2]}if(o.HW[t][3]){n=o.HW[t][3]}return this.createChar(s,[n,o.HW[t][1]],q).With({stretched:true})}}if(o.stretch){this["extendDelimiter"+o.dir](u,v,o.stretch,s,q)}return u},createChar:function(u,s,p){var t="",r={fonts:[s[1]],noRemap:true};if(p&&p===i.VARIANT.BOLD){r.fonts=[s[1]+"-bold",s[1]]}if(typeof(s[1])!=="string"){r=s[1]}if(s[0] instanceof Array){for(var q=0,n=s[0].length;qt){var n=this.createChar(q,o.ext,p);var r=(o.mid?2:1),x=(C-t)/r,D=(x+100)/(n.h+n.d);while(r-->0){var v=a.Element("g",{transform:"translate("+n.y+","+(z-D*n.h+50+n.y)+") 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l=a.BBOX=MathJax.Object.Subclass({type:"g",removeable:true,Init:function(n){this.h=this.d=-a.BIGDIMEN;this.H=this.D=0;this.w=this.r=0;this.l=a.BIGDIMEN;this.x=this.y=0;this.scale=1;this.n=0;if(this.type){this.element=a.Element(this.type,n)}},With:function(n){return e.Insert(this,n)},Add:function(q,w,v,n,u){if(w){q.x+=w}if(v){q.y+=v}if(q.element){if(q.removeable&&q.element.childNodes.length===1&&q.n===1){var o=q.element.firstChild,s=o.nodeName.toLowerCase();if(s==="use"||s==="rect"){q.element=o;q.scale=q.childScale;var t=q.childX,r=q.childY;q.x+=t;q.y+=r;q.h-=r;q.d+=r;q.H-=r;q.D+=r;q.w-=t;q.r-=t;q.l+=t;q.removeable=false;o.setAttribute("x",Math.floor(q.x/q.scale));o.setAttribute("y",Math.floor(q.y/q.scale))}}if(Math.abs(q.x)<1&&Math.abs(q.y)<1){q.remove=q.removeable}else{s=q.element.nodeName.toLowerCase();if(s==="g"){if(!q.element.firstChild){q.remove=q.removeable}else{q.element.setAttribute("transform","translate("+Math.floor(q.x)+","+Math.floor(q.y)+")")}}else{if(s==="line"||s==="polygon"||s==="path"||s==="a"){var p=q.element.getAttribute("transform")||"";if(p){p=" 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(c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/TeX/config.js", + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/output/SVG/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/tex2jax.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/extensions/TeX/noErrors.js", + "[MathJax]/extensions/TeX/noUndefined.js", + "[MathJax]/jax/input/TeX/jax.js", + "[MathJax]/extensions/TeX/AMSmath.js", + "[MathJax]/extensions/TeX/AMSsymbols.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.6",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); 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s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var 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"[MathJax]/jax/output/CommonHTML/autoload/mtable.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.6",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); 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s}});d.mo.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLgetVariant();this.CHTMLhandleScale(v);a.BBOX.empty(this.CHTML);var t=this.getValues("displaystyle","largeop");t.variant=this.CHTMLvariant;t.text=this.data.join("");if(t.text==""){if(this.fence){v.style.width=a.Em(a.TEX.nulldelimiterspace)}}else{this.CHTMLadjustAccent(t);this.CHTMLadjustVariant(t);for(var u=0,s=this.data.length;u0){if(!this.hasValue("lspace")){t.lspace=0.15}if(!this.hasValue("rspace")){t.rspace=0.15}}var s=this,u=this.Parent();while(u&&u.isEmbellished()&&u.Core()===s){s=u;u=u.Parent();v=s.CHTMLnodeElement()}if(t.lspace){v.style.paddingLeft=a.Em(t.lspace)}if(t.rspace){v.style.paddingRight=a.Em(t.rspace)}this.CHTML.L=t.lspace;this.CHTML.R=t.rspace}else{this.SUPER(arguments).CHTMLhandleSpace.apply(this,arguments)}},CHTMLadjustAccent:function(u){var t=this.CoreParent();u.parent=t;if(a.isChar(u.text)&&t&&t.isa(d.munderover)){var v=t.data[t.over],s=t.data[t.under];if(v&&this===v.CoreMO()&&t.Get("accent")){u.remapchars=a.FONTDATA.REMAPACCENT}else{if(s&&this===s.CoreMO()&&t.Get("accentunder")){u.remapchars=a.FONTDATA.REMAPACCENTUNDER}}}},CHTMLadjustVariant:function(t){var s=t.parent,u=(s&&s.isa(d.msubsup)&&this!==s.data[s.base]);if(t.largeop){t.mathvariant=(t.displaystyle?"-largeOp":"-smallOp")}if(u){t.remapchars=this.remapChars;if(t.text.match(/['`"\u00B4\u2032-\u2037\u2057]/)){t.mathvariant="-TeX-variant"}}},CHTMLfixCombiningChar:function(s){s=s.firstChild;var t=a.Element("mjx-box",{style:{width:".25em","margin-left":"-.25em"}});s.insertBefore(t,s.firstChild)},CHTMLcenterOp:function(s){var u=this.CHTML;var t=(u.h-u.d)/2-a.TEX.axis_height;if(Math.abs(t)>0.001){s.style.verticalAlign=a.Em(-t)}u.h-=t;u.d+=t;if(u.r>u.w){u.ic=u.r-u.w;u.w=u.r;s.style.paddingRight=a.Em(u.ic)}},CHTMLcanStretch:function(w,u,v){if(!this.Get("stretchy")){return false}var x=this.data.join("");if(!a.isChar(x)){return false}var t={text:x};this.CHTMLadjustAccent(t);if(t.remapchars){x=t.remapchars[x]||x}x=a.FONTDATA.DELIMITERS[x.charCodeAt(0)];var s=(x&&x.dir===w.substr(0,1));if(s){s=(this.CHTML.h!==u||this.CHTML.d!==v||!!this.Get("minsize",true)||!!this.Get("maxsize",true));if(s){this.CHTML.stretch=true}}return s},CHTMLstretchV:function(v,y){var w=this.CHTMLnodeElement(),x=this.CHTML;var t=this.getValues("symmetric","maxsize","minsize");var u,s=a.TEX.axis_height;if(t.symmetric){u=2*Math.max(v-s,y+s)}else{u=v+y}t.maxsize=this.CHTMLlength2em(t.maxsize,x.h+x.d);t.minsize=this.CHTMLlength2em(t.minsize,x.h+x.d);u=Math.max(t.minsize,Math.min(t.maxsize,u));if(u!==x.sH){if(u!=t.minsize){u=[Math.max(u*a.TEX.delimiterfactor/1000,u-a.TEX.delimitershortfall),u]}while(w.firstChild){w.removeChild(w.firstChild)}this.CHTML=x=a.createDelimiter(w,this.data.join("").charCodeAt(0),u,x);x.sH=(u instanceof Array?u[1]:u);if(t.symmetric){u=(x.h+x.d)/2+s}else{u=(x.h+x.d)*v/(v+y)}u-=x.h;if(Math.abs(u)>0.05){w.style.verticalAlign=a.Em(u);x.h+=u;x.d-=u;x.t+=u;x.b-=u}}return this.CHTML},CHTMLstretchH:function(u,s){var v=this.CHTML;var t=this.getValues("maxsize","minsize","mathvariant","fontweight");if((t.fontweight==="bold"||(this.removedStyles||{}).fontWeight==="bold"||parseInt(t.fontweight)>=600)&&!this.Get("mathvariant",true)){t.mathvariant=d.VARIANT.BOLD}t.maxsize=this.CHTMLlength2em(t.maxsize,v.w);t.minsize=this.CHTMLlength2em(t.minsize,v.w);s=Math.max(t.minsize,Math.min(t.maxsize,s));if(s!==v.sW){while(u.firstChild){u.removeChild(u.firstChild)}this.CHTML=v=a.createDelimiter(u,this.data.join("").charCodeAt(0),s,v,t.mathvariant);v.sW=s}return this.CHTML}});d.mtext.Augment({CHTMLgetVariant:function(){if(a.config.mtextFontInherit||this.Parent().type==="merror"){var u=(a.config.scale/100)/a.scale;var t={cache:{},fonts:[],className:"MJXc-font-inherit",rscale:u,style:{"font-size":a.Percent(u)}};var s=this.Get("mathvariant");if(s.match(/bold/)){t.style["font-weight"]="bold"}if(s.match(/italic|-tex-mathit/)){t.style["font-style"]="italic"}if(s==="monospace"){t.className+=" MJXc-monospace-font"}if(s==="double-struck"){t.className+=" MJXc-double-struck-font"}if(s.match(/fraktur/)){t.className+=" MJXc-fraktur-font"}if(s.match(/sans-serif/)){t.className+=" MJXc-sans-serif-font"}if(s.match(/script/)){t.className+=" MJXc-script-font"}this.CHTMLvariant=t}else{this.SUPER(arguments).CHTMLgetVariant.call(this)}}});d.merror.Augment({toCommonHTML:function(s){s=this.CHTMLdefaultNode(s);var t=this.CHTML;t.rescale(0.9);t.h+=3/a.em;if(t.h>t.t){t.t=t.h}t.d+=3/a.em;if(t.d>t.b){t.b=t.d}t.w+=8/a.em;t.r=t.w;t.l=0;return s}});d.mspace.