def _getEigvecs(modes, row_norm=False, dummy_mode=False):
la = importLA()
if isinstance(modes, (Mode, ModeSet, NMA)):
model = modes._model
if isinstance(model, MaskedGNM):
masked = model.masked
model.masked = True
V = modes.getArray()
model.masked = masked
else:
V = modes.getArray()
elif isinstance(modes, np.ndarray):
V = modes
else:
try:
mode0 = modes[0]
if isinstance(mode0, Mode):
V = np.empty((len(mode0), 0))
for mode in modes:
assert isinstance(mode,
Mode), 'Modes should be a list of modes.'
v = mode.getEigvec()
v = np.expand_dims(v, axis=1)
V = np.hstack((V, v))
else:
V = np.array(modes)
except TypeError:
raise TypeError('Modes should be a list of modes.')
if V.ndim == 1:
V = np.expand_dims(V, axis=1)
# add a dummy zero mode to the modeset
if dummy_mode:
v0 = V[:, 0]
if np.allclose(v0, np.mean(v0)):
dummy_mode = False
LOGGER.warn(
'at least one zero mode is detected therefore dummy mode will NOT be added'
)
if dummy_mode:
n, _ = V.shape
v0 = np.ones((n, 1), dtype=V.dtype)
v0 /= la.norm(v0)
V = np.hstack((v0, V))
LOGGER.debug('a dummy zero mode is added')
# normalize the rows so that feature vectors are unit vectors
if row_norm:
norms = la.norm(V, axis=1)
N = np.diag(div0(1., norms))
V = np.dot(N, V)
return V
def _getEigvecs(modes, row_norm=False, remove_zero_rows=False):
if isinstance(modes, (ModeSet, NMA)):
V = modes.getEigvecs()
elif isinstance(modes, Mode):
V = modes.getEigvec()
elif isinstance(modes, np.ndarray):
V = modes
else:
try:
mode0 = modes[0]
if isinstance(mode0, Mode):
V = np.empty((len(mode0), 0))
for mode in modes:
assert isinstance(mode,
Mode), 'Modes should be a list of modes.'
v = mode.getEigvec()
v = np.expand_dims(v, axis=1)
V = np.hstack((V, v))
else:
V = np.array(modes)
except TypeError:
TypeError('Modes should be a list of modes.')
if V.ndim == 1:
V = np.expand_dims(V, axis=1)
# normalize the rows so that feature vectors are unit vectors
if row_norm:
la = importLA()
norms = la.norm(V, axis=1)
N = np.diag(div0(1., norms))
V = np.dot(N, V)
# remove rows with all zeros
m, _ = V.shape
mask = np.ones(m, dtype=bool)
if remove_zero_rows:
mask = V.any(axis=1)
V = V[mask]
return V, mask
def _getEigvecs(modes, row_norm=False, remove_zero_rows=False):
if isinstance(modes, (ModeSet, NMA)):
V = modes.getEigvecs()
elif isinstance(modes, Mode):
V = modes.getEigvec()
elif isinstance(modes, np.ndarray):
V = modes
else:
try:
mode0 = modes[0]
if isinstance(mode0, Mode):
V = np.empty((len(mode0),0))
for mode in modes:
assert isinstance(mode, Mode), 'Modes should be a list of modes.'
v = mode.getEigvec()
v = np.expand_dims(v, axis=1)
V = np.hstack((V, v))
else:
V = np.array(modes)
except TypeError:
TypeError('Modes should be a list of modes.')
if V.ndim == 1:
V = np.expand_dims(V, axis=1)
# normalize the rows so that feature vectors are unit vectors
if row_norm:
la = importLA()
norms = la.norm(V, axis=1)
N = np.diag(div0(1., norms))
V = np.dot(N, V)
# remove rows with all zeros
m, _ = V.shape
mask = np.ones(m, dtype=bool)
if remove_zero_rows:
mask = V.any(axis=1)
V = V[mask]
return V, mask
def calcPerturbResponse(model, **kwargs):
"""This function implements the perturbation response scanning (PRS) method
described in [CA09]_ and [IG14]_. It returns a PRS matrix, and effectiveness
and sensitivity profiles.
Rows of the matrix are the average magnitude of the responses obtained by
perturbing the atom/node position at that row index, i.e. ``prs_matrix[i,j]``
will give the response of residue/node *j* to perturbations in residue/node *i*.
PRS is performed using the covariance matrix from a *model*, e.g.
a :class:`.ANM` instance. To use an external matrix, please provide it to
a :class:`.PCA` instance using the :meth:`.PCA.setCovariance`.
