How do you compute the product of a matrix and each column of another matrix without a for loop in MATLAB, or is this just not possible?

Question

Simon 2024-7-4，12:41

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https://ww2.mathworks.cn/matlabcentral/answers/2134471-how-do-you-compute-the-product-of-a-matrix-and-each-column-of-another-matrix-without-a-for-loop-in-m

评论： Simon 2024-7-4，14:06

A 4x14 matrix (C) is multiplied by each column of a 14xN matrix (x) - hence by N individual 14 element column vectors - to form N individual 4 element column vectors - represented by a 4xN matrix (y) -, where N is a known yet large number, let's assume N = 132 for simplicity.

I use a for loop for this operation:

N = 132;
C = [0,1,0,0,0,0,0,0,0,-1,0,-0.68,0, 1.53;
     0,0,0,1,0,0,0,0,0,-1,0,-0.64,0,-1.92;
     0,0,0,0,0,1,0,0,0,-1,0, 0.86,0,-1.92;
     0,0,0,0,0,0,0,1,0,-1,0, 0.91,0, 1.53];
x = rand(14,N);
for n = 1:N
    y(:,n) = C*x(:,n);
end
y
y = 4x132
    0.8171    0.6519   -0.1231   -0.3986    0.0067    0.5236    0.5635   -0.0142   -0.1589    0.7049    0.0493    0.8107    0.0467    0.3760    0.1629   -0.5810   -0.0014    0.0753    0.1952    0.9694    0.9893    1.0198    0.3636    1.1546   -0.1246    0.2960    0.6670    1.2503    0.7362    0.3130
   -1.5713   -0.2918   -2.0231   -1.5203   -0.4916   -1.5073   -0.6379   -1.3672   -1.6384   -2.3884   -1.0684   -1.7009   -1.4159   -1.6700   -0.7916   -0.8800   -0.6646   -0.3746   -1.3475   -0.9698   -2.3454   -0.8660   -1.2379   -1.0661   -2.0218   -0.7671   -1.8403   -1.7703   -1.3348   -1.1637
   -0.7278   -0.1535   -0.8238   -0.5070    0.4447   -0.4600   -0.1615    0.2374   -1.0285   -1.2346   -0.3279   -0.5324    0.3478   -1.8978    0.6776   -0.8982    0.0732   -0.0802    0.0912   -0.1890   -2.0549   -1.3461   -1.2515   -0.6147   -1.0407   -1.1961   -1.0804   -1.5745    0.1213   -0.2728
    1.0967    1.6059    1.5573    0.2685    1.8956    1.9566    1.2679    1.4401    0.3141    2.0937    0.3331    1.9022    1.2138    1.1691    1.4234    0.3172    0.7299   -0.4859    1.4454    0.6288    1.6082    1.1965    1.0090    2.0954    1.3740    0.2839    1.4502    2.1792    1.8181    0.8593
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This works fine, however, I wondered how this operation could be implemented without a for loop in MATLAB - all variables in the loop are available prior to the first iteration - to utilize MATLAB's matrix multiplication optimization and thus improve runtime performance, or is this just not possible?

Thanks in advance for any help!

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Answer 1

Torsten 2024-7-4，12:47

在 MATLAB Online 中打开

y = C*x

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Simon 2024-7-4，14:06

Oh ... When I implemented the multiplication like that prior to posting the question, MATLAB responded with 'Arrays have incompatible sizes for this operation' and I couldn't figure out why. Because of your answer I tried again and just realized that this error message actually concerned the next line. Now, I honestly feel a little bit embarrassed to having asked such a question. Nonetheless, thank you for your answer and for making me realize the bug! I think I should take a break.

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