def getAsubdiag(self, tInd):
assert tInd >= 0 and tInd < self.nT
eye = sp.eye(self.mesh.nF)
dt = self.timeSteps[tInd]
if self._makeASymmetric:
return -1./dt * self.MfRho.T
return -1./dt * eye
def getAsubdiag(self, tInd):
dt = self.timeSteps[tInd]
MfMui = self.MfMui
Asubdiag = -1. / dt * sp.eye(self.mesh.nF)
if self._makeASymmetric is True:
return MfMui.T * Asubdiag
return Asubdiag
def getAsubdiag(self, tInd):
dt = self.timeSteps[tInd]
MfMui = self.MfMui
Asubdiag = - 1./dt * sp.eye(self.mesh.nF)
if self._makeASymmetric is True:
return MfMui.T * Asubdiag
return Asubdiag
def getA(self, freq):
"""
:param float freq: Frequency
:rtype: scipy.sparse.csr_matrix
:return: A
"""
mui = self.MfMui
sigI = self.MeSigmaI
C = self.mesh.edgeCurl
iomega = 1j * omega(freq) * sp.eye(self.mesh.nF)
A = C*sigI*C.T*mui + iomega
if self._makeASymmetric is True:
return mui.T*A
return A
def getAdiag(self, tInd):
"""
System matrix at a given time index
"""
assert tInd >= 0 and tInd < self.nT
dt = self.timeSteps[tInd]
C = self.mesh.edgeCurl
MfRho = self.MfRho
MeMuI = self.MeMuI
eye = sp.eye(self.mesh.nF)
A = C * (MeMuI * (C.T * MfRho)) + 1./dt * eye
if self._makeASymmetric:
return MfRho.T * A
return A
def getA(self, freq):
"""
.. math ::
\mathbf{A} = \mathbf{C} \mathbf{M^e_{\sigma}}^{-1} \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} + i \omega
:param float freq: Frequency
:rtype: scipy.sparse.csr_matrix
:return: A
"""
MfMui = self.MfMui
MeSigmaI = self.MeSigmaI(freq)
C = self.mesh.edgeCurl
iomega = 1j * omega(freq) * sp.eye(self.mesh.nF)
A = C * (MeSigmaI * (C.T * MfMui)) + iomega
if self._makeASymmetric is True:
return MfMui.T * A
return A
def getA(self, freq):
"""
.. math ::
\mathbf{A} = \mathbf{C} \mathbf{M^e_{\sigma}}^{-1} \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} + i \omega
:param float freq: Frequency
:rtype: scipy.sparse.csr_matrix
:return: A
"""
MfMui = self.MfMui
MeSigmaI = self.MeSigmaI(freq)
C = self.mesh.edgeCurl
iomega = 1j * omega(freq) * sp.eye(self.mesh.nF)
A = C * (MeSigmaI * (C.T * MfMui)) + iomega
if self._makeASymmetric is True:
return MfMui.T*A
return A
def getA(self, freq):
"""
.. math ::
\\mathbf{A} = \\mathbf{C} \\mathbf{M^e_{mu^{-1}}} \\mathbf{C}^T \\mathbf{M^f_{\\sigma^{-1}}} + i\\omega
:param float freq: Frequency
:rtype: scipy.sparse.csr_matrix
:return: A
"""
MeMuI = self.MeMuI
MfRho = self.MfRho
C = self.mesh.edgeCurl
iomega = 1j * omega(freq) * sp.eye(self.mesh.nF)
A = C * MeMuI * C.T * MfRho + iomega
if self._makeASymmetric is True:
return MfRho.T*A
return A
def getA(self, freq):
"""
Here, we form the operator \(\\mathbf{A}\) to solce
.. math::
\\mathbf{A} = \\mathbf{C} \\mathbf{M^e_{mu^{-1}}} \\mathbf{C^T} \\mathbf{M^f_{\\sigma^{-1}}} + i\\omega
:param float freq: Frequency
:rtype: scipy.sparse.csr_matrix
:return: A
"""
MeMuI = self.MeMuI
MfSigi = self.MfSigmai
C = self.mesh.edgeCurl
iomega = 1j * omega(freq) * sp.eye(self.mesh.nF)
A = C * MeMuI * C.T * MfSigi + iomega
if self._makeASymmetric is True:
return MfSigi.T*A
return A
def getA(self, freq):
"""
System matrix
.. math ::
\\mathbf{A} = \\mathbf{C} \\mathbf{M^e_{\\mu^{-1}}} \\mathbf{C}^{\\top} \\mathbf{M^f_{\\sigma^{-1}}} + i\\omega
:param float freq: Frequency
:rtype: scipy.sparse.csr_matrix
:return: A
"""
MeMuI = self.MeMuI
MfRho = self.MfRho
C = self.mesh.edgeCurl
iomega = 1j * omega(freq) * sp.eye(self.mesh.nF)
A = C * MeMuI * C.T * MfRho + iomega
if self._makeASymmetric is True:
return MfRho.T*A
return A
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