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
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
ornumpy.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.