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLhandleScale(v);var t=this.getValues("height","depth","width");var s=this.CHTMLlength2em(t.width),u=this.CHTMLlength2em(t.height),y=this.CHTMLlength2em(t.depth);var x=this.CHTML;x.w=x.r=s;x.h=x.t=u;x.d=x.b=y;x.l=0;if(s<0){v.style.marginRight=a.Em(s);s=0}v.style.width=a.Em(s);v.style.height=a.Em(Math.max(0,u+y));if(y){v.style.verticalAlign=a.Em(-y)}this.CHTMLhandleBBox(v);this.CHTMLhandleColor(v);return v}});d.mpadded.Augment({toCommonHTML:function(t,F){var s;if(F&&F.stretch){t=t.firstChild;s=t.firstChild}else{t=this.CHTMLdefaultNode(t,{childNodes:"mjx-box",forceChild:true});s=t.firstChild;t=a.addElement(t,"mjx-block");t.appendChild(s);a.addElement(t,"mjx-strut")}var z=this.CHTMLbboxFor(0);var D=this.getValues("width","height","depth","lspace","voffset");var B=0,A=0,C=z.w,u=z.h,v=z.d;s.style.width=0;s.style.margin=a.Em(-u)+" 0 "+a.Em(-v);if(D.width!==""){C=this.CHTMLdimen(D.width,"w",C,0)}if(D.height!==""){u=this.CHTMLdimen(D.height,"h",u,0)}if(D.depth!==""){v=this.CHTMLdimen(D.depth,"d",v,0)}if(D.voffset!==""){A=this.CHTMLdimen(D.voffset);if(A){s.style.position="relative";s.style.top=a.Em(-A)}}if(D.lspace!==""){B=this.CHTMLdimen(D.lspace);if(B){s.style.position="relative";s.style.left=a.Em(B)}}t.style.width=0;t.style.marginTop=a.Em(u-k);t.style.padding="0 "+a.Em(C)+" "+a.Em(v)+" 0";var E=a.BBOX({w:C,h:u,d:v,l:0,r:C,t:u,b:v,scale:this.CHTML.scale,rscale:this.CHTML.rscale});E.combine(z,B,A);E.w=C;E.h=u;E.d=v;this.CHTML=E;return t.parentNode},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLdimen:function(w,y,x,s){if(s==null){s=-i}w=String(w);var t=w.match(/width|height|depth/);var u=(t?this.CHTML[t[0].charAt(0)]:(y?this.CHTML[y]:0));var v=(this.CHTMLlength2em(w,u)||0);if(w.match(/^[-+]/)&&x!=null){v+=x}if(s!=null){v=Math.max(s,v)}return v}});d.munderover.Augment({toCommonHTML:function(w,G){var E=this.getValues("displaystyle","accent","accentunder","align");var u=this.data[this.base];if(!E.displaystyle&&u!=null&&(u.movablelimits||u.CoreMO().Get("movablelimits"))){return d.msubsup.prototype.toCommonHTML.call(this,w,t)}var B,z,s=[],t=false;if(G&&G.stretch){if(this.data[this.base]){u=a.getNode(w,"mjx-op")}if(this.data[this.under]){B=a.getNode(w,"mjx-under")}if(this.data[this.over]){z=a.getNode(w,"mjx-over")}s[0]=u;s[1]=B||z;s[2]=z;t=true}else{var y=["mjx-op","mjx-under","mjx-over"];if(this.over===1){y[1]=y[2]}w=this.CHTMLdefaultNode(w,{childNodes:y,noBBox:true,forceChild:true,minChildren:2});s[0]=u=w.removeChild(w.firstChild);s[1]=B=z=w.removeChild(w.firstChild);if(w.firstChild){s[2]=z=w.removeChild(w.firstChild)}}var x=[],v=this.CHTMLgetBBoxes(x,s,E);var F=x[this.base],C=this.CHTML;C.w=v;C.h=F.h;C.d=F.d;if(F.h<0.35){u.style.marginTop=a.Em(F.h-0.35)}if(E.accent&&F.hu){u=s}}if(u===-i){u=s}for(y=0;yD.w){D.skew+=(D.w-(A.x+u*A.w))/2}}}else{y=a.TEX.big_op_spacing1;x=a.TEX.big_op_spacing3;v=Math.max(y,x-Math.max(0,u*A.d))}A.x+=E/2;A.y=D.h+v+w+u*A.d;if(v){B.style.paddingBottom=a.Em(v/u)}if(w){B.style.paddingTop=a.Em(w/u)}return C},CHTMLaddUnderscript:function(B,z,E,D,t,A,s){var C=this.CHTML;var y,x,w=a.TEX.big_op_spacing5,v;var F=z[this.under],u=F.rscale;if(!s){a.addElement(t,"mjx-itable",{},[["mjx-row",{},[["mjx-cell"]]],["mjx-row"]]);t.firstChild.firstChild.firstChild.appendChild(A);t.firstChild.lastChild.appendChild(B)}if(F.D){F.d=F.D}if(F.d<0){B.firstChild.style.verticalAlign="top";t.firstChild.style.marginBottom=a.Em(F.d)}if(E.accentunder){v=2*a.TEX.rule_thickness;w=0}else{y=a.TEX.big_op_spacing2;x=a.TEX.big_op_spacing4;v=Math.max(y,x-u*F.h)}F.x=-D/2;F.y=-(C.d+v+w+u*F.h);if(v){B.style.paddingTop=a.Em(v/u)}if(w){B.style.paddingBottom=a.Em(w/u)}},CHTMLplaceBoxes:function(s,B,A,E,z){var t=this.CHTML.w,y,v=z.length,x;var D=a.BBOX.zero();D.scale=this.CHTML.scale;D.rscale=this.CHTML.rscale;z[this.base].x=z[this.base].y=0;var F=i;for(y=0;y0){L+=Q;J-=Q}}L=Math.max(L,A.superscriptshift);J=Math.max(J,A.subscriptshift);H.style.paddingRight=a.Em(N/B);z.style.paddingBottom=a.Em(L/w+J/B-W.d-P.h/B*w);z.style.paddingLeft=a.Em(Y/w);z.style.paddingRight=a.Em(N/w);E.style.verticalAlign=a.Em(-J);G.combine(W,I+Y,L);G.combine(P,I,-J)}}G.clean();return S},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLchildNode:function(u,t){var s=["mjx-base","mjx-sub","mjx-sup"];if(this.over===1){s[1]=s[2]}return a.getNode(u,s[t])}});d.mfrac.Augment({toCommonHTML:function(N){N=this.CHTMLdefaultNode(N,{childNodes:["mjx-numerator","mjx-denominator"],childOptions:{autowidth:true},forceChild:true,noBBox:true,minChildren:2});var x=this.getValues("linethickness","displaystyle","numalign","denomalign","bevelled");var O=x.displaystyle;var D=N.firstChild,w=N.lastChild;var y=a.addElement(N,"mjx-box");y.appendChild(D);y.appendChild(w);N.appendChild(y);if(x.numalign!=="center"){D.style.textAlign=x.numalign}if(x.denomalign!=="center"){w.style.textAlign=x.denomalign}var P=this.CHTMLbboxFor(0),B=this.CHTMLbboxFor(1),C=a.BBOX.empty(this.CHTML),F=P.rscale,z=B.rscale;x.linethickness=Math.max(0,a.thickness2em(x.linethickness||"0",C.scale));var M=a.TEX.min_rule_thickness/a.em,T=a.TEX.axis_height;var J=x.linethickness,L,K,I,G;if(x.bevelled){y.className+=" MJXc-bevelled";var S=(O?0.4:0.15);var E=Math.max(F*(P.h+P.d),z*(B.h+B.d))+2*S;var R=a.Element("mjx-bevel");y.insertBefore(R,w);var s=a.createDelimiter(R,47,E);I=F*(P.d-P.h)/2+T+S;G=z*(B.d-B.h)/2+T-S;if(I){D.style.verticalAlign=a.Em(I/F)}if(G){w.style.verticalAlign=a.Em(G/z)}R.style.marginLeft=R.style.marginRight=a.Em(-S/2);C.combine(P,0,I);C.combine(s,F*P.w-S/2,0);C.combine(B,F*P.w+s.w-S,G);C.clean()}else{y.className+=" MJXc-stacked";if(O){I=a.TEX.num1;G=a.TEX.denom1}else{I=(J===0?a.TEX.num3:a.TEX.num2);G=a.TEX.denom2}if(J===0){L=Math.max((O?7:3)*a.TEX.rule_thickness,2*M);K=(I-P.d*F)-(B.h*z-G);if(KD){s=((A.h+A.d)-(D-G))/2}D=F.h+s+G;var B=this.CHTMLaddRoot(w,A,A.h+A.d-D);v.style.paddingTop=a.Em(s);v.style.borderTop=a.Px(y*F.scale,1)+" solid";E.style.paddingTop=a.Em(2*G-y);F.h+=s+2*G;C.combine(A,B,D-A.h);C.combine(F,B+A.w,0);C.clean();return w},CHTMLaddRoot:function(){return 0},CHTMLhandleBBox:function(s){var t=this.CHTMLbboxFor(0);delete t.pwidth;this.SUPER(arguments).CHTMLhandleBBox.apply(this,arguments)}});d.mroot.Augment({toCommonHTML:d.msqrt.prototype.toCommonHTML,CHTMLhandleBBox:d.msqrt.prototype.CHTMLhandleBBox,CHTMLaddRoot:function(A,u,v){if(!this.data[1]){return}var z=this.CHTML,B=this.data[1].CHTML,x=A.firstChild;var s=B.rscale;var t=this.CHTMLrootHeight(B,u,s)-v;var y=Math.min(B.w,B.r);var C=Math.max(y,u.offset/s);if(t){x.style.verticalAlign=a.Em(t/s)}if(C>y){x.firstChild.style.paddingLeft=a.Em(C-y)}C-=u.offset/s;x.style.width=a.Em(C);z.combine(B,0,t);return C*s},CHTMLrootHeight:function(u,s,t){return 0.45*(s.h+s.d-0.9)+s.offset+Math.max(0,u.d-0.075)}});d.mfenced.