def _getEdgeP(self, edge0, edge1, edge2):
I, J, V = [], [], []
for cell in self.sortedCells:
if self.dim == 2:
e2f = lambda e: ('f' + {'X':'Y','Y':'X'}[e[1]]
+ {'0':'m','1':'p'}[e[2]])
face = cell.faceDict[e2f(edge0)]
if face.isleaf:
j = face.index
else:
j = face.children[0 if 'm' in e2f(edge1) else 1].index
# Need to flip the numbering for edges
if 'X' in edge0:
j = [jj - self.nFx for jj in j]
elif 'Y' in edge0:
j = [jj + self.nFy for jj in j]
elif self.dim == 3:
edge = cell.edgeDict[edge0]
if edge.isleaf:
j = edge.index
else:
mSide = lambda e: {'0':True,'1':True,'2':False,'3':False}[e[2]]
j = edge.children[0 if mSide(edge1) else 1,
0 if mSide(edge2) else 1].index
lenj = len(j)
I += [cell.num]*lenj
J += j
V += [1./lenj]*lenj
return sp.csr_matrix((V,(I,J)), shape=(self.nC, self.nE))
def _fastInnerProductDeriv(self, projType, prop, invProp=False, invMat=False):
"""
:param str projType: 'E' or 'F'
:param TensorType tensorType: type of the tensor
:param bool invProp: inverts the material property
:param bool invMat: inverts the matrix
:rtype: function
:return: dMdmu, the derivative of the inner product matrix
"""
assert projType in ['F', 'E'], "projType must be 'F' for faces or 'E' for edges"
tensorType = Utils.TensorType(self, prop)
dMdprop = None
if invMat:
MI = self._fastInnerProduct(projType, prop, invProp=invProp, invMat=invMat)
if tensorType == 0:
Av = getattr(self, 'ave'+projType+'2CC')
V = Utils.sdiag(self.vol)
ones = sp.csr_matrix((np.ones(self.nC), (range(self.nC), np.zeros(self.nC))), shape=(self.nC,1))
if not invMat and not invProp:
dMdprop = self.dim * Av.T * V * ones
elif invMat and invProp:
dMdprop = self.dim * Utils.sdiag(MI.diagonal()**2) * Av.T * V * ones * Utils.sdiag(1./prop**2)
if tensorType == 1:
Av = getattr(self, 'ave'+projType+'2CC')
V = Utils.sdiag(self.vol)
if not invMat and not invProp:
dMdprop = self.dim * Av.T * V
elif invMat and invProp:
dMdprop = self.dim * Utils.sdiag(MI.diagonal()**2) * Av.T * V * Utils.sdiag(1./prop**2)
if tensorType == 2: # anisotropic
Av = getattr(self, 'ave'+projType+'2CCV')
V = sp.kron(sp.identity(self.dim), Utils.sdiag(self.vol))
if not invMat and not invProp:
dMdprop = Av.T * V
elif invMat and invProp:
dMdprop = Utils.sdiag(MI.diagonal()**2) * Av.T * V * Utils.sdiag(1./prop**2)
if dMdprop is not None:
def innerProductDeriv(v=None):
if v is None:
print 'Depreciation Warning: TensorMesh.innerProductDeriv. You should be supplying a vector. Use: sdiag(u)*dMdprop'
return dMdprop
return Utils.sdiag(v) * dMdprop
return innerProductDeriv
else:
return None
def _getFaceP(self, face0, face1, face2):
I, J, V = [], [], []
for cell in self.sortedCells:
face = cell.faceDict[face0]
if face.isleaf:
j = face.index
elif self.dim == 2:
j = face.children[0 if 'm' in face1 else 1].index
elif self.dim == 3:
j = face.children[0 if 'm' in face1 else 1,
0 if 'm' in face2 else 1].index
lenj = len(j)
I += [cell.num]*lenj
J += j
V += [1./lenj]*lenj
return sp.csr_matrix((V,(I,J)), shape=(self.nC, self.nF))
def faceDiv(self):
if getattr(self, '_faceDiv', None) is None:
self.number()
# TODO: Preallocate!
I, J, V = [], [], []
for cell in self.sortedCells:
faces = cell.faceDict
for face in faces:
j = faces[face].index
I += [cell.num]*len(j)
J += j
V += [-1 if 'm' in face else 1]*len(j)
VOL = self.vol
D = sp.csr_matrix((V,(I,J)), shape=(self.nC, self.nF))
S = self.area
self._faceDiv = Utils.sdiag(1/VOL)*D*Utils.sdiag(S)
return self._faceDiv
def edgeCurl(self):
"""Construct the 3D curl operator."""
