hypergeometric function in ‘ mvtnorm’

[statfan]

Is there any way to know how the "dmvt" function computes the hypergeometric function needed in the calculation for the density of multivariate t distribution?  

[Michael Weylandt]

To view the source of (most) functions, simply type funcname without
parentheses: here, you get

> dmvt

function (x, delta, sigma, df = 1, log = TRUE, type = "shifted")
{
    if (df == 0)
        return(dmvnorm(x, mean = delta, sigma = sigma, log = log))
    if (is.vector(x)) {
        x <- matrix(x, ncol = length(x))
    }
    if (missing(delta)) {
        delta <- rep(0, length = ncol(x))
    }
    if (missing(sigma)) {
        sigma <- diag(ncol(x))
    }
    if (NCOL(x) != NCOL(sigma)) {
        stop("x and sigma have non-conforming size")
    }
    if (!isSymmetric(sigma, tol = sqrt(.Machine$double.eps),
        check.attributes = FALSE)) {
        stop("sigma must be a symmetric matrix")
    }
    if (length(delta) != NROW(sigma)) {
        stop("mean and sigma have non-conforming size")
    }
    m <- NCOL(sigma)
    distval <- mahalanobis(x, center = delta, cov = sigma)
    logdet <- sum(log(eigen(sigma, symmetric = TRUE, only.values =
TRUE)$values))
    logretval <- lgamma((m + df)/2) - (lgamma(df/2) + 0.5 * (logdet +
        m * logb(pi * df))) - 0.5 * (df + m) * logb(1 + distval/df)
    if (log)
        return(logretval)
    return(exp(logretval))
}


Most of the functions in here you can see code for the same way: the
only ones you won't be able to are eigen, lgamma, log, exp, but these
methods are pretty well-documented and you shouldn't need to find code
for them. If you do, you'll need to read the underlying C.

Michael

On Sun, Mar 18, 2012 at 11:12 PM, statfan <[hidden email]> wrote:

> Is there any way to know how the "dmvt" function computes the hypergeometric
> function needed in the calculation for the density of multivariate t
> distribution?
>
> --
> View this message in context: http://r.789695.n4.nabble.com/hypergeometric-function-in-mvtnorm-tp4483730p4483730.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
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> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

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[statfan]

Thanks for your advice.  I actually meant to ask about the "pmvt" for the distribution function.  Viewing the source code "pmvt" uses the function "mvt" which uses the function "probval" which sources the fortran code:

Fortran("mvtdst", N = as.integer(n), NU = as.integer(df),
        LOWER = as.double(lower), UPPER = as.double(upper), INFIN = as.integer(infin),
        CORREL = as.double(corrF), DELTA = as.double(delta),
        MAXPTS = as.integer(x$maxpts), ABSEPS = as.double(x$abseps),
        RELEPS = as.double(x$releps), error = as.double(error),
        value = as.double(value), inform = as.integer(inform),
        PACKAGE = "mvtnorm")

I wish to look at how this "mvtdst" calculates the hypergeometric function (2_F_1).  Anyway that I can see that?
Thanks

[Berend Hasselman]

On 19-03-2012, at 16:54, statfan wrote:

> Thanks for your advice.  I actually meant to ask about the "pmvt" for the
> distribution function.  Viewing the source code "pmvt" uses the function
> "mvt" which uses the function "probval" which sources the fortran code:
>

No  it doesn't "source". It call a compiled Fortran subroutine.

> Fortran("mvtdst", N = as.integer(n), NU = as.integer(df),
>        LOWER = as.double(lower), UPPER = as.double(upper), INFIN =
> as.integer(infin),
>        CORREL = as.double(corrF), DELTA = as.double(delta),
>        MAXPTS = as.integer(x$maxpts), ABSEPS = as.double(x$abseps),
>        RELEPS = as.double(x$releps), error = as.double(error),
>        value = as.double(value), inform = as.integer(inform),
>        PACKAGE = "mvtnorm")
>
> I wish to look at how this "mvtdst" calculates the hypergeometric function
> (2_F_1).  Anyway that I can see that?

Yes. Download the source code of the package.
Obtainable from CRAN.
Unpack and browse.

Berend

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