getRand.m File Reference

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Functions
function	getRand (in mean, in cholow, in s1)
	Return a (set of) multivariate Uniform random vector(s), from within a hyper-ellipsoidal domain. More...

Function Documentation

getRand()

function getRand	(	in	mean,
		in	cholow,
		in	s1
	)

Return a (set of) multivariate Uniform random vector(s), from within a hyper-ellipsoidal domain.

The returned random vectors are uniformly distributed within the hyper-ellipsoidal domain of the Uniform distribution.

Parameters

[in]	mean	: The input vector of MATLAB real, representing the mean of a Multivariate Uniform distribution in size(mean) dimensional space. (optional. default = []. It must be present if cholow is missing.)
[in]	cholow	: The input square matrix of MATLAB real, representing the lower-triangle of the Cholesky factorization of the Gramian matrix of the target Multivariate Uniform distribution in numel(mean) dimensional space. This argument can be obtained by passing the Gramian matrix gramian of the distribution to the MATLAB intrinsic function chol(gramian, "lower"). (optional. default = []. It must be present if mean is missing.)
[in]	s1	: The input vector of MATLAB real, representing the mean of a Multivariate Uniform distribution in size(mean) dimensional space. (optional. default = 1)

Returns

rand : The output vector of MATLAB real of shape (numel(mean), 1) containing a random vector from the specified Multivariate Uniform distribution.

Possible calling interfaces ⛓

rand = pm.stats.dist.mvu.getRand(mean)
rand = pm.stats.dist.mvu.getRand([], cholow)
rand = pm.stats.dist.mvu.getRand(mean, cholow)
rand = pm.stats.dist.mvu.getRand([], cholow, s1)
rand = pm.stats.dist.mvu.getRand(mean, cholow, s1)

Example usage ⛓

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('pm.stats.dist.mvu.getRand(zeros(2, 1))')
pm.matlab.show( pm.stats.dist.mvu.getRand(zeros(2, 1)) )
 
pm.matlab.show()
pm.matlab.show('figure("color", "white"); histogram(pm.stats.dist.mvu.getRand(zeros(2, 1), [], 10000));')
                figure("color", "white"); histogram(pm.stats.dist.mvu.getRand(zeros(2, 1), [], 10000));
pm.matlab.show('pm.vis.figure.savefig("mvu.getRand.hist1.png");')
                pm.vis.figure.savefig("mvu.getRand.hist1.png");
 
pm.matlab.show()
pm.matlab.show('figure("color", "white"); histogram(pm.stats.dist.mvu.getRand([-3, 3], chol([1 .5; .5, 1], "lower"), 10000));')
                figure("color", "white"); histogram(pm.stats.dist.mvu.getRand([-3, 3], chol([1 .5; .5, 1], "lower"), 10000));
pm.matlab.show('pm.vis.figure.savefig("mvu.getRand.hist2.png");')
                pm.vis.figure.savefig("mvu.getRand.hist2.png");
 
pm.matlab.show()
pm.matlab.show('rand = pm.stats.dist.mvu.getRand([-3, 3], chol([1 .9; .9, 1], "lower"), 10000);')
                rand = pm.stats.dist.mvu.getRand([-3, 3], chol([1 .9; .9, 1], "lower"), 10000);
pm.matlab.show('figure("color", "white"); scatter(rand(1, :), rand(2, :), 5, ".");')
                figure("color", "white"); scatter(rand(1, :), rand(2, :), 5, ".");
pm.matlab.show('pm.vis.figure.savefig("mvu.getRand.scatter1.png");')
                pm.vis.figure.savefig("mvu.getRand.scatter1.png");

Visualization of the example output ⛓

Final Remarks ⛓

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For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
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Copyright

Computational Data Science Lab

Author:

Joshua Alexander Osborne, May 21 2024, 4:03 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