def __init__(self, atoms, unitcell=None):
"""*atoms* must be an :class:`.Atomic` instance.
:arg unitcell: orthorhombic unitcell dimension array with shape
``(3,)`` for KDTree. Default is **None**.
:type unitcell: :class:`~numpy.ndarray`"""
try:
self._acsi = atoms.getACSIndex()
except AttributeError:
try:
self._ag = atoms.getAtoms()
unitcell = unitcell or atoms.getUnitcell()[:3]
self._indices = atoms.getSelection()
except AttributeError:
try:
ndim, shape = atoms.ndim, atoms.shape
except AttributeError:
raise TypeError('atoms must be an Atomic or Frame instance'
', not a {0}'.format(type(atoms)))
else:
if not (ndim == 2 and shape[1] == 3):
raise ValueError('atoms.shape must be (n_atoms, 3) or '
'(3,).')
self._ag = None
self._indices = None
self._kdtree = KDTree(atoms, unitcell=unitcell)
else:
if self._ag is not None:
self._acsi = self._ag.getACSIndex()
if self._indices is not None:
self._indices = self._indices.getIndices()
else:
self._acsi = None
self._kdtree = KDTree(atoms._getCoords(), unitcell=unitcell)
else:
try:
self._ag = atoms.getAtomGroup()
except AttributeError:
self._ag = atoms
self._indices = None
self._kdtree = KDTree(atoms._getCoords(), unitcell=unitcell)
else:
self._indices = atoms._getIndices()
self._kdtree = KDTree(atoms._getCoords(), unitcell=unitcell)
self._unitcell = unitcell
self._atoms = atoms
def __init__(self, atoms, unitcell=None):
"""*atoms* must be an :class:`.Atomic` instance. When an orthorhombic
*unitcell* array is given"""
try:
self._acsi = atoms.getACSIndex()
except AttributeError:
try:
self._ag = atoms.getAtoms()
unitcell = unitcell or atoms.getUnitcell()[:3]
self._indices = atoms.getSelection()
except AttributeError:
try:
ndim, shape = atoms.ndim, atoms.shape
except AttributeError:
raise TypeError('atoms must be an Atomic or Frame instance'
', not a {0}'.format(type(atoms)))
else:
if not (ndim == 2 and shape[1] == 3):
raise ValueError('atoms.shape must be (n_atoms, 3) or '
'(3,).')
self._ag = None
self._indices = None
self._kdtree = KDTree(atoms, unitcell=unitcell)
else:
if self._ag is not None:
self._acsi = self._ag.getACSIndex()
if self._indices is not None:
self._indices = self._indices.getIndices()
else:
self._acsi = None
self._kdtree = KDTree(self._atoms._getCoords(),
unitcell=unitcell)
else:
try:
self._ag = atoms.getAtomGroup()
except AttributeError:
self._ag = atoms
self._indices = None
self._kdtree = KDTree(atoms._getCoords(), unitcell=unitcell)
else:
self._indices = atoms._getIndices()
self._kdtree = KDTree(atoms._getCoords(), unitcell=unitcell)
self._unitcell = unitcell
self._atoms = atoms
def _getKDTree(self, index=None):
"""Return KDTree for coordinate set at given index."""
if self._n_csets:
if index is None:
index = self._acsi
kdtree = self._kdtrees[index]
if kdtree is None:
kdtree = KDTree(self._coords[index])
self._kdtrees[index] = kdtree
return kdtree
else:
return None
def calcDistanceMatrix(coords, cutoff=None):
"""Calculate matrix of distances between coordinates within *cutoff*.
Other matrix entries are set to maximum of calculated distances.
:arg coords: a coordinate set or an object with :meth:`getCoords` method.
:type coords: :class:`~numpy.ndarray`, :class:`.Atomic`
:arg cutoff: cutoff distance for searching the KDTree.
Default (**None**) is to use the length of the longest coordinate axis.
:type cutoff: None, float
"""
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')
n_atoms = coords.shape[0]
dist_mat = zeros((n_atoms, n_atoms))
if cutoff is None:
cutoff = max(coords.max(axis=0) - coords.min(axis=0))
kdtree = KDTree(coords)
kdtree.search(cutoff)
dists = kdtree.getDistances()
r = 0
for i, j in kdtree.getIndices():
dist_mat[i, j] = dist_mat[j, i] = dists[r]
r += 1
for i in range(n_atoms):
for j in range(i + 1, n_atoms):
if dist_mat[i, j] == 0.:
dist_mat[i, j] = dist_mat[j, i] = max(dists)
return dist_mat
def buildKirchhoff(self, coords, cutoff=10., gamma=1., **kwargs):
"""Build Kirchhoff matrix for given coordinate set.
