def invPropertyTensor(M, tensor, returnMatrix=False):
propType = TensorType(M, tensor)
if isScalar(tensor):
T = 1./tensor
elif propType < 3: # Isotropic or Diagonal
T = 1./mkvc(tensor) # ensure it is a vector.
elif M.dim == 2 and tensor.size == M.nC*3: # Fully anisotropic, 2D
tensor = tensor.reshape((M.nC,3), order='F')
B = inv2X2BlockDiagonal(tensor[:,0], tensor[:,2],
tensor[:,2], tensor[:,1],
returnMatrix=False)
b11, b12, b21, b22 = B
T = np.r_[b11, b22, b12]
elif M.dim == 3 and tensor.size == M.nC*6: # Fully anisotropic, 3D
tensor = tensor.reshape((M.nC,6), order='F')
B = inv3X3BlockDiagonal(tensor[:,0], tensor[:,3], tensor[:,4],
tensor[:,3], tensor[:,1], tensor[:,5],
tensor[:,4], tensor[:,5], tensor[:,2],
returnMatrix=False)
b11, b12, b13, b21, b22, b23, b31, b32, b33 = B
T = np.r_[b11, b22, b33, b12, b13, b23]
else:
raise Exception('Unexpected shape of tensor')
if returnMatrix:
return makePropertyTensor(M, T)
return T
def makePropertyTensor(M, tensor):
if tensor is None: # default is ones
tensor = np.ones(M.nC)
if isScalar(tensor):
tensor = tensor * np.ones(M.nC)
propType = TensorType(M, tensor)
if propType == 1: # Isotropic!
Sigma = sp.kron(sp.identity(M.dim), sdiag(mkvc(tensor)))
elif propType == 2: # Diagonal tensor
Sigma = sdiag(mkvc(tensor))
elif M.dim == 2 and tensor.size == M.nC * 3: # Fully anisotropic, 2D
tensor = tensor.reshape((M.nC, 3), order='F')
row1 = sp.hstack((sdiag(tensor[:, 0]), sdiag(tensor[:, 2])))
row2 = sp.hstack((sdiag(tensor[:, 2]), sdiag(tensor[:, 1])))
Sigma = sp.vstack((row1, row2))
elif M.dim == 3 and tensor.size == M.nC * 6: # Fully anisotropic, 3D
tensor = tensor.reshape((M.nC, 6), order='F')
row1 = sp.hstack(
(sdiag(tensor[:, 0]), sdiag(tensor[:, 3]), sdiag(tensor[:, 4])))
row2 = sp.hstack(
(sdiag(tensor[:, 3]), sdiag(tensor[:, 1]), sdiag(tensor[:, 5])))
row3 = sp.hstack(
(sdiag(tensor[:, 4]), sdiag(tensor[:, 5]), sdiag(tensor[:, 2])))
Sigma = sp.vstack((row1, row2, row3))
else:
raise Exception('Unexpected shape of tensor')
return Sigma
def makePropertyTensor(M, tensor):
if tensor is None: # default is ones
tensor = np.ones(M.nC)
if isScalar(tensor):
tensor = tensor * np.ones(M.nC)
propType = TensorType(M, tensor)
if propType == 1: # Isotropic!
Sigma = sp.kron(sp.identity(M.dim), sdiag(mkvc(tensor)))
elif propType == 2: # Diagonal tensor
Sigma = sdiag(mkvc(tensor))
elif M.dim == 2 and tensor.size == M.nC*3: # Fully anisotropic, 2D
tensor = tensor.reshape((M.nC,3), order='F')
row1 = sp.hstack((sdiag(tensor[:, 0]), sdiag(tensor[:, 2])))
row2 = sp.hstack((sdiag(tensor[:, 2]), sdiag(tensor[:, 1])))
Sigma = sp.vstack((row1, row2))
elif M.dim == 3 and tensor.size == M.nC*6: # Fully anisotropic, 3D
tensor = tensor.reshape((M.nC,6), order='F')
row1 = sp.hstack((sdiag(tensor[:, 0]), sdiag(tensor[:, 3]), sdiag(tensor[:, 4])))
row2 = sp.hstack((sdiag(tensor[:, 3]), sdiag(tensor[:, 1]), sdiag(tensor[:, 5])))
row3 = sp.hstack((sdiag(tensor[:, 4]), sdiag(tensor[:, 5]), sdiag(tensor[:, 2])))
Sigma = sp.vstack((row1, row2, row3))
else:
raise Exception('Unexpected shape of tensor')
return Sigma
def meshTensor(value):
"""
**meshTensor** takes a list of numbers and tuples that have the form::
mT = [ float, (cellSize, numCell), (cellSize, numCell, factor) ]
For example, a time domain mesh code needs
many time steps at one time::
[(1e-5, 30), (1e-4, 30), 1e-3]
Means take 30 steps at 1e-5 and then 30 more at 1e-4,
and then one step of 1e-3.
Tensor meshes can also be created by increase factors::
[(10.0, 5, -1.3), (10.0, 50), (10.0, 5, 1.3)]
When there is a third number in the tuple, it
refers to the increase factor, if this number
is negative this section of the tensor is flipped right-to-left.
