def timescales_from_eigenvalues(ev, tau=1):
r"""Compute implied time scales from given eigenvalues
Parameters
----------
eval : eigenvalues
tau : lag time
Returns
-------
ts : ndarray
The implied time scales to the given eigenvalues, in the same order.
"""
"""Check for dominant eigenvalues with large imaginary part"""
if not np.allclose(ev.imag, 0.0):
warnings.warn('Using eigenvalues with non-zero imaginary part '
'for implied time scale computation', ImaginaryEigenValueWarning)
"""Check for multiple eigenvalues of magnitude one"""
ind_abs_one = isclose(np.abs(ev), 1.0)
if sum(ind_abs_one) > 1:
warnings.warn('Multiple eigenvalues with magnitude one.', SpectralWarning)
"""Compute implied time scales"""
ts = np.zeros(len(ev))
"""Eigenvalues of magnitude one imply infinite timescale"""
ts[ind_abs_one] = np.inf
"""All other eigenvalues give rise to finite timescales"""
ts[np.logical_not(ind_abs_one)] = \
-1.0 * tau / np.log(np.abs(ev[np.logical_not(ind_abs_one)]))
return ts
def timescales_from_eigenvalues(eval, tau=1):
r"""Compute implied time scales from given eigenvalues
Parameters
----------
eval : eigenvalues
tau : lag time
Returns
-------
ts : ndarray
The implied time scales to the given eigenvalues, in the same order.
"""
"""Check for dominant eigenvalues with large imaginary part"""
if not np.allclose(eval.imag, 0.0):
warnings.warn('Using eigenvalues with non-zero imaginary part '
'for implied time scale computation', ImaginaryEigenValueWarning)
"""Check for multiple eigenvalues of magnitude one"""
ind_abs_one=isclose(np.abs(eval), 1.0)
if sum(ind_abs_one)>1:
warnings.warn('Multiple eigenvalues with magnitude one.', SpectralWarning)
"""Compute implied time scales"""
ts=np.zeros(len(eval))
"""Eigenvalues of magnitude one imply infinite timescale"""
ts[ind_abs_one]=np.inf
"""All other eigenvalues give rise to finite timescales"""
ts[np.logical_not(ind_abs_one)]=\
-1.0*tau/np.log(np.abs(eval[np.logical_not(ind_abs_one)]))
return ts
def timescales(T, tau=1, k=None, ncv=None):
r"""Compute implied time scales of given transition matrix
Parameters
----------
T : transition matrix
tau : lag time
k : int (optional)
Compute the first k implied time scales.
ncv : int (optional)
The number of Lanczos vectors generated, `ncv` must be greater than k;
it is recommended that ncv > 2*k
Returns
-------
ts : ndarray
The implied time scales of the transition matrix.
"""
if k is None:
raise ValueError(
"Number of time scales required for decomposition of sparse matrix"
)
values = scipy.sparse.linalg.eigs(T,
k=k,
which='LM',
return_eigenvectors=False,
ncv=ncv)
"""Sort by absolute value"""
ind = np.argsort(np.abs(values))[::-1]
values = values[ind]
"""Check for dominant eigenvalues with large imaginary part"""
if not np.allclose(values.imag, 0.0):
warnings.warn(
'Using eigenvalues with non-zero imaginary part '
'for implied time scale computation', ImaginaryEigenValueWarning)
"""Check for multiple eigenvalues of magnitude one"""
ind_abs_one = isclose(np.abs(values), 1.0)
if sum(ind_abs_one) > 1:
warnings.warn('Multiple eigenvalues with magnitude one.',
SpectralWarning)
"""Compute implied time scales"""
ts = np.zeros(len(values))
"""Eigenvalues of magnitude one imply infinite rate"""
ts[ind_abs_one] = np.inf
"""All other eigenvalues give rise to finite rates"""
ts[np.logical_not(ind_abs_one)] = \
-1.0 * tau / np.log(np.abs(values[np.logical_not(ind_abs_one)]))
return ts
def timescales(T, tau=1, k=None, ncv=None):
r"""Compute implied time scales of given transition matrix
Parameters
----------
T : transition matrix
tau : lag time
k : int (optional)
Compute the first k implied time scales.
ncv : int (optional)
The number of Lanczos vectors generated, `ncv` must be greater than k;
it is recommended that ncv > 2*k
Returns
-------
ts : ndarray
The implied time scales of the transition matrix.
"""
if k is None:
raise ValueError("Number of time scales required for decomposition of sparse matrix")
values = scipy.sparse.linalg.eigs(T, k=k, which='LM', return_eigenvectors=False, ncv=ncv)
"""Sort by absolute value"""
ind = np.argsort(np.abs(values))[::-1]
values = values[ind]
"""Check for dominant eigenvalues with large imaginary part"""
if not np.allclose(values.imag, 0.0):
warnings.warn('Using eigenvalues with non-zero imaginary part '
'for implied time scale computation', ImaginaryEigenValueWarning)
"""Check for multiple eigenvalues of magnitude one"""
ind_abs_one = isclose(np.abs(values), 1.0)
if sum(ind_abs_one) > 1:
warnings.warn('Multiple eigenvalues with magnitude one.', SpectralWarning)
"""Compute implied time scales"""
ts = np.zeros(len(values))
"""Eigenvalues of magnitude one imply infinite rate"""
ts[ind_abs_one] = np.inf
"""All other eigenvalues give rise to finite rates"""
ts[np.logical_not(ind_abs_one)] = \
-1.0 * tau / np.log(np.abs(values[np.logical_not(ind_abs_one)]))
return ts