I have an M-by-M-by-N matrix, which is a concatenation of N M-by-M matrices. I want to reduce this matrix to an M-by-N matrix by taking the diagonals of each M-by-M submatrix and concatenating them together. How can I do this in a simple vectorized way?
You can do it by getting the linear indices of the diagonals and using it to form a new matrix
[M,~,N]=size(A);%# A is your matrix
indx=cumsum([1:(M+1):M^2; M^2.*ones(N-1,M)]);%#diagonal indices
B=A(indx');%'# transpose to get MxN
In the above, I've used ~ to disregard that output from the function. However, this works only if you're using MATLAB R2009b and above. If your version is older than that, use a dummy variable instead.
Related
Assume there is a data matrix (MATLAB)
X = [0.8147, 0.9134, 0.2785, 0.9649, 0.9572;
0.9058, 0.6324, 0.5469, 0.1576, 0.4854;
0.1270, 0.0975, 0.9575, 0.9706, 0.8003]
Each column represent a feature vector for a sample.
What is the fastest way to get the pairwise consine similarity measure in X in MATLAB? such as we want to compute the symmetric S is 5X5 matrix, the element in S(3,4) is the consine between the third column and fourth column.
Note: The consine measurment cos(a,b) means the angle bettween vector a and b.
If you have the Statistics Toolbox, use pdist with the 'cosine' option, followed by squareform. Note that:
pdist considers rows, not columns, as observations. So you need to transpose the input.
The output is 1 minus the cosine similarity. So you need to subtract the result from 1.
To get the result in the form of a symmetric matrix apply squareform.
So, you can use
S = 1 - squareform(pdist(X.', 'cosine'));
In Matlab, I have created a matrix A with size (244x2014723)
and a matrix B with size (244x1)
I was able to calculate the correlation matrix using corr(A,B) which yielded in a matrix of size 2014723x1. So, every column of matrix A correlates with matrix B and gives one row value in the matrix of size 2014723x1.
My question is when I ask for a covariance matrix using cov(A,B), I get an error saying A and B should be of same sizes. Why do I get this error? How is the method to find corr(A,B) any different from cov(A,B)?
The answer is pretty clear if you read the documentation:
cov:
If A and B are matrices of observations, cov(A,B) treats A and B as vectors and is equivalent to cov(A(:),B(:)). A and B must have equal size.
corr
corr(X,Y) returns a p1-by-p2 matrix containing the pairwise correlation coefficient between each pair of columns in the n-by-p1 and n-by-p2 matrices X and Y.
The difference between corr(X,Y) and the MATLAB® function corrcoef(X,Y) is that corrcoef(X,Y) returns a matrix of correlation coefficients for the two column vectors X and Y. If X and Y are not column vectors, corrcoef(X,Y) converts them to column vectors.
One way you could get the covariances of your vector with each column of you matrix is to use a loop. Another way (might be in-efficient depending on the size) is
C = cov([B,A])
and then look at the first row (or column) or C.
See link
In the more about section, the equation describing how cov is computed for cov(A,B) makes it clear why they need to be the same size. The summation is over only one variable which enumerates the elements of A,B.
Because it is possible to create a (non-constant) diagonal matrix in Matlab, f.i. A = diag([1;2;3]), I wonder if there is an easy way to create a non-constant tridiagonal matrix. Because the gallery('tridiag',...) command is only working with constant tridiagonal matrices.
If I understood your question correctly, then you can create random tridiagonal matrices using the below line of code
n=10;
p=3;
T=toeplitz([1 randn(1,n-p-1) zeros(1,p)], [1 randn(1,n-p-1) zeros(1,p)])*diag(randn(1,n))
Note, you can also change the 1 in the toeplitz function or you can remove it all along, but then you get a warning.
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;