assert self.dim > 2, "Edge Curl only programed for 3D."
if getattr(self, '_edgeCurl', None) is None:
self.number()
# TODO: Preallocate!
I, J, V = [], [], []
for face in self.faces:
for ii, edge in enumerate([face.edge0, face.edge1, face.edge2, face.edge3]):
j = edge.index
I += [face.num]*len(j)
J += j
isNeg = [True, False, True, False]
V += [-1 if isNeg[ii] else 1]*len(j)
C = sp.csr_matrix((V,(I,J)), shape=(self.nF, self.nE))
S = self.area
L = self.edge
self._edgeCurl = Utils.sdiag(1/S)*C*Utils.sdiag(L)
return self._edgeCurl
def nodalGrad(self):
if getattr(self, '_nodalGrad', None) is None:
self.number()
# TODO: Preallocate!
I, J, V = [], [], []
# kinda a hack for the 2D gradient
# because edges are not stored
edges = self.faces if self.dim == 2 else self.edges
for edge in edges:
if self.dim == 3:
I += [edge.num, edge.num]
elif self.dim == 2 and edge.faceType == 'x':
I += [edge.num + self.nFy, edge.num + self.nFy]
elif self.dim == 2 and edge.faceType == 'y':
I += [edge.num - self.nFx, edge.num - self.nFx]
J += [edge.node0.num, edge.node1.num]
V += [-1, 1]
G = sp.csr_matrix((V,(I,J)), shape=(self.nE, self.nN))
L = self.edge
self._nodalGrad = Utils.sdiag(1/L)*G
return self._nodalGrad
def _fastInnerProductDeriv(self,
projType,
prop,
invProp=False,
invMat=False):
"""
:param str projType: 'E' or 'F'
:param TensorType tensorType: type of the tensor
:param bool invProp: inverts the material property
:param bool invMat: inverts the matrix
:rtype: function
:return: dMdmu, the derivative of the inner product matrix
"""
assert projType in [
'F', 'E'
], "projType must be 'F' for faces or 'E' for edges"
tensorType = Utils.TensorType(self, prop)
dMdprop = None
if invMat:
MI = self._fastInnerProduct(projType,
prop,
invProp=invProp,
invMat=invMat)
if tensorType == 0:
Av = getattr(self, 'ave' + projType + '2CC')
V = Utils.sdiag(self.vol)
ones = sp.csr_matrix(
(np.ones(self.nC), (range(self.nC), np.zeros(self.nC))),
shape=(self.nC, 1))
if not invMat and not invProp:
dMdprop = self.dim * Av.T * V * ones
elif invMat and invProp:
dMdprop = self.dim * Utils.sdiag(
MI.diagonal()**2) * Av.T * V * ones * Utils.sdiag(
1. / prop**2)
if tensorType == 1:
Av = getattr(self, 'ave' + projType + '2CC')
V = Utils.sdiag(self.vol)
if not invMat and not invProp:
dMdprop = self.dim * Av.T * V
elif invMat and invProp:
dMdprop = self.dim * Utils.sdiag(
MI.diagonal()**2) * Av.T * V * Utils.sdiag(1. / prop**2)
if tensorType == 2: # anisotropic
Av = getattr(self, 'ave' + projType + '2CCV')
V = sp.kron(sp.identity(self.dim), Utils.sdiag(self.vol))
if not invMat and not invProp:
dMdprop = Av.T * V
elif invMat and invProp:
dMdprop = Utils.sdiag(MI.diagonal()**
2) * Av.T * V * Utils.sdiag(1. / prop**2)
if dMdprop is not None:
def innerProductDeriv(v=None):
if v is None:
print 'Depreciation Warning: TensorMesh.innerProductDeriv. You should be supplying a vector. Use: sdiag(u)*dMdprop'
