def to_ao(self, mo_operator):
""" Transform an operator from this orbital basis into the AO basis
Given the matrix elements :math:`\hat O_{ij}` of an operator over orbital basis indices
:math:`i,j`, returns the operator's matrix elements :math:`\hat O_{\mu \nu}` over
orbital indices :math:`\mu, \nu`:
..math::
\hat O_{\mu \nu} =
\left \langle \mu \right| \hat O \left| \nu \right \rangle =
\sum_{i,j,\lambda,\kappa}S_{\mu \lambda} C_{i \lambda} O_{ij} C_{j \kappa} S_{\kappa \nu}
where :math:`S_{\mu \nu} = \left \langle \mu | \nu \right \rangle` is the AO overlap matrix
and :math:`C_{i \mu}` is the expansion coefficient for AO basis function :math:`\mu` in
molecular orbital _i_.
Args:
mo_operator (u.Array): matrix elements of the operator in this orbital basis
Returns:
u.Array: matrix elements of the operator in the AO basis
"""
units = u.get_units(mo_operator)
s = self.wfn.aobasis.overlaps
o_ao = s.dot(self.coeffs.T).dot(mo_operator).dot(self.coeffs).dot(s)
return o_ao * units
def _validate(self, change):
import pint
self._validated_value = None
self._error_msg = False
# Check that we can parse this
try:
val = u.ureg(change['new'])
except (pint.UndefinedUnitError, pint.DimensionalityError,
pint.compat.tokenize.TokenError):
self._error_msg = "Failed to parse '%s'" % self.textbox.value
except Exception as e: # unfortunately, pint's parser sometimes raises bare exception class
if e.__class__ != Exception:
raise # this isn't what we want
self._error_msg = "Failed to parse '%s'" % self.textbox.value
else: # Check dimensionality
valdim = u.get_units(val).dimensionality
if self.dimensionality is not None and valdim != self.dimensionality:
self._error_msg = "Requires dimensionality %s" % self.dimensionality
if not self._error_msg:
self.validated.value = '<span title="Valid quantity">%s</span>' % self.VALID
self._validated_value = val
else:
self.validated.value = '<span title="%s">%s</span>' % (
self._error_msg, self.INVALID)
def to_ao(self, mo_operator):
""" Transform an operator from this orbital basis into the AO basis
Given the matrix elements :math:`\hat O_{ij}` of an operator over orbital basis indices
:math:`i,j`, returns the operator's matrix elements :math:`\hat O_{\mu \nu}` over
orbital indices :math:`\mu, \nu`:
..math::
\hat O_{\mu \nu} =
\left \langle \mu \right| \hat O \left| \nu \right \rangle =
\sum_{i,j,\lambda,\kappa}S_{\mu \lambda} C_{i \lambda} O_{ij} C_{j \kappa} S_{\kappa \nu}
where :math:`S_{\mu \nu} = \left \langle \mu | \nu \right \rangle` is the AO overlap matrix
and :math:`C_{i \mu}` is the expansion coefficient for AO basis function :math:`\mu` in
molecular orbital _i_.
Args:
mo_operator (u.Array): matrix elements of the operator in this orbital basis
Returns:
u.Array: matrix elements of the operator in the AO basis
"""
units = u.get_units(mo_operator)
s = self.wfn.aobasis.overlaps
o_ao = s.dot(self.coeffs.T).dot(mo_operator).dot(self.coeffs).dot(s)
return o_ao * units
def from_ao(self, ao_operator):
""" Transform an operator into this orbital basis from the ao basis
Given the matrix elements :math:`\hat O_{\mu \nu}` of an operator over AO basis indices
:math:`\mu,\nu`, returns the operator's matrix elements :math:`\hat O_{ij}` over
orbital indices :math:`i,j`:
..math::
\hat O_{ij} =
\left \langle i \right| \hat O \left| j \right \rangle =
\sum_{\mu \nu}C_{i \mu} O_{\mu \nu} C_{j \nu}
where :math:`C_{i \mu}` is the expansion coefficient for AO basis function :math:`\mu` in
molecular orbital _i_.
