initial commit

demos.xml

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+<?xml version="1.0" encoding="utf-8"?>
+<demos><!--This is an autogenerated file, please do not modify-->
+   <name>Generalized chi-square distribution</name>
+   <type>toolbox</type>
+   <icon>HelpIcon.DEMOS</icon>
+   <website/>
+   <description>The generalized chi-square variable is a quadratic form of a normal variable, or equivalently, a linear sum of independent non-central chi-square variables and a normal variable. Try the Getting Started guide for a quick demo of all the functions.</description>
+   <demosection>
+      <label>doc</label>
+      <demoitem>
+         <label>GettingStarted</label>
+         <type>other</type>
+         <source>GettingStarted</source>
+         <file>doc/html/GettingStarted.html</file>
+      </demoitem>
+   </demosection>
+</demos>

gx2.prj

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+<deployment-project plugin="plugin.toolbox" plugin-version="1.0">
+  <configuration build-checksum="2263924193" file="C:\Users\abhra\Google Drive\Geisler Lab\IntClassNorm\gx2\gx2.prj" location="C:\Users\abhra\Google Drive\Geisler Lab\IntClassNorm\gx2" name="gx2" target="target.toolbox" target-name="Package Toolbox">
+    <param.appname>Generalized chi-square distribution</param.appname>
+    <param.authnamewatermark>Abhranil Das</param.authnamewatermark>
+    <param.email>abhranil.das@utexas.edu</param.email>
+    <param.company>The University of Texas at Austin</param.company>
+    <param.summary>Compute the statistics, pdf, cdf, inverse cdf and random numbers of the generalized chi-square distribution.</param.summary>
+    <param.description>The generalized chi-square variable is a quadratic form of a normal variable, or equivalently, a linear sum of independent non-central chi-square variables and a normal variable. Try the Getting Started guide for a quick demo of all the functions.</param.description>
+    <param.screenshot>${PROJECT_ROOT}\gx2_icon.png</param.screenshot>
+    <param.version>1.6.1</param.version>
+    <param.output>${PROJECT_ROOT}\Generalized chi-square distribution.mltbx</param.output>
+    <param.products.name>
+      <item>Statistics and Machine Learning Toolbox</item>
+      <item>Symbolic Math Toolbox</item>
+    </param.products.name>
+    <param.products.id>
+      <item>19</item>
+      <item>15</item>
+    </param.products.id>
+    <param.products.version>
+      <item>12.0</item>
+      <item>8.6</item>
+    </param.products.version>
+    <param.platforms />
+    <param.guid>6f9f2474-f422-495e-a245-dd928544dd14</param.guid>
+    <param.exclude.filters>% List files contained in your toolbox folder that you would like to exclude
+% from packaging.  Excludes should be listed relative to the toolbox folder.
+% Some examples of how to specify excludes are provided below:
+%
+% A single file in the toolbox folder:
+% .svn
+%
+% A single file in a subfolder of the toolbox folder:
+% example/.svn
+%
+% All files in a subfolder of the toolbox folder:
+% example/*
+%
+% All files of a certain name in all subfolders of the toolbox folder:
+% **/.svn
+%
+% All files matching a pattern in all subfolders of the toolbox folder:
+% **/*.bak
+%
+gx2_icon.png</param.exclude.filters>
+    <param.exclude.pcodedmfiles>true</param.exclude.pcodedmfiles>
+    <param.examples>&lt;?xml version="1.0" encoding="utf-8"?&gt;
+&lt;examples&gt;
+   &lt;exampleCategory name="doc"&gt;
+      &lt;example name="GettingStarted" type="html"&gt;
+         &lt;file type="source"&gt;/doc/html/GettingStarted.html&lt;/file&gt;
+         &lt;file type="main"&gt;/doc/GettingStarted.mlx&lt;/file&gt;
+         &lt;file type="thumbnail"/&gt;
+      &lt;/example&gt;
+   &lt;/exampleCategory&gt;
+&lt;/examples&gt;</param.examples>
+    <param.demosxml />
+    <param.apps />
+    <param.registered.apps />
+    <param.docs />
+    <param.getting.started.guide>${PROJECT_ROOT}\doc\GettingStarted.mlx</param.getting.started.guide>
+    <param.matlabpath.excludes />
+    <param.javaclasspath.excludes />
+    <param.exported.on.package>true</param.exported.on.package>
+    <param.required.addons />
+    <param.matlab.project.id />
+    <param.matlab.project.name />
+    <param.release.start />
+    <param.release.end />
+    <param.release.current.only>false</param.release.current.only>
+    <param.compatiblity.windows>true</param.compatiblity.windows>
+    <param.compatiblity.macos>true</param.compatiblity.macos>
+    <param.compatiblity.linux>true</param.compatiblity.linux>
+    <param.compatiblity.matlabonline>true</param.compatiblity.matlabonline>
+    <param.installation.map />
+    <param.additional.sw.names />
+    <param.additional.sw.licenses />
+    <param.additional.sw.win.url />
+    <param.additional.sw.mac.url />
+    <param.additional.sw.linux.url />
+    <unset>
+      <param.authnamewatermark />
+      <param.email />
+      <param.company />
+      <param.output />
+      <param.platforms />
+      <param.exclude.pcodedmfiles />
+      <param.demosxml />
+      <param.apps />
+      <param.registered.apps />
+      <param.docs />
+      <param.matlabpath.excludes />
+      <param.javaclasspath.excludes />
+      <param.required.addons />
+      <param.matlab.project.id />
+      <param.matlab.project.name />
+      <param.release.current.only />
+      <param.compatiblity.windows />
+      <param.compatiblity.macos />
+      <param.compatiblity.linux />
+      <param.compatiblity.matlabonline />
+      <param.installation.map />
+      <param.additional.sw.names />
+      <param.additional.sw.licenses />
+      <param.additional.sw.win.url />
+      <param.additional.sw.mac.url />
+      <param.additional.sw.linux.url />
+    </unset>
+    <fileset.rootdir>
+      <file>${PROJECT_ROOT}</file>
+    </fileset.rootdir>
+    <fileset.rootfiles>
+      <file>${PROJECT_ROOT}\demos.xml</file>
+      <file>${PROJECT_ROOT}\doc</file>
+      <file>${PROJECT_ROOT}\gx2_params_norm_quad.m</file>
+      <file>${PROJECT_ROOT}\gx2cdf.m</file>
+      <file>${PROJECT_ROOT}\gx2cdf_davies.m</file>
+      <file>${PROJECT_ROOT}\gx2cdf_imhof.m</file>
+      <file>${PROJECT_ROOT}\gx2cdf_ruben.m</file>
+      <file>${PROJECT_ROOT}\gx2inv.m</file>
+      <file>${PROJECT_ROOT}\gx2pdf.m</file>
+      <file>${PROJECT_ROOT}\gx2rnd.m</file>
+      <file>${PROJECT_ROOT}\gx2stat.m</file>
+    </fileset.rootfiles>
+    <fileset.depfun.included />
+    <fileset.depfun.excluded />
+    <fileset.package />
+    <build-deliverables>
+      <file location="${PROJECT_ROOT}" name="Generalized chi-square distribution.mltbx" optional="false">C:\Users\abhra\Google Drive\Geisler Lab\IntClassNorm\gx2\Generalized chi-square distribution.mltbx</file>
+    </build-deliverables>
+    <workflow />
+    <matlab>
+      <root>C:\Program Files\MATLAB\R2020b</root>
+      <toolboxes />
+    </matlab>
+    <platform>
+      <unix>false</unix>
+      <mac>false</mac>
+      <windows>true</windows>
+      <win2k>false</win2k>
+      <winxp>false</winxp>
+      <vista>false</vista>
+      <linux>false</linux>
+      <solaris>false</solaris>
+      <osver>10.0</osver>
+      <os32>false</os32>
+      <os64>true</os64>
+      <arch>win64</arch>
+      <matlab>true</matlab>
+    </platform>
+  </configuration>
+</deployment-project>

