scipy.linalg.

ishermitian#

scipy.linalg.ishermitian(a, atol=None, rtol=None)#

Check if a square 2D array is Hermitian.

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 Batched Linear Operations for details.

Parameters:

andarray: Input array of size (N, N)
atolfloat, optional: Absolute error bound
rtolfloat, optional: Relative error bound

Returns:

herbool: 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