Args:
ao_operator (u.Array): matrix elements of the operator in the ao basis
Returns:
u.Array: matrix elements of the operator in this orbital basis
Note:
Assumes that this set of orbitals is orthogonal
"""
# Dot doesn't place nice with units, so we need to pass them explicitly
ao_units = u.get_units(ao_operator)
return self.coeffs.dot(ao_operator.dot(self.coeffs.T)) * ao_units
def from_ao(self, ao_operator):
""" Transform an operator into this orbital basis from the ao basis
Given the matrix elements :math:`\hat O_{\mu \nu}` of an operator over AO basis indices
:math:`\mu,\nu`, returns the operator's matrix elements :math:`\hat O_{ij}` over
orbital indices :math:`i,j`:
..math::
\hat O_{ij} =
\left \langle i \right| \hat O \left| j \right \rangle =
\sum_{\mu \nu}C_{i \mu} O_{\mu \nu} C_{j \nu}
where :math:`C_{i \mu}` is the expansion coefficient for AO basis function :math:`\mu` in
molecular orbital _i_.
Args:
ao_operator (u.Array): matrix elements of the operator in the ao basis
Returns:
u.Array: matrix elements of the operator in this orbital basis
Note:
Assumes that this set of orbitals is orthogonal
"""
# Dot doesn't place nice with units, so we need to pass them explicitly
ao_units = u.get_units(ao_operator)
return self.coeffs.dot(ao_operator.dot(self.coeffs.T)) * ao_units
def _validate(self, change):
import pint
self._validated_value = None
self._error_msg = False
# Check that we can parse this
try:
val = u.ureg(change['new'])
except (pint.UndefinedUnitError,
pint.DimensionalityError,
pint.compat.tokenize.TokenError):
self._error_msg = "Failed to parse '%s'" % self.textbox.value
except Exception as e: # unfortunately, pint's parser sometimes raises bare exception class
if e.__class__ != Exception:
raise # this isn't what we want
self._error_msg = "Failed to parse '%s'" % self.textbox.value
else: # Check dimensionality
valdim = u.get_units(val).dimensionality
if self.dimensionality is not None and valdim != self.dimensionality:
self._error_msg = "Requires dimensionality %s" % self.dimensionality
if not self._error_msg:
self.validated.value = '<span title="Valid quantity">%s</span>' % self.VALID
self._validated_value = val
else:
self.validated.value = '<span title="%s">%s</span>' % (self._error_msg, self.INVALID)
def draw_atom_vectors(self,
vecs,
rescale_to=1.75,
scale_factor=None,
opacity=0.85,
radius=0.11,
**kwargs):
""" Draw a 3D vector on each atom
Args:
vecs (Matrix[shape=(*,3)]): list of vectors for each atom
rescale_to (Scalar[length]): vectors so the largest is this long
scale_factor (Scalar[length/units]): factor for conversion between input units and
length
kwargs (dict): keyword arguments for self.draw_arrow
"""
kwargs['radius'] = radius
kwargs['opacity'] = opacity
if vecs.shape == (self.mol.ndims, ):
vecs = vecs.reshape(self.mol.num_atoms, 3)
assert vecs.shape == (self.mol.num_atoms, 3), '`vecs` must be a num_atoms X 3 matrix or' \
' 3*num_atoms vector'
assert not np.allclose(vecs, 0.0), "Input vectors are 0."
# strip units and scale the vectors appropriately
if scale_factor is not None: # scale all arrows by this quantity
if (u.get_units(vecs) /
scale_factor).dimensionless: # allow implicit scale factor
scale_factor = scale_factor / self.DISTANCE_UNITS
vecarray = vecs / scale_factor
try:
arrowvecs = vecarray.value_in(self.DISTANCE_UNITS)
except AttributeError:
arrowvecs = vecarray
else: # rescale the maximum length arrow length to rescale_to
try:
vecarray = vecs.magnitude
unit = vecs.getunits()
except AttributeError:
vecarray = vecs
unit = ''
lengths = np.sqrt((vecarray * vecarray).sum(axis=1))
scale = (lengths.max() / rescale_to
) # units of [vec units] / angstrom
if hasattr(scale, 'defunits'):
scale = scale.defunits()
arrowvecs = vecarray / scale
print('Arrow scale: {q:.3f} {unit} per {native}'.format(
q=scale, unit=unit, native=self.DISTANCE_UNITS))
shapes = []
for atom, vecarray in zip(self.mol.atoms, arrowvecs):
if mathutils.norm(vecarray) < 0.2:
continue
shapes.append(
self.draw_arrow(atom.position, vector=vecarray, **kwargs))
return shapes
def draw_atom_vectors(self,
vecs,
rescale_to=1.75,
scale_factor=None,
opacity=0.85,
radius=0.11,
**kwargs):
"""
For displaying atom-centered vector data (e.g., momenta, forces)
:param rescale_to: rescale to this length (in angstroms) (not used if scale_factor is passed)
:param scale_factor: Scaling factor for arrows: dimensions of [vecs dimensions] / [length]
:param kwargs: keyword arguments for self.draw_arrow
"""
kwargs['radius'] = radius
kwargs['opacity'] = opacity
if vecs.shape == (self.mol.ndims, ):
vecs = vecs.reshape(self.mol.num_atoms, 3)
assert vecs.shape == (self.mol.num_atoms, 3), '`vecs` must be a num_atoms X 3 matrix or' \
' 3*num_atoms vector'
assert not np.allclose(vecs, 0.0), "Input vectors are 0."