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLhandleScale(v);this.CHTMLaddChild(v,"open",{});for(var u=0,s=this.data.length;ua.linebreakWidth)||this.hasNewline()},CHTMLstretchV:function(s,t){this.CHTMLstretchChildV(this.CoreIndex(),s,t);return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLstretchChildH(this.CoreIndex(),s,t);return this.CHTML}});d.TeXAtom.Augment({toCommonHTML:function(x,w){if(!w||!w.stretch){x=this.CHTMLdefaultNode(x)}if(this.texClass===d.TEXCLASS.VCENTER){var s=a.TEX.axis_height,u=this.CHTML;var t=s-(u.h+u.d)/2+u.d;if(Math.abs(t)>0.001){x.style.verticalAlign=a.Em(t);u.h+=t;u.t+=t;u.d-=t;u.b-=t}}return x},CHTMLstretchV:function(s,t){this.CHTMLupdateFrom(this.Core().CHTMLstretchV(s,t));this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,s));this.toCommonHTML(t,{stretch:true});return this.CHTML}});d.semantics.Augment({toCommonHTML:function(s){s=this.CHTMLcreateNode(s);if(this.data[0]){this.data[0].toCommonHTML(s);this.CHTMLupdateFrom(this.data[0].CHTML);this.CHTMLhandleBBox(s)}return s}});d.annotation.Augment({toCommonHTML:function(s){return this.CHTMLcreateNode(s)}});d["annotation-xml"].Augment({toCommonHTML:d.mbase.CHTMLautoload});d.ms.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mglyph.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.menclose.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.maction.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mmultiscripts.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mtable.Augment({toCommonHTML:d.mbase.CHTMLautoload});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(f.config.menuSettings.zoom!=="None"){o.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.CommonHTML); +MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var g="2.7.6";var b=MathJax.ElementJax.mml,a=MathJax.Hub.config,e=MathJax.OutputJax.CommonHTML,d=MathJax.Hub.SplitList;var c=-1,f=1000000;b.mtable.Augment({toCommonHTML:function(l){var m={rows:[],labels:[],labeled:false};l=this.CHTMLdefaultNode(l,{noBBox:true,childOptions:m});var k=e.Element("mjx-table");while(l.firstChild){k.appendChild(l.firstChild)}l.appendChild(k);var h=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width","side","minlabelspacing","useHeight");var j=e.TEX.min_rule_thickness/e.em;m.t=e.Px(j*this.CHTML.scale,1);this.CHTMLgetBoxSizes(h,m);this.CHTMLgetAttributes(h,m);this.CHTMLadjustCells(h,m);if(h.frame){k.style.border=m.t+" "+h.frame}this.CHTMLalignV(h,m,l);this.CHTMLcolumnWidths(h,m,l);this.CHTMLstretchCells(h,m);if(m.labeled){this.CHTMLaddLabels(h,m,l,k)}var i=this.CHTML;i.w=i.r=m.R;i.h=i.t=m.T-m.B;i.d=i.b=m.B;if(!h.frame&&!i.pwidth){l.style.padding="0 "+e.Em(1/6);i.L=i.R=1/6}this.CHTMLhandleSpace(l);this.CHTMLhandleBBox(l);this.CHTMLhandleColor(l);return 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2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/TeX/config.js", + "[MathJax]/jax/output/CommonHTML/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/tex2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/extensions/TeX/noErrors.js", + "[MathJax]/extensions/TeX/noUndefined.js", + "[MathJax]/jax/input/TeX/jax.js", + "[MathJax]/extensions/TeX/AMSmath.js", + "[MathJax]/extensions/TeX/AMSsymbols.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + 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s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var 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n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" 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s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var 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n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 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MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" 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q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" 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i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible 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+ * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/TeX/config.js", + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/input/AsciiMath/config.js", + "[MathJax]/jax/output/CommonHTML/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/tex2jax.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/asciimath2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/extensions/TeX/noErrors.js", + "[MathJax]/extensions/TeX/noUndefined.js", + "[MathJax]/jax/input/TeX/jax.js", + "[MathJax]/extensions/TeX/AMSmath.js", + "[MathJax]/extensions/TeX/AMSsymbols.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/input/AsciiMath/jax.js", + "[MathJax]/jax/output/CommonHTML/jax.js", + "[MathJax]/jax/output/CommonHTML/autoload/mtable.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.6",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); +MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.6",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); +MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.7.6",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{fixphi:true,useMathMLspacing:true,displaystyle:true,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js"); 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+MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.tex2jax={version:"2.7.6",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" 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s}});d.mo.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLgetVariant();this.CHTMLhandleScale(v);a.BBOX.empty(this.CHTML);var t=this.getValues("displaystyle","largeop");t.variant=this.CHTMLvariant;t.text=this.data.join("");if(t.text==""){if(this.fence){v.style.width=a.Em(a.TEX.nulldelimiterspace)}}else{this.CHTMLadjustAccent(t);this.CHTMLadjustVariant(t);for(var u=0,s=this.data.length;u0){if(!this.hasValue("lspace")){t.lspace=0.15}if(!this.hasValue("rspace")){t.rspace=0.15}}var s=this,u=this.Parent();while(u&&u.isEmbellished()&&u.Core()===s){s=u;u=u.Parent();v=s.CHTMLnodeElement()}if(t.lspace){v.style.paddingLeft=a.Em(t.lspace)}if(t.rspace){v.style.paddingRight=a.Em(t.rspace)}this.CHTML.L=t.lspace;this.CHTML.R=t.rspace}else{this.SUPER(arguments).CHTMLhandleSpace.apply(this,arguments)}},CHTMLadjustAccent:function(u){var t=this.CoreParent();u.parent=t;if(a.isChar(u.text)&&t&&t.isa(d.munderover)){var v=t.data[t.over],s=t.data[t.under];if(v&&this===v.CoreMO()&&t.Get("accent")){u.remapchars=a.FONTDATA.REMAPACCENT}else{if(s&&this===s.CoreMO()&&t.Get("accentunder")){u.remapchars=a.FONTDATA.REMAPACCENTUNDER}}}},CHTMLadjustVariant:function(t){var s=t.parent,u=(s&&s.isa(d.msubsup)&&this!==s.data[s.base]);if(t.largeop){t.mathvariant=(t.displaystyle?"