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Hello, I am attempting to multiply a 5D 3x3x3x3x3 matrix and a 5D 3x3x3x3x1 matrix in order to produce a 4D matrix of 3x3x3x3 after squeeze operation is applied.

Here's is what it would look like in an equation.

Multiplying a 3x3 by a 3x1 works no problem,

A = ones(3,1);

B = ones(3,3);

C = B*A;

However when I try to extend this to higher orders, I recieve and error

A = ones(3,3,3,3,1);

B = ones(3,3,3,3,3);

C = B*A;

The error suggests I use pagemtimes, but I'm not so sure those are the correct operations for my application. How would I go about coding this correctly?

EDIT: I believe I might have found the right answer, but not sure. The code below leads me to believe this might be correct

A = ones(3,1,3);

B = ones(3,3,3);

C = pagemtimes(B,A);

which would then exent to

A = ones(3,1,3,3,3);

B = ones(3,3,3,3,3);

C = pagemtimes(B,A);

EDIT2: Yes the above works, you can check it will the code below

clear all

a = 10;

%% Convert 3D matrix to 5D for tensor matrix multiplication

Bx = 1*ones(a,a,a);

By = 2*ones(a,a,a);

Bz = 3*ones(a,a,a);

B(1,1,:,:,:) = Bx;

B(2,1,:,:,:) = By;

B(3,1,:,:,:) = Bz;

%% Generate 5D tensor matrix

exx = 1*ones(a,a,a);

exy = 2*ones(a,a,a);

exz = 3*ones(a,a,a);

eyx = 4*ones(a,a,a);

eyy = 5*ones(a,a,a);

eyz = 6*ones(a,a,a);

ezx = 7*ones(a,a,a);

ezy = 8*ones(a,a,a);

ezz = 9*ones(a,a,a);

eT(1,1,:,:,:) = exx;

eT(1,2,:,:,:) = exy;

eT(1,3,:,:,:) = exz;

eT(2,1,:,:,:) = eyx;

eT(2,2,:,:,:) = eyy;

eT(2,3,:,:,:) = eyz;

eT(3,1,:,:,:) = ezx;

eT(3,2,:,:,:) = ezy;

eT(3,3,:,:,:) = ezz;

%% Multiply 3x3 3D matrix by 3x1 3D matrix

A = pagemtimes(eT,B);

%% Convert 5D matrix into 3 3D matrix components

Ax = squeeze(A(1,1,:,:,:));

Ay = squeeze(A(2,1,:,:,:));

Az = squeeze(A(3,1,:,:,:));

%% Ax should = 14 at each location

%% Ay should = 32 at each location

%% Az should = 50 at each location

James Tursa
on 25 May 2021

You may need to permute your arrays first to get your desired 2D slices in the first two dimensions.

A = whatever

B = whatever

Ap = permute(A,[4 5 1 2 3]);

Bp = permute(B,[4 5 1 2 3]);

Then use pagemtimes

C = pagemtimes(Bp,Ap);

Then if needed you can permute the answer back

C = permute(C,[3 4 5 1 2]);

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