When an *atoms* instance is given, the PRS matrix will be added as data,
which can be retrieved with ``atoms.getData('prs_matrix')``.
*model* and *atoms* must have the same number of atoms. *atoms* must be an
:class:`.AtomGroup` instance.
.. [CA09] Atilgan C, Atilgan AR, Perturbation-Response Scanning
Reveals Ligand Entry-Exit Mechanisms of Ferric Binding Protein.
*PLoS Comput Biol* **2009** 5(10):e1000544.
.. [IG14] General IJ, Liu Y, Blackburn ME, Mao W, Gierasch LM, Bahar I.
ATPase subdomain IA is a mediator of interdomain allostery in Hsp70
molecular chaperones. *PLoS Comput. Biol.* **2014** 10:e1003624.
If *turbo* is **True** (default), then PRS is approximated by the limit of
large numbers of forces and no perturbation forces are explicitly applied.
If set to **False**, then each residue/node is perturbed *repeats* times (default 100)
with a random unit force vector as in ProDy v1.8 and earlier.
"""
if not isinstance(model, (NMA, ModeSet, Mode)):
raise TypeError('model must be an NMA, ModeSet, or Mode instance')
if isinstance(model, NMA) and len(model) == 0:
raise ValueError('model must have normal modes calculated')
atoms = kwargs.get('atoms', None)
suppress_diag = kwargs.get('suppress_diag', False)
no_diag = kwargs.get('no_diag', suppress_diag)
if atoms is not None:
if isinstance(atoms, Selection):
atoms = atoms.copy()
if not isinstance(atoms, AtomGroup):
raise TypeError('atoms must be an AtomGroup instance')
elif atoms.numAtoms() != model.numAtoms():
raise ValueError('model and atoms must have the same number atoms')
n_atoms = model.numAtoms()
# LOGGER.timeit('_prody_prs_all')
# LOGGER.info('Calculating covariance matrix')
# LOGGER.timeit('_prody_cov')
cov = model.getCovariance()
turbo = kwargs.get('turbo', True)
if turbo:
if not model.is3d():
prs_matrix = cov**2
else:
cov_squared = cov**2
n_by_3n_cov_squared = np.zeros((n_atoms, 3 * n_atoms))
prs_matrix = np.zeros((n_atoms, n_atoms))
i3 = -3
i3p3 = 0
for i in range(n_atoms):
i3 += 3
i3p3 += 3
n_by_3n_cov_squared[i, :] = (cov_squared[i3:i3p3, :]).sum(0)
j3 = -3
j3p3 = 0
for j in range(n_atoms):
j3 += 3
j3p3 += 3
prs_matrix[:, j] = (n_by_3n_cov_squared[:, j3:j3p3]).sum(1)
else:
repeats = kwargs.pop('repeats', 100)
LOGGER.info(
'Calculating perturbation response with {0} repeats'.format(
repeats))
LOGGER.timeit('_prody_prs_mat')
response_matrix = np.zeros((n_atoms, n_atoms))
LOGGER.progress('Calculating perturbation response', n_atoms,
'_prody_prs')
i3 = -3
i3p3 = 0
for i in range(n_atoms):
i3 += 3
i3p3 += 3
forces = np.random.rand(repeats * 3).reshape((repeats, 3))
forces /= ((forces**2).sum(1)**0.5).reshape((repeats, 1))
for force in forces:
response_matrix[i] += (np.dot(cov[:, i3:i3p3],
force)**2).reshape(
(n_atoms, 3)).sum(1)
LOGGER.update(i, '_prody_prs')
response_matrix /= repeats
LOGGER.clear()
LOGGER.report('Perturbation response matrix calculated in %.1fs.',
'_prody_prs_mat')
norm_prs_matrix = np.zeros((n_atoms, n_atoms))
self_dp = np.diag(prs_matrix)
self_dp = self_dp.reshape(n_atoms, 1)
re_self_dp = np.repeat(self_dp, n_atoms, axis=1)
norm_prs_matrix = div0(prs_matrix, re_self_dp)
if no_diag:
# suppress the diagonal (self displacement) to facilitate
# visualizing the response profile
norm_prs_matrix = norm_prs_matrix - np.diag(np.diag(norm_prs_matrix))
W = 1 - np.eye(n_atoms)
effectiveness = np.average(norm_prs_matrix, weights=W, axis=1)
sensitivity = np.average(norm_prs_matrix, weights=W, axis=0)
# LOGGER.report('Perturbation response scanning completed in %.1fs.',
# '_prody_prs_all')
if atoms is not None:
try:
ag = atoms.getAtomGroup()
defdata = np.zeros(ag.numAtoms(), dtype=float)
ag.setData('effectiveness', defdata.copy())
ag.setData('sensitivity', defdata.copy())
except AttributeError:
pass
atoms.setData('effectiveness', effectiveness)
atoms.setData('sensitivity', sensitivity)
#atoms.setData('prs_matrix', norm_prs_matrix)
return norm_prs_matrix, effectiveness, sensitivity
def calcCrossCorr(modes, n_cpu=1, norm=True):
"""Returns cross-correlations matrix. For a 3-d model, cross-correlations
matrix is an NxN matrix, where N is the number of atoms. Each element of
this matrix is the trace of the submatrix corresponding to a pair of atoms.