-largeOp":"-smallOp")}if(u){t.remapchars=this.remapChars;if(t.text.match(/['`"\u00B4\u2032-\u2037\u2057]/)){t.mathvariant="-TeX-variant"}}},CHTMLfixCombiningChar:function(s){s=s.firstChild;var t=a.Element("mjx-box",{style:{width:".25em","margin-left":"-.25em"}});s.insertBefore(t,s.firstChild)},CHTMLcenterOp:function(s){var u=this.CHTML;var t=(u.h-u.d)/2-a.TEX.axis_height;if(Math.abs(t)>0.001){s.style.verticalAlign=a.Em(-t)}u.h-=t;u.d+=t;if(u.r>u.w){u.ic=u.r-u.w;u.w=u.r;s.style.paddingRight=a.Em(u.ic)}},CHTMLcanStretch:function(w,u,v){if(!this.Get("stretchy")){return false}var x=this.data.join("");if(!a.isChar(x)){return false}var t={text:x};this.CHTMLadjustAccent(t);if(t.remapchars){x=t.remapchars[x]||x}x=a.FONTDATA.DELIMITERS[x.charCodeAt(0)];var s=(x&&x.dir===w.substr(0,1));if(s){s=(this.CHTML.h!==u||this.CHTML.d!==v||!!this.Get("minsize",true)||!!this.Get("maxsize",true));if(s){this.CHTML.stretch=true}}return s},CHTMLstretchV:function(v,y){var w=this.CHTMLnodeElement(),x=this.CHTML;var t=this.getValues("symmetric","maxsize","minsize");var u,s=a.TEX.axis_height;if(t.symmetric){u=2*Math.max(v-s,y+s)}else{u=v+y}t.maxsize=this.CHTMLlength2em(t.maxsize,x.h+x.d);t.minsize=this.CHTMLlength2em(t.minsize,x.h+x.d);u=Math.max(t.minsize,Math.min(t.maxsize,u));if(u!==x.sH){if(u!=t.minsize){u=[Math.max(u*a.TEX.delimiterfactor/1000,u-a.TEX.delimitershortfall),u]}while(w.firstChild){w.removeChild(w.firstChild)}this.CHTML=x=a.createDelimiter(w,this.data.join("").charCodeAt(0),u,x);x.sH=(u instanceof Array?u[1]:u);if(t.symmetric){u=(x.h+x.d)/2+s}else{u=(x.h+x.d)*v/(v+y)}u-=x.h;if(Math.abs(u)>0.05){w.style.verticalAlign=a.Em(u);x.h+=u;x.d-=u;x.t+=u;x.b-=u}}return this.CHTML},CHTMLstretchH:function(u,s){var v=this.CHTML;var t=this.getValues("maxsize","minsize","mathvariant","fontweight");if((t.fontweight==="bold"||(this.removedStyles||{}).fontWeight==="bold"||parseInt(t.fontweight)>=600)&&!this.Get("mathvariant",true)){t.mathvariant=d.VARIANT.BOLD}t.maxsize=this.CHTMLlength2em(t.maxsize,v.w);t.minsize=this.CHTMLlength2em(t.minsize,v.w);s=Math.max(t.minsize,Math.min(t.maxsize,s));if(s!==v.sW){while(u.firstChild){u.removeChild(u.firstChild)}this.CHTML=v=a.createDelimiter(u,this.data.join("").charCodeAt(0),s,v,t.mathvariant);v.sW=s}return this.CHTML}});d.mtext.Augment({CHTMLgetVariant:function(){if(a.config.mtextFontInherit||this.Parent().type==="merror"){var u=(a.config.scale/100)/a.scale;var t={cache:{},fonts:[],className:"MJXc-font-inherit",rscale:u,style:{"font-size":a.Percent(u)}};var s=this.Get("mathvariant");if(s.match(/bold/)){t.style["font-weight"]="bold"}if(s.match(/italic|-tex-mathit/)){t.style["font-style"]="italic"}if(s==="monospace"){t.className+=" MJXc-monospace-font"}if(s==="double-struck"){t.className+=" MJXc-double-struck-font"}if(s.match(/fraktur/)){t.className+=" MJXc-fraktur-font"}if(s.match(/sans-serif/)){t.className+=" MJXc-sans-serif-font"}if(s.match(/script/)){t.className+=" MJXc-script-font"}this.CHTMLvariant=t}else{this.SUPER(arguments).CHTMLgetVariant.call(this)}}});d.merror.Augment({toCommonHTML:function(s){s=this.CHTMLdefaultNode(s);var t=this.CHTML;t.rescale(0.9);t.h+=3/a.em;if(t.h>t.t){t.t=t.h}t.d+=3/a.em;if(t.d>t.b){t.b=t.d}t.w+=8/a.em;t.r=t.w;t.l=0;return s}});d.mspace.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLhandleScale(v);var t=this.getValues("height","depth","width");var s=this.CHTMLlength2em(t.width),u=this.CHTMLlength2em(t.height),y=this.CHTMLlength2em(t.depth);var x=this.CHTML;x.w=x.r=s;x.h=x.t=u;x.d=x.b=y;x.l=0;if(s<0){v.style.marginRight=a.Em(s);s=0}v.style.width=a.Em(s);v.style.height=a.Em(Math.max(0,u+y));if(y){v.style.verticalAlign=a.Em(-y)}this.CHTMLhandleBBox(v);this.CHTMLhandleColor(v);return v}});d.mpadded.Augment({toCommonHTML:function(t,F){var s;if(F&&F.stretch){t=t.firstChild;s=t.firstChild}else{t=this.CHTMLdefaultNode(t,{childNodes:"mjx-box",forceChild:true});s=t.firstChild;t=a.addElement(t,"mjx-block");t.appendChild(s);a.addElement(t,"mjx-strut")}var z=this.CHTMLbboxFor(0);var D=this.getValues("width","height","depth","lspace","voffset");var B=0,A=0,C=z.w,u=z.h,v=z.d;s.style.width=0;s.style.margin=a.Em(-u)+" 0 "+a.Em(-v);if(D.width!==""){C=this.CHTMLdimen(D.width,"w",C,0)}if(D.height!==""){u=this.CHTMLdimen(D.height,"h",u,0)}if(D.depth!==""){v=this.CHTMLdimen(D.depth,"d",v,0)}if(D.voffset!==""){A=this.CHTMLdimen(D.voffset);if(A){s.style.position="relative";s.style.top=a.Em(-A)}}if(D.lspace!==""){B=this.CHTMLdimen(D.lspace);if(B){s.style.position="relative";s.style.left=a.Em(B)}}t.style.width=0;t.style.marginTop=a.Em(u-k);t.style.padding="0 "+a.Em(C)+" "+a.Em(v)+" 0";var E=a.BBOX({w:C,h:u,d:v,l:0,r:C,t:u,b:v,scale:this.CHTML.scale,rscale:this.CHTML.rscale});E.combine(z,B,A);E.w=C;E.h=u;E.d=v;this.CHTML=E;return t.parentNode},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLdimen:function(w,y,x,s){if(s==null){s=-i}w=String(w);var t=w.match(/width|height|depth/);var u=(t?this.CHTML[t[0].charAt(0)]:(y?this.CHTML[y]:0));var v=(this.CHTMLlength2em(w,u)||0);if(w.match(/^[-+]/)&&x!=null){v+=x}if(s!=null){v=Math.max(s,v)}return v}});d.munderover.Augment({toCommonHTML:function(w,G){var E=this.getValues("displaystyle","accent","accentunder","align");var u=this.data[this.base];if(!E.displaystyle&&u!=null&&(u.movablelimits||u.CoreMO().Get("movablelimits"))){return d.msubsup.prototype.toCommonHTML.call(this,w,t)}var B,z,s=[],t=false;if(G&&G.stretch){if(this.data[this.base]){u=a.getNode(w,"mjx-op")}if(this.data[this.under]){B=a.getNode(w,"mjx-under")}if(this.data[this.over]){z=a.getNode(w,"mjx-over")}s[0]=u;s[1]=B||z;s[2]=z;t=true}else{var y=["mjx-op","mjx-under","mjx-over"];if(this.over===1){y[1]=y[2]}w=this.CHTMLdefaultNode(w,{childNodes:y,noBBox:true,forceChild:true,minChildren:2});s[0]=u=w.removeChild(w.firstChild);s[1]=B=z=w.removeChild(w.firstChild);if(w.firstChild){s[2]=z=w.removeChild(w.firstChild)}}var x=[],v=this.CHTMLgetBBoxes(x,s,E);var F=x[this.base],C=this.CHTML;C.w=v;C.h=F.h;C.d=F.d;if(F.h<0.35){u.style.marginTop=a.Em(F.h-0.35)}if(E.accent&&F.hu){u=s}}if(u===-i){u=s}for(y=0;yD.w){D.skew+=(D.w-(A.x+u*A.w))/2}}}else{y=a.TEX.big_op_spacing1;x=a.TEX.big_op_spacing3;v=Math.max(y,x-Math.max(0,u*A.d))}A.x+=E/2;A.y=D.h+v+w+u*A.d;if(v){B.style.paddingBottom=a.Em(v/u)}if(w){B.style.paddingTop=a.Em(w/u)}return C},CHTMLaddUnderscript:function(B,z,E,D,t,A,s){var C=this.CHTML;var y,x,w=a.TEX.big_op_spacing5,v;var F=z[this.under],u=F.rscale;if(!s){a.addElement(t,"mjx-itable",{},[["mjx-row",{},[["mjx-cell"]]],["mjx-row"]]);t.firstChild.firstChild.firstChild.appendChild(A);t.firstChild.lastChild.appendChild(B)}if(F.D){F.d=F.D}if(F.d<0){B.firstChild.style.verticalAlign="top";t.firstChild.style.marginBottom=a.Em(F.d)}if(E.accentunder){v=2*a.TEX.rule_thickness;w=0}else{y=a.TEX.big_op_spacing2;x=a.TEX.big_op_spacing4;v=Math.max(y,x-u*F.h)}F.x=-D/2;F.y=-(C.d+v+w+u*F.h);if(v){B.style.paddingTop=a.Em(v/u)}if(w){B.style.paddingBottom=a.Em(w/u)}},CHTMLplaceBoxes:function(s,B,A,E,z){var