3d arrays Matrix multiplication with a vector

i have 3 D matrix <64x64x64 double> i want to mutiply it with a vector <64x1 double>.

Answer 1

[BhaTTa]

To multiply a 3D matrix by a vector in MATLAB, you need to decide how you want this multiplication to behave. Since direct multiplication like this isn't standard in linear algebra, you have a few options depending on what you're trying to achieve.Element-wise multiplication for each slice

If you want to multiply each slice (a 64x64 matrix) of your 3D matrix by the vector (64x1) element-wise, where each element of the vector multiplies the corresponding row of each 64x64 slice, you can use the following approach:

% Assuming A is your 3D matrix (64x64x64) and v is your vector (64x1)
result = zeros(size(A)); % Initialize the result array with the same size as A

for i = 1:size(A,3) % Loop through each slice
    for j = 1:length(v) % Loop through each element of the vector
        result(:,j,i) = A(:,j,i) * v(j); % Multiply each row of the slice by the vector element
    end
end

Answer 2

[Steven Lord]

This wasn't an option when the question was asked originally, but since release R2020b you can use pagemtimes. Let's make a small sample data set.

A = randi(5, [4 4 3]);
b = [1; 2; 3; 4];
C = pagemtimes(A, b)

C = 
C(:,:,1) =

    22
    24
    50
    44


C(:,:,2) =

    30
    39
    29
    30


C(:,:,3) =

    28
    26
    30
    37

To check the answer we can multiply one of the pages of A by b and check it against the corresponding page in C.

pageOfA = A(:, :, 2)*b

pageOfA = 4x1

30 39 29 30

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pageOfC = C(:, :, 2)

pageOfC = 4x1

30 39 29 30

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