如何在Matlab的多维数组中应用corr2函数?

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问题描述

假设我有两个矩阵A和B

Let's say I have two matrices A and B

A = rand(4,5,3);
B = rand(4,5,6)

我想应用函数'corr2'计算相关系数.

I want to apply the function 'corr2' to calculate the correlation coefficients.

corr2(A(:,:,1),B(:,:,1))
corr2(A(:,:,1),B(:,:,2))
corr2(A(:,:,1),B(:,:,3))
...
corr2(A(:,:,1),B(:,:,6))
...
corr2(A(:,:,2),B(:,:,1))
corr2(A(:,:,2),B(:,:,2))
...
corr2(A(:,:,3),B(:,:,6))

如何避免使用循环来创建这样的向量化?

How to avoid using loops to create such a vectorization?

推荐答案

已添加到corr2的m文件中，以创建用于处理3D数组的自定义矢量化版本.建议使用bsxfun的两种方法(当然！)

Hacked into the m-file for corr2 to create a customized vectorized version for working with 3D arrays. Proposed here are two approaches with bsxfun (of course!)

方法1

szA = size(A);
szB = size(B);

a1 = bsxfun(@minus,A,mean(mean(A)));
b1 = bsxfun(@minus,B,mean(mean(B)));

sa1 = sum(sum(a1.*a1));
sb1 = sum(sum(b1.*b1));

v1 = reshape(b1,[],szB(3)).'*reshape(a1,[],szA(3));
v2 = sqrt(sb1(:)*sa1(:).');

corr3_out = v1./v2; %// desired output

corr3_out在A和B的所有3D切片之间存储corr2结果.

corr3_out stores corr2 results between all 3D slices of A and B.

因此，对于A = rand(4,5,3), B = rand(4,5,6)，我们将corr3_out作为6x3数组.

Thus, for A = rand(4,5,3), B = rand(4,5,6), we would have corr3_out as a 6x3 array.

方法2

通过使用reshape代替-

szA = size(A);
szB = size(B);
dim12 = szA(1)*szA(2);

a1 = bsxfun(@minus,A,mean(reshape(A,dim12,1,[])));
b1 = bsxfun(@minus,B,mean(reshape(B,dim12,1,[])));

v1 = reshape(b1,[],szB(3)).'*reshape(a1,[],szA(3));
v2 = sqrt(sum(reshape(b1.*b1,dim12,[])).'*sum(reshape(a1.*a1,dim12,[])));

corr3_out = v1./v2; %// desired output

基准化

基准代码-

Benchmarking

Benchmark code -

%// Create random input arrays
N = 55; %// datasize scaling factor
A = rand(4*N,5*N,3*N);
B = rand(4*N,5*N,6*N);

%// Warm up tic/toc
for k = 1:50000
    tic(); elapsed = toc();
end

%// Run vectorized and loopy approach codes on the input arrays

%// 1. Vectorized approach
%//... solution code (Approach #2) posted earlier
%// clear variables used

%// 2. Loopy approach
tic
s_A=size(A,3);
s_B=size(B,3);
out1 = zeros(s_B,s_A);
for ii=1:s_A
    for jj=1:s_B
        out1(jj,ii)=corr2(A(:,:,ii),B(:,:,jj));
    end
end
toc

结果-

-------------------------- With BSXFUN vectorized solution
Elapsed time is 1.231230 seconds.
-------------------------- With loopy approach
Elapsed time is 139.934719 seconds.

MATLAB-JIT爱好者在这里表现出一些爱！:)

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Corr2