# strip units and scale the vectors appropriately
if scale_factor is not None: # scale all arrows by this quantity
if (u.get_units(vecs) /
scale_factor).dimensionless: # allow implicit scale factor
scale_factor = scale_factor / self.DISTANCE_UNITS
vecarray = vecs / scale_factor
try:
arrowvecs = vecarray.value_in(self.DISTANCE_UNITS)
except AttributeError:
arrowvecs = vecarray
else: # rescale the maximum length arrow length to rescale_to
try:
vecarray = vecs.magnitude
unit = vecs.getunits()
except AttributeError:
vecarray = vecs
unit = ''
lengths = np.sqrt((vecarray * vecarray).sum(axis=1))
scale = (lengths.max() / rescale_to
) # units of [vec units] / angstrom
if hasattr(scale, 'defunits'): scale = scale.defunits()
arrowvecs = vecarray / scale
print 'Arrow scale: {q:.3f} {unit} per {native}'.format(
q=scale, unit=unit, native=self.DISTANCE_UNITS)
shapes = []
for atom, vecarray in zip(self.mol.atoms, arrowvecs):
if vecarray.norm() < 0.2: continue
shapes.append(
self.draw_arrow(atom.position, vector=vecarray, **kwargs))
return shapes
def draw_atom_vectors(self, vecs, rescale_to=1.75,
scale_factor=None, opacity=0.85,
radius=0.11, **kwargs):
""" Draw a 3D vector on each atom
Args:
vecs (Matrix[shape=(*,3)]): list of vectors for each atom
rescale_to (Scalar[length]): vectors so the largest is this long
scale_factor (Scalar[length/units]): factor for conversion between input units and
length
kwargs (dict): keyword arguments for self.draw_arrow
"""
kwargs['radius'] = radius
kwargs['opacity'] = opacity
if vecs.shape == (self.mol.ndims,):
vecs = vecs.reshape(self.mol.num_atoms, 3)
assert vecs.shape == (self.mol.num_atoms, 3), '`vecs` must be a num_atoms X 3 matrix or' \
' 3*num_atoms vector'
assert not np.allclose(vecs, 0.0), "Input vectors are 0."
