从MATLAB矩阵中提取数据而无需for循环 [英] Extract data from MATLAB matrix without for-loop

问题描述

在MATLAB中，假设我有一个10 x 100的矩阵，称为M.我想做的是提取此矩阵的特定索引，并以行矢量化的方式基于行索引立即对它们进行操作.

In MATLAB, let us say I have a 10 x 100 matrix, called M. What I would like to do, is extract particular indicies of this matrix, and do an operation on them immediately, based on the row index, in a vectorized fashion.

例如，对于第一行，我想计算sum(M(1, 1:1:100)).然后对于第二行，我想要sum(M(2, 1:2:100)).对于第三行，我要sum(M(3, 1:3:100))，依此类推.对于第十行，我当然要sum(M(10, 1:10:100)).

For example, for the first row, I want to compute sum(M(1, 1:1:100)). Then for row two, I want sum(M(2, 1:2:100)). For row three, I want sum(M(3, 1:3:100)), etc etc. For row ten, I have of course sum(M(10, 1:10:100)).

我在for循环中有这个，但是我想看看是否有一种方法可以在没有for循环的情况下提取此数据.谢谢.

I have this in a for loop, but I want to see if there is a way to extract this data without a for loop. Thank you.

推荐答案

您可以尝试使用单线

S=arrayfun(@(n) sum(M(n,1:n:100)), 1:10)

或者，您可以预先创建稀疏矩阵

Alternatively, you can create a sparse matrix beforehand

A=sparse(100,10);
for n=1:10, 
   A(1:n:100, n)=1; 
end

并通过以下方式求和

S=diag(M*A);

可以通过定义A=sparse(10,100)和

S=sum(M.*A,2);

我快速的卧推

M=rand(10,100);
sz = size(M);
tic;
for k=1:10000,
    for n=1:sz(1),
        B(n)=sum(M(n,1:n:end));
    end
end
toc

tic;
for k=1:10000,
    B=arrayfun(@(n) sum(M(n,1:n:end)), 1:sz(1));
end
toc

tic;
for k=1:10000,
    A=sparse(sz(2), sz(1));
    for n=1:sz(1),
        A(1:n:end, n)=1;
    end
    B=diag(M*A);
end
toc

tic;
A=sparse(sz(2),sz(1));
for n=1:sz(1),
    A(1:n:end, n)=1;
end
for k=1:10000,
    B=diag(M*A);
end
toc

tic;
A=sparse(sz(1),sz(2));
for n=1:sz(1),
    A(n, 1:n:end)=1;
end
for k=1:10000,
    B=sum(M.*A,2);
end
toc

返回

Elapsed time is 0.552470 seconds.
Elapsed time is 2.409102 seconds.
Elapsed time is 0.638072 seconds.
Elapsed time is 0.052246 seconds.
Elapsed time is 0.061893 seconds.

用于30 x 1000矩阵

for 30-by-1000 matrix

Elapsed time is 1.785664 seconds.
Elapsed time is 3.954034 seconds.
Elapsed time is 4.760436 seconds.
Elapsed time is 0.926118 seconds.
Elapsed time is 0.865330 seconds.

以及1000 x 100矩阵

and for 1000-by-100 matrix

Elapsed time is 51.389322 seconds.
Elapsed time is 63.443414 seconds.
Elapsed time is 68.327187 seconds.
Elapsed time is 29.056304 seconds.
Elapsed time is 1.147215 seconds.

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