naginterfaces.library.matop.complex_gen_matrix_sqrt¶
- naginterfaces.library.matop.complex_gen_matrix_sqrt(a)[source]¶
complex_gen_matrix_sqrt
computes the principal matrix square root, , of a complex matrix .For full information please refer to the NAG Library document for f01fn
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f01/f01fnf.html
- Parameters
- acomplex, array-like, shape
The matrix .
- Returns
- acomplex, ndarray, shape
Contains, if no exception or warning is raised, the principal matrix square root, . Alternatively, if = 1, contains an non-principal square root of .
- Raises
- NagValueError
- (errno )
On entry, .
Constraint: .
- (errno )
has a defective vanishing eigenvalue. The square root cannot be found in this case.
- (errno )
An internal error occurred. It is likely that the function was called incorrectly.
- Warns
- NagAlgorithmicWarning
- (errno )
has a negative or semisimple vanishing eigenvalue. A non-principal square root is returned.
- Notes
A square root of a matrix is a solution to the equation . A nonsingular matrix has multiple square roots. For a matrix with no eigenvalues on the closed negative real line, the principal square root, denoted by , is the unique square root whose eigenvalues lie in the open right half-plane.
is computed using the algorithm described in Björck and Hammarling (1983). In addition a blocking scheme described in Deadman et al. (2013) is used.
- References
Björck, Å and Hammarling, S, 1983, A Schur method for the square root of a matrix, Linear Algebra Appl. (52/53), 127–140
Deadman, E, Higham, N J and Ralha, R, 2013, Blocked Schur Algorithms for Computing the Matrix Square Root, Applied Parallel and Scientific Computing: 11th International Conference, (PARA 2012, Helsinki, Finland), P. Manninen and P. Öster, Eds, Lecture Notes in Computer Science (7782), 171–181, Springer–Verlag
Higham, N J, 2008, Functions of Matrices: Theory and Computation, SIAM, Philadelphia, PA, USA