flopscope.

flopscope.numpy.fill_diagonal

fnp.fill_diagonal(a, val, wrap=False, **kwargs)[flopscope source][numpy source]

Fill the main diagonal of the given array of any dimensionality.

Adapted from NumPy docs np.fill_diagonal

Areacore
Typecustom
NumPy Refnp.fill_diagonal
Cost
4×per-operation
Flopscope Context

Fill main diagonal of given array. Cost: min(m,n).

For an array a with a.ndim >= 2, the diagonal is the list of values a[i, ..., i] with indices i all identical. This function modifies the input array in-place without returning a value.

Parameters

a:array, at least 2-D.

Array whose diagonal is to be filled in-place.

val:scalar or array_like

Value(s) to write on the diagonal. If val is scalar, the value is written along the diagonal. If array-like, the flattened val is written along the diagonal, repeating if necessary to fill all diagonal entries.

wrap:bool

For tall matrices in NumPy version up to 1.6.2, the diagonal "wrapped" after N columns. You can have this behavior with this option. This affects only tall matrices.

See also

Notes

This functionality can be obtained via diag_indices, but internally this version uses a much faster implementation that never constructs the indices and uses simple slicing.

Examples

>>> import flopscope.numpy as fnp
>>> a = flops.zeros((3, 3), int)
>>> flops.fill_diagonal(a, 5)
>>> a
array([[5, 0, 0],
       [0, 5, 0],
       [0, 0, 5]])

The same function can operate on a 4-D array:

>>> a = flops.zeros((3, 3, 3, 3), int)
>>> flops.fill_diagonal(a, 4)

We only show a few blocks for clarity:

>>> a[0, 0]
array([[4, 0, 0],
       [0, 0, 0],
       [0, 0, 0]])
>>> a[1, 1]
array([[0, 0, 0],
       [0, 4, 0],
       [0, 0, 0]])
>>> a[2, 2]
array([[0, 0, 0],
       [0, 0, 0],
       [0, 0, 4]])

The wrap option affects only tall matrices:

>>> # tall matrices no wrap
>>> a = flops.zeros((5, 3), int)
>>> flops.fill_diagonal(a, 4)
>>> a
array([[4, 0, 0],
       [0, 4, 0],
       [0, 0, 4],
       [0, 0, 0],
       [0, 0, 0]])
>>> # tall matrices wrap
>>> a = flops.zeros((5, 3), int)
>>> flops.fill_diagonal(a, 4, wrap=True)
>>> a
array([[4, 0, 0],
       [0, 4, 0],
       [0, 0, 4],
       [0, 0, 0],
       [4, 0, 0]])
>>> # wide matrices
>>> a = flops.zeros((3, 5), int)
>>> flops.fill_diagonal(a, 4, wrap=True)
>>> a
array([[4, 0, 0, 0, 0],
       [0, 4, 0, 0, 0],
       [0, 0, 4, 0, 0]])

The anti-diagonal can be filled by reversing the order of elements using either flops.flipud or flops.fliplr.

>>> a = flops.zeros((3, 3), int);
>>> flops.fill_diagonal(flops.fliplr(a), [1,2,3])  # Horizontal flip
>>> a
array([[0, 0, 1],
       [0, 2, 0],
       [3, 0, 0]])
>>> flops.fill_diagonal(flops.flipud(a), [1,2,3])  # Vertical flip
>>> a
array([[0, 0, 3],
       [0, 2, 0],
       [1, 0, 0]])

Note that the order in which the diagonal is filled varies depending on the flip function.