FooBar - 1 year ago 285
Python Question

# Numpy: Affect diagonal elements of matrix prior to 1.10

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 Source

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 `i`th upper diagonal with

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

and the `i`th 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]
``````
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