t=this.CHTML.w,y,v=z.length,x;var D=a.BBOX.zero();D.scale=this.CHTML.scale;D.rscale=this.CHTML.rscale;z[this.base].x=z[this.base].y=0;var F=i;for(y=0;y0){L+=Q;J-=Q}}L=Math.max(L,A.superscriptshift);J=Math.max(J,A.subscriptshift);H.style.paddingRight=a.Em(N/B);z.style.paddingBottom=a.Em(L/w+J/B-W.d-P.h/B*w);z.style.paddingLeft=a.Em(Y/w);z.style.paddingRight=a.Em(N/w);E.style.verticalAlign=a.Em(-J);G.combine(W,I+Y,L);G.combine(P,I,-J)}}G.clean();return S},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLchildNode:function(u,t){var s=["mjx-base","mjx-sub","mjx-sup"];if(this.over===1){s[1]=s[2]}return a.getNode(u,s[t])}});d.mfrac.Augment({toCommonHTML:function(N){N=this.CHTMLdefaultNode(N,{childNodes:["mjx-numerator","mjx-denominator"],childOptions:{autowidth:true},forceChild:true,noBBox:true,minChildren:2});var x=this.getValues("linethickness","displaystyle","numalign","denomalign","bevelled");var O=x.displaystyle;var D=N.firstChild,w=N.lastChild;var y=a.addElement(N,"mjx-box");y.appendChild(D);y.appendChild(w);N.appendChild(y);if(x.numalign!=="center"){D.style.textAlign=x.numalign}if(x.denomalign!=="center"){w.style.textAlign=x.denomalign}var P=this.CHTMLbboxFor(0),B=this.CHTMLbboxFor(1),C=a.BBOX.empty(this.CHTML),F=P.rscale,z=B.rscale;x.linethickness=Math.max(0,a.thickness2em(x.linethickness||"0",C.scale));var M=a.TEX.min_rule_thickness/a.em,T=a.TEX.axis_height;var J=x.linethickness,L,K,I,G;if(x.bevelled){y.className+=" MJXc-bevelled";var S=(O?0.4:0.15);var E=Math.max(F*(P.h+P.d),z*(B.h+B.d))+2*S;var R=a.Element("mjx-bevel");y.insertBefore(R,w);var s=a.createDelimiter(R,47,E);I=F*(P.d-P.h)/2+T+S;G=z*(B.d-B.h)/2+T-S;if(I){D.style.verticalAlign=a.Em(I/F)}if(G){w.style.verticalAlign=a.Em(G/z)}R.style.marginLeft=R.style.marginRight=a.Em(-S/2);C.combine(P,0,I);C.combine(s,F*P.w-S/2,0);C.combine(B,F*P.w+s.w-S,G);C.clean()}else{y.className+=" MJXc-stacked";if(O){I=a.TEX.num1;G=a.TEX.denom1}else{I=(J===0?a.TEX.num3:a.TEX.num2);G=a.TEX.denom2}if(J===0){L=Math.max((O?7:3)*a.TEX.rule_thickness,2*M);K=(I-P.d*F)-(B.h*z-G);if(KD){s=((A.h+A.d)-(D-G))/2}D=F.h+s+G;var B=this.CHTMLaddRoot(w,A,A.h+A.d-D);v.style.paddingTop=a.Em(s);v.style.borderTop=a.Px(y*F.scale,1)+" solid";E.style.paddingTop=a.Em(2*G-y);F.h+=s+2*G;C.combine(A,B,D-A.h);C.combine(F,B+A.w,0);C.clean();return w},CHTMLaddRoot:function(){return 0},CHTMLhandleBBox:function(s){var t=this.CHTMLbboxFor(0);delete t.pwidth;this.SUPER(arguments).CHTMLhandleBBox.apply(this,arguments)}});d.mroot.Augment({toCommonHTML:d.msqrt.prototype.toCommonHTML,CHTMLhandleBBox:d.msqrt.prototype.CHTMLhandleBBox,CHTMLaddRoot:function(A,u,v){if(!this.data[1]){return}var z=this.CHTML,B=this.data[1].CHTML,x=A.firstChild;var s=B.rscale;var t=this.CHTMLrootHeight(B,u,s)-v;var y=Math.min(B.w,B.r);var C=Math.max(y,u.offset/s);if(t){x.style.verticalAlign=a.Em(t/s)}if(C>y){x.firstChild.style.paddingLeft=a.Em(C-y)}C-=u.offset/s;x.style.width=a.Em(C);z.combine(B,0,t);return C*s},CHTMLrootHeight:function(u,s,t){return 0.45*(s.h+s.d-0.9)+s.offset+Math.max(0,u.d-0.075)}});d.mfenced.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLhandleScale(v);this.CHTMLaddChild(v,"open",{});for(var u=0,s=this.data.length;ua.linebreakWidth)||this.hasNewline()},CHTMLstretchV:function(s,t){this.CHTMLstretchChildV(this.CoreIndex(),s,t);return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLstretchChildH(this.CoreIndex(),s,t);return this.CHTML}});d.TeXAtom.Augment({toCommonHTML:function(x,w){if(!w||!w.stretch){x=this.CHTMLdefaultNode(x)}if(this.texClass===d.TEXCLASS.VCENTER){var s=a.TEX.axis_height,u=this.CHTML;var t=s-(u.h+u.d)/2+u.d;if(Math.abs(t)>0.001){x.style.verticalAlign=a.Em(t);u.h+=t;u.t+=t;u.d-=t;u.b-=t}}return x},CHTMLstretchV:function(s,t){this.CHTMLupdateFrom(this.Core().CHTMLstretchV(s,t));this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,s));this.toCommonHTML(t,{stretch:true});return this.CHTML}});d.semantics.Augment({toCommonHTML:function(s){s=this.CHTMLcreateNode(s);if(this.data[0]){this.data[0].toCommonHTML(s);this.CHTMLupdateFrom(this.data[0].CHTML);this.CHTMLhandleBBox(s)}return s}});d.annotation.Augment({toCommonHTML:function(s){return this.CHTMLcreateNode(s)}});d["annotation-xml"].Augment({toCommonHTML:d.mbase.CHTMLautoload});d.ms.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mglyph.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.menclose.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.maction.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mmultiscripts.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mtable.Augment({toCommonHTML:d.mbase.CHTMLautoload});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(f.config.menuSettings.zoom!=="None"){o.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.CommonHTML); +MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var g="2.7.6";var b=MathJax.ElementJax.mml,a=MathJax.Hub.config,e=MathJax.OutputJax.CommonHTML,d=MathJax.Hub.SplitList;var c=-1,f=1000000;b.mtable.Augment({toCommonHTML:function(l){var m={rows:[],labels:[],labeled:false};l=this.CHTMLdefaultNode(l,{noBBox:true,childOptions:m});var k=e.Element("mjx-table");while(l.firstChild){k.appendChild(l.firstChild)}l.appendChild(k);var h=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width","side","minlabelspacing","useHeight");var j=e.TEX.min_rule_thickness/e.em;m.t=e.Px(j*this.CHTML.scale,1);this.CHTMLgetBoxSizes(h,m);this.CHTMLgetAttributes(h,m);this.CHTMLadjustCells(h,m);if(h.frame){k.style.border=m.t+" "+h.frame}this.CHTMLalignV(h,m,l);this.CHTMLcolumnWidths(h,m,l);this.CHTMLstretchCells(h,m);if(m.labeled){this.CHTMLaddLabels(h,m,l,k)}var i=this.CHTML;i.w=i.r=m.R;i.h=i.t=m.T-m.B;i.d=i.b=m.B;if(!h.frame&&!i.pwidth){l.style.padding="0 "+e.Em(1/6);i.L=i.R=1/6}this.CHTMLhandleSpace(l);this.CHTMLhandleBBox(l);this.CHTMLhandleColor(l);return l},CHTMLgetBoxSizes:function(z,k){var r=e.FONTDATA.lineH*z.useHeight,t=e.FONTDATA.lineD*z.useHeight;var y=[],h=[],l=[],w=-1,q,n;for(q=0,n=this.data.length;qw){w=p}}var u=B.data[p-A].CHTML;if(u.h>y[q]){y[q]=u.h}if(u.d>h[q]){h[q]=u.d}if(u.w>l[p]){l[p]=u.w}}}if(z.equalrows){k.HD=true;var x=Math.max.apply(Math,y);var o=Math.max.apply(Math,h);for(q=0,n=y.length;qt||m<=0){m=null}}else{w.align=this.defaults.align}var p=0,l=0,u=e.TEX.axis_height;if(w.fspace){p+=k.FSPACE[1]}if(w.frame){p+=2/e.em;l+=1/e.em}for(var q=0;q=m){l+=r+s+x[q]}}}if(!m){l=({top:p,bottom:0,center:p/2,baseline:p/2,axis:p/2-u})[w.align]}if(l){o.style.verticalAlign=e.Em(-l)}k.T=p;k.B=l},CHTMLcolumnWidths:function(l,r,A){var I=r.CWIDTH,K=r.CSPACE,u=r.J,F;var G=0,n=false,y=l.width.match(/%$/);var H,B,v;if(l.width!=="auto"&&!y){G=Math.max(0,this.CHTMLlength2em(l.width,r.R));n=true}if(l.equalcolumns){if(y){var z=e.Percent(1/(u+1));for(F=0;F<=u;F++){I[F]=z}}else{v=Math.max.apply(Math,r.W);if(l.width!