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hermite_five_1d.m
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167 lines (138 loc) · 4.2 KB
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function e = hermite_five_1d(p)
%
% hermite_five_1d.m - Evaluate the inner product of 1d Hermite-chaos with
% entries
%
% Syntax e = hermite_five_1d(p)
%
% Input: p = order of Hermite-chaos
%
% Output: e = (p+1)^5 matrix containing the result
% as integers.
%
% By Dongbin Xiu 9/11/2002
%
e = zeros(p+1,p+1,p+1,p+1, p+1);
np = ceil((5*p+1)/2);
[z,w] = HermiteZW(np);
factor = sqrt(pi);
J = zeros(p+1, np);
for order=0:p
J(order+1, :) = HermiteF(z', order);
end
for i=1:p+1
for j=i:p+1
for k=j:p+1
for l=k:p+1
for m=l:p+1
e(i,j,k,l,m)=sum(J(i,:).*J(j,:).*J(k,:).*J(l,:).*J(m,:).*w')/factor;
e(i,j,k,l,m) = round(e(i,j,k,l,m)); % e_ijk are integers
e(i,k,j,l,m) = e(i,j,k,l,m);
e(j,i,k,l,m) = e(i,j,k,l,m);
e(j,k,i,l,m) = e(i,j,k,l,m);
e(k,i,j,l,m) = e(i,j,k,l,m);
e(k,j,i,l,m) = e(i,j,k,l,m);
e(i,k,l,j,m) = e(i,j,k,l,m);
e(j,i,l,k,m) = e(i,j,k,l,m);
e(j,k,l,i,m) = e(i,j,k,l,m);
e(k,i,l,j,m) = e(i,j,k,l,m);
e(k,j,l,i,m) = e(i,j,k,l,m);
e(i,l,k,j,m) = e(i,j,k,l,m);
e(j,l,i,k,m) = e(i,j,k,l,m);
e(j,l,k,i,m) = e(i,j,k,l,m);
e(k,l,i,j,m) = e(i,j,k,l,m);
e(k,l,j,i,m) = e(i,j,k,l,m);
e(l,i,k,j,m) = e(i,j,k,l,m);
e(l,j,i,k,m) = e(i,j,k,l,m);
e(l,j,k,i,m) = e(i,j,k,l,m);
e(l,k,i,j,m) = e(i,j,k,l,m);
e(l,k,j,i,m) = e(i,j,k,l,m);
% ------------------------------------------
e(i,k,j,m,l) = e(i,j,k,l,m);
e(j,i,k,m,l) = e(i,j,k,l,m);
e(j,k,i,m,l) = e(i,j,k,l,m);
e(k,i,j,m,l) = e(i,j,k,l,m);
e(k,j,i,m,l) = e(i,j,k,l,m);
e(i,k,l,m,j) = e(i,j,k,l,m);
e(j,i,l,m,k) = e(i,j,k,l,m);
e(j,k,l,m,i) = e(i,j,k,l,m);
e(k,i,l,m,j) = e(i,j,k,l,m);
e(k,j,l,m,i) = e(i,j,k,l,m);
e(i,l,k,m,j) = e(i,j,k,l,m);
e(j,l,i,m,k) = e(i,j,k,l,m);
e(j,l,k,m,i) = e(i,j,k,l,m);
e(k,l,i,m,j) = e(i,j,k,l,m);
e(k,l,j,m,i) = e(i,j,k,l,m);
e(l,i,k,m,j) = e(i,j,k,l,m);
e(l,j,i,m,k) = e(i,j,k,l,m);
