I attempted to use the solution from this post: Multiply a 3D matrix with a 2D matrix, to vectorize the multiplication of a one dimensional with a three dimensional, but to no avail. Any help would be greatly appreciated!
for s = 1: s_length
for a = 1: a_length
for g = g_length
two_dim(s,a) = two_dim(s,a) + one_dim(g) * three_dim(s,a,g);
end
end
end
I think this does what you want.
two_dim = reshape(three_dim, [], size(three_dim,3))*one_dim(:);
two_dim = reshape(two_dim, size(three_dim,1), size(three_dim,2));
This works as follows:
First line reshapes your 3D array into a matrix, collapsing the first two dimensions into one. That way the operation you want is standard multiplication of the resulting matrix times a column vector.
Second line reshapes the result into matrix shape.
mtimes does not work with inputs with dimension larger than 2, so you have to find a way to do the multiplication by yourself. The solution of Luis Mendo is a nice solution; here is another one using bsxfun:
two_dim = two_dim + squeeze(sum(bsxfun(#times, three_dim, reshape(one_dim,[1 1 g_length])),3));
Here is how it works:
reshape makes the vector one_dim looking like a 3D array. This must be done because the multiplication between the vector and the 3D array is performed along the 3rd dimension, so Matlab need a hint on sizes.
bsxfun perfoms the element-wise multiplcation, so the result must be sumed up along the 3rd dimension (and squeezed to be compliant with a 2D matrix format)
Related
Did a quick search and couldn't find much about this. Say I have a 2D matrix and a 1D 'response function'. I want to convolve each row of the 2D matrix with the response function. I can do this by:
for i=1:numrows
answer(:,i) = conv(2dmatrix(:,i),response_function,'same');
end
but it's super slow! Any tips to accelerate this?
Thanks
This code reproduces your results on randomly generated matrices:
conv2(response_function,1,2dmatrix,'same')
conv2 allows you to convolute along rows and columns separately, so do nothing to the rows, 1, and convolve the columns by response_function.
To convolve along each row, swap the order of the first two function arguments.
conv2 has somewhat weird syntax, I would prefer using convn for generalized n dimensional convolution. When one of the inputs is just a row vector then convolution in every other dimension is essentially a convolution with [1] so it doesn't change anything, only preforming convolution along each row. Similarly if your a matrix convoluted with a column vector then it would do convolution along each column.
answer = convn(2dmatrix, response_function);
In my current analysis, I am trying to multiply a matrix (flm), of dimension nxm, with the inverse of a matrix nxmxp, and then use this result to multiply it by the inverse of the matrix (flm).
I was trying using the following code:
flm = repmat(Data.fm.flm(chan,:),[1 1 morder]); %chan -> is a vector 1by3
A = (flm(:,:,:)/A_inv(:,:,:))/flm(:,:,:);
However. due to the problem of dimensions, I am getting the following error message:
Error using ==> mrdivide
Inputs must be 2-D, or at least one
input must be scalar.
To compute elementwise RDIVIDE, use
RDIVIDE (./) instead.
I have no idea on how to proceed without using a for loop, so anyone as any suggestion?
I think you are looking for a way to conveniently multiply matrices when one is of higher dimensionality than the other. In that case you can use bxsfun to automatically 'expand' the smaller matrix.
x = rand(3,4);
y = rand(3,4,5);
bsxfun(#times,x,y)
It is quite simple, and very efficient.
Make sure to check out doc bsxfun for more examples.
I have N kx1 sparse vectors and I need to multiply each of them by their transpose, creating N square matrices, which I then have to sum over. The desired output is a k by k matrix. I have tried doing this in a loop and using arrayfun, but both solutions are too slow. Perhaps one of you can come up with something faster. Below are specific details about the best solution I've come up with.
mdev_big is k by N sparse matrix, containing each of the N vectors.
fun_sigma_i = #(i) mdev_big(:,i)*mdev_big(:,i)';
sigma_i = arrayfun(fun_sigma_i,1:N,'UniformOutput',false);
sigma = sum(reshape(full([sigma_i{:}]),k,k,N),3);
The slow part of this process is making sigma_i full, but I cannot reshape it into a 3d array otherwise. I've also tried cat instead of reshape (slower), ndSparse instead of full (way slower), and making fun_sigma_i return a full matrix rather than a sparse one (slower).
Thanks for the help! ,
I need a 3D matrix in matlab, I have another 2D matrix (7570x3) too,
The 3D matrix should have zero number except of all dimensions in 2D matrix that should have 1 value. How can I do that.
i.e. 2D matrix (1,:) = 28,64,27 then 3d(27,64,27) should be 1
how can i do that?
Assuming a is your 2-d matrix, and b is the 3-d one, use sub2ind as follows:
b=false(max(a)); % preallocate memory for a logical zeros matrix b
b(sub2ind(size(b),a(:,1),a(:,2),a(:,3))) = 1;
Check to see what max(a) gives you to see if you can host a 3-d matrix of size(max(a) to begin with. Since you are interested in a logcial matrix (ones and zeros), the size of that matrix in memory is the same as the # of elements, n*m*l, so a 1000x1000x1000 will take 1 GB.
Note, it very well may be that b is very sparse, if that is the case you can refer to this thread to see how to deal with it. Know that at the moment, and to the best of my knowledge, matlab doesn't support 3d sparse matrices. So you may want to check this option from the FEX. When I think of it, you already have a sparse look-up table of the 3D matrix! it is just your 2D matrix you started with...
Thanks a lot #natan
for non-integer matrix also can use:
b=false(floor(max(a))); % preallocate memory for a logical zeros matrix b
b(sub2ind(size(b),floor(a(:,1)),floor(a(:,2)),floor(a(:,3)))) = 1;
or use round function:
b=false(round(max(a))); % preallocate memory for a logical zeros matrix b
b(sub2ind(size(b),round(a(:,1)),round(a(:,2)),round(a(:,3)))) = 1;
I have to create a very big 3D matrix (such as: 500000x60x60). Is there any way to do this in matlab?
When I try
omega = zeros(500000,60,60,'single');
I get an out-of-memory error.
The sparse function is no option since it is only meant for 2D matrices. So is there any alternative to that for higher dimensional matrices?
Matlab only has support for sparse matrices (2D). For 3D tensors/arrays, you'll have to use a workaround. I can think of two:
linear indexing
cell arrays
Linear indexing
You can create a sparse vector like so:
A = spalloc(500000*60*60, 1, 100);
where the last entry (100) refers to the amount of non-zeros eventually to be assigned to A. If you know this amount beforehand it makes memory usage for A more efficient. If you don't know it beforehand just use some number close to it, it'll still work, but A can consume more memory in the end than it strictly needs to.
Then you can refer to elements as if it is a 3D array like so:
A(sub2ind(size(A), i,j,k))
where i, j and k are the indices to the 1st, 2nd and 3rd dimension, respectively.
Cell arrays
Create each 2D page in the 3D tensor/array as a cell array:
a = cellfun(#(x) spalloc(500000, 60, 100), cell(60,1), 'UniformOutput', false);
The same story goes for this last entry into spalloc. Then concatenate in 3D like so:
A = cat(3, a{:});
then you can refer to individual elements like so:
A{i,j,k}
where i, j and k are the indices to the 1st, 2nd and 3rd dimension, respectively.
Since your matrix is sparse, try to use ndsparse (N-dimensional sparse arrays FEX)