Covariance matrix may be calculated using all modes or a subset of modes
of an NMA instance. For large systems, calculation of cross-correlations
matrix may be time consuming. Optionally, multiple processors may be
employed to perform calculations by passing ``n_cpu=2`` or more."""
if not isinstance(n_cpu, int):
raise TypeError('n_cpu must be an integer')
elif n_cpu < 1:
raise ValueError('n_cpu must be equal to or greater than 1')
if not isinstance(modes, (Mode, NMA, ModeSet)):
if isinstance(modes, list):
try:
is3d = modes[0].is3d()
except:
raise TypeError(
'modes must be a list of Mode or Vector instances, '
'not {0}'.format(type(modes)))
else:
raise TypeError('modes must be a Mode, NMA, or ModeSet instance, '
'not {0}'.format(type(modes)))
else:
is3d = modes.is3d()
if is3d:
model = modes
if isinstance(modes, (Mode, ModeSet)):
model = modes._model
if isinstance(modes, (Mode)):
indices = [modes.getIndex()]
n_modes = 1
else:
indices = modes.getIndices()
n_modes = len(modes)
else:
n_modes = len(modes)
indices = np.arange(n_modes)
array = model._getArray()
n_atoms = model._n_atoms
variances = model._vars
if n_cpu == 1:
s = (n_modes, n_atoms, 3)
arvar = (array[:, indices] * variances[indices]).T.reshape(s)
array = array[:, indices].T.reshape(s)
covariance = np.tensordot(array.transpose(2, 0, 1),
arvar.transpose(0, 2, 1),
axes=([0, 1], [1, 0]))
else:
import multiprocessing
n_cpu = min(multiprocessing.cpu_count(), n_cpu)
queue = multiprocessing.Queue()
size = n_modes / n_cpu
for i in range(n_cpu):
if n_cpu - i == 1:
indices = modes.indices[i * size:]
else:
indices = modes.indices[i * size:(i + 1) * size]
process = multiprocessing.Process(target=_crossCorrelations,
args=(queue, n_atoms, array,
variances, indices))
process.start()
while queue.qsize() < n_cpu:
time.sleep(0.05)
covariance = queue.get()
while queue.qsize() > 0:
covariance += queue.get()
else:
covariance = calcCovariance(modes)
if norm:
diag = np.power(covariance.diagonal(), 0.5)
D = np.outer(diag, diag)
covariance = div0(covariance, D)
return covariance
def solveEig(M, n_modes=None, zeros=False, turbo=True, is3d=False):
linalg = importLA()
dof = M.shape[0]
expct_n_zeros = 6 if is3d else 1
if n_modes is None:
eigvals = None
n_modes = dof
else:
if n_modes >= dof:
eigvals = None
n_modes = dof
else:
eigvals = (0, n_modes+expct_n_zeros-1)
def _eigh(M, eigvals=None, turbo=True):
if linalg.__package__.startswith('scipy'):
from scipy.sparse import issparse
if eigvals:
turbo = False
if not issparse(M):
values, vectors = linalg.eigh(M, turbo=turbo, eigvals=eigvals)
else:
try:
from scipy.sparse import linalg as scipy_sparse_la
except ImportError:
raise ImportError('failed to import scipy.sparse.linalg, '
'which is required for sparse matrix '
'decomposition')
if eigvals:
j = eigvals[0]
k = eigvals[-1] + 1
else:
j = 0
k = dof
if k >= dof:
k -= 1
LOGGER.warning('Cannot calculate all eigenvalues for sparse matrices, thus '
'the last eigenvalue is omitted. See scipy.sparse.linalg.eigsh '
'for more information')
values, vectors = scipy_sparse_la.eigsh(M, k=k, which='SA')
values = values[j:k]
vectors = vectors[:, j:k]
else:
if n_modes is not None:
LOGGER.info('Scipy is not found, all modes were calculated.')