return dMdprop
return Utils.sdiag(v) * dMdprop
return innerProductDeriv
else:
return None
def _fastInnerProductDeriv(self, projType, prop, invProp=False,
invMat=False):
"""
:param str projType: 'E' or 'F'
:param TensorType tensorType: type of the tensor
:param bool invProp: inverts the material property
:param bool invMat: inverts the matrix
:rtype: function
:return: dMdmu, the derivative of the inner product matrix
"""
assert projType in ['F', 'E'], ("projType must be 'F' for faces or 'E'"
" for edges")
tensorType = Utils.TensorType(self, prop)
dMdprop = None
if invMat or invProp:
MI = self._fastInnerProduct(projType, prop, invProp=invProp,
invMat=invMat)
# number of elements we are averaging (equals dim for regular
# meshes, but for cyl, where we use symmetry, it is 1 for edge
# variables and 2 for face variables)
if self._meshType == 'CYL':
n_elements = np.sum(getattr(self, 'vn'+projType).nonzero())
else:
n_elements = self.dim
if tensorType == 0: # isotropic, constant
Av = getattr(self, 'ave'+projType+'2CC')
V = Utils.sdiag(self.vol)
ones = sp.csr_matrix((np.ones(self.nC), (range(self.nC),
np.zeros(self.nC))),
shape=(self.nC, 1))
if not invMat and not invProp:
dMdprop = n_elements * Av.T * V * ones
elif invMat and invProp:
dMdprop = n_elements * (Utils.sdiag(MI.diagonal()**2) * Av.T *
V * ones * Utils.sdiag(1./prop**2))
elif invProp:
dMdprop = n_elements * Av.T * V * Utils.sdiag(- 1./prop**2)
elif invMat:
dMdprop = n_elements * (Utils.sdiag(- MI.diagonal()**2) * Av.T
* V)
elif tensorType == 1: # isotropic, variable in space
Av = getattr(self, 'ave'+projType+'2CC')
V = Utils.sdiag(self.vol)
if not invMat and not invProp:
dMdprop = n_elements * Av.T * V
elif invMat and invProp:
dMdprop = n_elements * (Utils.sdiag(MI.diagonal()**2) * Av.T *
V * Utils.sdiag(1./prop**2))
elif invProp:
dMdprop = n_elements * Av.T * V * Utils.sdiag(-1./prop**2)
elif invMat:
dMdprop = n_elements * (Utils.sdiag(- MI.diagonal()**2) * Av.T
* V)
elif tensorType == 2: # anisotropic
Av = getattr(self, 'ave'+projType+'2CCV')
V = sp.kron(sp.identity(self.dim), Utils.sdiag(self.vol))
if self._meshType == 'CYL':
Zero = sp.csr_matrix((self.nC, self.nC))
Eye = sp.eye(self.nC)
if projType == 'E':
P = sp.hstack([Zero, Eye, Zero])
# print P.todense()
elif projType == 'F':
P = sp.vstack([sp.hstack([Eye, Zero, Zero]),
sp.hstack([Zero, Zero, Eye])])
# print P.todense()
else:
P = sp.eye(self.nC*self.dim)
if not invMat and not invProp:
dMdprop = Av.T * P * V
elif invMat and invProp:
dMdprop = (Utils.sdiag(MI.diagonal()**2) * Av.T * P * V *
Utils.sdiag(1./prop**2))
elif invProp:
dMdprop = Av.T * P * V * Utils.sdiag(-1./prop**2)
elif invMat:
dMdprop = Utils.sdiag(- MI.diagonal()**2) * Av.T * P * V
if dMdprop is not None:
def innerProductDeriv(v=None):
if v is None:
warnings.warn("Depreciation Warning: "
"TensorMesh.innerProductDeriv."
