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Module « scipy.linalg »

Fonction pinvh - module scipy.linalg

Signature de la fonction pinvh

def pinvh(a, atol=None, rtol=None, lower=True, return_rank=False, check_finite=True) 

Description

help(scipy.linalg.pinvh)

Compute the (Moore-Penrose) pseudo-inverse of a Hermitian matrix.

Calculate a generalized inverse of a complex Hermitian/real symmetric
matrix using its eigenvalue decomposition and including all eigenvalues
with 'large' absolute value.

Parameters
----------
a : (N, N) array_like
    Real symmetric or complex hermetian matrix to be pseudo-inverted

atol : float, optional
    Absolute threshold term, default value is 0.

    .. versionadded:: 1.7.0

rtol : float, optional
    Relative threshold term, default value is ``N * eps`` where
    ``eps`` is the machine precision value of the datatype of ``a``.

    .. versionadded:: 1.7.0

lower : bool, optional
    Whether the pertinent array data is taken from the lower or upper
    triangle of `a`. (Default: lower)
return_rank : bool, optional
    If True, return the effective rank of the matrix.
check_finite : bool, optional
    Whether to check that the input matrix contains only finite numbers.
    Disabling may give a performance gain, but may result in problems
    (crashes, non-termination) if the inputs do contain infinities or NaNs.

Returns
-------
B : (N, N) ndarray
    The pseudo-inverse of matrix `a`.
rank : int
    The effective rank of the matrix.  Returned if `return_rank` is True.

Raises
------
LinAlgError
    If eigenvalue algorithm does not converge.

See Also
--------
pinv : Moore-Penrose pseudoinverse of a matrix.

Examples
--------

For a more detailed example see `pinv`.

>>> import numpy as np
>>> from scipy.linalg import pinvh
>>> rng = np.random.default_rng()
>>> a = rng.standard_normal((9, 6))
>>> a = np.dot(a, a.T)
>>> B = pinvh(a)
>>> np.allclose(a, a @ B @ a)
True
>>> np.allclose(B, B @ a @ B)
True

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