Between what variables is this kron function doing the Kronecker product? (MATLAB)
y = kron(x,[1:size(x)]);
I understand what the first variable is, but what does [1:size(x)] mean? Don't you need to put an array/list before it so it means something?
If x is a column vector, then n=size(x) will be its length and 1:size(x) will be the row vector [1...n].
If x is a matrix or higher dimensions, the expression 1:size(x) will take the row count only.
IF the Kronecker Product between those quantities makes sense or not, it depends on your application.
[1:size(x)] will produce a vector the size of vector x, and his entries will be:
[1,2,3,...,n]
Related
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.
I am generating a random binary matrix with a specific number of ones in each row. Now, I want to take each row in the matrix and multiply it by its transpose (i.e row1'*row1).
So, I am using row1=rnd_mat(1,:) to get the first row. However, in the multiplication step I get this error
"Both logical inputs must be scalar. To compute elementwise TIMES, use TIMES (.*) instead."
Knowing that I don't want to compute element-wise, I want to generate a matrix using the outer product. I tried to write row1 manually using [0 0 1 ...], and tried to find the outer product. I managed to get the matrix I wanted.
So, does anyone have some ideas on how I can do this?
Matrix multiplication of logical matrices or vectors is not supported in MATLAB. That is the reason why you are getting that error. You need to convert your matrix into double or another valid numeric input before attempting to do that operation. Therefore, do something like this:
rnd_mat = double(rnd_mat); %// Cast to double
row1 = rnd_mat(1,:);
result = row1.'*row1;
What you are essentially computing is the outer product of two vectors. If you want to avoid casting to double, consider using bsxfun to do the job for you instead:
result = bsxfun(#times, row1.', row1);
This way, you don't need to cast your matrix before doing the outer product. Remember, the outer product of two vectors is simply an element-wise multiplication of two matrices where one matrix is consists of a row vector where each row is a copy of the row vector while the other matrix is a column vector, where each column is a copy of the column vector.
bsxfun automatically broadcasts each row vector and column vector so that we produce two matrices of compatible dimensions, and performs an element by element multiplication, thus producing the outer product.
I have two 50 x 6 matrices, say A and B. I want to assign weights to each element of columns in matrix - more weight to elements occurring earlier in a column and less weight to elements occurring later in the same column...likewise for all 6 columns. Something like this:
cumsum(weight(row)*(A(row,col)-B(row,col)); % cumsum is for cumulative sum of matrix
How can we do it efficiently without using loops?
If you have your weight vector w as a 50x1 vector, then you can rewrite your code as
cumsum(repmat(w,1,6).*(A-B))
BTW, I don't know why you have the cumsum operating on a scalar in a loop... it has no effect. I'm assuming that you meant that's what you wanted to do with the entire matrix. Calling cumsum on a matrix will operate along each column by default. If you need to operate along the rows, you should call it with the optional dimension argument as cumsum(x,2), where x is whatever matrix you have.
I am trying to take a matrix and normalize the values in each cell around the average for that column. By normalize I mean subtract the value in each cell from the mean value in that column i.e. subtract the mean for Column1 from the values in Column1...subtract mean for ColumnN from the values in ColumnN. I am looking for script in Matlab. Thanks!
You could use the function mean to get the mean of each column, then the function bsxfun to subtract that from each column:
M = bsxfun(#minus, M, mean(M, 1));
Additionally, starting in version R2016b, you can take advantage of the fact that MATLAB will perform implicit expansion of operands to the correct size for the arithmetic operation. This means you can simply do this:
M = M-mean(M, 1);
Try the mean function for starters. Passing a matrix to it will result in all the columns being averaged and returns a row vector.
Next, you need to subtract off the mean. To do that, the matrices must be the same size, so use repmat on your mean row vector.
a=rand(10);
abar=mean(a);
abar=repmat(abar,size(a,1),1);
anorm=a-abar;
or the one-liner:
anorm=a-repmat(mean(a),size(a,1),1);
% Assuming your matrix is in A
m = mean(A);
A_norm = A - repmat(m,size(A,1),1)
As has been pointed out, you'll want the mean function, which when called without any additional arguments gives the mean of each column in the input. A slight complication then comes up because you can't simply subtract the mean -- its dimensions are different from the original matrix.
So try this:
a = magic(4)
b = a - repmat(mean(a),[size(a,1) 1]) % subtract columnwise mean from elements in a
repmat replicates the mean to match the data dimensions.
Is there a way in Octave to compute and store only the diagonal of a matrix product?
Basically like doing: vector = diag(A*B);
I don't care about any of the values of A*B except those on the diagonal. The matrix sizes are around 80k x 12 and 12 x 80k, so even if I didn't care about the speed/extra memory it simply wont fit in RAM.
Strange, since Octave is a package for huge data sets and diagonals are very important, so it should be possible.
The first element in the diagonal is the scalar product of the first row of A with the first column of B. The second element in the diagonal is the scalar product of the second row of A with the second column of B.
In other words:
vector = sum(A.*B',2);
This is how you could do it in MATLAB (probably similar to Octave syntax):
vector = sum(A.*B',2);
This will compute only the resulting diagonal of the operation A*B as a column vector vector.
actually I think it's the dot product of the first row of A with the first column of B... the second diagonal element is the dot product of the second row and the second column... etc