scipy.linalg.coshm

scipy.linalg.coshm(A)

Compute the hyperbolic matrix cosine.

This routine uses expm to compute the matrix exponentials.

Parameters:

A(N, N) array_like

Input array.

Returns:

coshm(N, N) ndarray

Hyperbolic matrix cosine of A

Examples

>>> import numpy as np
>>> from scipy.linalg import tanhm, sinhm, coshm
>>> a = np.array([[1.0, 3.0], [1.0, 4.0]])
>>> c = coshm(a)
>>> c
array([[ 11.24592233,  38.76236492],
       [ 12.92078831,  50.00828725]])

Verify tanhm(a) = sinhm(a).dot(inv(coshm(a)))

>>> t = tanhm(a)
>>> s = sinhm(a)
>>> t - s.dot(np.linalg.inv(c))
array([[  2.72004641e-15,   4.55191440e-15],
       [  0.00000000e+00,  -5.55111512e-16]])