matlab - 从张量的每个正面切片中提取对角线元素

Question

我有一个 p×p×n 张量。我想为每个 p-by-p 切片提取对角线元素。有没有人知道如何在不循环的情况下做到这一点？

谢谢。

Answer 1

Behold永远强大的 bsxfun 对于 vectorizing MATLAB problems使用 MATLAB's linear indexing 非常有效地完成这项任务-

diags = A(bsxfun(@plus,[1:p+1:p*p]',[0:n-1]*p*p))

使用 4 x 4 x 3 大小的输入数组运行示例 -

A(:,:,1) =
    0.7094    0.6551    0.9597    0.7513
    0.7547    0.1626    0.3404    0.2551
    0.2760    0.1190    0.5853    0.5060
    0.6797    0.4984    0.2238    0.6991
A(:,:,2) =
    0.8909    0.1493    0.8143    0.1966
    0.9593    0.2575    0.2435    0.2511
    0.5472    0.8407    0.9293    0.6160
    0.1386    0.2543    0.3500    0.4733
A(:,:,3) =
    0.3517    0.9172    0.3804    0.5308
    0.8308    0.2858    0.5678    0.7792
    0.5853    0.7572    0.0759    0.9340
    0.5497    0.7537    0.0540    0.1299
diags =
    0.7094    0.8909    0.3517
    0.1626    0.2575    0.2858
    0.5853    0.9293    0.0759
    0.6991    0.4733    0.1299

基准测试

这里有一些运行时测试将这种基于 bsxfun 的方法与 repmat + eye based approach 进行了比较对于大数据量 -

***** Datasize: 500 x 500 x 500 *****
----------------------- With BSXFUN
Elapsed time is 0.008383 seconds.
----------------------- With REPMAT + EYE
Elapsed time is 0.163341 seconds.

***** Datasize: 800 x 800 x 500 *****
----------------------- With BSXFUN
Elapsed time is 0.012977 seconds.
----------------------- With REPMAT + EYE
Elapsed time is 0.402111 seconds.

***** Datasize: 1000 x 1000 x 500 *****
----------------------- With BSXFUN
Elapsed time is 0.017058 seconds.
----------------------- With REPMAT + EYE
Elapsed time is 0.690199 seconds.