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Full anisotropic tensor derivatives.

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rowanc1
2014-03-03 11:01:12 -08:00
parent 8eaff94e48
commit 3dd54bc0e3
3 changed files with 186 additions and 63 deletions
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SimPEG/Mesh/InnerProducts.py
+102 -21
View File
@@ -1,5 +1,5 @@
from scipy import sparse as sp
from SimPEG.Utils import sub2ind, ndgrid, mkvc, getSubArray, sdiag, inv3X3BlockDiagonal, inv2X2BlockDiagonal, makePropertyTensor, invPropertyTensor
from SimPEG.Utils import sub2ind, ndgrid, mkvc, getSubArray, sdiag, inv3X3BlockDiagonal, inv2X2BlockDiagonal, makePropertyTensor, invPropertyTensor, spzeros
import numpy as np
@@ -11,7 +11,7 @@ class InnerProducts(object):
raise Exception('InnerProducts is a base class providing inner product matrices for meshes and cannot run on its own. Inherit to your favorite Mesh class.')
def getFaceInnerProduct(self, materialProperty=None, returnP=False,
invertProperty=False):
invertProperty=False, doFast=True):
"""
:param numpy.array materialProperty: material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
:param bool returnP: returns the projection matrices
@@ -21,7 +21,7 @@ class InnerProducts(object):
"""
fast = None
if returnP is False and hasattr(self, '_fastFaceInnerProduct'):
if returnP is False and hasattr(self, '_fastFaceInnerProduct') and doFast:
fast = self._fastFaceInnerProduct(materialProperty=materialProperty, invertProperty=invertProperty)
if fast is not None:
@@ -71,7 +71,7 @@ class InnerProducts(object):
else:
return A
def getFaceInnerProductDeriv(self, materialProperty=None, P=None):
def getFaceInnerProductDeriv(self, materialProperty=None, v=None, P=None, doFast=True):
"""
:param numpy.array materialProperty: material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
:rtype: scipy.csr_matrix
@@ -79,24 +79,18 @@ class InnerProducts(object):
"""
fast = None
if hasattr(self, '_fastFaceInnerProductDeriv'):
fast = self._fastFaceInnerProductDeriv(materialProperty=materialProperty)
if hasattr(self, '_fastFaceInnerProductDeriv') and doFast:
fast = self._fastFaceInnerProductDeriv(materialProperty=materialProperty, v=v)
if fast is not None:
return fast
raise NotImplementedError('Derivatives for the material property specified are not yet implemented.')
if P is None:
M, P = getFaceInnerProduct(self, materialProperty=materialProperty, returnP=True)
M, P = self.getFaceInnerProduct(materialProperty=materialProperty, returnP=True)
d = self.dim
return self._getInnerProductDeriv(materialProperty, v, P, self.nF)
if d == 1:
P[0].T * sp.identity(n) * P[0]
def getEdgeInnerProduct(self, materialProperty=None, returnP=False, invertProperty=False):
def getEdgeInnerProduct(self, materialProperty=None, returnP=False, invertProperty=False, doFast=True):
"""
:param numpy.array materialProperty: material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
:param bool returnP: returns the projection matrices
@@ -106,7 +100,7 @@ class InnerProducts(object):
"""
fast = None
if returnP is False and hasattr(self, '_fastEdgeInnerProduct'):
if returnP is False and hasattr(self, '_fastEdgeInnerProduct') and doFast:
fast = self._fastEdgeInnerProduct(materialProperty=materialProperty, invertProperty=invertProperty)
if fast is not None:
@@ -151,8 +145,7 @@ class InnerProducts(object):
else:
return A
def getEdgeInnerProductDeriv(self, materialProperty=None, P=None):
def getEdgeInnerProductDeriv(self, materialProperty=None, v=None, P=None, doFast=True):
"""
:param numpy.array materialProperty: material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
:rtype: scipy.csr_matrix
@@ -161,14 +154,102 @@ class InnerProducts(object):
fast = None
if hasattr(self, '_fastEdgeInnerProductDeriv'):
fast = self._fastEdgeInnerProductDeriv(materialProperty=materialProperty)
if hasattr(self, '_fastEdgeInnerProductDeriv') and doFast:
fast = self._fastEdgeInnerProductDeriv(materialProperty=materialProperty, v=v)
if fast is not None:
return fast
raise NotImplementedError('Derivatives for the material property specified are not yet implemented.')
if P is None:
M, P = self.getEdgeInnerProduct(materialProperty=materialProperty, returnP=True)
return self._getInnerProductDeriv(materialProperty, v, P, self.nE)
def _getInnerProductDeriv(self, materialProperty, v, P, n):
if v is None:
raise Exception('v must be supplied for this implementation.')
