split long 2D matrix into the third dimension

问题:

Say I have the following matrix:

A = randi(10, [6 3])
     7    10     3
     5     5     7
    10     5     1
     6     5    10
     4     9     1
     4    10     1

And I would like to extract each 2 rows and put them into the third dimension, so the result would be like:

B(:,:,1) =
     7    10     3
     5     5     7
B(:,:,2) =
    10     5     1
     6     5    10
B(:,:,3) =
     4     9     1
     4    10     1

I can obviously do this with a for loop, just wondering how to do it more elegantly as one-liner using permute/reshape/.. (note matrix size and step must be parameters)

% params
step = 5;
r = 15;
c = 3;

% data
A = randi(10, [r c]);
B = zeros(step, c, r/step); % assuming step evenly divides r

% fill
counter = 1;
for i=1:step:r
    B(:,:,counter) = A(i:i+step-1, :);
    counter = counter + 1;
end

回答1:

Here's a one-line solution using RESHAPE and PERMUTE:

C = 3;          % Number of columns
R = 6;          % Number of rows
newR = 2;       % New number of rows
A = randi(10,[R C]);  % 6-by-3 array of random integers
B = permute(reshape(A',[C newR R/newR]),[2 1 3]);

This of course requires that newR divides evenly into R.

回答2:

Here's a one-liner with reshape and permute, but without transposing the input array -

out = permute(reshape(A,newR,size(A,1)/newR,[]),[1 3 2]);

, where newR is the number of rows in the 3D array output.

---

Benchmarking

This section compares the proposed aproach in this post against the other solution with reshape, permute & transpose on performance. The datasizes are inflated proportionality to the ones listed in the question. Thus, A is 60000 x 300 sized and we would split it such that the 3D output would have 200 rows and thus dim-3 would have 300 entries.

Benchmarking code -

%// Input
A = randi(10, [60000 300]); %// 2D matrix
newR = 200;                 %// New number of rows

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

N_iter = 5; %// Number of iterations for each approach to run with

disp('---------------------- With PERMUTE, RESHAPE & TRANSPOSE')
tic
for iter = 1:N_iter
    [R,C] = size(A);
    B = permute(reshape(A',[C newR R/newR]),[2 1 3]); %//'
end
toc, clear B R C iter

disp('---------------------- With PERMUTE & RESHAPE')
tic
for iter = 1:N_iter
    out = permute(reshape(A,newR,size(A,1)/newR,[]),[1 3 2]);
end
toc

Output -

---------------------- With PERMUTE, RESHAPE & TRANSPOSE
Elapsed time is 2.236350 seconds.
---------------------- With PERMUTE & RESHAPE
Elapsed time is 1.049184 seconds.