.. plot::
from SimPEG import Mesh
tx = [(10.0,10,-1.3),(10.0,40),(10.0,10,1.3)]
ty = [(10.0,10,-1.3),(10.0,40)]
M = Mesh.TensorMesh([tx, ty])
M.plotGrid(showIt=True)
"""
if type(value) is not list:
raise Exception('meshTensor must be a list of scalars and tuples.')
proposed = []
for v in value:
if isScalar(v):
proposed += [float(v)]
elif type(v) is tuple and len(v) == 2:
proposed += [float(v[0])] * int(v[1])
elif type(v) is tuple and len(v) == 3:
start = float(v[0])
num = int(v[1])
factor = float(v[2])
pad = (
(np.ones(num) * np.abs(factor))**(np.arange(num) + 1)) * start
if factor < 0: pad = pad[::-1]
proposed += pad.tolist()
else:
raise Exception(
'meshTensor must contain only scalars and len(2) or len(3) tuples.'
)
return np.array(proposed)
def meshTensor(value):
"""
**meshTensor** takes a list of numbers and tuples that have the form::
mT = [ float, (cellSize, numCell), (cellSize, numCell, factor) ]
For example, a time domain mesh code needs
many time steps at one time::
[(1e-5, 30), (1e-4, 30), 1e-3]
Means take 30 steps at 1e-5 and then 30 more at 1e-4,
and then one step of 1e-3.
Tensor meshes can also be created by increase factors::
[(10.0, 5, -1.3), (10.0, 50), (10.0, 5, 1.3)]
When there is a third number in the tuple, it
refers to the increase factor, if this number
is negative this section of the tensor is flipped right-to-left.
.. plot::
from SimPEG import Mesh
tx = [(10.0,10,-1.3),(10.0,40),(10.0,10,1.3)]
ty = [(10.0,10,-1.3),(10.0,40)]
M = Mesh.TensorMesh([tx, ty])
M.plotGrid(showIt=True)
"""
if type(value) is not list:
raise Exception('meshTensor must be a list of scalars and tuples.')
proposed = []
for v in value:
if isScalar(v):
proposed += [float(v)]
elif type(v) is tuple and len(v) == 2:
proposed += [float(v[0])]*int(v[1])
elif type(v) is tuple and len(v) == 3:
start = float(v[0])
num = int(v[1])
factor = float(v[2])
pad = ((np.ones(num)*np.abs(factor))**(np.arange(num)+1))*start
if factor < 0: pad = pad[::-1]
proposed += pad.tolist()
else:
raise Exception('meshTensor must contain only scalars and len(2) or len(3) tuples.')
return np.array(proposed)
def __init__(self, M, tensor):
if tensor is None: # default is ones
self._tt = -1
self._tts = 'none'
elif isScalar(tensor):
self._tt = 0
self._tts = 'scalar'
elif tensor.size == M.nC:
self._tt = 1
self._tts = 'isotropic'
elif ((M.dim == 2 and tensor.size == M.nC*2) or
(M.dim == 3 and tensor.size == M.nC*3)):
self._tt = 2
self._tts = 'anisotropic'
elif ((M.dim == 2 and tensor.size == M.nC*3) or
(M.dim == 3 and tensor.size == M.nC*6)):
self._tt = 3
self._tts = 'tensor'
else:
raise Exception('Unexpected shape of tensor')
def __init__(self, M, tensor):
if tensor is None: # default is ones
self._tt = -1
self._tts = 'none'
elif isScalar(tensor):
self._tt = 0
self._tts = 'scalar'
elif tensor.size == M.nC:
self._tt = 1
self._tts = 'isotropic'
elif ((M.dim == 2 and tensor.size == M.nC * 2)
or (M.dim == 3 and tensor.size == M.nC * 3)):
self._tt = 2
self._tts = 'anisotropic'
elif ((M.dim == 2 and tensor.size == M.nC * 3)
or (M.dim == 3 and tensor.size == M.nC * 6)):
self._tt = 3
self._tts = 'tensor'
else:
raise Exception('Unexpected shape of tensor')
def invPropertyTensor(M, tensor, returnMatrix=False):
propType = TensorType(M, tensor)
if isScalar(tensor):
T = 1. / tensor
elif propType < 3: # Isotropic or Diagonal
T = 1. / mkvc(tensor) # ensure it is a vector.
elif M.dim == 2 and tensor.size == M.nC * 3: # Fully anisotropic, 2D
tensor = tensor.reshape((M.nC, 3), order='F')
B = inv2X2BlockDiagonal(tensor[:, 0],
tensor[:, 2],
tensor[:, 2],
tensor[:, 1],
returnMatrix=False)
b11, b12, b21, b22 = B
T = np.r_[b11, b22, b12]
elif M.dim == 3 and tensor.size == M.nC * 6: # Fully anisotropic, 3D
tensor = tensor.reshape((M.nC, 6), order='F')
B = inv3X3BlockDiagonal(tensor[:, 0],
tensor[:, 3],
tensor[:, 4],
tensor[:, 3],
tensor[:, 1],
tensor[:, 5],
tensor[:, 4],
tensor[:, 5],
tensor[:, 2],
returnMatrix=False)
b11, b12, b13, b21, b22, b23, b31, b32, b33 = B
T = np.r_[b11, b22, b33, b12, b13, b23]
else:
raise Exception('Unexpected shape of tensor')
if returnMatrix:
return makePropertyTensor(M, T)
return T
