How can I get counterdiagonals of a matrix and concatenate them? - matlab

Question

Short Version
How can I do concatMap in MATLAB? I'm trying to build a single vector from a series of smaller, differently sized vectors. I know I can do:
result = [];
for i=1:N
result = [result nextPart(i)];
end
but that has a serious speed impact and there must be a smarter way to do concatMap.
Long Version
I'm trying to write a MATLAB function that returns the counterdiagonals of a block. For example, if you have the block:
1 2 4
3 5 7
6 8 9
then counterDiagonals(block) should return [1 2 3 4 5 6 7 8 9].
I have a function that will find a single counter diagonal of a block. i.e. counterDiagonal(x, 3) will return [4 5 6].
Therefore, counterDiagonals should be as simple as concatMap counterDiagonal(x, i) (1:N) where N is (2*length(block)-1). How can I do this in MATLAB in an efficient way?

Answer 1

One problem with the accepted answer: if the matrix A had zeros, they will be incorrectly removed from the result.. Instead you should work on the indices of the elements:
A = [0 2 4; 3 5 7; 6 8 9]; %# Sample matrix (contains zeros)
ind = reshape(1:numel(A), size(A)); %# indices of elements
ind = fliplr( spdiags( fliplr(ind) ) ); %# get the anti-diagonals (or use ROT90)
ind(ind==0) = []; %# keep non-zero indices
result = A(ind); %# get elements in desired order
This is very similar to this answer I gave in a previous question (the difference was that the anti-digaonals were in reverse order).

Answer 2

I believe what you want to do can be accomplished using the functions ROT90 and SPDIAGS:
A = [1 2 4; 3 5 7; 6 8 9]; %# Sample matrix
result = rot90(A); %# Rotate the matrix counter-clockwise
result = spdiags(result); %# Find all the diagonals
result = result(result ~= 0).'; %'# Remove zero padding and format the results
%# into a row vector
And you should end up with result = [1 2 3 4 5 6 7 8 9].
EDIT: As Amro mentions in a comment, the above code assumes that there are no zeroes in the original matrix A. If there are zeroes in the original matrix, one solution is to replace them with a non-zero flag value that you know doesn't appear in the original matrix (like, for example, NaN), run the above code, then replace the flag values in the result:
A = [0 2 4; 3 0 7; 6 8 0]; %# Sample matrix
result = rot90(A); %# Rotate the matrix counter-clockwise
result(result == 0) = nan; %# Replace zeroes with NaN
result = spdiags(result); %# Find all the diagonals
result = result(result ~= 0).'; %'# Remove zero padding and format the results
%# into a row vector
result(isnan(result)) = 0; %# Put the original zeroes back

Answer 3

Short version:
If you preassign your result array, everything will be a lot faster.
result = zeros(1,knownLengthOfResultsArray); %# such as "numel(block)"
ct = 1;
for i=1:N
tmp = nextPart(i);
nTmp = length(tmp);
result(ct:ct+nTmp-1) = tmp;
ct = ct + nTmp;
end
Long version:
However, it may be even more efficient to rewrite your algorithm. See e.g. the answers to this question (use fliplr on your array first), or #gnovice's answer.