gx2_params_norm_quad.m

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+function [lambda,m,delta,sigma,c]=gx2_params_norm_quad(mu,v,quad)
+
+	% GX2_PARAMS_NORM_QUAD A quadratic form of a normal variable is distributed
+	% as a generalized chi-squared. This function takes the normal parameters
+	% and the quadratic coeffs and returns the parameters of the generalized
+	% chi-squared.
+	%
+	% Abhranil Das <abhranil.das@utexas.edu>
+	% Center for Perceptual Systems, University of Texas at Austin
+	% If you use this code, please cite:
+	% <a href="matlab:web('https://arxiv.org/abs/2012.14331')"
+	% >A method to integrate and classify normal distributions</a>.
+	%
+	% Example:
+	% mu=[1;2]; % mean
+	% v=[2 1; 1 3]; % covariance matrix
+	% % Say q(x)=(x1+x2)^2-x1-1 = [x1;x2]'*[1 1; 1 1]*[x1;x2] + [-1;0]'*[x1;x2] - 1:
+	% quad.q2=[1 1; 1 1];
+	% quad.q1=[-1;0];
+	% quad.q0=-1;
+	%
+	% [lambda,m,delta,sigma,c]=gx2_params_norm_quad(mu,v,quad)
+	%
+	% Required inputs:
+	% mu        column vector of normal mean
+	% v         normal covariance matrix
+	% quad      struct with quadratic form coefficients:
+	%               q2      matrix of quadratic coefficients
+	%               q1      column vector of linear coefficients
+	%               q0      scalar constant
+	%
+	% Outputs:
+	% lambda    row vector of coefficients of the non-central chi-squares
+	% m         row vector of degrees of freedom of the non-central chi-squares
+	% delta     row vector of non-centrality paramaters (sum of squares of
+	%           means) of the non-central chi-squares
+	% sigma     sd of normal term
+	% c         constant term
+    %
+    % See also:
+	% <a href="matlab:open(strcat(fileparts(which('gx2cdf')),filesep,'doc',filesep,'GettingStarted.mlx'))">Interactive demos</a>
+	% gx2rnd
+	% gx2stat
+    % gx2cdf
+    % gx2pdf
+
+	% standardize the space
+	q2s=0.5*(quad.q2+quad.q2'); % symmetrize q2
+	q2=sqrtm(v)*q2s*sqrtm(v);
+	q1=sqrtm(v)*(2*q2s*mu+quad.q1);
+	q0=mu'*q2s*mu+quad.q1'*mu+quad.q0;
+
+	[R,D]=eig(q2);
+	d=diag(D)';
+	b=(R'*q1)';
+
+	[lambda,~,ic]=unique(nonzeros(d)'); % unique non-zero eigenvalues
+	m=accumarray(ic,1)'; % total dof of each eigenvalue
+	delta=arrayfun(@(x) sum((b(d==x)).^2),lambda)./(4*lambda.^2); % total non-centrality for each eigenvalue
+	sigma=norm(b(~d));
+	c=q0-sum(lambda.*delta);

