Issues with generating the following block matrix using horizontal stacking and vertical stacking-CodePudding

I am trying to generate the following block matrix consisting of submatrices A and B, and N is a positive integer. So far, my code is as follows:

C_lower = B
for j in range(0,N):
    for i in range(0,N-j):
        col = np.linalg.matrix_power(A,i) @ B
        C = np.hstack(np.vstack((C_lower,col)))

However, it seems like my code is not working because the loop continues forever. Any suggestions?

Similarly, I'm also having issues with constructing the following block diagonal matrices:

I tried using block_diag from scipy, but there is no way I can repeat Q as many times as N is equal to (i.e., N = 50 in my case). I had to do block_diag(Q,Q,Q,Q,Q,Q,Q.......) in order to get the block diagonal matrix I want.

CodePudding user response：

Here's the answer to your first question. There are a number of issues in your code. This is a better way of achieving what you want:

C = np.zeros((N, N, A.shape[0], B.shape[1]))
for i in range(N):
    for j in range(i   1):
        C[i, j] = np.linalg.matrix_power(A, i - j) @ B

Similarly for your second question:

Q_ = np.zeros((N, N, *Q.shape))
for i in range(N):
    Q_[i, i] = Q