Question

如何有效地对10对阵列进行矩阵乘法并对乘法矩阵的相应结果求和？例如：

创建两个数组，A1和B1。

A1 = [1 3 5; 2 4 7];
B1 = [-5 8 11; 3 9 21; 4 0 8];

计算A1和B1的乘积。

C1 = A1*B1

C1 =

    24    35   114
    30    52   162

创建另外两个数组，A2和B2。

A2 = [7 9 11; 3 5 6];
B2 = [-1 2 3; 4 5 6; 4 1 8];

计算A2和B2的乘积。

C2 = A2*B2



sum_of_products1 = sum(C1,C2);
sum_of_products2 = sum(C3,C4); and so on till 


    .
    .
    .
sum_of_products5 = sum(C9,C10);

更新

根据回复，我输入了矢量。总结的结果是不正确的。

clc;
clear all;

%VECTORS
A1(:,1) = [1 2 3 4].';
A1(:,2) = [5 6 7 8].';

%// Concatenate all An and Bn arrays along third dim to have A, B as 3D arrays
A = cat(3,A1(:,1),A1(:,2));
B = cat(3,A1(:,1)',A1(:,2)');

%// You may clear A1, A2,...A10, B1, B2.., B10 at this point for a cleaner workspace

%// Get the product values into a 3D array
multvals = squeeze(sum(bsxfun(@times,permute(A,[1 2 4 3]),permute(B,[4 1 2 3])),2))

%// Finally get the sum of product values
sumvals = squeeze(sum(reshape(multvals,size(A,1),size(A,2),2,[]),3))

答案

多个人（：，：，1）=

 1     2     3     4
 2     4     6     8
 3     6     9    12
 4     8    12    16

多个人（：，：，2）=

25    30    35    40
30    36    42    48
35    42    49    56
40    48    56    64

sumvals =

 3     7    55    75
 6    14    66    90
 9    21    77   105
12    28    88   120

正确的答案应该是

s1 = multvals(:,:,1);
s2 = multvals(:,:,2); 

sumvals = s1 + s2;

sumvals = 
26  32  38  44
32  40  48  56
38  48  58  68
44  56  68  80

Answer 1

您可以将它们连接成两个3D数组并使用它们，而不是遍历所有这些数组。

%// Concatenate all An and Bn arrays along third dim to have A, B as 3D arrays
A = cat(3,A1,A2,...)
B = cat(3,B1,B2,...)

%// You may clear A1, A2,..., B1, B2..., at this point for a cleaner workspace

%// Get the product values into a 3D array
multvals = sum(bsxfun(@times,permute(A,[1 2 4 3]),permute(B,[4 1 2 3])),2)

%// Finally get the sum of product values
[m1,m2,m3,m4] = size(multvals);
sumvals = squeeze(sum(reshape(multvals,m1,m2,m3,2,[]),4))

multvals的最后一个维度中的每个切片都对应于这些C数组中的每一个。最后，3D的每个sumvals切片都对应于每个sum_of_products数组。

样品使用载体和基质运行

1）矢量案例

clear all;clc;

%// VECTORS
A1 = [1 2 3 4].';
B1 = [5 6 7 8];

A2 = [11 12 13 14].';
B2 = [15 16 17 18];

A = cat(3,A1,A2);
B = cat(3,B1,B2);

multvals = sum(bsxfun(@times,permute(A,[1 2 4 3]),permute(B,[4 1 2 3])),2);
[m1,m2,m3,m4] = size(multvals);
sumvals = squeeze(sum(reshape(multvals,m1,m2,m3,2,[]),4))

solution_with_approach_from_question = A1*B1 + A2*B2 
%// this should yield values identical to sumvals(:,:,1)

输出 -

sumvals =
   170   182   194   206
   190   204   218   232
   210   226   242   258
   230   248   266   284
solution_with_approach_from_question =
   170   182   194   206
   190   204   218   232
   210   226   242   258
   230   248   266   284

2）矩阵案例

clear all;clc;

%// MATRICES
A1 = [1 3 5; 2 4 7];
B1 = [-5 8 11; 3 9 21; 4 0 8];

A2 = [7 9 11; 3 5 6];
B2 = [-1 2 3; 4 5 6; 4 1 8];

A = cat(3,A1,A2);
B = cat(3,B1,B2);

multvals = sum(bsxfun(@times,permute(A,[1 2 4 3]),permute(B,[4 1 2 3])),2);
[m1,m2,m3,m4] = size(multvals);
sumvals = squeeze(sum(reshape(multvals,m1,m2,m3,2,[]),4))

solution_with_approach_from_question = A1*B1 + A2*B2 
%// this should yield values identical to sumvals(:,:,1)

输出 -

sumvals =
    97   105   277
    71    89   249
solution_with_approach_from_question =
    97   105   277
    71    89   249

Matlab：乘法和乘积之和

1 个答案:

样品使用载体和基质运行