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These generate random samples from a multivariate distribution | These generate random samples from a multivariate distribution | ||
| − | - You can use mvnrnd(mu,sigma) function in Matlab. (See details below) | + | - You can use mvnrnd(mu,sigma) function in Matlab. (See details below) |
| − | - You can use the technique of [Generating Gaussian Samples] (which is good theory to know). | + | - You can use the technique of [Generating Gaussian Samples] (which is good theory to know). |
This calculates the [pdf] function of the multivariate distribution | This calculates the [pdf] function of the multivariate distribution | ||
| − | - You can use `multigauss.m <multigauss.m>`_ | + | - You can use `multigauss.m <multigauss.m>`_ |
| + | |||
| + | Forum | ||
| + | ========= | ||
From jin-young.kim.1 Tue Feb 12 11:54:56 -0500 2008 | From jin-young.kim.1 Tue Feb 12 11:54:56 -0500 2008 | ||
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Message-ID: <20080212115456-0500@https://engineering.purdue.edu> | Message-ID: <20080212115456-0500@https://engineering.purdue.edu> | ||
| − | => You can use mvnrnd(mu,sigma) function in Matlab. | + | => You can use mvnrnd(mu,sigma) function in Matlab. |
:: | :: | ||
| − | MVNRND Random vectors from the multivariate normal distribution. | + | MVNRND Random vectors from the multivariate normal distribution. |
| − | R = MVNRND(MU,SIGMA) returns an N-by-D matrix R of random vectors | + | R = MVNRND(MU,SIGMA) returns an N-by-D matrix R of random vectors |
| − | chosen from the multivariate normal distribution with mean vector MU, | + | chosen from the multivariate normal distribution with mean vector MU, |
| − | and covariance matrix SIGMA. MU is an N-by-D matrix, and MVNRND | + | and covariance matrix SIGMA. MU is an N-by-D matrix, and MVNRND |
| − | generates each row of R using the corresponding row of MU. SIGMA is a | + | generates each row of R using the corresponding row of MU. SIGMA is a |
| − | D-by-D symmetric positive semi-definite matrix, or a D-by-D-by-N array. | + | D-by-D symmetric positive semi-definite matrix, or a D-by-D-by-N array. |
| − | If SIGMA is an array, MVNRND generates each row of R using the | + | If SIGMA is an array, MVNRND generates each row of R using the |
| − | corresponding page of SIGMA, i.e., MVNRND computes R(I,:) using MU(I,:) | + | corresponding page of SIGMA, i.e., MVNRND computes R(I,:) using MU(I,:) |
| − | and SIGMA(:,:,I). If MU is a 1-by-D vector, MVNRND replicates it to | + | and SIGMA(:,:,I). If MU is a 1-by-D vector, MVNRND replicates it to |
| − | match the trailing dimension of SIGMA. | + | match the trailing dimension of SIGMA. |
| − | + | ||
| − | R = MVNRND(MU,SIGMA,N) returns a N-by-D matrix R of random vectors | + | R = MVNRND(MU,SIGMA,N) returns a N-by-D matrix R of random vectors |
| − | chosen from the multivariate normal distribution with 1-by-D mean | + | chosen from the multivariate normal distribution with 1-by-D mean |
| − | vector MU, and D-by-D covariance matrix SIGMA. | + | vector MU, and D-by-D covariance matrix SIGMA. |
| − | + | ||
| − | Example: | + | Example: |
| − | mu = [1 -1]; Sigma = [.9 .4; .4 .3]; | + | mu = [1 -1]; Sigma = [.9 .4; .4 .3]; |
| − | r = mvnrnd(mu, Sigma, 500); | + | r = mvnrnd(mu, Sigma, 500); |
| − | plot(r(:,1),r(:,2),'.'); | + | plot(r(:,1),r(:,2),'.'); |
| − | + | ||
| − | See also mvtrnd, mvnpdf, mvncdf, normrnd. | + | |
| + | See also mvtrnd, mvnpdf, mvncdf, normrnd. | ||
| − | Reference page in Help browser | + | Reference page in Help browser |
| − | doc mvnrnd | + | doc mvnrnd |
Ref: Matlab Help | Ref: Matlab Help | ||
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Message-ID: <20080212230917-0500@https://engineering.purdue.edu> | Message-ID: <20080212230917-0500@https://engineering.purdue.edu> | ||
| − | I worked out a proof for using the Cholsky decomposition of the covariance matrix for [Generating Gaussian Samples]. I suppose you could use this if you were not going to use Matlab, which, as I have found here, already has a canned function for this type of sampling | + | I worked out a proof for using the Cholsky decomposition of the covariance matrix for [Generating Gaussian Samples]. I suppose you could use this if you were not going to use Matlab, which, as I have found here, already has a canned function for this type of sampling |
Revision as of 17:42, 19 March 2008
There are several ways to create multi-variate data in matlab
These generate random samples from a multivariate distribution
- You can use mvnrnd(mu,sigma) function in Matlab. (See details below) - You can use the technique of [Generating Gaussian Samples] (which is good theory to know).
This calculates the [pdf] function of the multivariate distribution
- You can use `multigauss.m <multigauss.m>`_
Forum
=
From jin-young.kim.1 Tue Feb 12 11:54:56 -0500 2008 From: jin-young.kim.1 Date: Tue, 12 Feb 2008 11:54:56 -0500 Subject: How to generate multivariate normal distribution using Matlab Message-ID: <20080212115456-0500@https://engineering.purdue.edu>
=> You can use mvnrnd(mu,sigma) function in Matlab.
MVNRND Random vectors from the multivariate normal distribution.
R = MVNRND(MU,SIGMA) returns an N-by-D matrix R of random vectors
chosen from the multivariate normal distribution with mean vector MU,
and covariance matrix SIGMA. MU is an N-by-D matrix, and MVNRND
generates each row of R using the corresponding row of MU. SIGMA is a
D-by-D symmetric positive semi-definite matrix, or a D-by-D-by-N array.
If SIGMA is an array, MVNRND generates each row of R using the
corresponding page of SIGMA, i.e., MVNRND computes R(I,:) using MU(I,:)
and SIGMA(:,:,I). If MU is a 1-by-D vector, MVNRND replicates it to
match the trailing dimension of SIGMA.
R = MVNRND(MU,SIGMA,N) returns a N-by-D matrix R of random vectors
chosen from the multivariate normal distribution with 1-by-D mean
vector MU, and D-by-D covariance matrix SIGMA.
Example:
mu = [1 -1]; Sigma = [.9 .4; .4 .3];
r = mvnrnd(mu, Sigma, 500);
plot(r(:,1),r(:,2),'.');
See also mvtrnd, mvnpdf, mvncdf, normrnd.
Reference page in Help browser
doc mvnrnd
Ref: Matlab Help
Here is another way to do so (probably what mvnrnd.m is doing in the first place): GeneratingGaussianSamples
From landis.m.huffman.1 Tue Feb 12 23:09:17 -0500 2008 From: landis.m.huffman.1 Date: Tue, 12 Feb 2008 23:09:17 -0500 Subject: Generating Gaussian Samples Message-ID: <20080212230917-0500@https://engineering.purdue.edu>
I worked out a proof for using the Cholsky decomposition of the covariance matrix for [Generating Gaussian Samples]. I suppose you could use this if you were not going to use Matlab, which, as I have found here, already has a canned function for this type of sampling
