`scipy.linalg._cythonized_array_utils:ishermitian`

Signature

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

Summary

Check if a square 2D array is Hermitian.

Extended Summary

The documentation is written assuming array arguments are of specified "core" shapes. However, array argument(s) of this function may have additional "batch" dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see linalg_batch for details. Note that calls with zero-size batches are unsupported and will raise a ValueError.

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.

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)
A = np.array([[1., 2. + 3.j], [2. - 3.j, 4.]])
ishermitian(A)
Ac = np.array([[1. + 1.j, 3.j], [3.j, 2.]])
ishermitian(Ac)  # not Hermitian but symmetric
Af = np.array([[0, 1 + 1j], [1 - (1+1e-12)*1j, 0]])
ishermitian(Af)
ishermitian(Af, atol=5e-11) # almost hermitian with atol

✓

Aliases

scipy.linalg.ishermitian

Referenced by

This package

release:1.8.0-notes