Sum over all diagonals in lower matrix

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Hi, I have a matrix which I will take the sum over the diagonals in the lower matrix. So for example my matrix A=rand(4,4); the result I want is following vector
P=[sum(diag(A)); sum(diag(A,-1)); sum(diag(A,-2)); sum(diag(A,-3))]
My matrix is much larger, how can this be done without looping?

回答(3 个)

Jan
Jan 2017-2-25
编辑:Jan 2017-2-25
Why do you prefer a solution without a loop?
function speedtest
A = rand(1000, 1000);
tic
for k = 1:20
P = test1(A);
end
toc
tic
for k = 1:20
P = test2(A);
end
toc
function P = test1(A)
rowdest = toeplitz(1:size(A, 1), [1, repelem(size(A, 1)+1, size(A, 2)-1)]);
P = accumarray(rowdest(:), A(:));
P = P(1:end-1);
function P = test2(A)
n = size(A, 1);
P = zeros(n, 1);
for k = 1:n
P(k) = sum(diag(A, 1-k));
end
Matlab 2016b/64, Win7, Core2Duo:
Elapsed time is 1.139792 seconds. % Toeplitz
Elapsed time is 0.182293 seconds. % Loop
I could not estimate, if the overhead for the loops or for creating the large index matrix are more expensive. But this short test seems, like the loop is efficient.
  3 个评论
Jan
Jan 2017-2-27
@Lenovo: I share your preference for smart commands and clever solutions. This dull loop does not really satisfy me. But it is simple and fast.
Guillaume
Guillaume 2017-2-27
The dull loop is also the simplest to understand, which I'd actually value over speed and conciseness. It's immediately clear what it does without having to do any mental gymnastic.
Another version of the loop, in my opinion even clearer (albeit probably slightly slower):
arrayfun(@(d), sum(diag(A, 1-d)), 1:size(A, 1))

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Guillaume
Guillaume 2017-2-25
A = reshape(1:30, 5, 6) %demo data
rowdest = toeplitz(1:size(A, 1), [1, repelem(size(A, 1)+1, size(A, 2)-1)]);
P = accumarray(rowdest(:), A(:));
P = P(1:end-1)
  2 个评论
Stephen23
Stephen23 2017-2-25
Or without repelem:
>> A = randi(9,4,4)
A =
8 1 6 8
4 2 1 1
3 9 3 1
4 9 4 2
>> X = toeplitz(2:1+size(A,1),[2,ones(1,size(A,2)-1)]);
>> V = accumarray(X(:),A(:));
>> V = V(2:end)
V =
15
17
12
4
Jan
Jan 2017-2-25
编辑:Jan 2017-2-25
@Guillaume: Your solution is nice and Matlabish. I could not predict, if it is faster or slower than a simple loop, therefore I tried it.
After the measurement, I assume the creation of the large index matrix needs more time than the loop overhead costs.

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Andrei Bobrov
Andrei Bobrov 2017-2-25
编辑:Andrei Bobrov 2017-2-28
P = sum(spdiags(A.',0:size(A,1)-1)).';
  2 个评论
Orongo
Orongo 2017-2-26
Given it is a matrix manipulation and it is Matlab, I'm convinced there are clever solutions out there handling this type of calculations.
spdiags looks promising, however if a diagonal is zero I must have it return as zero so number of rows in the result matches number of rows in the matrix.
Andrei Bobrov
Andrei Bobrov 2017-2-26
编辑:Andrei Bobrov 2017-2-28
[EDIT]
I'm corrected. Please read about spdiags.

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