else:
n_modes = dof
values, vectors = linalg.eigh(M)
return values, vectors
def _calc_n_zero_modes(M):
from scipy.sparse import issparse
if not issparse(M):
w = linalg.eigvalsh(M)
else:
try:
from scipy.sparse import linalg as scipy_sparse_la
except ImportError:
raise ImportError('failed to import scipy.sparse.linalg, '
'which is required for sparse matrix '
'decomposition')
w, _ = scipy_sparse_la.eigsh(M, k=dof-1, which='SA')
n_zeros = sum(w < ZERO)
return n_zeros
values, vectors = _eigh(M, eigvals, turbo)
n_zeros = sum(values < ZERO)
if n_zeros < n_modes + expct_n_zeros:
if n_zeros < expct_n_zeros:
LOGGER.warning('Fewer than %d (%d) zero eigenvalues were calculated.'%(expct_n_zeros, n_zeros))
elif n_zeros > expct_n_zeros:
LOGGER.warning('More than %d (%d) zero eigenvalues were calculated.'%(expct_n_zeros, n_zeros))
else:
LOGGER.warning('More than %d zero eigenvalues were detected.'%expct_n_zeros)
if not zeros:
if n_zeros > expct_n_zeros:
if n_zeros == n_modes + expct_n_zeros and n_modes != dof:
LOGGER.debug('Determing the number of zero eigenvalues...')
# find the actual number of zero modes
n_zeros = _calc_n_zero_modes(M)
LOGGER.debug('%d zero eigenvalues detected.'%n_zeros)
LOGGER.debug('Solving for additional eigenvalues...')
start = min(n_modes+expct_n_zeros, dof-1); end = min(n_modes+n_zeros-1, dof-1)
values_, vectors_ = _eigh(M, eigvals=(start, end))
values = np.concatenate((values, values_))
vectors = np.hstack((vectors, vectors_))
# final_n_modes may exceed len(eigvals) - no need to fix for the sake of the simplicity of the code
final_n_modes = n_zeros + n_modes
eigvals = values[n_zeros:final_n_modes]
eigvecs = vectors[:, n_zeros:final_n_modes]
vars = 1 / eigvals
else:
eigvals = values[:n_modes]
eigvecs = vectors[:, :n_modes]
vars = div0(1, values)
vars[:n_zeros] = 0.
vars = vars[:n_modes]
return eigvals, eigvecs, vars
def solveEig(M, n_modes=None, zeros=False, turbo=True, is3d=False):
linalg = importLA()
dof = M.shape[0]
expct_n_zeros = 6 if is3d else 1
if n_modes is None:
eigvals = None
n_modes = dof
else:
if n_modes >= dof:
eigvals = None
n_modes = dof
else:
eigvals = (0, n_modes+expct_n_zeros-1)
def _eigh(M, eigvals=None, turbo=True):
if linalg.__package__.startswith('scipy'):
from scipy.sparse import issparse
if eigvals:
turbo = False
if not issparse(M):
values, vectors = linalg.eigh(M, turbo=turbo, eigvals=eigvals)
else:
try:
from scipy.sparse import linalg as scipy_sparse_la
except ImportError:
raise ImportError('failed to import scipy.sparse.linalg, '
'which is required for sparse matrix '
'decomposition')
if eigvals:
j = eigvals[0]
k = eigvals[-1] + 1
else:
j = 0
k = dof
if k >= dof:
k -= 1
LOGGER.warning('Cannot calculate all eigenvalues for sparse matrices, thus '
'the last eigenvalue is omitted. See scipy.sparse.linalg.eigsh '
'for more information')
values, vectors = scipy_sparse_la.eigsh(M, k=k, which='SA')
values = values[j:k]
vectors = vectors[:, j:k]
else:
if n_modes is not None:
LOGGER.info('Scipy is not found, all modes were calculated.')