" You should be supplying a vector. "
"Use: sdiag(u)*dMdprop", FutureWarning)
return dMdprop
return Utils.sdiag(v) * dMdprop
return innerProductDeriv
else:
return None
def _fastInnerProductDeriv(self, projType, prop, invProp=False, invMat=False):
"""
:param str projType: 'E' or 'F'
:param TensorType tensorType: type of the tensor
:param bool invProp: inverts the material property
:param bool invMat: inverts the matrix
:rtype: function
:return: dMdmu, the derivative of the inner product matrix
"""
assert projType in ["F", "E"], "projType must be 'F' for faces or 'E'" " for edges"
tensorType = Utils.TensorType(self, prop)
dMdprop = None
if invMat or invProp:
MI = self._fastInnerProduct(projType, prop, invProp=invProp, invMat=invMat)
# number of elements we are averaging (equals dim for regular
# meshes, but for cyl, where we use symmetry, it is 1 for edge
# variables and 2 for face variables)
if self._meshType == "CYL":
n_elements = np.sum(getattr(self, "vn" + projType).nonzero())
else:
n_elements = self.dim
if tensorType == 0: # isotropic, constant
Av = getattr(self, "ave" + projType + "2CC")
V = Utils.sdiag(self.vol)
ones = sp.csr_matrix((np.ones(self.nC), (range(self.nC), np.zeros(self.nC))), shape=(self.nC, 1))
if not invMat and not invProp:
dMdprop = n_elements * Av.T * V * ones
elif invMat and invProp:
dMdprop = n_elements * (
Utils.sdiag(MI.diagonal() ** 2) * Av.T * V * ones * Utils.sdiag(1.0 / prop ** 2)
)
elif invProp:
dMdprop = n_elements * Av.T * V * Utils.sdiag(-1.0 / prop ** 2)
elif invMat:
dMdprop = n_elements * (Utils.sdiag(-MI.diagonal() ** 2) * Av.T * V)
elif tensorType == 1: # isotropic, variable in space
Av = getattr(self, "ave" + projType + "2CC")
V = Utils.sdiag(self.vol)
if not invMat and not invProp:
dMdprop = n_elements * Av.T * V
elif invMat and invProp:
dMdprop = n_elements * (Utils.sdiag(MI.diagonal() ** 2) * Av.T * V * Utils.sdiag(1.0 / prop ** 2))
elif invProp:
dMdprop = n_elements * Av.T * V * Utils.sdiag(-1.0 / prop ** 2)
elif invMat:
dMdprop = n_elements * (Utils.sdiag(-MI.diagonal() ** 2) * Av.T * V)
elif tensorType == 2: # anisotropic
Av = getattr(self, "ave" + projType + "2CCV")
V = sp.kron(sp.identity(self.dim), Utils.sdiag(self.vol))
if self._meshType == "CYL":
Zero = sp.csr_matrix((self.nC, self.nC))
Eye = sp.eye(self.nC)
if projType == "E":
P = sp.hstack([Zero, Eye, Zero])
# print(P.todense())
elif projType == "F":
P = sp.vstack([sp.hstack([Eye, Zero, Zero]), sp.hstack([Zero, Zero, Eye])])
# print(P.todense())
else:
P = sp.eye(self.nC * self.dim)
if not invMat and not invProp:
dMdprop = Av.T * P * V
elif invMat and invProp:
dMdprop = Utils.sdiag(MI.diagonal() ** 2) * Av.T * P * V * Utils.sdiag(1.0 / prop ** 2)
elif invProp:
dMdprop = Av.T * P * V * Utils.sdiag(-1.0 / prop ** 2)
elif invMat:
dMdprop = Utils.sdiag(-MI.diagonal() ** 2) * Av.T * P * V
if dMdprop is not None:
def innerProductDeriv(v=None):
if v is None:
warnings.warn(
"Depreciation Warning: "
"TensorMesh.innerProductDeriv."
" You should be supplying a vector. "
"Use: sdiag(u)*dMdprop",
FutureWarning,
)
return dMdprop
return Utils.sdiag(v) * dMdprop
return innerProductDeriv
else:
return None