def get_eigs(Ei, Eij, T=0.05):
from pele.utils.hessian import sort_eigs
m = make_rate_matrix(Ei, Eij, T=T)
lam, v = np.linalg.eig(m)
lam, v = sort_eigs(lam, v)
print "exact eigenvalues", sorted(-lam)
print "exact eigenvectors"
print v
def normalmodes(hessian, metric=None, eps=1e-4, symmetric=False):
"""calculate (squared) normal mode frequencies and normal mode vectors
Parameters
----------
hessian: array
hessian marix
metric: array
mass weighted metric tensor
symmetric: bool
If true, the Hessian times the metric tensor is assumed to be symmetric. This is
not usually the case, even if the metric tensor is symmetric. It is
true if the metric tensor is the identity.
Returns
-------
freq, evecs tuple array of squared frequencies and normal modes
"""
if metric is None:
A = hessian
symmetric = True
else:
A = np.dot(np.linalg.pinv(metric), hessian)
if symmetric:
freq, evecs = np.linalg.eigh(A)
else:
freq, evecs = np.linalg.eig(A)
if np.max(np.abs(np.imag(freq))) > eps:
print freq
raise ValueError(
"imaginary eigenvalue in frequency calculation"
", check hessian + metric tensor\nthe largest imaginary part is %g"
% np.max(np.abs(np.imag(freq))))
freq = np.real(freq)
freq, evecs = sort_eigs(freq, evecs)
return freq, evecs
def normalmodes(hessian, metric=None, eps=1e-4, symmetric=False):
"""calculate (squared) normal mode frequencies and normal mode vectors
Parameters
----------
hessian: array
hessian marix
metric: array
mass weighted metric tensor
symmetric: bool
If true, the Hessian times the metric tensor is assumed to be symmetric. This is
not usually the case, even if the metric tensor is symmetric. It is
true if the metric tensor is the identity.
Returns
-------
freq, evecs tuple array of squared frequencies and normal modes
"""
if metric is None:
A = hessian
symmetric = True
else:
A = np.dot(np.linalg.pinv(metric), hessian)
if symmetric:
freq, evecs = np.linalg.eigh(A)
else:
freq, evecs = np.linalg.eig(A)
if np.max(np.abs(np.imag(freq))) > eps:
print(freq)
raise ValueError("imaginary eigenvalue in frequency calculation"
", check hessian + metric tensor\nthe largest imaginary part is %g" % np.max(
np.abs(np.imag(freq))))
freq = np.real(freq)
freq, evecs = sort_eigs(freq, evecs)
return freq, evecs