Suppose you have an N x 1 cell array where each constituent cell is an m x m matrix. I would like the matrix product (i.e. not entry-by-entry multiplication) of these matrices, so if E_i is the ith matrix in the cell array. I would like to compute E_1 * E_2 * ... * E_N. Any ideas for a vectorized approach to this?
The most direct way is to do this (where p is your answer and cellarray is your cell array). * is the matrix multiplication while .* is the element-by-element multiplication you wish to avoid.
p = 1;
for i = 1:N,
p = p*cellarray{i};
end
I don't think this can be vectorized since the iterations aren't independent of each other. A multiplication at some step is dependent on all the multiplications prior to it.
Related
I have a m * n * k Matrix called M which I want to index to get the mean of some Data.
I have a logical m * n matrix called EZG and want to apply this on every of the k-th dimension from 1:(end-1) (call this vector V).
Any chance to write it without a loop like this:
M=rand(3,3,3)
EZG=logical([1,1,1;0,1,0;0,0,1])
V=1:size(M,3)-1
mean(mean(M(EZG,V)1),2)
Result should be a onedimensional vector of the length of V.
Thank you
I think this is what you want:
M=rand(3,3,3);
EZG=logical([1,1,1;0,1,0;0,0,1]);
% repeat EZG K-1 times, and add zeros to the Kth slice
V=cat(3,repmat(EZG,1,1,size(M,3)-1),false(size(M,1),size(M,2)));
% logical index and mean
m=mean(M(V));
I have two sparse matrices in Matlab, A and B,
and I want to compute a three-dimensional matrix C such that
C(i,j,k) = A(i,j) * B(j,k)
can I do this without a loop?
(Side question: Is there a name for this operation?)
Edit:
Seems my question has already been asked (just for full matrices):
Create a 3-dim matrix from two 2-dim matrices
For full matrices:
You can do it using bsxfun and shiftdim:
C = bsxfun(#times, A, shiftdim(B,-1))
Explanation: Let A be of size M x N and B of size N x P. Applying shiftdim(B,-1) gives a 1 x N x P array. bsxfun implicitly replicates A along the third dimension and shiftdim(B,-1) along the first to compute the desired element-wise product.
Another possibility, usually less efficient than bsxfun, is to repeat the arrays explicity along the desired dimensions, using repmat:
C = repmat(A, [1 1 size(B,2)]) .* repmat(shiftdim(B,-1), [size(A,1) 1 1])
For sparse matrices:
The result cannot be sparse, as sparse ND-arrays are not supported.. But you can do the computations with sparse A and B using linear indexing:
ind1 = repmat(1:numel(A),1,size(B,2));
ind2 = repmat(1:numel(B),size(A,1),1);
ind2 = ind2(:).';
C = NaN([size(A,1),size(A,2),size(B,2)]); %// preallocate with appropriate shape
C(:) = full(A(ind1).*B(ind2)); %// need to use full if C is to be 3D
Answer to your side question: the name for this operation is a hash join.
For a specific problem, I need to design the resizing of a matrix process using multiplication of matrices alone.
Given a matrix of A of dimensions (a*b,1) where a and b are integers, I need to find a way to resize A to dimensions (a,b) like this:
M*A*N = resize(A,a,b)
where dim(M) = (a,a*b) and dim(N) = (1,b). It doesn't have to be two matrices but I don't think it is possible any other way.
If you can't use reshape or vec2mat, you need to do your manipulation for each element of A separately.
There is no such M and N that you are searching for.
Suppose:
resh_A = M*A*N;
Let's study one row of this equation. Assume one row of M*A :
temp_i = M(i, :) * A;
Since M(i, :) is 1 x a*b and A is a*b x 1; temp_i whould be a 1 x 1 matrix.
Now temp_i * N should result in the ith row of your result (or resh_A).
Thus resh_A will look like:
(note N is 1 x b)
temp_1 * N % row1
temp_2 * N % row2
temp_3 * N % row3
...
which is not a general matrix (it's a matrix with rank 1).
Suppose I have a matrix A=rand(2,14,24) and a vector x=10*ones(1,14)
I want element wise multiplication of A and x, such that B(i,j,k)=A(i,j,k)*x(j) for all j=1,2,..14.
I want to be able to do this without running a loop. What is the most efficient way to do this in matlab?
If you're multiplying A by a vector of 10's element-wise, wouldn't it be easier to simply multiply by a scalar instead?
B = A * 10;
For a general case, there is no need for repmat logic here. bsxfun can do the trick (and it's faster). :
B = bsxfun(#times, A, x);
You first use repmat to tile x the right number of times, then do element-wise multiplication.
repX = repmat(x, [size(A, 1), 1, size(A, 3)]);
B = A.*repX;
I have a M x N matrix. I want to multiply each of the N columns by a M x M matrix. The following does this in a loop, but I have no idea how to vectorize it.
u=repmat(sin(2*pi*f*t),[n 1]);
W = rand(n);
answer = size(u);
for i=1:size(u,2)
answer(:,i) = W*u(:,i);
end
You simply need to multiply the two matrices:
answer = W*u;
Think about it: in every iteration of your loop you multiply a matrix by a vector. The result of that operation is a vector, which you save into your answer in column i. Matrix multiplication is a similar thing: you can understand it as multiplication of a matrix (W) by a set of vectors, which form your matrix u.
So your code is good, just remove the loop :)