def buildHessian(self, coords, cutoff=15.0, gamma=1.0, **kwargs):
"""Build Hessian matrix for given coordinate set.
:arg coords: a coordinate set or anything with getCoordinates method
:type coords: :class:`~numpy.ndarray` or :class:`~prody.atomic.Atomic`
:arg cutoff: cutoff distance (Å) for pairwise interactions,
default is 15.0 Å, minimum is 4.0 Å
:type cutoff: float
:arg gamma: spring constant, default is 1.0
:type gamma: float, :class:`Gamma`
:arg sparse: slect to use sparse matrices. Default is ``False``. If
Scipy is not found, :class:`ImportError` is raised.
:type sparse: bool
Instances of :class:`Gamma` classes and custom functions are
accepted as *gamma* argument.
When Scipy is available, user can select to use sparse matrices for
efficient usage of memory at the cost of computation speed."""
slow = kwargs.get("slow", False)
try:
from KDTree import KDTree
except ImportError:
KDTree = False
if not slow and not KDTree:
LOGGER.info("Using a slower method for building the Hessian " "matrix.")
if not isinstance(coords, np.ndarray):
try:
coords = coords.getCoords()
except AttributeError:
raise TypeError("coords must be a Numpy array or must have " "getCoordinates attribute")
coords = checkCoords(coords, "coords")
cutoff, g, gamma = checkENMParameters(cutoff, gamma)
self._reset()
self._cutoff = cutoff
self._gamma = g
n_atoms = coords.shape[0]
dof = n_atoms * 3
start = time.time()
if kwargs.get("sparse", False):
try:
from scipy import sparse as scipy_sparse
except ImportError:
raise ImportError("failed to import scipy.sparse, which is " "required for sparse matrix calculations")
kirchhoff = scipy_sparse.lil_matrix((n_atoms, n_atoms))
hessian = scipy_sparse.lil_matrix((dof, dof))
else:
kirchhoff = np.zeros((n_atoms, n_atoms), "d")
hessian = np.zeros((dof, dof), float)
if not slow and KDTree:
kdtree = getKDTree(coords)
kdtree.all_search(cutoff)
for i, j in kdtree.all_get_indices():
i2j = coords[j] - coords[i]
dist2 = np.dot(i2j, i2j)
g = gamma(dist2, i, j)
super_element = np.outer(i2j, i2j) * (-g / dist2)
res_i3 = i * 3
res_i33 = res_i3 + 3
res_j3 = j * 3
res_j33 = res_j3 + 3
hessian[res_i3:res_i33, res_j3:res_j33] = super_element
hessian[res_j3:res_j33, res_i3:res_i33] = super_element
hessian[res_i3:res_i33, res_i3:res_i33] = hessian[res_i3:res_i33, res_i3:res_i33] - super_element
hessian[res_j3:res_j33, res_j3:res_j33] = hessian[res_j3:res_j33, res_j3:res_j33] - super_element
kirchhoff[i, j] = -g
kirchhoff[j, i] = -g
kirchhoff[i, i] = kirchhoff[i, i] - g
kirchhoff[j, j] = kirchhoff[j, j] - g
else:
cutoff2 = cutoff * cutoff
for i in range(n_atoms):
res_i3 = i * 3
res_i33 = res_i3 + 3
xyz_i = coords[i, :]
for j in range(i + 1, n_atoms):
i2j = coords[j, :] - xyz_i
dist2 = np.dot(i2j, i2j)
if dist2 > cutoff2:
continue
g = gamma(dist2, i, j)
res_j3 = j * 3
res_j33 = res_j3 + 3
super_element = np.outer(i2j, i2j) * (-g / dist2)
hessian[res_i3:res_i33, res_j3:res_j33] = super_element
hessian[res_j3:res_j33, res_i3:res_i33] = super_element
hessian[res_i3:res_i33, res_i3:res_i33] = hessian[res_i3:res_i33, res_i3:res_i33] - super_element
hessian[res_j3:res_j33, res_j3:res_j33] = hessian[res_j3:res_j33, res_j3:res_j33] - super_element
kirchhoff[i, j] = -g
kirchhoff[j, i] = -g
kirchhoff[i, i] = kirchhoff[i, i] - g
kirchhoff[j, j] = kirchhoff[j, j] - g
LOGGER.info("Hessian was built in {0:.2f}s.".format(time.time() - start))
self._kirchhoff = kirchhoff
self._hessian = hessian
self._n_atoms = n_atoms
self._dof = dof
def buildHessian(self, coords, cutoff=15., gamma=1., **kwargs):
"""Build Hessian matrix for given coordinate set.
