HermiteF_nd.m

function poly = HermiteF_nd(x, ndim, norder)
%
% HermiteF_nd.m - Compute multi-dimensional Hermite polynomials
%           up to a given order at a given coordinate.
%
% Syntax:   poly = HermiteF_nd(x, ndim, norder);
%
% Input :   x = (1,ndim) array containing a ndim-coordinates
%           ndim = dimension of space
%           norder = highest order of polynomials returned.
%
% Output:   poly = (1, nterm) array. All nterm polynomials evaluated at x.
%
% by Dongbin Xiu   11/09/2005
%

ntmp = length(x);

if ntmp ~= ndim
    fprintf('Incompatible dimension in JacobiF_nd! Quit.\n');
end

pmatrix = chaos_sequence(ndim,norder);
ptmp = zeros(norder+1,ndim);
for n=0:norder
    ptmp(n+1,:) = HermiteF(x,n);
end

[nterm,ntmp]=size(pmatrix);
poly = ones(1, nterm);

for m=2:nterm
    for n=1:ndim
        poly(m) = poly(m) * ptmp(pmatrix(m,n)+1,n);
    end
end