GlobalMoran.tex

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\documentclass{article}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{graphicx}
\usepackage{color}
\usepackage{listings}
\usepackage{hyperref}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{epstopdf}
\usepackage{matlab}

\sloppy
\epstopdfsetup{outdir=./}
\graphicspath{ {./GlobalMoran_images/} }

\begin{document}

\matlabtitle{Global Moran's I}

\begin{par}
\begin{flushleft}
calculate global moran's I with mask.
\end{flushleft}
\end{par}

\begin{par}
\begin{flushleft}
Formula: 
\end{flushleft}
\end{par}

\begin{par}
$$I = \frac{\sum_i\sum_j(y_i – \overline{y})(y_j – \overline{y})}{s^2\sum_i\sum_j w_{ij}}$$
\end{par}

\begin{par}
\begin{flushleft}
where $s^2 = \frac{\sum (y_i - \overline{y})^2}{n}$, $\overline{y} = \sum^{n}_{i=1} \frac{y_i}{n}$
\end{flushleft}
\end{par}

\begin{matlabcode}
function [moran_global] = GlobalMoran(image, mask)
    [x,y] = size(image);
    image(mask==0)=NaN;
    x_avg = nanmean(image(:));
    for xi = 1:x
        for yi = 1:y
            % if current pixel is not empty
            if ~isnan(image(xi,yi))
                left = xi -1;
                right = xi +1;
                upper = yi -1;
                lower = yi +1;
                coords = [left, right, upper, lower];
                if left <= 1
                    left = 1;
                end
                if right >= x
                    right = x;
                end
                if upper <= 1
                    upper = 1;
                end
                if lower >= y
                    lower = y;
                end
                windowIM = image(left:right,upper:lower);
                windowWt = windowIM;
                windowWt(isnan(windowIM)) = 0;
                windowWt(~isnan(windowIM)) = 1;
                reshape(windowWt,size(windowIM));
                % current pixel not empty
            end
        end
    end
end
\end{matlabcode}

\end{document}