:arg coords: a coordinate set or an object with ``getCoords`` method
:type coords: :class:`numpy.ndarray`
:arg cutoff: cutoff distance (Å) for pairwise interactions,
default is 15.0 Å, minimum is 4.0 Å
:type cutoff: float
:arg gamma: spring constant, default is 1.0
:type gamma: float, :class:`Gamma`
:arg sparse: elect to use sparse matrices, default is **False**. If
Scipy is not found, :class:`ImportError` is raised.
:type sparse: bool
:arg kdtree: elect to use KDTree for building Hessian matrix,
default is **False** since KDTree method is slower
:type kdtree: bool
Instances of :class:`Gamma` classes and custom functions are
accepted as *gamma* argument.
When Scipy is available, user can select to use sparse matrices for
efficient usage of memory at the cost of computation speed."""
try:
coords = (coords._getCoords() if hasattr(coords, '_getCoords') else
coords.getCoords())
except AttributeError:
try:
checkCoords(coords)
except TypeError:
raise TypeError('coords must be a Numpy array or an object '
'with `getCoords` method')
cutoff, g, gamma = checkENMParameters(cutoff, gamma)
self._reset()
self._cutoff = cutoff
self._gamma = g
n_atoms = coords.shape[0]
dof = n_atoms * 3
start = time.time()
if kwargs.get('sparse', False):
try:
from scipy import sparse as scipy_sparse
except ImportError:
raise ImportError('failed to import scipy.sparse, which is '
'required for sparse matrix calculations')
kirchhoff = scipy_sparse.lil_matrix((n_atoms, n_atoms))
hessian = scipy_sparse.lil_matrix((dof, dof))
else:
kirchhoff = np.zeros((n_atoms, n_atoms), 'd')
hessian = np.zeros((dof, dof), float)
if kwargs.get('kdtree', False):
LOGGER.info('Using KDTree for building the Hessian.')
kdtree = KDTree(coords)
kdtree.search(cutoff)
for i, j in kdtree.getIndices():
i2j = coords[j] - coords[i]
dist2 = np.dot(i2j, i2j)
g = gamma(dist2, i, j)
super_element = np.outer(i2j, i2j) * (- g / dist2)
res_i3 = i*3
res_i33 = res_i3+3
res_j3 = j*3
res_j33 = res_j3+3
hessian[res_i3:res_i33, res_j3:res_j33] = super_element
hessian[res_j3:res_j33, res_i3:res_i33] = super_element
hessian[res_i3:res_i33, res_i3:res_i33] = \
hessian[res_i3:res_i33, res_i3:res_i33] - super_element
hessian[res_j3:res_j33, res_j3:res_j33] = \
hessian[res_j3:res_j33, res_j3:res_j33] - super_element
kirchhoff[i, j] = -g
kirchhoff[j, i] = -g
kirchhoff[i, i] = kirchhoff[i, i] - g
kirchhoff[j, j] = kirchhoff[j, j] - g
else:
cutoff2 = cutoff * cutoff
for i in range(n_atoms):
res_i3 = i*3
res_i33 = res_i3+3
i_p1 = i+1
i2j_all = coords[i_p1:, :] - coords[i]
for j, dist2 in enumerate((i2j_all ** 2).sum(1)):
if dist2 > cutoff2:
continue
i2j = i2j_all[j]
j += i_p1
g = gamma(dist2, i, j)
res_j3 = j*3
res_j33 = res_j3+3
super_element = np.outer(i2j, i2j) * (- g / dist2)
hessian[res_i3:res_i33, res_j3:res_j33] = super_element
hessian[res_j3:res_j33, res_i3:res_i33] = super_element
hessian[res_i3:res_i33, res_i3:res_i33] = \
hessian[res_i3:res_i33, res_i3:res_i33] - super_element
hessian[res_j3:res_j33, res_j3:res_j33] = \
hessian[res_j3:res_j33, res_j3:res_j33] - super_element
kirchhoff[i, j] = -g
kirchhoff[j, i] = -g
kirchhoff[i, i] = kirchhoff[i, i] - g
kirchhoff[j, j] = kirchhoff[j, j] - g
LOGGER.info('Hessian was built in {0:.2f}s.'.format(time.time()-start))
self._kirchhoff = kirchhoff
self._hessian = hessian
self._n_atoms = n_atoms
self._dof = dof