else:
n_modes = dof
values, vectors = linalg.eigh(M)
return values, vectors
def _calc_n_zero_modes(M):
from scipy.sparse import issparse
if not issparse(M):
w = linalg.eigvalsh(M)
else:
try:
from scipy.sparse import linalg as scipy_sparse_la
except ImportError:
raise ImportError('failed to import scipy.sparse.linalg, '
'which is required for sparse matrix '
'decomposition')
w, _ = scipy_sparse_la.eigsh(M, k=dof-1, which='SA')
n_zeros = sum(w < ZERO)
return n_zeros
values, vectors = _eigh(M, eigvals, turbo)
n_zeros = sum(values < ZERO)
if n_zeros < n_modes + expct_n_zeros:
if n_zeros < expct_n_zeros:
LOGGER.warning('Fewer than %d (%d) zero eigenvalues were calculated.'%(expct_n_zeros, n_zeros))
elif n_zeros > expct_n_zeros:
LOGGER.warning('More than %d (%d) zero eigenvalues were calculated.'%(expct_n_zeros, n_zeros))
else:
LOGGER.warning('More than %d zero eigenvalues were detected.'%expct_n_zeros)
if not zeros:
if n_zeros > expct_n_zeros:
if n_zeros == n_modes + expct_n_zeros and n_modes != dof:
LOGGER.debug('Determing the number of zero eigenvalues...')
# find the actual number of zero modes
n_zeros = _calc_n_zero_modes(M)
LOGGER.debug('%d zero eigenvalues detected.'%n_zeros)
LOGGER.debug('Solving for additional eigenvalues...')
start = min(n_modes+expct_n_zeros, dof-1); end = min(n_modes+n_zeros-1, dof-1)
values_, vectors_ = _eigh(M, eigvals=(start, end))
values = np.concatenate((values, values_))
vectors = np.hstack((vectors, vectors_))
# final_n_modes may exceed len(eigvals) - no need to fix for the sake of the simplicity of the code
final_n_modes = n_zeros + n_modes
eigvals = values[n_zeros:final_n_modes]
eigvecs = vectors[:, n_zeros:final_n_modes]
vars = 1 / eigvals
else:
eigvals = values[:n_modes]
eigvecs = vectors[:, :n_modes]
vars = div0(1, values)
vars[:n_zeros] = 0.
vars = vars[:n_modes]
return eigvals, eigvecs, vars
def calcCrossCorr(modes, n_cpu=1, norm=True):
"""Returns cross-correlations matrix. For a 3-d model, cross-correlations
matrix is an NxN matrix, where N is the number of atoms. Each element of
this matrix is the trace of the submatrix corresponding to a pair of atoms.
Covariance matrix may be calculated using all modes or a subset of modes
of an NMA instance. For large systems, calculation of cross-correlations
matrix may be time consuming. Optionally, multiple processors may be
employed to perform calculations by passing ``n_cpu=2`` or more."""
if not isinstance(n_cpu, int):
raise TypeError('n_cpu must be an integer')
elif n_cpu < 1:
raise ValueError('n_cpu must be equal to or greater than 1')
if not isinstance(modes, (Mode, NMA, ModeSet)):
if isinstance(modes, list):
try:
is3d = modes[0].is3d()
except:
raise TypeError('modes must be a list of Mode or Vector instances, '
'not {0}'.format(type(modes)))
else:
raise TypeError('modes must be a Mode, NMA, or ModeSet instance, '
'not {0}'.format(type(modes)))
else:
is3d = modes.is3d()
if is3d:
model = modes
if isinstance(modes, (Mode, ModeSet)):
model = modes._model
if isinstance(modes, (Mode)):
indices = [modes.getIndex()]
n_modes = 1
else:
indices = modes.getIndices()
n_modes = len(modes)
else:
n_modes = len(modes)
indices = np.arange(n_modes)
array = model._getArray()
n_atoms = model._n_atoms
variances = model._vars
if n_cpu == 1:
s = (n_modes, n_atoms, 3)
arvar = (array[:, indices]*variances[indices]).T.reshape(s)
array = array[:, indices].T.reshape(s)
covariance = np.tensordot(array.transpose(2, 0, 1),
arvar.transpose(0, 2, 1),
axes=([0, 1], [1, 0]))
else:
import multiprocessing
n_cpu = min(multiprocessing.cpu_count(), n_cpu)
queue = multiprocessing.Queue()
size = n_modes / n_cpu
for i in range(n_cpu):
if n_cpu - i == 1:
indices = modes.indices[i*size:]
else:
indices = modes.indices[i*size:(i+1)*size]
process = multiprocessing.Process(
target=_crossCorrelations,
args=(queue, n_atoms, array, variances, indices))
process.start()
while queue.qsize() < n_cpu:
time.sleep(0.05)
covariance = queue.get()
while queue.qsize() > 0:
covariance += queue.get()
else:
covariance = calcCovariance(modes)
if norm:
diag = np.power(covariance.diagonal(), 0.5)
D = np.outer(diag, diag)
covariance = div0(covariance, D)
return covariance