e(l,j,k,m,i) = e(i,j,k,l,m);
e(l,k,i,m,j) = e(i,j,k,l,m);
e(l,k,j,m,i) = e(i,j,k,l,m);
% ------------------------------------------
e(i,k,m,j,l) = e(i,j,k,l,m);
e(j,i,m,k,l) = e(i,j,k,l,m);
e(j,k,m,i,l) = e(i,j,k,l,m);
e(k,i,m,j,l) = e(i,j,k,l,m);
e(k,j,m,i,l) = e(i,j,k,l,m);
e(i,k,m,l,j) = e(i,j,k,l,m);
e(j,i,m,l,k) = e(i,j,k,l,m);
e(j,k,m,l,i) = e(i,j,k,l,m);
e(k,i,m,l,j) = e(i,j,k,l,m);
e(k,j,m,l,i) = e(i,j,k,l,m);
e(i,l,m,k,j) = e(i,j,k,l,m);
e(j,l,m,i,k) = e(i,j,k,l,m);
e(j,l,m,k,i) = e(i,j,k,l,m);
e(k,l,m,i,j) = e(i,j,k,l,m);
e(k,l,m,j,i) = e(i,j,k,l,m);
e(l,i,m,k,j) = e(i,j,k,l,m);
e(l,j,m,i,k) = e(i,j,k,l,m);
e(l,j,m,k,i) = e(i,j,k,l,m);
e(l,k,m,i,j) = e(i,j,k,l,m);
e(l,k,m,j,i) = e(i,j,k,l,m);
% ------------------------------------------
e(i,m,k,j,l) = e(i,j,k,l,m);
e(j,m,i,k,l) = e(i,j,k,l,m);
e(j,m,k,i,l) = e(i,j,k,l,m);
e(k,m,i,j,l) = e(i,j,k,l,m);
e(k,m,j,i,l) = e(i,j,k,l,m);
e(i,m,k,l,j) = e(i,j,k,l,m);
e(j,m,i,l,k) = e(i,j,k,l,m);
e(j,m,k,l,i) = e(i,j,k,l,m);
e(k,m,i,l,j) = e(i,j,k,l,m);
e(k,m,j,l,i) = e(i,j,k,l,m);
e(i,m,l,k,j) = e(i,j,k,l,m);
e(j,m,l,i,k) = e(i,j,k,l,m);
e(j,m,l,k,i) = e(i,j,k,l,m);
e(k,m,l,i,j) = e(i,j,k,l,m);
e(k,m,l,j,i) = e(i,j,k,l,m);
e(l,m,i,k,j) = e(i,j,k,l,m);
e(l,m,j,i,k) = e(i,j,k,l,m);
e(l,m,j,k,i) = e(i,j,k,l,m);
e(l,m,k,i,j) = e(i,j,k,l,m);
e(l,m,k,j,i) = e(i,j,k,l,m);
% ------------------------------------------
e(m,i,k,j,l) = e(i,j,k,l,m);
e(m,j,i,k,l) = e(i,j,k,l,m);
e(m,j,k,i,l) = e(i,j,k,l,m);
e(m,k,i,j,l) = e(i,j,k,l,m);
e(m,k,j,i,l) = e(i,j,k,l,m);
e(m,i,k,l,j) = e(i,j,k,l,m);
e(m,j,i,l,k) = e(i,j,k,l,m);
e(m,j,k,l,i) = e(i,j,k,l,m);
e(m,k,i,l,j) = e(i,j,k,l,m);
e(m,k,j,l,i) = e(i,j,k,l,m);
e(m,i,l,k,j) = e(i,j,k,l,m);
e(m,j,l,i,k) = e(i,j,k,l,m);
e(m,j,l,k,i) = e(i,j,k,l,m);
e(m,k,l,i,j) = e(i,j,k,l,m);
e(m,k,l,j,i) = e(i,j,k,l,m);
e(m,l,i,k,j) = e(i,j,k,l,m);
e(m,l,j,i,k) = e(i,j,k,l,m);
e(m,l,j,k,i) = e(i,j,k,l,m);
e(m,l,k,i,j) = e(i,j,k,l,m);
e(m,l,k,j,i) = e(i,j,k,l,m);
end
end
end
end
end