MATLAB：在单元阵列中将2D矩阵与3D矩阵相乘

Question

I have a constant 2D double matrix mat1 . I also have a 2D cell array mat2 where every cell contains a 2D or 3D double matrix. These double matrices have the same number of rows and columns as mat1 . I need to dot multiply (.*) mat1 with every slice of each double matrix within mat2 . The result needs to be another cell array results with the same size as mat2 , whereby the contatining double matrices must equal the double matrices of mat2 in terms of size.

Here's my code to generate mat1 and mat2 for illustrating purposes. I am struggling at the point where the multiplication should take place.

rowCells = 5;
colCells = 3;
rowTimeSeries = 300;
colTimeSeries = 5;
slices = [1;10];

% Create 2D double matrix
mat1 = rand(rowTimeSeries, colTimeSeries);

% Create 2D cell matrix comprisiong 2D and/or 3D double matrices
mat2 = cell(rowCells,colCells);

for c = 1:colCells
    for r = 1:rowCells
        slice = randsample(slices, 1, true);
        mat2{r,c} = rand(rowTimeSeries, colTimeSeries, slice);
    end
end

% Multiply (.*) mat1 with mat2 (every slice)

results = cell(rowCells,colCells);

for c = 1:colCells
    for r = 1:rowCells
        results{r,c} = ... % I am struggling here!!!
    end
end

Answer 1

You could use bsxfun to remove the need for your custom function multiply2D3D , it works in a similar way! Updated code:

results = cell(rowCells,colCells);
for c = 1:colCells
    for r = 1:rowCells
        results{r,c} = bsxfun(@times, mat1, mat2{r,c});
    end
end

This will work for 2D and 3D matrices where the number of rows and cols is the same in each of your "slices", so it should work in your case.

---

You also don't need to loop over the rows and the columns of your cell array separately. This loop has the same number of iterations, but it is one loop not two, so the code is a little more streamlined:

results = cell(size(mat2));
for n = 1:numel(mat2)   % Loop over every element of mat2. numel(mat2) = rowCells*colCells
    results{n} = bsxfun(@times, mat1, mat2{n});
end

Answer 2

I had almost the exact same answer as Wolfie but he beat me to it.

Anyway, here is a one liner that I think is slightly nicer:

nR = rowCells; % Number of Rows
nC = colCells; % Number of Cols
results = arrayfun(@(I) bsxfun(@times, mat1, mat2{I}), reshape(1:nR*nC,[],nC), 'un',0);

This uses arrayfun to perform the loop indexing and bsxfun for the multiplications.

---

A few advantages

1) Specifying 'UniformOutput' ( 'un' ) in arrayfun returns a cell array so the results variable is also a cell array and doesn't need to be initialised (in contrast to using loops).

2) The dimensions of the indexes determine the dimensions of results at the output, so they can match what you like.

3) The single line can be used directly as an input argument to a function.

Disadvantage

1) Can run slower than using for loops as Wolfie pointed out in the comments.

Answer 3

One solution I came up with is to outsource the multiplication of a 2D with a 3D matrix into a function. However, I am curious to know whether this is the most efficient way to solve this problem?

rowCells = 5;
colCells = 3;
rowTimeSeries = 300;
colTimeSeries = 5;
slices = [1;10];

% Create 2D double matrix
mat1 = rand(rowTimeSeries, colTimeSeries);

% Create 2D cell matrix comprisiong 2D and/or 3D double matrices
mat2 = cell(rowCells,colCells);

for c = 1:colCells
    for r = 1:rowCells
        slice = randsample(slices, 1, true);
        mat2{r,c} = rand(rowTimeSeries, colTimeSeries, slice);
    end
end

% Multiply (.*) mat1 with mat2 (every slice)

results = cell(rowCells,colCells);

for c = 1:colCells
    for r = 1:rowCells
        results{r,c} = multiply2D3D(mat1, mat2{r,c});
    end
end


function vout = multiply2D3D(mat2D, mat3D)
%MULTIPLY2D3D multiplies a 2D double matrix with every slice of a 3D
% double matrix.
%
% INPUTs:
%   mat2D:
%   2D double matrix
%
%   mat3D:
%   3D double matrix where the third dimension is equal or greater than 1.
%
% OUTPUT:
%   vout:
%   3D double matrix with the same size as mat3D. Every slice in vout
%   is the result of a multiplication of mat2D with every individual slice
%   of mat3D.

[rows, cols,  slices] = size(mat3D);
vout = zeros(rows, cols, slices);

for s = 1 : slices
    vout(:,:,s) = mat2D .* mat3D(:,:,s);
end

end