=="auto"){var 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document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var 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n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var 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r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var 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r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return 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q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" 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i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var 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Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/TeX/config.js", + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/input/AsciiMath/config.js", + "[MathJax]/jax/output/CommonHTML/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/tex2jax.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/asciimath2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/extensions/TeX/noErrors.js", + "[MathJax]/extensions/TeX/noUndefined.js", + "[MathJax]/jax/input/TeX/jax.js", + "[MathJax]/extensions/TeX/AMSmath.js", + "[MathJax]/extensions/TeX/AMSsymbols.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/input/AsciiMath/jax.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.6",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); +MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.6",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); +MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.7.6",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{fixphi:true,useMathMLspacing:true,displaystyle:true,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js"); 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n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return 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q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" 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i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var 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Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/TeX/config.js", + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/input/AsciiMath/config.js", + "[MathJax]/jax/output/SVG/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/tex2jax.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/asciimath2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/extensions/TeX/noErrors.js", + "[MathJax]/extensions/TeX/noUndefined.js", + "[MathJax]/jax/input/TeX/jax.js", + "[MathJax]/extensions/TeX/AMSmath.js", + "[MathJax]/extensions/TeX/AMSsymbols.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/input/AsciiMath/jax.js", + "[MathJax]/jax/output/SVG/jax.js", + "[MathJax]/jax/output/SVG/autoload/mtable.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.6",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); +MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.6",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); +MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.7.6",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{fixphi:true,useMathMLspacing:true,displaystyle:true,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js"); +MathJax.OutputJax.SVG=MathJax.OutputJax({id:"SVG",version:"2.7.6",directory:MathJax.OutputJax.directory+"/SVG",extensionDir:MathJax.OutputJax.extensionDir+"/SVG",autoloadDir:MathJax.OutputJax.directory+"/SVG/autoload",fontDir:MathJax.OutputJax.directory+"/SVG/fonts",config:{scale:100,minScaleAdjust:50,font:"TeX",blacker:1,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",addMMLclasses:false,useFontCache:true,useGlobalCache:true,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},merrorStyle:{fontSize:"90%",color:"#C00",background:"#FF8",border:"1px solid #C00",padding:"3px"},styles:{".MathJax_SVG_Display":{"text-align":"center",margin:"1em 0em"},".MathJax_SVG .MJX-monospace":{"font-family":"monospace"},".MathJax_SVG .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_SVG_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 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s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var 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i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right 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License. + */ + +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 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Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +(function(d,c){var f="2.7.6";var 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index 0000000..165f53a --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/TeX/AMScd.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/TeX/AMScd.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Extension["TeX/AMScd"]={version:"2.7.6",config:MathJax.Hub.CombineConfig("TeX.CD",{colspace:"5pt",rowspace:"5pt",harrowsize:"2.75em",varrowsize:"1.75em",hideHorizontalLabels:false})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,e=MathJax.InputJax.TeX,d=e.Stack.Item,c=e.Definitions,a=MathJax.Extension["TeX/AMScd"].config;c.environment.CD="CD_env";c.special["@"]="CD_arrow";c.macros.minCDarrowwidth="CD_minwidth";c.macros.minCDarrowheight="CD_minheight";e.Parse.Augment({CD_env:function(f){this.Push(f);return d.array().With({arraydef:{columnalign:"center",columnspacing:a.colspace,rowspacing:a.rowspace,displaystyle:true},minw:this.stack.env.CD_minw||a.harrowsize,minh:this.stack.env.CD_minh||a.varrowsize})},CD_arrow:function(g){var l=this.string.charAt(this.i);if(!l.match(/[>":"\u2192","<":"\u2190",V:"\u2193",A:"\u2191"}[l];var p=this.GetUpTo(g+l,l),m=this.GetUpTo(g+l,l);if(l===">"||l==="<"){h=b.mo(r).With(f);if(!p){p="\\kern 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Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Extension["TeX/AMSmath"]={version:"2.7.6",number:0,startNumber:0,IDs:{},eqIDs:{},labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,h=MathJax.InputJax.TeX,g=MathJax.Extension["TeX/AMSmath"];var d=h.Definitions,f=h.Stack.Item,a=h.config.equationNumbers;var c=function(k){var n=[];for(var l=0,j=k.length;l0){p+="rl";o.push("0em 0em");q--}o=o.join(" ");if(i){return this.AMSarray(l,j,i,p,o)}var m=this.AMSarray(l,j,i,p,o);return this.setArrayAlign(m,k)},EquationBegin:function(i,j){this.checkEqnEnv();this.stack.global.forcetag=(j&&a.autoNumber!