Multiple a matrix by every column of another matrix and stack the results in some form

Question

Deepayan Bhadra 2022-3-14

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https://ww2.mathworks.cn/matlabcentral/answers/1671609-multiple-a-matrix-by-every-column-of-another-matrix-and-stack-the-results-in-some-form

回答： Voss 2022-3-14

Hello, I have a matrix A: 3xn and a matrix B: 3x6. What I wish to do is subtract each column of B from A as follows:

B_11 is subtracted from A_1i for i = 1:n, B_21 is subtracted from A_2i for i = 1:n, B_31 is subtracted from A_3i for i = 1:n.

This is repeated for each column of B with the whole A matrix and the results stacked each time, giving a resultant matrix that's 18xn.

Or storing the 3xn matrices for the 6 different B columns in a structure is also okay.

I have tried combinations of repmat but nothing useful yet. Can we do this without a loop, preferably?

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Answer 1

Voss 2022-3-14

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https://ww2.mathworks.cn/matlabcentral/answers/1671609-multiple-a-matrix-by-every-column-of-another-matrix-and-stack-the-results-in-some-form#answer_917544

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I think this will do it:

n = 10;
A = 100+2*reshape(1:3*n,3,[])
A = 3×10
 108   114   120   126   132   138   144   150   156
 110   116   122   128   134   140   146   152   158
 112   118   124   130   136   142   148   154   160
B = reshape(1:3*6,3,[])
B = 3×6
   4     7    10    13    16
   5     8    11    14    17
   6     9    12    15    18
new_A = repmat(A,size(B,2),1);
new_B = repmat(B(:),1,size(A,2));
result = new_A-new_B;
disp(result);
 107   113   119   125   131   137   143   149   155
 108   114   120   126   132   138   144   150   156
 109   115   121   127   133   139   145   151   157
 104   110   116   122   128   134   140   146   152
 105   111   117   123   129   135   141   147   153
 106   112   118   124   130   136   142   148   154
 101   107   113   119   125   131   137   143   149
 102   108   114   120   126   132   138   144   150
 103   109   115   121   127   133   139   145   151
  98   104   110   116   122   128   134   140   146
  99   105   111   117   123   129   135   141   147
 100   106   112   118   124   130   136   142   148
  95   101   107   113   119   125   131   137   143
  96   102   108   114   120   126   132   138   144
  97   103   109   115   121   127   133   139   145
  92    98   104   110   116   122   128   134   140
  93    99   105   111   117   123   129   135   141
  94   100   106   112   118   124   130   136   142