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## Documentation | ||
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For detailed information about the SPRAL packages and API see [Fortran | ||
documentation](http://www.numerical.rl.ac.uk/spral/doc/latest/Fortran/) | ||
documentation](https://ralna.github.io/spral/_build/html/Fortran/) | ||
or [C | ||
documentation](http://www.numerical.rl.ac.uk/spral/doc/latest/C/). | ||
documentation](https://ralna.github.io/spral/_build/html/C/). | ||
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## Packages | ||
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# Sphinx build info version 1 | ||
# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done. | ||
config: 9be5e82a2ad22e9a17dcfcb91ca0981e | ||
tags: 645f666f9bcd5a90fca523b33c5a78b7 |
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========================= | ||
Coordinate (Coord) Format | ||
========================= | ||
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This standard data format consists of the following data: | ||
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.. code-block:: C | ||
int m; /* number of rows (unsymmetric only) */ | ||
int n; /* number of columns */ | ||
int ne; /* number of entries in matrix (may have type int64_t) */ | ||
int row[ne]; /* row indices */ | ||
int col[ne]; /* column indices */ | ||
double val[ne]; /* numerical values */ | ||
The arrays should be set such that the ``k``-th entry is in row | ||
``row[k]`` and column ``col[k]`` with value ``val[k]``. Entries that are | ||
zero, including those on the diagonal, need not be specified. | ||
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For **symmetric matrices**, only the lower *or* upper triangular entries of | ||
:math:`A` should be supplied. For **unsymmetric matrices**, all entries in the | ||
matrix should be supplied. Duplicate entries will be summed and out-of-range | ||
entries will be ignored. | ||
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Some SPRAL routines offer only input in :doc:`CSC format<csc_format>`, you | ||
may need to use routines from the :doc:`matrix_util` package to convert | ||
data from Coordinate to CSC format. | ||
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To illustrate the Coordinate format, the matrix | ||
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.. math:: | ||
\left( \begin{array}{ccccc} | ||
1.1 & 2.2 & & 3.3 & \\ | ||
2.2 & & 4.4 & & \\ | ||
& 4.4 & 5.5 & & 6.6 \\ | ||
3.3 & & & 7.7 & 8.8 \\ | ||
& & 6.6 & 8.8 & 9.9 | ||
\end{array} \right) | ||
is described by the following data: | ||
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.. code-block:: C | ||
int n = 5; | ||
int ne = 9; | ||
int row[] = { 1, 2, 3, 4, 3, 5, 4, 5, 5 }; | ||
int col[] = { 1, 1, 2, 1, 3, 3, 4, 4, 5 }; | ||
double val[] = { 1.1, 2.2, 4.4, 3.3, 5.5, 6.6, 7.7, 8.8, 9.9 }; |
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===================================== | ||
Compressed Sparse Column (CSC) Format | ||
===================================== | ||
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This standard data format consists of the following data: | ||
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.. code-block:: C | ||
int m; /* number of rows (unsymmetric only) */ | ||
int n; /* number of columns */ | ||
int ptr[n+1]; /* column pointers (may have type int64_t) */ | ||
int row[ ptr[n]-1 ]; /* row indices */ | ||
double val[ ptr[n]-1 ]; /* numerical values */ | ||
Non-zero matrix entries are ordered by increasing column index and stored in | ||
the arrays `row[]` and `val[]` such that `row[k]` holds | ||
the row number and `val[k]` holds the value of the k-th entry. | ||
The `ptr[]` array stores column pointers such that `ptr[i]` is | ||
the position in `row[]` and `val[]` of | ||
the first entry in the i-th column, and `ptr[n]` is | ||
the total number of entries. `ptr[]` may be either `int` or `int64_t`. | ||
There must be no duplicate or out of range entries. | ||
Entries that are zero, including those on the diagonal, need not be specified. | ||
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For **symmetric matrices**, only the lower triangular entries of :math:`A` | ||
should be supplied. For **unsymmetric matrices**, all entries in the matrix | ||
should be supplied. | ||
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Note that most SPRAL routines offer **no checking** of user data, and the | ||
behaviour of these routines with misformatted data is undefined. You may use | ||
routines from the :doc:`matrix_util` package to convert data to and | ||
check data stored in this format. | ||
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To illustrate the CSC format, the matrix | ||
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.. math:: | ||
\left( \begin{array}{ccccc} | ||
1.1 & 2.2 & & 3.3 & \\ | ||
2.2 & & 4.4 & & \\ | ||
& 4.4 & 5.5 & & 6.6 \\ | ||
3.3 & & & 7.7 & 8.8 \\ | ||
& & 6.6 & 8.8 & 9.9 | ||
\end{array} \right) | ||
is described by the following data: | ||
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.. code-block:: C | ||
int n = 5; | ||
int ptr[] = { 1, 4, 5, 7, 9, 10 }; | ||
int row[] = { 1, 2, 4, 3, 3, 5, 4, 5, 5 }; | ||
double val[] = { 1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.8, 9.9 }; |
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.. spral documentation master file, created by | ||
sphinx-quickstart on Mon Feb 15 15:20:34 2016. | ||
You can adapt this file completely to your liking, but it should at least | ||
contain the root `toctree` directive. | ||
The Sparse Parallel Robust Algorithms Library | ||
============================================= | ||
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Introduction | ||
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.. toctree:: | ||
:maxdepth: 1 | ||
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install | ||
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Data Formats | ||
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.. toctree:: | ||
:maxdepth: 1 | ||
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csc_format | ||
coord_format | ||
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Packages: | ||
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.. toctree:: | ||
:maxdepth: 1 | ||
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lsmr | ||
matrix_util | ||
random | ||
random_matrix | ||
rutherford_boeing | ||
scaling | ||
ssids | ||
ssmfe | ||
ssmfe_expert | ||
ssmfe_core | ||
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Indices and tables | ||
================== | ||
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* :ref:`genindex` | ||
* :ref:`modindex` | ||
* :ref:`search` | ||
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