=="none");return 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f=[this.top,this.stack.length-this.top].concat(e.stack.slice(1));this.stack.splice.apply(this.stack,f);this.top=this.stack.length},Reset:function(){this.top=this.stack.length},Clear:function(e){this.stack=[this.stack[0].Clear()];this.top=this.stack.length}},{nsFrame:a});b.Add({macros:{begingroup:"BeginGroup",endgroup:"EndGroup",global:"Global",gdef:["Macro","\\global\\def"]}},null,true);d.Parse.Augment({BeginGroup:function(e){d.eqnStack.Push(a())},EndGroup:function(e){if(d.eqnStack.top>1){d.eqnStack.Pop()}else{if(d.rootStack.top===1){d.Error(["ExtraEndMissingBegin","Extra %1 or missing \\begingroup",e])}else{d.eqnStack.Clear();d.rootStack.Pop()}}},csFindMacro:function(e){return(d.eqnStack.Find(e,"macros")||d.rootStack.Find(e,"macros"))},envFindName:function(e){return(d.eqnStack.Find(e,"environments")||d.rootStack.Find(e,"environments"))},setDef:function(e,f){f.isUser=true;d.eqnStack.Def(e,f,"macros",this.stack.env.isGlobal);delete this.stack.env.isGlobal},setEnv:function(e,f){f.isUser=true;d.eqnStack.Def(e,f,"environments")},Global:function(e){var f=this.i;var g=this.GetCSname(e);this.i=f;if(g!=="let"&&g!=="def"&&g!=="newcommand"&&g!=="DeclareMathOperator"&&g!=="Newextarrow"){d.Error(["GlobalNotFollowedBy","%1 not followed by \\let, \\def, or \\newcommand",e])}this.stack.env.isGlobal=true}});d.rootStack=c();d.eqnStack=c(true);d.prefilterHooks.Add(function(){d.rootStack.Reset();d.eqnStack.Clear(true)});d.postfilterHooks.Add(function(){d.rootStack.Merge(d.eqnStack)});MathJax.Hub.Startup.signal.Post("TeX begingroup Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/begingroup.js"); diff --git a/revisions_report_files/mathjax-27/extensions/TeX/boldsymbol.js b/revisions_report_files/mathjax-27/extensions/TeX/boldsymbol.js new file mode 100644 index 0000000..63f2545 --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/TeX/boldsymbol.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/TeX/boldsymbol.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Extension["TeX/boldsymbol"]={version:"2.7.6"};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var a=MathJax.ElementJax.mml;var d=MathJax.InputJax.TeX;var b=d.Definitions;var c={};c[a.VARIANT.NORMAL]=a.VARIANT.BOLD;c[a.VARIANT.ITALIC]=a.VARIANT.BOLDITALIC;c[a.VARIANT.FRAKTUR]=a.VARIANT.BOLDFRAKTUR;c[a.VARIANT.SCRIPT]=a.VARIANT.BOLDSCRIPT;c[a.VARIANT.SANSSERIF]=a.VARIANT.BOLDSANSSERIF;c["-tex-caligraphic"]="-tex-caligraphic-bold";c["-tex-oldstyle"]="-tex-oldstyle-bold";b.Add({macros:{boldsymbol:"Boldsymbol"}},null,true);d.Parse.Augment({mmlToken:function(f){if(this.stack.env.boldsymbol){var e=f.Get("mathvariant");if(e==null){f.mathvariant=a.VARIANT.BOLD}else{f.mathvariant=(c[e]||e)}}return f},Boldsymbol:function(h){var e=this.stack.env.boldsymbol,f=this.stack.env.font;this.stack.env.boldsymbol=true;this.stack.env.font=null;var g=this.ParseArg(h);this.stack.env.font=f;this.stack.env.boldsymbol=e;this.Push(g)}});MathJax.Hub.Startup.signal.Post("TeX boldsymbol Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/boldsymbol.js"); diff --git a/revisions_report_files/mathjax-27/extensions/TeX/cancel.js 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Please report."]}return n}, +H:function(t){switch(t){case"->":case"\u2192":case"\u27f6":return"rightarrow";case"<-":return"leftarrow";case"<->":return"leftrightarrow";case"<--\x3e":return"leftrightarrows";case"<=>":case"\u21cc":return"rightleftharpoons";case"<=>>":return"Rightleftharpoons";case"<<=>":return"Leftrightharpoons";default:throw["MhchemBugT","mhchem bug T. Please report."]}}, +j:function(t){switch(t){case"-":case"1":return"{-}";case"=":case"2":return"{=}";case"#":case"3":return"{\\equiv}";case"~":return"{\\tripledash}";case"~-":return"{\\rlap{\\lower.1em{-}}\\raise.1em{\\tripledash}}";case"~=":case"~--":return"{\\rlap{\\lower.2em{-}}\\rlap{\\raise.2em{\\tripledash}}-}";case"-~-":return"{\\rlap{\\lower.2em{-}}\\rlap{\\raise.2em{-}}\\tripledash}";case"...":return"{{\\cdot}{\\cdot}{\\cdot}}";case"....":return"{{\\cdot}{\\cdot}{\\cdot}{\\cdot}}";case"->":return"{\\rightarrow}";case"<-":return"{\\leftarrow}";case"<":return"{<}";case">":return"{>}";default:throw["MhchemBugT","mhchem bug T. Please report."]}}, +J:function(t){switch(t){case"+":return" {}+{} ";case"-":return" {}-{} ";case"=":return" {}={} ";case"<":return" {}<{} ";case">":return" {}>{} ";case"<<":return" {}\\ll{} ";case">>":return" {}\\gg{} ";case"\\pm":return" {}\\pm{} ";case"\\approx":case"$\\approx$":return" {}\\approx{} ";case"v":case"(v)":return" \\downarrow{} ";case"^":case"(^)":return" \\uparrow{} ";default:throw["MhchemBugT","mhchem bug T. Please report."]}}};MathJax.Extension["TeX/mhchem"].CE=n,t.Definitions.Add({macros:{ce:"CE",pu:"PU",xleftrightarrow:["Extension","AMSmath"],xrightleftharpoons:["Extension","AMSmath"],xRightleftharpoons:["Extension","AMSmath"],xLeftrightharpoons:["Extension","AMSmath"],longrightleftharpoons:["Macro","\\stackrel{\\textstyle{-}\\!\\!{\\rightharpoonup}}{\\smash{{\\leftharpoondown}\\!\\!{-}}}"],longRightleftharpoons:["Macro","\\stackrel{\\textstyle{-}\\!\\!{\\rightharpoonup}}{\\smash{\\leftharpoondown}}"],longLeftrightharpoons:["Macro","\\stackrel{\\textstyle\\vphantom{{-}}{\\rightharpoonup}}{\\smash{{\\leftharpoondown}\\!\\!{-}}}"],longleftrightarrows:["Macro","\\stackrel{\\longrightarrow}{\\smash{\\longleftarrow}\\Rule{0px}{.25em}{0px}}"],tripledash:["Macro","\\vphantom{-}\\raise2mu{\\kern2mu\\tiny\\text{-}\\kern1mu\\text{-}\\kern1mu\\text{-}\\kern2mu}"]}}, +null,!0),MathJax.Extension["TeX/AMSmath"]||t.Definitions.Add({macros:{xrightarrow:["Extension","AMSmath"],xleftarrow:["Extension","AMSmath"]}}, +null,!0),MathJax.Hub.Register.StartupHook("TeX AMSmath Ready",function(){t.Definitions.Add({macros:{xleftrightarrow:["xArrow",8596,6,6],xrightleftharpoons:["xArrow",8652,5,7],xRightleftharpoons:["xArrow",8652,5,7],xLeftrightharpoons:["xArrow",8652,5,7]}}, +null,!0)}),t.Parse.Augment({ +CE:function(t){var e=this.GetArgument(t),a=n(e).Parse();this.string=a+this.string.substr(this.i),this.i=0}, +PU:function(t){var e=this.GetArgument(t),a=n(e).Parse("pu");this.string=a+this.string.substr(this.i),this.i=0}}),MathJax.Hub.Startup.signal.Post("TeX mhchem Ready")}),MathJax.Ajax.loadComplete("[mhchem]/mhchem.js"); + diff --git a/revisions_report_files/mathjax-27/extensions/TeX/newcommand.js b/revisions_report_files/mathjax-27/extensions/TeX/newcommand.js new file mode 100644 index 0000000..be7bdee --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/TeX/newcommand.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/TeX/newcommand.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Extension["TeX/newcommand"]={version:"2.7.6"};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.InputJax.TeX;var a=b.Definitions;a.Add({macros:{newcommand:"NewCommand",renewcommand:"NewCommand",newenvironment:"NewEnvironment",renewenvironment:"NewEnvironment",def:"MacroDef",let:"Let"}},null,true);b.Parse.Augment({NewCommand:function(c){var e=this.trimSpaces(this.GetArgument(c)),g=this.GetBrackets(c),d=this.GetBrackets(c),f=this.GetArgument(c);if(e.charAt(0)==="\\"){e=e.substr(1)}if(!e.match(/^(.