:arg coords: a coordinate set or an object with ``getCoords`` method
:type coords: :class:`numpy.ndarray` or :class:`.Atomic`
:arg cutoff: cutoff distance (Å) for pairwise interactions
default is 10.0 Å, , minimum is 4.0 Å
:type cutoff: float
:arg gamma: spring constant, default is 1.0
:type gamma: float
: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 Kirchhoff matrix faster,
default is **True**
: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]
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))
else:
kirchhoff = np.zeros((n_atoms, n_atoms), 'd')
if kwargs.get('kdtree', True):
kdtree = KDTree(coords)
kdtree.search(cutoff)
dist2 = kdtree.getDistances() ** 2
r = 0
for i, j in kdtree.getIndices():
g = gamma(dist2[r], i, j)
kirchhoff[i, j] = -g
kirchhoff[j, i] = -g
kirchhoff[i, i] = kirchhoff[i, i] + g
kirchhoff[j, j] = kirchhoff[j, j] + g
r += 1
else:
LOGGER.info('Using slower method for building the Kirchhoff.')
cutoff2 = cutoff * cutoff
mul = np.multiply
for i in range(n_atoms):
xyz_i = coords[i, :]
i_p1 = i+1
i2j = coords[i_p1:, :] - xyz_i
mul(i2j, i2j, i2j)
for j, dist2 in enumerate(i2j.sum(1)):
if dist2 > cutoff2:
continue
j += i_p1
g = gamma(dist2, i, j)
kirchhoff[i, j] = -g
kirchhoff[j, i] = -g
kirchhoff[i, i] = kirchhoff[i, i] + g
kirchhoff[j, j] = kirchhoff[j, j] + g
LOGGER.debug('Kirchhoff was built in {0:.2f}s.'
.format(time.time()-start))
self._kirchhoff = kirchhoff
self._n_atoms = n_atoms
self._dof = n_atoms
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
LOGGER.timeit('_anm_hessian')
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.report('Hessian was built in %.2fs.', label='_anm_hessian')
self._kirchhoff = kirchhoff
self._hessian = hessian
self._n_atoms = n_atoms
self._dof = dof
def iterNeighbors(atoms, radius, atoms2=None, unitcell=None):
"""Yield pairs of *atoms* that are within *radius* of each other and the
distance between them. If *atoms2* is also provided, one atom from *atoms*
and another from *atoms2* will be yielded. If one of *atoms* or *atoms2*
is a coordinate array, pairs of indices and distances will be yielded.
When orthorhombic *unitcell* dimensions are provided, periodic boundary
conditions will be taken into account (see :class:`.KDTree` and also
:func:`wrapAtoms` for details). If *atoms* is a :class:`.Frame` instance
and *unitcell* is not provided, unitcell information from frame will be
if available."""
radius = float(radius)
if radius <= 0:
raise ValueError('radius must be a positive number')
try:
acsi = atoms.getACSIndex()
except AttributeError:
try:
ndim, shape = atoms.ndim, atoms.shape
except AttributeError:
try:
uc = atoms.getUnitcell()[:3]
except AttributeError:
raise TypeError('atoms must be an Atomic or Frame instance or '
'a coordinate array')
else:
coords = atoms._getCoords()
ag = atoms.getAtoms()
if unitcell is None:
unitcell = uc
if ag is not None:
acsi = ag.getACSIndex()
_ = atoms.getSelection()
if _:
indices = _._getIndices()
index = lambda i: indices[i]
else:
index = lambda i: i
else:
if ndim > 2:
raise ValueError('number of dimensions of coordinate array '
'must be 1 or 2')
coords = atoms
ag = None
acsi = None
else:
coords = atoms._getCoords()
try:
ag = atoms.getAtomGroup()
indices = atoms.getIndices()
index = lambda i: indices[i]
except AttributeError:
ag = atoms
index = lambda i: i
if coords.ndim == 1:
coords = array([coords])
if atoms2 is None:
if len(coords) <= 1:
raise ValueError('atoms must be more than 1')
kdtree = KDTree(coords, unitcell=unitcell, none=list)
_dict = {}
if ag is None:
for (i, j), r in zip(*kdtree(radius)):
yield (i, j, r)
else:
for (i, j), r in zip(*kdtree(radius)):
a1 = _dict.get(i)
if a1 is None:
a1 = Atom(ag, index(i), acsi)
_dict[i] = a1
a2 = _dict.get(j)
if a2 is None:
a2 = Atom(ag, index(j), acsi)
_dict[j] = a2
yield (a1, a2, r)
else:
try:
coords2 = atoms2._getCoords()
except AttributeError:
try:
ndim, shape = atoms2.ndim, atoms2.shape
except AttributeError:
raise TypeError(
