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Module « scipy.linalg »

Fonction funm - module scipy.linalg

Signature de la fonction funm

def funm(A, func, disp=True) 

Description

help(scipy.linalg.funm)

Evaluate a matrix function specified by a callable.

Returns the value of matrix-valued function ``f`` at `A`. The
function ``f`` is an extension of the scalar-valued function `func`
to matrices.

Parameters
----------
A : (N, N) array_like
    Matrix at which to evaluate the function
func : callable
    Callable object that evaluates a scalar function f.
    Must be vectorized (eg. using vectorize).
disp : bool, optional
    Print warning if error in the result is estimated large
    instead of returning estimated error. (Default: True)

Returns
-------
funm : (N, N) ndarray
    Value of the matrix function specified by func evaluated at `A`
errest : float
    (if disp == False)

    1-norm of the estimated error, ||err||_1 / ||A||_1

Notes
-----
This function implements the general algorithm based on Schur decomposition
(Algorithm 9.1.1. in [1]_).

If the input matrix is known to be diagonalizable, then relying on the
eigendecomposition is likely to be faster. For example, if your matrix is
Hermitian, you can do

>>> from scipy.linalg import eigh
>>> def funm_herm(a, func, check_finite=False):
...     w, v = eigh(a, check_finite=check_finite)
...     ## if you further know that your matrix is positive semidefinite,
...     ## you can optionally guard against precision errors by doing
...     # w = np.maximum(w, 0)
...     w = func(w)
...     return (v * w).dot(v.conj().T)

References
----------
.. [1] Gene H. Golub, Charles F. van Loan, Matrix Computations 4th ed.

Examples
--------
>>> import numpy as np
>>> from scipy.linalg import funm
>>> a = np.array([[1.0, 3.0], [1.0, 4.0]])
>>> funm(a, lambda x: x*x)
array([[  4.,  15.],
       [  5.,  19.]])
>>> a.dot(a)
array([[  4.,  15.],
       [  5.,  19.]])

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