def powerm(x, power):
ndim = x.ndim
new_x = to_ndarray(x, to_ndim=3)
if is_symmetric(new_x):
eigvals, eigvecs = np.linalg.eigh(new_x)
eigvals = eigvals**power
if (eigvals > 0).all():
eigvals = np.vectorize(np.diag, signature='(n)->(n,n)')(eigvals)
transp_eigvecs = np.transpose(eigvecs, axes=(0, 2, 1))
result = np.matmul(eigvecs, eigvals)
result = np.matmul(result, transp_eigvecs)
else:
log_x = np.vectorize(scipy.linalg.logm,
signature='(n,m)->(n,m)')(new_x)
p_log_x = power * log_x
result = np.vectorize(scipy.linalg.expm,
signature='(n,m)->(n,m)')(p_log_x)
else:
log_x = np.vectorize(scipy.linalg.logm,
signature='(n,m)->(n,m)')(new_x)
p_log_x = power * log_x
result = np.vectorize(scipy.linalg.expm,
signature='(n,m)->(n,m)')(p_log_x)
if ndim == 2:
return result[0]
return result
def expm(x):
ndim = x.ndim
new_x = to_ndarray(x, to_ndim=3)
if is_symmetric(new_x):
result = expsym(new_x)
else:
result = np.vectorize(scipy.linalg.expm,
signature='(n,m)->(n,m)')(new_x)
if ndim == 2:
return result[0]
return result
def is_symmetric(x):
new_x = to_ndarray(x, to_ndim=3)
return (new_x - np.transpose(new_x, axes=(0, 2, 1)) == 0).all()
def is_symmetric(x, tol=TOL):
new_x = to_ndarray(x, to_ndim=3)
return (np.abs(new_x - np.transpose(new_x, axes=(0, 2, 1))) < tol).all()
