def test_invPropertyTensor2D(self):
M = discretize.TensorMesh([6, 6])
a1 = np.random.rand(M.nC)
a2 = np.random.rand(M.nC)
a3 = np.random.rand(M.nC)
prop1 = a1
prop2 = np.c_[a1, a2]
prop3 = np.c_[a1, a2, a3]
for prop in [4, prop1, prop2, prop3]:
b = invPropertyTensor(M, prop)
A = makePropertyTensor(M, prop)
B1 = makePropertyTensor(M, b)
B2 = invPropertyTensor(M, prop, returnMatrix=True)
Z = B1 * A - sp.identity(M.nC * 2)
self.assertTrue(np.linalg.norm(Z.todense().ravel(), 2) < TOL)
Z = B2 * A - sp.identity(M.nC * 2)
self.assertTrue(np.linalg.norm(Z.todense().ravel(), 2) < TOL)
def _getInnerProduct(self, projType, prop=None, invProp=False, invMat=False, doFast=True):
"""get the inner product matrix
Parameters
----------
str : projType
'F' for faces 'E' for edges
numpy.ndarray : prop
material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
bool : invProp
inverts the material property
bool : invMat
inverts the matrix
bool : doFast
do a faster implementation if available.
Returns
-------
scipy.sparse.csr_matrix
M, the inner product matrix (nE, nE)
"""
assert projType in ['F', 'E'], "projType must be 'F' for faces or 'E' for edges"
fast = None
if hasattr(self, '_fastInnerProduct') and doFast:
fast = self._fastInnerProduct(projType, prop=prop, invProp=invProp, invMat=invMat)
if fast is not None:
return fast
if invProp:
prop = invPropertyTensor(self, prop)
tensorType = TensorType(self, prop)
Mu = makePropertyTensor(self, prop)
Ps = self._getInnerProductProjectionMatrices(projType, tensorType)
A = np.sum([P.T * Mu * P for P in Ps])
if invMat and tensorType < 3:
A = sdInv(A)
elif invMat and tensorType == 3:
raise Exception('Solver needed to invert A.')
return A