This question already has answers here:
Vector norm of an array of vectors in MATLAB
(4 answers)
Closed 5 years ago.
I have a 3 columns, n rows matrix:
[ a,b,c;
d,e,f;
g,h,i; ]
I want to apply the norm function to each of the rows, and get a 1xn matrix containing the norms:
[ norm([a,b,c]);
norm([d,e,f]);
norm([g,h,i]); ]
I could do this with a for-loop, but is there a better way?
What about
norms = sqrt(sum(A.^2,1))
or
norms = sqrt(sum(A.^2,2))?
depending on whether your coordinates are in rows or in columns.
If readability is a bigger consideration than performance you might also consider:
norms = cellfun(#norm,num2cell(A,2));
This pattern is also adaptable to other operations along one dimension you might want to perform where MATLAB doesn't support it natively.
if the first dimension is not too large:
norms = sqrt(diag(A * A'));
Related
This question already has answers here:
Multiply a 3D matrix with a 2D matrix
(10 answers)
Closed 5 years ago.
I try to use svd in my work which will return the vector as below.
A=rand(10,5);
b=rand(10,5,100);
[U, S , V]=svd(A);
What I'm trying to do is to multiply each slice of b with U. With one specific slice, this operation is valid:
c=U'*b(:,:,1);
However when I try to use a vectorized method as below, it return array dimensions mismatch error.
Utran=U.';
c = cellfun(#(x) x.*b,num2cell(Utran,[1 2]),'UniformOutput',false);
I could probably use loop for the first method, but it's not efficient if I have a large matrix. Any idea what's my mistake here?
The following is a vectorized solution.
Not sure if it's faster than using loops; and even if it is, note that it uses more memorry for intermediate computations:
result = permute(sum(permute(conj(U), [1 3 4 2]).*b), [4 2 3 1]);
This question already has answers here:
Fast Algorithms for Finding Pairwise Euclidean Distance (Distance Matrix)
(3 answers)
Closed 5 years ago.
I am trying to calculate the Square Euclidean Distance between each column from two matrices and store in matrix D.
im_patches is 81*60840 double
codebook is 81*456 double
SquareEuclidean = #(x, y) x'*x+y'*y-2*x'*y;
% Get N*K distance matrix D between the N patches extracted
% from the image (im patches) and the K prototypes in the codebook
D=zeros(size(im_patches,2),size(codebook, 2));
for i=1:size(im_patches,2)
for j=1:size(codebook, 2)
D(i,j)=SquareEuclidean(im_patches(:,i),codebook(:,j));
end
end
However, this is very inefficient that cost more than 10 minutes in my laptop.
I am wondering is there a better way of using bsxfun. So I tried:
D2 = bsxfun(#(x,y) x'.*x+y'.*y-2.*x'.*y,im_patches,codebook);
which gives an error:
Error using bsxfun: Non-singleton dimensions of the two input arrays must match each other.
I think bsxfun or arrayfun would be a nice way of dealing such problem. But don't know the correct way of doing this.
Thank you in advance.
Your loop can be reduced to:
bsxfun(#plus,sum(im_patches.'.^2,2),sum(codebook.^2)-2*im_patches.'*codebook)
In MATLAB r2016b there is no need to bsxfun:
sum(im_patches.'.^2,2)+sum(codebook.^2)-2*im_patches.'*codebook
This question already has answers here:
Sum over blocks in a 2D matrix - MATLAB
(4 answers)
Closed 6 years ago.
I'm sure this is basic, but I can't come up to an easy way to reduce a matrix of population count by grid cell by adding up all the elements of the "small" cells which would fit in the new ones.
My matrix is 720x360 and would like to change it to 360x180. I thought about using imresize with 0.5 scale, and then assume the value per new grid is 4 times the old one.
I fell uneasy doing so though, as I can't find examples of similar cases. It'll be nice to have "sum" or "average" as an "interpolation" option or something like that.
Thanks in advance for any help
Cheers
Maria
If you have the Image Processing Toolbox:
x = randi(10,6,8); % example matrix
bs = [2 2]; % block size
y = col2im(sum(im2col(x, bs, 'distinct'), 1), [1 1], size(x)./bs, 'distinct');
How this works:
im2col(... 'distinct') arranges each distinct block of the given size into a column. sum(...,1) then sums each column. Finally, im2col(..., 'distinct') arranges the results back into a matrix of reduced size.
This question already has answers here:
How to divide an image into blocks in MATLAB?
(5 answers)
Closed 8 years ago.
I was wondering: I have a 100x100 matrix. I would like to split it in several 10x10 sub-matrices the first including columns and rows 1-10, then second including columns 11-20 and rows 1-10 and son on until eventually I have a set of 10x10 matrices.
Is there any way of doing this without needing to build an extremely complex array of for loops?
Thanks :)
If you need to extract the sub-matrices explicitly than mat2cell would be a reasonable choice:
sm = mat2cell( M, 10*ones(1,size(M,1)/10), 10*ones(1,size(M,2)/10) );
However, if you only need these submatrices for a local processing you can use blockproc
blockproc( M, [10 10], #myFun );
This question already has answers here:
applying norm function to rows of matrix - Matlab [duplicate]
(3 answers)
Closed 9 years ago.
I have a Nx3 matrix (A) the columns are X,Y,Z respectively. I want to calculate the norm that is sqrt(X^2+Y^2+Z^2) for each row. I did a for loop for that:
for i = 1:length(A)
Result(i) = norm(A(i,:))
end
is there any other way to do it avoiding for loop?
Thanks
You can do it like this:
sqrt(sum(A.^2, 2))
Your method returns a 1x3 where this returns a 3x1. So if you want you can transpose it but I doubt you really need to.