gx2cdf.m

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+function p=gx2cdf(x,lambda,m,delta,sigma,c,varargin)
+
+	% GX2CDF Returns the cdf of a generalized chi-squared (a weighted sum of
+	% non-central chi-squares and a normal), using Ruben's [1962] method,
+	% Davies' [1973] method, or the native ncx2cdf, depending on the input.
+	%
+	% Abhranil Das <abhranil.das@utexas.edu>
+	% Center for Perceptual Systems, University of Texas at Austin
+	% If you use this code, please cite:
+	% <a href="matlab:web('https://arxiv.org/abs/2012.14331')"
+	% >A method to integrate and classify normal distributions</a>.
+	%
+	% Usage:
+	% p=gx2cdf(x,lambda,m,delta,sigma,c)
+	% p=gx2cdf(x,lambda,m,delta,sigma,c,'upper')
+	% p=gx2cdf(x,lambda,m,delta,sigma,c,'AbsTol',0,'RelTol',1e-7)
+	%
+	% Example:
+	% f=gx2pdf(25,[1 -5 2],[1 2 3],[2 3 7],5,0)
+	%
+	% Required inputs:
+	% x         points at which to evaluate the CDF
+	% lambda    row vector of coefficients of the non-central chi-squares
+	% m         row vector of degrees of freedom of the non-central chi-squares
+	% delta     row vector of non-centrality paramaters (sum of squares of
+	%           means) of the non-central chi-squares
+	% sigma     sd of normal term
+	% c         constant term
+	%
+	% Optional positional input:
+	% 'upper'   more accurate estimate of the complementary CDF when it's small
+	%
+	% Optional name-value inputs:
+	% 'AbsTol'  absolute error tolerance for the output
+	% 'RelTol'  relative error tolerance for the output
+	%           The absolute OR the relative tolerance is satisfied.
+	%
+	% Output:
+	% p         computed cdf
+    %
+	% See also:
+	% <a href="matlab:open(strcat(fileparts(which('gx2cdf')),filesep,'doc',filesep,'GettingStarted.mlx'))">Interactive demos</a>
+	% gx2cdf_davies
+	% gx2cdf_imhof
+    % gx2cdf_ruben
+    % gx2pdf
+
+	parser = inputParser;
+	parser.KeepUnmatched = true;
+	addRequired(parser,'x',@(x) isreal(x));
+	addRequired(parser,'lambda',@(x) isreal(x) && isrow(x));
+	addRequired(parser,'m',@(x) isreal(x) && isrow(x));
+	addRequired(parser,'delta',@(x) isreal(x) && isrow(x));
+	addRequired(parser,'sigma',@(x) isreal(x) && isscalar(x));
+	addRequired(parser,'c',@(x) isreal(x) && isscalar(x));
+	addOptional(parser,'side','lower',@(x) strcmpi(x,'lower') || strcmpi(x,'upper') );
+	addParameter(parser,'AbsTol',1e-10,@(x) isreal(x) && isscalar(x) && (x>=0));
+	addParameter(parser,'RelTol',1e-6,@(x) isreal(x) && isscalar(x) && (x>=0));
+
+	parse(parser,x,lambda,m,delta,sigma,c,varargin{:});
+	side=parser.Results.side;
+
+	if ~sigma && length(unique(lambda))==1
+		% native ncx2 fallback
+		if (sign(unique(lambda))==1 && strcmpi(side,'lower')) || (sign(unique(lambda))==-1 && strcmpi(side,'upper'))
+			p=ncx2cdf((x-c)/unique(lambda),sum(m),sum(delta));
+		else
+			p=ncx2cdf((x-c)/unique(lambda),sum(m),sum(delta),'upper');
+		end
+	elseif ~sigma && (all(lambda>0)||all(lambda<0))
+		try
+			p=gx2cdf_ruben(x,lambda,m,delta,c,varargin{:});
+		catch
+			p=gx2cdf_davies(x,lambda,m,delta,sigma,c,varargin{:});
+		end
+	else
+		p=gx2cdf_davies(x,lambda,m,delta,sigma,c,varargin{:});
+	end