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Module « scipy.linalg »

Fonction ishermitian - module scipy.linalg

Signature de la fonction ishermitian

def ishermitian(a, atol=None, rtol=None) 

Description

help(scipy.linalg.ishermitian)

ishermitian(a, atol=None, rtol=None)
Check if a square 2D array is Hermitian.

    Parameters
    ----------
    a : ndarray
        Input array of size (N, N)

    atol : float, optional
        Absolute error bound

    rtol : float, optional
        Relative error bound

    Returns
    -------
    her : bool
        Returns True if the array Hermitian.

    Raises
    ------
    TypeError
        If the dtype of the array is not supported, in particular, NumPy
        float16, float128 and complex256 dtypes.

    See Also
    --------
    issymmetric : Check if a square 2D array is symmetric

    Notes
    -----
    For square empty arrays the result is returned True by convention.

    `numpy.inf` will be treated as a number, that is to say ``[[1, inf],
    [inf, 2]]`` will return ``True``. On the other hand `numpy.nan` is never
    symmetric, say, ``[[1, nan], [nan, 2]]`` will return ``False``.

    When ``atol`` and/or ``rtol`` are set to , then the comparison is performed
    by `numpy.allclose` and the tolerance values are passed to it. Otherwise an
    exact comparison against zero is performed by internal functions. Hence
    performance can improve or degrade depending on the size and dtype of the
    array. If one of ``atol`` or ``rtol`` given the other one is automatically
    set to zero.

    Examples
    --------
    >>> import numpy as np
    >>> from scipy.linalg import ishermitian
    >>> A = np.arange(9).reshape(3, 3)
    >>> A = A + A.T
    >>> ishermitian(A)
    True
    >>> A = np.array([[1., 2. + 3.j], [2. - 3.j, 4.]])
    >>> ishermitian(A)
    True
    >>> Ac = np.array([[1. + 1.j, 3.j], [3.j, 2.]])
    >>> ishermitian(Ac)  # not Hermitian but symmetric
    False
    >>> Af = np.array([[0, 1 + 1j], [1 - (1+1e-12)*1j, 0]])
    >>> ishermitian(Af)
    False
    >>> ishermitian(Af, atol=5e-11) # almost hermitian with atol
    True

    

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