I am looking to implement a constraint on an optimization on all diagonals of a matrix using CVXPY. The diag function in CVXPY only returns the main diagonal. Is there a simple way to implement the numbered diagonal function in numpy using a CVXPY variable, in order to iterate over all diagonals adding a constraint for each?
Answers:
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Method 1
I wound up using (though the final result used this code inline in a different function) the following:
def diagat(mat, n, i, j):
""" return the diagonal containing mat[i][j] (mat is a square matrix of dimension n)"""
return [mat[i + k][j + k] for k in range(-n, n) if 0 <= i + k < n and 0 <= j + k < n]
def diag90at(mat, n, i, j):
""" return the diagonal orthogonal to the regular diagonal containing mat[i][j] """
return [mat[i - k][j + k] for k in range(-n, n) if 0 <= i - k < n and 0 <= j + k < n]
A = [[ 1, 2, 3, 4],
[ 5, 6, 7, 8],
[ 9,10,11,12],
[13,14,15,16]]
print(diagat(A, 4, 0, 1))
print(diagat(A, 4, 2, 2))
print(diagat(A, 4, 3, 0))
print(diag90at(A, 4, 0, 1))
print(diag90at(A, 4, 2, 2))
print(diag90at(A, 4, 3, 0))
"""
[2, 7, 12]
[1, 6, 11, 16]
[13]
[5, 2]
[14, 11, 8]
[13, 10, 7, 4]
"""
All methods was sourced from stackoverflow.com or stackexchange.com, is licensed under cc by-sa 2.5, cc by-sa 3.0 and cc by-sa 4.0