Arrays Matlab：乘积的乘法和求和

如何有效地对10对数组执行矩阵乘法，并对乘法矩阵的相应结果求和？例如：

创建两个阵列，A1和B1

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

C1 = A1*B1

C1 =

    24    35   114
    30    52   162

计算A1和B1的乘积

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

C1 = A1*B1

C1 =

    24    35   114
    30    52   162

创建另外两个阵列，A2和B2

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

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);

计算A2和B2的乘积

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

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，我输入向量。求和的结果不正确

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))

回答

多变量（：，：，1）=

多变量（：，：，2）=

盛宴=

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

正确答案应该是

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

---

您可以将它们连接成两个三维阵列并使用它们，而不是遍历所有这些阵列

%// 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片都对应于这些

C

数组中的每个。最后，

3D

的每个

summals

片段将对应于每个

产品的总和

数组

---

样本使用向量和矩阵运行 1）向量大小写

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)

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 =
   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

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

2）矩阵情况

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)

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 =
   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

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

---

至少对于工作空间效率，考虑使用3D阵列来包含所有这5对阵列。对于您的代码和预期的输出，您已经在为一个混乱的工作区调用15个变量了。@Divakar:我不熟悉使用3D数组。你能告诉我如何循环乘法和求和吗？谢谢查看发布的解决方案？谢谢您的回复。你能解释一下permute[1 2 4 3]和其他数字的含义吗？另外，同样的方法也适用于向量，比如A1=[1 2 3]”，B1是[5 6 7]？当输入是一维向量时，我检查了代码。求和的结果不正确。我已在我的问题中公布了结果。您能看一看吗？@SrishtiM如果您想在最低级别上测试解决方案中的代码，请看这里，看看这是否有意义-@SrishtiM，我很抱歉，但我不明白您在问题的更新部分试图做什么。最初，你有A1，A2，。。。B1，B2。。。数组和我的解决方案建议将这些数组连接到一个3D数组中，而在更新中，您将a的列连接到

a=cat（3，A1（：，1），A1（：，2））。这两件事完全是两码事。更重要的是，最初是将
A1
和
B1
相乘，以此类推。您在更新中是如何做到这一点的？@SrishtiM以及官方声明，
cat
只是沿着指定维度连接元素。因为我们知道这里处理的是1D（向量）和2D（矩阵），所以第三维是“空的”，元素可以沿着该维连接。这基本上就是猫在这里所做的。关于你的时间序列问题，我认为这与这里的上下文无关，可以作为一个单独的问题。祝你好运