| (2 intermediate revisions by the same user not shown) | |||
| Line 2: | Line 2: | ||
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 the technique of [Generating Gaussian Samples] (which is good theory to know). | |
| − | This calculates the [ | + | This calculates the [[pdf_Old Kiwi]] function of the multivariate distribution |
| − | + | * You can use `multigauss.m <multigauss.m>`_ | |
| − | + | '''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 | + | |
From: jin-young.kim.1 | From: jin-young.kim.1 | ||
Date: Tue, 12 Feb 2008 11:54:56 -0500 | Date: Tue, 12 Feb 2008 11:54:56 -0500 | ||
Subject: How to generate multivariate normal distribution using Matlab | Subject: How to generate multivariate normal distribution using Matlab | ||
| − | 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. | |
| − | + | 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 | Ref: Matlab Help | ||
| Line 53: | Line 48: | ||
Here is another way to do so (probably what mvnrnd.m is doing in the first place): GeneratingGaussianSamples | 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 Tue Feb 12 23:09:17 -0500 2008 |
From: landis.m.huffman.1 | From: landis.m.huffman.1 | ||
Date: Tue, 12 Feb 2008 23:09:17 -0500 | Date: Tue, 12 Feb 2008 23:09:17 -0500 | ||
Subject: Generating Gaussian Samples | Subject: Generating Gaussian Samples | ||
| − | 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 | + | I worked out a proof for using the Cholsky decomposition of the covariance matrix for [[Generating Gaussian Samples_Old Kiwi]]. 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 |
Latest revision as of 16:44, 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_Old Kiwi function of the multivariate distribution
- You can use `multigauss.m <multigauss.m>`_
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_Old Kiwi. 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