|[a-z]+)$/i)){b.Error(["IllegalControlSequenceName","Illegal control sequence name for %1",c])}if(g){g=this.trimSpaces(g);if(!g.match(/^[0-9]+$/)){b.Error(["IllegalParamNumber","Illegal number of parameters specified in %1",c])}}this.setDef(e,["Macro",f,g,d])},NewEnvironment:function(d){var f=this.trimSpaces(this.GetArgument(d)),h=this.GetBrackets(d),e=this.GetBrackets(d),g=this.GetArgument(d),c=this.GetArgument(d);if(h){h=this.trimSpaces(h);if(!h.match(/^[0-9]+$/)){b.Error(["IllegalParamNumber","Illegal number of parameters specified in %1",d])}}this.setEnv(f,["BeginEnv",[null,"EndEnv"],g,c,h,e])},MacroDef:function(c){var d=this.GetCSname(c),f=this.GetTemplate(c,"\\"+d),e=this.GetArgument(c);if(!(f instanceof Array)){this.setDef(d,["Macro",e,f])}else{this.setDef(d,["MacroWithTemplate",e].concat(f))}},Let:function(d){var e=this.GetCSname(d),f;var g=this.GetNext();if(g==="="){this.i++;g=this.GetNext()}if(g==="\\"){d=this.GetCSname(d);f=this.csFindMacro(d);if(!f){if(a.mathchar0mi.hasOwnProperty(d)){f=["csMathchar0mi",a.mathchar0mi[d]]}else{if(a.mathchar0mo.hasOwnProperty(d)){f=["csMathchar0mo",a.mathchar0mo[d]]}else{if(a.mathchar7.hasOwnProperty(d)){f=["csMathchar7",a.mathchar7[d]]}else{if(a.delimiter.hasOwnProperty("\\"+d)){f=["csDelimiter",a.delimiter["\\"+d]]}else{return}}}}}}else{f=["Macro",g];this.i++}this.setDef(e,f)},GetCSname:function(e){var f=this.GetNext();if(f!=="\\"){b.Error(["MissingCS","%1 must be followed by a control sequence",e])}var d=this.trimSpaces(this.GetArgument(e));return d.substr(1)},GetTemplate:function(f,e){var j,g=[],h=0;j=this.GetNext();var d=this.i;while(this.i0){return[h,g]}else{return h}}}this.i++}b.Error(["MissingReplacementString","Missing replacement string for definition of %1",f])},MacroWithTemplate:function(d,g,h,f){if(h){var c=[];this.GetNext();if(f[0]&&!this.MatchParam(f[0])){b.Error(["MismatchUseDef","Use of %1 doesn't match its definition",d])}for(var e=0;eb.config.MAXMACROS){b.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},BeginEnv:function(g,k,c,j,h){if(j){var e=[];if(h!=null){var d=this.GetBrackets("\\begin{"+name+"}");e.push(d==null?h:d)}for(var f=e.length;f1){var n=(q.h+q.d)/2,j=h.TeX.x_height/2;p.parentNode.style.verticalAlign=h.Em(q.d+(j-n));q.h=j+n;q.d=n-j}p.bbox={h:q.h,d:q.d,w:k,lw:0,rw:k};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.apply(this,arguments)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.apply(this,arguments)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.apply(this,arguments)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.apply(this,arguments)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Register.StartupHook("PreviewHTML Jax Config",function(){b.Config({PreviewHTML:{styles:{".MathJax_PHTML .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("PreviewHTML Jax Ready",function(){var f=MathJax.ElementJax.mml;var h=MathJax.HTML;var g=f.merror.prototype.toPreviewHTML;f.merror.Augment({toPreviewHTML:function(l){if(!this.isError){return g.apply(this,arguments)}l=this.PHTMLcreateSpan(l);l.className="noError";if(this.multiLine){l.style.display="inline-block"}var n=this.data[0].data[0].data.join("").split(/\n/);for(var k=0,j=n.length;k1){var l=1.2*j/2;o.h=l+0.25;o.d=l-0.25;n.style.verticalAlign=g.Em(0.45-l)}else{o.h=1;o.d=0.2+2/g.em}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); diff --git a/revisions_report_files/mathjax-27/extensions/TeX/noUndefined.js b/revisions_report_files/mathjax-27/extensions/TeX/noUndefined.js new file mode 100644 index 0000000..f4100a7 --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/TeX/noUndefined.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/TeX/noUndefined.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Extension["TeX/noUndefined"]={version:"2.7.6",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); diff --git a/revisions_report_files/mathjax-27/extensions/TeX/unicode.js b/revisions_report_files/mathjax-27/extensions/TeX/unicode.js new file mode 100644 index 0000000..9f82f47 --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/TeX/unicode.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/TeX/unicode.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Extension["TeX/unicode"]={version:"2.7.6",unicode:{},config:MathJax.Hub.CombineConfig("TeX.unicode",{fonts:"STIXGeneral,'Arial Unicode MS'"})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX;var a=MathJax.ElementJax.mml;var b=MathJax.Extension["TeX/unicode"].unicode;c.Definitions.Add({macros:{unicode:"Unicode"}},null,true);c.Parse.Augment({Unicode:function(e){var i=this.GetBrackets(e),d;if(i){if(i.replace(/ /g,"").match(/^(\d+(\.\d*)?|\.\d+),(\d+(\.\d*)?|\.\d+)$/)){i=i.replace(/ /g,"").split(/,/);d=this.GetBrackets(e)}else{d=i;i=null}}var j=this.trimSpaces(this.GetArgument(e)).replace(/^0x/,"x");if(!j.match(/^(x[0-9A-Fa-f]+|[0-9]+)$/)){c.Error(["BadUnicode","Argument to \\unicode must be a number"])}var h=parseInt(j.match(/^x/)?"0"+j:j);if(!b[h]){b[h]=[800,200,d,h]}else{if(!d){d=b[h][2]}}if(i){b[h][0]=Math.floor(i[0]*1000);b[h][1]=Math.floor(i[1]*1000)}var f=this.stack.env.font,g={};if(d){b[h][2]=g.fontfamily=d.replace(/"/g,"'");if(f){if(f.match(/bold/)){g.fontweight="bold"}if(f.match(/italic|-mathit/)){g.fontstyle="italic"}}}else{if(f){g.mathvariant=f}}g.unicode=[].concat(b[h]);this.Push(a.mtext(a.entity("#"+j)).With(g))}});MathJax.Hub.Startup.signal.Post("TeX unicode Ready")});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.ElementJax.mml;var c=MathJax.Extension["TeX/unicode"].config.fonts;var b=a.mbase.prototype.HTMLgetVariant;a.mbase.Augment({HTMLgetVariant:function(){var d=b.apply(this,arguments);if(d.unicode){delete d.unicode;delete d.FONTS}if(!this.unicode){return d}d.unicode=true;if(!d.defaultFont){d=MathJax.Hub.Insert({},d);d.defaultFont={family:c}}var e=this.unicode[2];if(e){e+=","+c}else{e=c}d.defaultFont[this.unicode[3]]=[this.unicode[0],this.unicode[1],500,0,500,{isUnknown:true,isUnicode:true,font:e}];return d}})});MathJax.Hub.Register.StartupHook("SVG Jax Ready",function(){var a=MathJax.ElementJax.mml;var c=MathJax.Extension["TeX/unicode"].config.fonts;var b=a.mbase.prototype.SVGgetVariant;a.mbase.Augment({SVGgetVariant:function(){var d=b.call(this);if(d.unicode){delete d.unicode;delete d.FONTS}if(!this.unicode){return d}d.unicode=true;if(!d.forceFamily){d=MathJax.Hub.Insert({},d)}d.defaultFamily=c;d.noRemap=true;d.h=this.unicode[0];d.d=this.unicode[1];return d}})});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/unicode.js"); diff --git a/revisions_report_files/mathjax-27/extensions/TeX/verb.js b/revisions_report_files/mathjax-27/extensions/TeX/verb.js new file mode 100644 index 0000000..7916c6d --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/TeX/verb.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/TeX/verb.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Extension["TeX/verb"]={version:"2.7.6"};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX;var b=c.Definitions;b.Add({macros:{verb:"Verb"}},null,true);c.Parse.Augment({Verb:function(d){var g=this.GetNext();var f=++this.i;if(g==""){c.Error(["MissingArgFor","Missing 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