从张量的每个正面切片中提取对角线元素

Question

我有一个p-by-p-by-n张量.我想为每个p-by-p切片提取对角元素.有没有人知道如何做到这一点没有循环？

谢谢.

Answer 1

Behold日益强大和不断强大bsxfun的vectorizing MATLAB problems非常有效地做这个任务使用MATLAB's linear indexing-

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

标杆

这里有一些运行时测试将这种bsxfun基于大数据的方法与repmat + eye基于大数据的方法进行比较-

***** 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.

Answer 2

我的一个建议是创建一个p x p逻辑单位矩阵,n在第三维中复制这个时间,然后使用这个矩阵来访问你的张量.这样的事情,假设你的张量存储在A:

ind = repmat(logical(eye(p)), [1 1 n]);
out = A(ind);

使用示例:

>> p = 5; n = 3;
>> A = reshape(1:75, p, p, n)

A(:,:,1) =

     1     6    11    16    21
     2     7    12    17    22
     3     8    13    18    23
     4     9    14    19    24
     5    10    15    20    25


A(:,:,2) =

    26    31    36    41    46
    27    32    37    42    47
    28    33    38    43    48
    29    34    39    44    49
    30    35    40    45    50


A(:,:,3) =

    51    56    61    66    71
    52    57    62    67    72
    53    58    63    68    73
    54    59    64    69    74
    55    60    65    70    75

>> ind = repmat(logical(eye(p)), [1 1 n]);
>> out = A(ind)

out =

     1
     7
    13
    19
    25
    26
    32
    38
    44
    50
    51
    57
    63
    69
    75

您会注意到我们抓住第一个切片的对角线,然后抓住第二个切片的对角线等,直到最后一个切片.这些值都连接成一个矢量.