d = self.dim
Z = spzeros(self.nC, self.nC)
if d == 1:
dMdm = spzeros(n, self.nC)
for i, p in enumerate(P):
dMdm = dMdm + p.T * sdiag( p * v )
elif d == 2:
if materialProperty is None or materialProperty.size == self.nC:
dMdm = spzeros(n, self.nC)
for i, p in enumerate(P):
Y = p * v
y1 = Y[:self.nC]
y2 = Y[self.nC:]
dMdm = dMdm + p.T * sp.vstack((sdiag( y1 ), sdiag( y2 )))
if materialProperty.size == self.nC*2:
dMdm1 = spzeros(n, self.nC)
dMdm2 = spzeros(n, self.nC)
for i, p in enumerate(P):
Y = p * v
y1 = Y[:self.nC]
y2 = Y[self.nC:]
dMdm1 = dMdm1 + p.T * sp.vstack(( sdiag( y1 ), Z))
dMdm2 = dMdm2 + p.T * sp.vstack(( Z, sdiag( y2 )))
dMdm = sp.hstack((dMdm1, dMdm2))
if materialProperty.size == self.nC*3:
dMdm1 = spzeros(n, self.nC)
dMdm2 = spzeros(n, self.nC)
dMdm3 = spzeros(n, self.nC)
for i, p in enumerate(P):
Y = p * v
y1 = Y[:self.nC]
y2 = Y[self.nC:]
dMdm1 = dMdm1 + p.T * sp.vstack(( sdiag( y1 ), Z))
dMdm2 = dMdm2 + p.T * sp.vstack(( Z, sdiag( y2 )))
dMdm3 = dMdm3 + p.T * sp.vstack(( sdiag( y2 ), sdiag( y1 )))
dMdm = sp.hstack((dMdm1, dMdm2, dMdm3))
elif d == 3:
if materialProperty is None or materialProperty.size == self.nC:
dMdm = spzeros(n, self.nC)
for i, p in enumerate(P):
Y = p * v
y1 = Y[:self.nC]
y2 = Y[self.nC:self.nC*2]
y3 = Y[self.nC*2:]
dMdm = dMdm + p.T * sp.vstack((sdiag( y1 ), sdiag( y2 ), sdiag( y3 )))
if materialProperty.size == self.nC*3:
dMdm1 = spzeros(n, self.nC)
dMdm2 = spzeros(n, self.nC)
dMdm3 = spzeros(n, self.nC)
for i, p in enumerate(P):
Y = p * v
y1 = Y[:self.nC]
y2 = Y[self.nC:self.nC*2]
y3 = Y[self.nC*2:]
dMdm1 = dMdm1 + p.T * sp.vstack(( sdiag( y1 ), Z, Z))
dMdm2 = dMdm2 + p.T * sp.vstack(( Z, sdiag( y2 ), Z))
dMdm3 = dMdm3 + p.T * sp.vstack(( Z, Z, sdiag( y3 )))
dMdm = sp.hstack((dMdm1, dMdm2, dMdm3))
if materialProperty.size == self.nC*6:
dMdm1 = spzeros(n, self.nC)
dMdm2 = spzeros(n, self.nC)
dMdm3 = spzeros(n, self.nC)
dMdm4 = spzeros(n, self.nC)
dMdm5 = spzeros(n, self.nC)
dMdm6 = spzeros(n, self.nC)
for i, p in enumerate(P):
Y = p * v
y1 = Y[:self.nC]
y2 = Y[self.nC:self.nC*2]
y3 = Y[self.nC*2:]
dMdm1 = dMdm1 + p.T * sp.vstack(( sdiag( y1 ), Z, Z))
dMdm2 = dMdm2 + p.T * sp.vstack(( Z, sdiag( y2 ), Z))
dMdm3 = dMdm3 + p.T * sp.vstack(( Z, Z, sdiag( y3 )))
dMdm4 = dMdm4 + p.T * sp.vstack(( sdiag( y2 ), sdiag( y1 ), Z))
dMdm5 = dMdm5 + p.T * sp.vstack(( sdiag( y3 ), Z, sdiag( y1 )))
dMdm6 = dMdm6 + p.T * sp.vstack(( Z, sdiag( y3 ), sdiag( y2 )))
dMdm = sp.hstack((dMdm1, dMdm2, dMdm3, dMdm4, dMdm5, dMdm6))
return dMdm
# ------------------------ Geometries ------------------------------
#
SimPEG/Mesh/TensorMesh.py
+12 -7
View File
@@ -549,25 +549,25 @@ class TensorMesh(BaseRectangularMesh, TensorView, DiffOperators, InnerProducts):
return Utils.sdiag(Av.T * V * Utils.mkvc(materialProperty))
def _fastFaceInnerProductDeriv(self, materialProperty=None):
def _fastFaceInnerProductDeriv(self, materialProperty=None, v=None):
"""
:param numpy.array materialProperty: material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
:rtype: scipy.csr_matrix
:return: M, the inner product matrix (nF, nF)
"""
return self._fastInnerProductDeriv('F', materialProperty=materialProperty)
return self._fastInnerProductDeriv('F', materialProperty=materialProperty, v=v)
def _fastEdgeInnerProductDeriv(self, materialProperty=None):
def _fastEdgeInnerProductDeriv(self, materialProperty=None, v=None):
"""
:param numpy.array materialProperty: material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
:rtype: scipy.csr_matrix
:return: M, the inner product matrix (nE, nE)
"""
return self._fastInnerProductDeriv('E', materialProperty=materialProperty)
return self._fastInnerProductDeriv('E', materialProperty=materialProperty, v=v)
def _fastInnerProductDeriv(self, AvType, materialProperty=None):
def _fastInnerProductDeriv(self, AvType, materialProperty=None, v=None):
"""
:param str AvType: 'E' or 'F'
:param numpy.array materialProperty: material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
@@ -576,11 +576,16 @@ class TensorMesh(BaseRectangularMesh, TensorView, DiffOperators, InnerProducts):
"""
if materialProperty is None or materialProperty.size == self.nC:
Av = getattr(self, 'ave'+AvType+'2CC')
return self.dim * Av.T * Utils.sdiag(self.vol)
V = Utils.sdiag(self.vol)
if v is None:
return self.dim * Av.T * Utils.sdiag(self.vol)
return Utils.sdiag(v) * self.dim * Av.T * V
if materialProperty.size == self.nC*self.dim: # anisotropic
Av = getattr(self, 'ave'+AvType+'2CCV')
V = sp.kron(sp.identity(self.dim), Utils.sdiag(self.vol))
return Av.T * V
if v is None:
return Av.T * V
return Utils.sdiag(v) * Av.T * V
if __name__ == '__main__':