getLogPDF.m File Reference

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Functions
function	getLogPDF (in x, in mean, in invcov)
	Return the corresponding natural logarithm(s) of Probability Density Function (PDF) of the input ndim-dimensional multivariate Normal random vector(s). More...

Function Documentation

getLogPDF()

function getLogPDF	(	in	x,
		in	mean,
		in	invcov
	)

Return the corresponding natural logarithm(s) of Probability Density Function (PDF) of the input ndim-dimensional multivariate Normal random vector(s).

This log-PDF function can be potentially faster and more flexible than the intrinsic MATLAB equivalent because it optionally accepts vectors of MVN random variates and returns the natural logarithm of the density function which avoids a costly exponentiation.

Parameters

[in]	x	: The input vector of shape [ndim, nvec] of MATLAB real, representing the set of nvec MVN vectors from the ndim-dimensional MVN space.
[in]	mean	: The input vector of shape [ndim, 1] of MATLAB real, representing the mean of a Multivariate Normal distribution in size(mean) dimensional space. If the input value is empty, it is set to the default value. (optional. default = zeros(ndim, 1).)
[in]	invcov	: The input positive-definite square matrix of shape [ndim, ndim] of MATLAB real, representing the inverse of the covariance matrix of the target Multivariate Normal distribution in numel(mean) dimensional space. If the input value is empty, it is set to the default value. Note that the inverse covariance matrix can be readily obtained from its lower or upper Cholesky factorization (cholow or choupp) via pm.matlab.inv(cholow) or pm.matlab.inv(choupp'). (optional. default = eye(ndim, ndim).)

Returns

logPDF : The output column vector of MATLAB real of shape [nvec, 1] containing the natural logarithm(s) of the input MVN vector(s).

Possible calling interfaces ⛓

logPDF = pm.stats.dist.mvn.getLogPDF(x)
logPDF = pm.stats.dist.mvn.getLogPDF(x, mean)
logPDF = pm.stats.dist.mvn.getLogPDF(x, [], invcov)
logPDF = pm.stats.dist.mvn.getLogPDF(x, mean, invcov)

Example usage ⛓

cd(fileparts(mfilename('fullpath'))); % Change working directory to source code directory.
addpath('../../../../../'); % Add the ParaMonte library root directory to the search path.
 
pm.matlab.show()
pm.matlab.show("pdf = exp(pm.stats.dist.mvn.getLogPDF([1, 2, 3]'))")
                pdf = exp(pm.stats.dist.mvn.getLogPDF([1, 2, 3]'))
pm.matlab.show("pdf_ref = mvnpdf([1, 2, 3]')")
                pdf_ref = mvnpdf([1, 2, 3]')
assert(abs(pdf - pdf_ref) < 1.e-12)
 
pm.matlab.show()
pm.matlab.show('mean = [-3, 3]; cholow = chol([1 -.9; -.9, 1], "lower")')
                mean = [-3, 3]; cholow = chol([1 -.9; -.9, 1], "lower");
pm.matlab.show('sample = pm.stats.dist.mvn.getRand(mean, cholow, 1000);')
                sample = pm.stats.dist.mvn.getRand(mean, cholow, 1000);
pm.matlab.show("sample = array2table([sample', exp(pm.stats.dist.mvn.getLogPDF(sample, mean, pm.matrix.inv(cholow)))]);")
                sample = array2table([sample', exp(pm.stats.dist.mvn.getLogPDF(sample, mean, pm.matrix.inv(cholow)))]);
pm.matlab.show('sample.Properties.VariableNames = ["X", "Y", "MVN PDF"];')
                sample.Properties.VariableNames = ["X", "Y", "MVN PDF"];
pm.matlab.show('p = pm.vis.PlotScatter3(sample, "colx", 1, "coly", 2, "colz", 3, "colc", 3); p.make();')
                p = pm.vis.PlotScatter3(sample, "colx", 1, "coly", 2, "colz", 3, "colc", 3); p.make();
pm.matlab.show('pm.vis.figure.savefig("mvn.getLogPDF.scatter.3d.png", "-m4");')
                pm.vis.figure.savefig("mvn.getLogPDF.scatter.3d.png", "-m4");

Example output ⛓

 
pdf = exp(pm.stats.dist.mvn.getLogPDF([1, 2, 3]'))
pdf =
     5.789870153591850e-05
pdf_ref = mvnpdf([1, 2, 3]')
pdf_ref =
     5.789870153591850e-05
 
mean = [-3, 3]; cholow = chol([1 -.9; -.9, 1], "lower")
sample = pm.stats.dist.mvn.getRand(mean, cholow, 1000);
sample = array2table([sample', exp(pm.stats.dist.mvn.getLogPDF(sample, mean, pm.matrix.inv(cholow)))]);
sample.Properties.VariableNames = ["X", "Y", "MVN PDF"];
p = pm.vis.PlotScatter3(sample, "colx", 1, "coly", 2, "colz", 3, "colc", 3); p.make();
pm.vis.figure.savefig("mvn.getLogPDF.scatter.3d.png", "-m4");

Visualization of the example output ⛓

Final Remarks ⛓

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Copyright

Computational Data Science Lab

Author:

Joshua Alexander Osborne, May 21 2024, 12:06 AM, University of Texas at Arlington
Fatemeh Bagheri, May 20 2024, 1:25 PM, NASA Goddard Space Flight Center (GSFC), Washington, D.C.
Amir Shahmoradi, May 16 2016, 9:03 AM, Oden Institute for Computational Engineering and Sciences (ICES), UT Austin