Numpy: Affect diagonal elements of matrix prior to 1.10

Question

I would like to change diagonal elements from a 2d matrix. These are both main and non-main diagonals.

numpy.diagonal() In NumPy 1.10, it will return a read/write view, Writing to the returned array will alter your original array.

numpy.fill_diagonal(), numpy.diag_indices() Only works with main-diagonal elements

Here is my use case: I want to recreate a matrix of the following form, which is very trivial using diagonal notation given that I have all the x, y, z as arrays.

Answer 1

You could always use slicing to assign a value or array to the diagonals.

Passing in a list of row indices and a list of column indices lets you access the locations directly (and efficiently). For example:

>>> z = np.zeros((5,5))
>>> z[np.arange(5), np.arange(5)] = 1 # diagonal is 1
>>> z[np.arange(4), np.arange(4) + 1] = 2 # first upper diagonal is 2
>>> z[np.arange(4) + 1, np.arange(4)] = [11, 12, 13, 14] # first lower diagonal values

changes the array of zeros z to:

array([[  1.,   2.,   0.,   0.,   0.],
       [ 11.,   1.,   2.,   0.,   0.],
       [  0.,  12.,   1.,   2.,   0.],
       [  0.,   0.,  13.,   1.,   2.],
       [  0.,   0.,   0.,  14.,   1.]])

In general for a k x k array called z, you can set the ith upper diagonal with

z[np.arange(k-i), np.arange(k-i) + i]

and the ith lower diagonal with

z[np.arange(k-i) + i, np.arange(k-i)]

Note: if you want to avoid calling np.arange several times, you can simply write ix = np.arange(k) once and then slice that range as needed:

np.arange(k-i) == ix[:-i]