'atoms2 must be an Atomic or Frame instance or '
'a coordinate array')
else:
if ndim > 2:
raise ValueError('number of dimensions of second '
'coordinate array must be 1 or 2')
coords2 = atoms2
ag2 = None
acsi2 = None
else:
try:
acsi2 = atoms2.getACSIndex()
except AttributeError:
acsi2 = None
ag2 = None
index2 = None
else:
try:
ag2 = atoms2.getAtomGroup()
indices2 = atoms2.getIndices()
index2 = lambda i: indices2[i]
except AttributeError:
ag2 = atoms2
index2 = lambda i: i
if coords2.ndim == 1:
coords2 = array([coords2])
if len(coords) >= len(coords2):
kdtree = KDTree(coords, unitcell=unitcell, none=list)
_dict = {}
if ag is None or ag2 is None:
for j, xyz in enumerate(coords2):
for i, r in zip(*kdtree(radius, xyz)):
yield (i, j, r)
else:
for a2 in atoms2.iterAtoms():
for i, r in zip(*kdtree(radius, a2._getCoords())):
a1 = _dict.get(i)
if a1 is None:
a1 = Atom(ag, index(i), acsi)
_dict[i] = a1
yield (a1, a2, r)
else:
kdtree = KDTree(coords2, unitcell=unitcell, none=list)
_dict = {}
if ag is None or ag2 is None:
for i, xyz in enumerate(coords):
for j, r in zip(*kdtree(radius, xyz)):
yield (i, j, r)
else:
for a1 in atoms.iterAtoms():
for i, r in zip(*kdtree(radius, a1._getCoords())):
a2 = _dict.get(i)
if a2 is None:
a2 = Atom(ag2, index2(i), acsi2)
_dict[i] = a2
yield (a1, a2, r)
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
LOGGER.timeit('_anm_hessian')
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.report('Hessian was built in %.2fs.', label='_anm_hessian')
self._kirchhoff = kirchhoff
self._hessian = hessian
self._n_atoms = n_atoms
self._dof = dof
def setUp(self):
self.coords = tile(arange(10), (3,1)).T.astype(float)
self.kdtree = KDTree(self.coords)
self.assertEqual(len(indices), 9, 'KDTree all search failed')
for pair, radius in zip(indices, radii):
x, y = coords[pair]
assert_allclose(((x - y)**2).sum()**0.5, radius,
rtol=RTOL, atol=ATOL,
err_msg='KDTree all search failed')
COORDS = array([[-1., -1., 0.],
[-1., 5., 0.],
[ 2., 2., 0.],
[ 5., -1., 0.],
[ 5., 5., 0.],])
UNITCELL = array([4., 4., 0.])
KDTREE = KDTree(COORDS)
KDTREE_PBC = KDTree(COORDS, unitcell=UNITCELL)
class TestKDTreePBC(unittest.TestCase):
def testPointNoPBC(self):
KDTREE.search(2, ones(3) * 2)
self.assertEqual(1, KDTREE.getCount())
def testPairNoPBC(self):
KDTREE.search(2)
self.assertEqual(0, KDTREE.getCount())
def testPointPBC(self):
def buildKirchhoff(self, coords, cutoff=10., gamma=1., **kwargs):
"""Build Kirchhoff matrix for given coordinate set.
:arg coords: a coordinate set or an object with ``getCoords`` method
:type coords: :class:`numpy.ndarray` or :class:`.Atomic`
:arg cutoff: cutoff distance (Å) for pairwise interactions
default is 10.0 Å, , minimum is 4.0 Å
:type cutoff: float
:arg gamma: spring constant, default is 1.0
:type gamma: float
: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 Kirchhoff matrix faster,
default is **True**
: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]
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))
else:
kirchhoff = np.zeros((n_atoms, n_atoms), 'd')
if kwargs.get('kdtree', True):
kdtree = KDTree(coords)
kdtree.search(cutoff)
dist2 = kdtree.getDistances()**2
r = 0
for i, j in kdtree.getIndices():
g = gamma(dist2[r], i, j)
kirchhoff[i, j] = -g
kirchhoff[j, i] = -g
kirchhoff[i, i] = kirchhoff[i, i] + g
kirchhoff[j, j] = kirchhoff[j, j] + g
r += 1
else:
LOGGER.info('Using slower method for building the Kirchhoff.')
cutoff2 = cutoff * cutoff
mul = np.multiply
for i in range(n_atoms):
xyz_i = coords[i, :]
i_p1 = i + 1
i2j = coords[i_p1:, :] - xyz_i
mul(i2j, i2j, i2j)
for j, dist2 in enumerate(i2j.sum(1)):
if dist2 > cutoff2:
continue
j += i_p1
g = gamma(dist2, i, j)
kirchhoff[i, j] = -g
kirchhoff[j, i] = -g
kirchhoff[i, i] = kirchhoff[i, i] + g
kirchhoff[j, j] = kirchhoff[j, j] + g
LOGGER.debug('Kirchhoff was built in {0:.2f}s.'.format(time.time() -
start))
self._kirchhoff = kirchhoff
self._n_atoms = n_atoms
self._dof = n_atoms
