# scipy.linalg.funm#

scipy.linalg.funm(A, func, disp=True)[source]#

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

funccallable

Callable object that evaluates a scalar function f. Must be vectorized (eg. using vectorize).

dispbool, 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

errestfloat

(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 ).

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



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.]])
```