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 returnTrue
. On the other handnumpy.nan
is never symmetric, say,[[1, nan], [nan, 2]]
will returnFalse
.When
atol
and/orrtol
are set to , then the comparison is performed bynumpy.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 ofatol
orrtol
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