Vectorisation of code for insertion of n x n matrices in a 3D array along the diagonal of a large matrix

2 次查看（过去 30 天）
Jason Tracey
Jason Tracey 2019-10-21
回答： Andrei Bobrov 2019-10-21
I am trying to insert small square matrices along the diagonal of a large matrix. These matrices are contained in a 3D array, and have different values. Overlapping values are to be added, and the small matrices are only inserted where they can fit fully inside the large matrix. The step dimension will always be equal to 1.
I have achieved an answer through the use of for-loops, but am attempting to vectorise this code for efficiency. How would I do this? The current, unvectorised code is shown below.
function M = TestDiagonal2()
N = 10;
n = 2;
maxRand = 3;
deepMiniM = randi(maxRand,n,n,N+1-n);
M = zeros(N);
for i = 1:N+1-n
M(i:i+1,i:i+1) = M(i:i+1,i:i+1) + deepMiniM(:,:,i);
end
end
The desired result is an `N`x`N` matrix with `n+1` diagonals populated:
3 1 0 0 0 0 0 0 0 0
4 5 3 0 0 0 0 0 0 0
0 3 3 3 0 0 0 0 0 0
0 0 1 6 3 0 0 0 0 0
0 0 0 4 4 4 0 0 0 0
0 0 0 0 2 3 2 0 0 0
0 0 0 0 0 2 6 2 0 0
0 0 0 0 0 0 4 2 2 0
0 0 0 0 0 0 0 3 3 1
0 0 0 0 0 0 0 0 3 3
  1 个评论
Stephen23
Stephen23 2019-10-21
"I have achieved an answer through the use of for-loops, but am attempting to vectorise this code for efficiency."
I don't see why that loop would be particularly slow. Have you profiled your code to see where the bottlenecks are?

请先登录，再进行评论。

请先登录，再回答此问题。

回答（2 个）

Guillaume
Guillaume 2019-10-21
Note: I don't see how you can get a 4 at M(2, 1) if maxRand is 3.
Here is one way, no guarantee that it's faster than a loop. Works for any size of deepMiniM:
[rstart, cstart] = ndgrid(1:size(deepMiniM, 1), 1:size(deepMiniM, 2)); %destination indices of the first matrix
rall = rstart(:) + (0:N-size(deepMiniM, 1)); %destination indices of the rows of ALL the matrices
call = cstart(:) + (0:N-size(deepMiniM, 2)); %same for columns
M = accumarray([rall(:), call(:)], deepMiniM(:)); %pass destination and values to accumarray. Default accumarray function is sum
Andrei Bobrov
Andrei Bobrov 2019-10-21
A = full(gallery('tridiag',Z(n,1,:),cat(3,Z(1,1,1),Z(n,n,1:end-1)+Z(1,1,2:end),Z(n,n,end)),Z(1,n,:)));

类别

在 Help Center 和 File Exchange 中查找有关 Creating and Concatenating Matrices 的更多信息

标签

产品

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by