pyyeti.ytools.mattype

pyyeti.ytools.mattype(A, mtype=None, return_cholesky=False)[source]

Checks contents of square matrix A to see if it is symmetric, hermitian, positive-definite, diagonal, and identity.

Parameters:

  • A (2d array_like or None) – If not square or if number of dimensions does not equal 2, the return type is 0. If None, just return the mattypes output (not a tuple).

  • mtype (string or None) – If string, it must be one of the mattypes listed below; in this case, True is returned if A is of the type specified or False otherwise. If None, Atype (if A is not None) and mattypes is returned. mtype is ignored if A is None.

  • return_cholesky (bool; optional) – If True, the output of scipy.linalg.cholesky() is returned if computed. Output will be None if A is not positive-definite. See example usages below.

Returns:

  • flag (bool) – True/False flag specifying whether or not A is of the type specified by mtype. Not returned if either A or mtype is None. If flag is returned, it is the only returned value.

  • Atype (integer) – Integer with bits set according to content. Not returned if A is None or if mtype is specified.

  • mattypes (dictionary) –

    Provided for reference:

    mattypes = {'symmetric': 1,
            'hermitian': 2,
            'posdef': 4,
            'diagonal': 8,
            'identity': 16}

    Not returned if mtype is specified. This is the only return if A is None.

  • chol (2d ndarray or None) – See return_cholesky above. If returned, chol will be the output of scipy.linalg.cholesky() (with default settings) or None, depending on whether matrix is positive-definite or not.

Notes

Here are some example usages:

Usage

Returns

mattype(A)

(Atype, mattypes)

mattype(A, return_cholesky=True)

(Atype, mattypes, chol)

mattype(A, ‘symmetric’)

True or False

mattype(A, ‘posdef’, return_cholesky=True)

(True or False, chol)

mattype(None)

mattypes

See also

isdiag()

Examples

>>> from pyyeti import ytools
>>> import numpy as np
>>> A = np.eye(5)
>>> ytools.mattype(A, 'identity')
True
>>> Atype, mattypes = ytools.mattype(A)
>>>
>>> Atype == 1 | 4 | 8 | 16
True
>>> if Atype & mattypes['identity']:
...     print('A is identity')
A is identity
>>> for i in sorted(mattypes):
...     print(f'{i:10s}: {mattypes[i]:2}')
diagonal  :  8
hermitian :  2
identity  : 16
posdef    :  4
symmetric :  1
>>> mattypes = ytools.mattype(None)
>>> for i in sorted(mattypes):
...     print(f'{i:10s}: {mattypes[i]:2}')
diagonal  :  8
hermitian :  2
identity  : 16
posdef    :  4
symmetric :  1