Matlab的：乘法和产品的总和 [英] Matlab: Multiplication and sum of products
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问题描述
我怎样才能effeciently进行矩阵乘法10对阵列，总结乘法矩阵相应的结果？例如：
创建两个数组，A1和B1。
A1 = [1 3 5; 2 4 7];
B1 = [-5 8月11日; 3 9月21日; 4 0 8]。
计算A1和B1的产品
C1 = A1 * B1C1 = 24 35 114
30 52 162
创建另一个两个数组，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的产品
C2 = A2 * B2sum_of_products1 =总和（C1，C2）;
sum_of_products2 =总和（C3，C4）;等等，直到
。
。
。
sum_of_products5 =总和（C9，C10）;
更新
根据的答复，I输入矢量。求和的结果来了不正确。
CLC;
清除所有;％向量
A1（：，1）= [1 2 3 4]';
A1（：，2）。= [5 6 7 8]';//％串连所有的和BN沿着昏暗的第三阵列有A，B三维阵列
A =猫（3，A 1（：，1），A 1（：，2））;
B =猫（3，A 1（：，1）'，A 1（：，2）'）;％//你可能会清除A1，A2，... A10，B1，B2 ...，B10在这一点上要清洁器工作区％//获取产品价值成3D阵列
multvals =挤压（SUM（bsxfun（@倍，置换（A，[1 2 4 3]），置换（B，[4 1 2 3]）），2））//％得到最终产品价值的总和
sumvals =挤压（SUM（重塑（multvals，尺寸（A，1），尺寸（A，2），2，[]），3））
答
multvals（：，：，1）=
1 2 3 4
2 4 6 8
3 6 9 12
4 8 12 16
multvals（：，：，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月21日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
解决方案
而不是通过所有的阵列循环的，你可以将它们连接起来成两个3D阵列，并与他们合作。
//％串连所有的和BN沿着昏暗的第三阵列有A，B三维阵列
A =猫（3，A1，A2，...）
B =猫（3，B1，B2，......）％//你可能会清除A1，A2，......，B1，B2 ...，在这一点上要清洁器工作区％//获取产品价值成3D阵列
multvals =总和（bsxfun（@倍，置换（A，[1 2 4 3]），置换（B，[4 1 2 3]）），2）//％得到最终产品价值的总和
[M1，M2，M3，M4 =尺寸（multvals）;
sumvals =挤压（总和（重塑（multvals，M1，M2，m3,2，[]），4））
在 multvals 的最后一维每个切片对应于每个那些 C 阵列。在结束 sumvals 的每个 3D 片将对应于每个 sum_of_products 阵列。
样品向量和矩阵
运行1）向案例
清除所有;中图分类号;//％向量
A1 = [1 2 3 4]'。
B1 = [5 6 7 8];A2 = [11 12 13 14]'。
B2 = [15 16 17 18];A =猫（3，A1，A2）;
B =猫（3，B1，B2）;multvals =总和（bsxfun（@倍，置换（A，[1 2 4 3]），置换（B，[4 1 2 3]）），2）;
[M1，M2，M3，M4 =尺寸（multvals）;
sumvals =挤压（总和（重塑（multvals，M1，M2，m3,2，[]），4））solution_with_approach_from_question = A1 * B1 + A2 * B2
//％这应该产生相同的值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）矩阵的情况下
清除所有;中图分类号;//％矩阵
A1 = [1 3 5; 2 4 7];
B1 = [-5 8月11日; 3 9月21日; 4 0 8]。A2 = [7 9 11; 3 5 6];
B2 = [-1 2 3; 4 5 6; 4 1 8];A =猫（3，A1，A2）;
B =猫（3，B1，B2）;multvals =总和（bsxfun（@倍，置换（A，[1 2 4 3]），置换（B，[4 1 2 3]）），2）;
[M1，M2，M3，M4 =尺寸（multvals）;
sumvals =挤压（总和（重塑（multvals，M1，M2，m3,2，[]），4））solution_with_approach_from_question = A1 * B1 + A2 * B2
//％这应该产生相同的值sumvals（：，：，1）
输出 -
sumvals =
97 105 277
71 89 249
solution_with_approach_from_question =
97 105 277
71 89 249
How can I effeciently perform matrix multiplication for 10 pairs of arrays and sum the corresponding result of multiplication matrices? For example:
Create two arrays, A1 and B1.
A1 = [1 3 5; 2 4 7];
B1 = [-5 8 11; 3 9 21; 4 0 8];
Calculate the product of A1 and B1.
C1 = A1*B1
C1 =
24 35 114
30 52 162
Create another two arrays, A2 and B2.
A2 = [7 9 11; 3 5 6];
B2 = [-1 2 3; 4 5 6; 4 1 8];
Calculate the product of A2 and B2.
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);
UPDATE
Based on the reply, I input vectors. The result of summation is coming incorrect.
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))
Answer
multvals(:,:,1) =
1 2 3 4
2 4 6 8
3 6 9 12
4 8 12 16
multvals(:,:,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
The correct answer should have been
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
解决方案
Instead of looping through all those arrays, you can concatenate them into two 3D arrays and work with them.
%// 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))
Each slice in the last dimension of multvals would correspond to each of those C arrays. At the end each 3D slice of sumvals would correspond to each sum_of_products array.
Samples runs with vectors and matrices
1) Vector case
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)
Output -
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) Matrix case
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)
Output -
sumvals =
97 105 277
71 89 249
solution_with_approach_from_question =
97 105 277
71 89 249
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