numpy.linalg.diagonal#

linalg.diagonal(x, /, *, offset=0)[source]#

Returns specified diagonals of a matrix (or a stack of matrices) x.

This function is Array API compatible, contrary to numpy.diagonal, the matrix is assumed to be defined by the last two dimensions.

Parameters:
x(…,M,N) array_like

Input array having shape (…, M, N) and whose innermost two dimensions form MxN matrices.

offsetint, optional

Offset specifying the off-diagonal relative to the main diagonal, where:

* offset = 0: the main diagonal.
* offset > 0: off-diagonal above the main diagonal.
* offset < 0: off-diagonal below the main diagonal.
Returns:
out(…,min(N,M)) ndarray

An array containing the diagonals and whose shape is determined by removing the last two dimensions and appending a dimension equal to the size of the resulting diagonals. The returned array must have the same data type as x.

See also

numpy.diagonal

Examples

>>> a = np.arange(4).reshape(2, 2); a
array([[0, 1],
       [2, 3]])
>>> np.linalg.diagonal(a)
array([0, 3])

A 3-D example:

>>> a = np.arange(8).reshape(2, 2, 2); a
array([[[0, 1],
        [2, 3]],
       [[4, 5],
        [6, 7]]])
>>> np.linalg.diagonal(a)
array([[0, 3],
       [4, 7]])

Diagonals adjacent to the main diagonal can be obtained by using the offset argument:

>>> a = np.arange(9).reshape(3, 3)
>>> a
array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])
>>> np.linalg.diagonal(a, offset=1)  # First superdiagonal
array([1, 5])
>>> np.linalg.diagonal(a, offset=2)  # Second superdiagonal
array([2])
>>> np.linalg.diagonal(a, offset=-1)  # First subdiagonal
array([3, 7])
>>> np.linalg.diagonal(a, offset=-2)  # Second subdiagonal
array([6])

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

>>> a = np.arange(9).reshape(3, 3)
>>> a
array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])
>>> np.linalg.diagonal(np.fliplr(a))  # Horizontal flip
array([2, 4, 6])
>>> np.linalg.diagonal(np.flipud(a))  # Vertical flip
array([6, 4, 2])

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

On this page