Use of tensorprod function to compute multilinear forms

Hi everyone,

I have to compute the multilinear form of a tensor and a vector. Suppose for example we have a 4-dimensional tensor A and a vector v. The 4-linear form is the multiplication of A by v 4 times. The only way that I found to do this is to use "for" loops. I think there must be a way to use the "tensorprod" function to perform the operation more efficiently but I can't find it. Thank you in advance to anyone who can help.

Cheers

n = 3;
A = rand(n,n,n,n);
v = rand(n,1);

for j = 1:n
    for k = 1:n
        G(:,k,j) = squeeze(v'*A(:,:,k,j));
    end
end
for j = 1:n
    J(:,j) = squeeze(v'*G(:,:,j));
end
res = v'*J*v;

Answer 1

[Matt J]

n = 3;
A = rand(n,n,n,n);
v = rand(n,1);


J=pagemtimes(v',pagemtimes(A,v));

res=v'*reshape(J,[n,n])*v

res = 2.4327

Answer 2

[Matt J]

res=A;
while ~isvector(res)
  res=pagemtimes(v',squeeze(res));
end
res=res*v

Answer 3

[Catalytic]

res=A;
for i=1:ndims(A)
 res = tensorprod(res,v,1);
end
res