Multi Dimension Matrix Elements multiplication

Hello,

I am strugling with some matrix multiplication...

I am having one M: matrix and one N: matrix with some given elements. Elements of M are given as whereas elements of N are given as . I wish to obtain maxtrix P: whose elements , and . Thus, matrix would be in my case.

Does anyone know how to perform this complex operation in the fastest way (without loops)?

Thanks in advance

Answer 1

[Rik]

Not completely without loops, but this should be fast enough. You should also be aware that loops can sometimes be the fastest way.

M=rand(3,2);N=rand(2,3,4);
%prime the execution engine to produce a more reliable comparison
timeit(@()option1(M,N));

timeit(@()option1(M,N))

ans = 1.5263e-05

timeit(@()option2(M,N))

ans = 5.3950e-06

isequal(option1(M,N),option2(M,N))

ans = logical
   1

function P=option1(M,N)
P=zeros(size(M,1),size(N,2),size(N,3));
for n=1:size(M,1)
    P(n,:,:)=M(n,1)*N(1,:,:)+M(n,2)*N(2,:,:);
end
end
function P=option2(M,N)
P=zeros(size(M,1),size(N,2),size(N,3));
for i=1:size(M,1)
    for j=1:size(N,2)
        for k=1:size(N,3)
            P(i,j,k)=M(i,1)*N(1,j,k)+M(i,2)*N(2,j,k);
        end
    end
end
end

Answer 2

[Steven Lord]

If you're using release R2020b or later, see the pagemtimes function.