# strip units and scale the vectors appropriately
if scale_factor is not None: # scale all arrows by this quantity
if (u.get_units(vecs)/scale_factor).dimensionless: # allow implicit scale factor
scale_factor = scale_factor/self.DISTANCE_UNITS
vecarray = vecs/scale_factor
try:
arrowvecs = vecarray.value_in(self.DISTANCE_UNITS)
except AttributeError:
arrowvecs = vecarray
else: # rescale the maximum length arrow length to rescale_to
try:
vecarray = vecs.magnitude
unit = vecs.getunits()
except AttributeError:
vecarray = vecs
unit = ''
lengths = np.sqrt((vecarray*vecarray).sum(axis=1))
scale = (lengths.max()/rescale_to) # units of [vec units] / angstrom
if hasattr(scale, 'defunits'):
scale = scale.defunits()
arrowvecs = vecarray/scale
print('Arrow scale: {q:.3f} {unit} per {native}'.format(q=scale, unit=unit,
native=self.DISTANCE_UNITS))
shapes = []
for atom, vecarray in zip(self.mol.atoms, arrowvecs):
if mathutils.norm(vecarray) < 0.2:
continue
shapes.append(self.draw_arrow(atom.position, vector=vecarray, **kwargs))
return shapes
def __init__(self, value=None, units=None, **kwargs):
super(UnitText, self).__init__(layout=ipy.Layout(display='flex',
flex_flow='row wrap'),
**kwargs)
self.textbox = ipy.Text()
self.textbox.observe(self._validate, 'value')
self._error_msg = None
if units is not None:
self.dimensionality = u.get_units(units).dimensionality
else:
self.dimensionality = None
self._validated_value = None
self.validated = ipy.HTML(self.INVALID)
self.children = [self.textbox, self.validated]
self._is_valid = False
if value is not None: self.value = value
def __init__(self, value=None, units=None, **kwargs):
super(UnitText, self).__init__(layout=ipy.Layout(display='flex', flex_flow='row wrap'),
**kwargs)
self.textbox = ipy.Text()
self.textbox.observe(self._validate, 'value')
self._error_msg = None
if units is not None:
self.dimensionality = u.get_units(units).dimensionality
else:
self.dimensionality = None
self._validated_value = None
self.validated = ipy.HTML(self.INVALID)
self.children = [self.textbox, self.validated]
self._is_valid = False
if value is not None:
self.value = value
def draw_atom_vectors(self, vecs, rescale_to=1.75,
scale_factor=None, opacity=0.85,
radius=0.11, **kwargs):
"""
For displaying atom-centered vector data (e.g., momenta, forces)
:param rescale_to: rescale to this length (in angstroms) (not used if scale_factor is passed)
:param scale_factor: Scaling factor for arrows: dimensions of [vecs dimensions] / [length]
:param kwargs: keyword arguments for self.draw_arrow
"""
kwargs['radius'] = radius
kwargs['opacity'] = opacity
if vecs.shape == (self.mol.ndims,):
vecs = vecs.reshape(self.mol.num_atoms, 3)
assert vecs.shape == (self.mol.num_atoms, 3), '`vecs` must be a num_atoms X 3 matrix or' \
' 3*num_atoms vector'
assert not np.allclose(vecs, 0.0), "Input vectors are 0."
# strip units and scale the vectors appropriately
if scale_factor is not None: # scale all arrows by this quantity
if (u.get_units(vecs)/scale_factor).dimensionless: # allow implicit scale factor
scale_factor = scale_factor / self.DISTANCE_UNITS
vecarray = vecs / scale_factor
try: arrowvecs = vecarray.value_in(self.DISTANCE_UNITS)
except AttributeError: arrowvecs = vecarray
else: # rescale the maximum length arrow length to rescale_to
try:
vecarray = vecs.magnitude
unit = vecs.getunits()
except AttributeError:
vecarray = vecs
unit = ''
lengths = np.sqrt((vecarray * vecarray).sum(axis=1))
scale = (lengths.max() / rescale_to) # units of [vec units] / angstrom
if hasattr(scale,'defunits'): scale = scale.defunits()
arrowvecs = vecarray / scale
print 'Arrow scale: {q:.3f} {unit} per {native}'.format(q=scale, unit=unit,
native=self.DISTANCE_UNITS)
shapes = []
for atom, vecarray in zip(self.mol.atoms, arrowvecs):
if vecarray.norm() < 0.2: continue
shapes.append(self.draw_arrow(atom.position, vector=vecarray, **kwargs))
return shapes
def _validate(self, change):
self._validated_value = None
self._error_msg = False
# Check that we can parse this
try:
val = u.ureg(change['new'])
except: # parsing failed, pint just raises generic "Exception"
self._error_msg = "Failed to parse '%s'" % self.textbox.value
else: # Check dimensionality
valdim = u.get_units(val).dimensionality
if self.dimensionality is not None and valdim != self.dimensionality:
self._error_msg = "Requires dimensionality %s" % self.dimensionality
if not self._error_msg:
self.validated.value = '<span title="Valid quantity">%s</span>' % self.VALID
self._validated_value = val
else:
self.validated.value = '<span title="%s">%s</span>' % (
self._error_msg, self.INVALID)
def test_getunits_doctests():
assert units.get_units(1.0 * units.angstrom) == units.MdtUnit('angstrom')
assert units.get_units(np.array([1.0, 2,
3.0])) == units.MdtUnit('dimensionless')
assert units.get_units([[1.0 * units.dalton, 3.0 * units.eV], ['a'],
'gorilla']) == units.MdtUnit('amu')