multivariate gaussian distribution

multivariate gaussian distribution

[Emmanuel Benazera]

Hi,

I've written a few lines of code that implement a multivariate
gaussian distribution. The function takes the eigenvalues/vectors
decomposition of the covariance matrix as input, and outputs a
random vector. In dimension n, it proceeds to n gsl_ran_gaussian
calls, plus a blas level 2 product. It fits in the GSL framework.

I guess it may be useful to other GSL users. Should it be added
to the library ? I can provide the piece of code + doc + theoretical 
reference.

Regards,

Emmanuel

Re: multivariate gaussian distribution

[Brian Gough]

Emmanuel Benazera writes:
 > I've written a few lines of code that implement a multivariate
 > gaussian distribution. The function takes the eigenvalues/vectors
 > decomposition of the covariance matrix as input, and outputs a
 > random vector. In dimension n, it proceeds to n gsl_ran_gaussian
 > calls, plus a blas level 2 product. It fits in the GSL framework.
 > 
 > I guess it may be useful to other GSL users. Should it be added
 > to the library ? I can provide the piece of code + doc + theoretical 
 > reference.

Certainly feel free to send it to the list or post it on a webpage
somewhere.

-- 
Brian Gough

Re: multivariate gaussian distribution (Code)

[Emmanuel Benazera]

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Hi,

here is a tarball. Hope it helps.

Happy holidays,

Emmanuel

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Re: multivariate gaussian distribution (Code)

[Brian Gough]

Emmanuel Benazera writes:
 > Hi,
 > 
 > here is a tarball. Hope it helps.
 > 

Is there any advantage of LU over Cholesky decomposition?

-- 
Brian Gough

Network Theory Ltd
15 Royal Park
Bristol BS8 3AL
United Kingdom

Tel: +44 (0)117 3179309
Fax: +44 (0)117 9048108
Web: http://www.network-theory.co.uk/

Re: multivariate gaussian distribution (Code)

[Emmanuel Benazera]

Hi Brian,

I remember reading that the matrix decomposition through
eigensystems was more 'stable', while Cholesky was
probably faster. See the implementation in R:
http://rweb.stat.umn.edu/R/library/MASS/html/mvrnorm.html

I used the LU for determinant and matrix inverse only.
I'm not an expert in this field though...

Emmanuel

P.S.: in my opinion the multivariate_gaussian_pdf_LU is rather
useless, because for repeated calls, you want the inverse
 to be computed once and for all.

On Mon, Dec 29, 2003 at 11:41:10AM +0000, Brian Gough wrote:
> Emmanuel Benazera writes:
>  > Hi,
>  > 
>  > here is a tarball. Hope it helps.
>  > 
> 
> Is there any advantage of LU over Cholesky decomposition?
> 
> -- 
> Brian Gough
> 
> Network Theory Ltd
> 15 Royal Park
> Bristol BS8 3AL
> United Kingdom
> 
> Tel: +44 (0)117 3179309
> Fax: +44 (0)117 9048108
> Web: http://www.network-theory.co.uk/

Re: multivariate gaussian distribution (Code) / bugfix

[Emmanuel Benazera]

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Hi Brian,

There was an ugly bug in files I sent to this list a few months
ago. Someone kindly pointed it to me. So here is an updated version.

I've added a function that uses the Cholesky decomposition. On a simple
example, results appear deceiving compared to the LU decomposition.
Someone here would like to investigate further (code + results) before
using this function.

Btw, alpha doesn't appear in functions for triangular matrix that are 
described p.117 of gsl-ref.

cheers,

Emmanuel

On Mon, Dec 29, 2003 at 11:41:10AM +0000, Brian Gough wrote:
> Emmanuel Benazera writes:
>  > Hi,
>  > 
>  > here is a tarball. Hope it helps.
>  > 
> 
> Is there any advantage of LU over Cholesky decomposition?
> 
> -- 
> Brian Gough
> 

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