scipy.linalg.ishermitian

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

Check if a square 2D array is Hermitian.

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

>>> 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