- scipy.linalg.issymmetric(a, atol=None, rtol=None)#
Check if a square 2D array is symmetric.
Input array of size (N, N).
- atolfloat, optional
Absolute error bound
- rtolfloat, optional
Relative error bound
Returns True if the array symmetric.
If the dtype of the array is not supported, in particular, NumPy float16, float128 and complex256 dtypes for exact comparisons.
Check if a square 2D array is Hermitian
For square empty arrays the result is returned True by convention. Complex valued arrays are tested for symmetricity and not for being Hermitian (see examples)
The diagonal of the array is not scanned. Thus if there are infs, NaNs or similar problematic entries on the diagonal, they will be ignored. However,
numpy.infwill be treated as a number, that is to say
[[1, inf], [inf, 2]]will return
True. On the other hand
numpy.NaNis never symmetric, say,
[[1, nan], [nan, 2]]will return
rtolare set to , then the comparison is performed by
numpy.allcloseand 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
rtolgiven the other one is automatically set to zero.
>>> import numpy as np >>> from scipy.linalg import issymmetric >>> A = np.arange(9).reshape(3, 3) >>> A = A + A.T >>> issymmetric(A) True >>> Ac = np.array([[1. + 1.j, 3.j], [3.j, 2.]]) >>> issymmetric(Ac) # not Hermitian but symmetric True