- naginterfaces.library.matop.real_gen_matrix_cond_std(fun, a)¶
real_gen_matrix_cond_stdcomputes an estimate of the absolute condition number of a matrix function at a real matrix in the -norm, where is either the exponential, logarithm, sine, cosine, hyperbolic sine (sinh) or hyperbolic cosine (cosh). The evaluation of the matrix function, , is also returned.
For full information please refer to the NAG Library document for f01ja
Indicates which matrix function will be used.
The matrix exponential, , will be used.
The matrix sine, , will be used.
The matrix cosine, , will be used.
The hyperbolic matrix sine, , will be used.
The hyperbolic matrix cosine, , will be used.
The matrix logarithm, , will be used.
- afloat, array-like, shape
The matrix .
- afloat, ndarray, shape
The matrix, .
An estimate of the absolute condition number of at .
The -norm of .
The -norm of .
The absolute condition number of at , is given by the norm of the Fréchet derivative of , , which is defined by
where is the Fréchet derivative in the direction . is linear in and can, therefore, be written as
where the operator stacks the columns of a matrix into one vector, so that is .
real_gen_matrix_cond_stdcomputes an estimate such that , where . The relative condition number can then be computed via
The algorithm used to find is detailed in Section 3.4 of Higham (2008).
Higham, N J, 2008, Functions of Matrices: Theory and Computation, SIAM, Philadelphia, PA, USA