mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-28 21:12:41 +08:00
rowanc1
371 lines
10 KiB
Python
371 lines
10 KiB
Python
import Utils, Parameters, numpy as np, scipy.sparse as sp
|
|
from Tests import checkDerivative
|
|
|
|
class BaseModel(object):
|
|
"""
|
|
SimPEG Model
|
|
|
|
"""
|
|
|
|
__metaclass__ = Utils.SimPEGMetaClass
|
|
|
|
counter = None #: A SimPEG.Utils.Counter object
|
|
mesh = None #: A SimPEG Mesh
|
|
|
|
def __init__(self, mesh):
|
|
self.mesh = mesh
|
|
|
|
def transform(self, m):
|
|
"""
|
|
:param numpy.array m: model
|
|
:rtype: numpy.array
|
|
:return: transformed model
|
|
|
|
The *transform* changes the model into the physical property.
|
|
|
|
"""
|
|
return m
|
|
|
|
def transformInverse(self, D):
|
|
"""
|
|
:param numpy.array D: physical property
|
|
:rtype: numpy.array
|
|
:return: model
|
|
|
|
The *transformInverse* changes the physical property into the model.
|
|
|
|
.. note:: The *transformInverse* may not be easy to create in general.
|
|
|
|
"""
|
|
raise NotImplementedError('The transformInverse is not implemented.')
|
|
|
|
def transformDeriv(self, m):
|
|
"""
|
|
:param numpy.array m: model
|
|
:rtype: scipy.csr_matrix
|
|
:return: derivative of transformed model
|
|
|
|
The *transform* changes the model into the physical property.
|
|
The *transformDeriv* provides the derivative of the *transform*.
|
|
"""
|
|
return sp.identity(m.size)
|
|
|
|
@property
|
|
def nP(self):
|
|
"""Number of parameters in the model."""
|
|
return self.mesh.nC
|
|
|
|
def example(self):
|
|
return np.random.rand(self.nP)
|
|
|
|
def test(self, m=None):
|
|
print 'Testing the %s Class!' % self.__class__.__name__
|
|
if m is None:
|
|
m = self.example()
|
|
return checkDerivative(lambda m : [self.transform(m), self.transformDeriv(m)], m, plotIt=False)
|
|
|
|
class BaseNonLinearModel(object):
|
|
"""
|
|
SimPEG BaseNonLinearModel
|
|
|
|
"""
|
|
|
|
__metaclass__ = Utils.SimPEGMetaClass
|
|
|
|
counter = None #: A SimPEG.Utils.Counter object
|
|
mesh = None #: A SimPEG Mesh
|
|
|
|
def __init__(self, mesh):
|
|
self.mesh = mesh
|
|
|
|
def transform(self, u, m):
|
|
"""
|
|
:param numpy.array u: fields
|
|
:param numpy.array m: model
|
|
:rtype: numpy.array
|
|
:return: transformed model
|
|
|
|
The *transform* changes the model into the physical property.
|
|
|
|
"""
|
|
return m
|
|
|
|
def transformDerivU(self, u, m):
|
|
"""
|
|
:param numpy.array u: fields
|
|
:param numpy.array m: model
|
|
:rtype: scipy.csr_matrix
|
|
:return: derivative of transformed model
|
|
|
|
The *transform* changes the model into the physical property.
|
|
The *transformDerivU* provides the derivative of the *transform* with respect to the fields.
|
|
"""
|
|
raise NotImplementedError('The transformDerivU is not implemented.')
|
|
|
|
|
|
def transformDerivM(self, u, m):
|
|
"""
|
|
:param numpy.array u: fields
|
|
:param numpy.array m: model
|
|
:rtype: scipy.csr_matrix
|
|
:return: derivative of transformed model
|
|
|
|
The *transform* changes the model into the physical property.
|
|
The *transformDerivU* provides the derivative of the *transform* with respect to the model.
|
|
"""
|
|
raise NotImplementedError('The transformDerivM is not implemented.')
|
|
|
|
@property
|
|
def nP(self):
|
|
"""Number of parameters in the model."""
|
|
return self.mesh.nC
|
|
|
|
def example(self):
|
|
raise NotImplementedError('The example is not implemented.')
|
|
|
|
def test(self, m=None):
|
|
raise NotImplementedError('The test is not implemented.')
|
|
|
|
|
|
class LogModel(BaseModel):
|
|
"""SimPEG LogModel"""
|
|
|
|
def __init__(self, mesh, **kwargs):
|
|
BaseModel.__init__(self, mesh, **kwargs)
|
|
|
|
def transform(self, m):
|
|
"""
|
|
:param numpy.array m: model
|
|
:rtype: numpy.array
|
|
:return: transformed model
|
|
|
|
The *transform* changes the model into the physical property.
|
|
|
|
A common example of this is to invert for electrical conductivity
|
|
in log space. In this case, your model will be log(sigma) and to
|
|
get back to sigma, you can take the exponential:
|
|
|
|
.. math::
|
|
|
|
m = \log{\sigma}
|
|
|
|
\exp{m} = \exp{\log{\sigma}} = \sigma
|
|
"""
|
|
return np.exp(Utils.mkvc(m))
|
|
|
|
|
|
def transformInverse(self, D):
|
|
"""
|
|
:param numpy.array D: physical property
|
|
:rtype: numpy.array
|
|
:return: model
|
|
|
|
The *transformInverse* changes the physical property into the model.
|
|
|
|
.. math::
|
|
|
|
m = \log{\sigma}
|
|
|
|
"""
|
|
return np.log(Utils.mkvc(D))
|
|
|
|
|
|
def transformDeriv(self, m):
|
|
"""
|
|
:param numpy.array m: model
|
|
:rtype: scipy.csr_matrix
|
|
:return: derivative of transformed model
|
|
|
|
The *transform* changes the model into the physical property.
|
|
The *transformDeriv* provides the derivative of the *transform*.
|
|
|
|
If the model *transform* is:
|
|
|
|
.. math::
|
|
|
|
m = \log{\sigma}
|
|
|
|
\exp{m} = \exp{\log{\sigma}} = \sigma
|
|
|
|
Then the derivative is:
|
|
|
|
.. math::
|
|
|
|
\\frac{\partial \exp{m}}{\partial m} = \\text{sdiag}(\exp{m})
|
|
"""
|
|
return Utils.sdiag(np.exp(Utils.mkvc(m)))
|
|
|
|
class Vertical1DModel(BaseModel):
|
|
"""Vertical1DModel
|
|
|
|
Given a 1D vector through the last dimension
|
|
of the mesh, this will extend to the full
|
|
model space.
|
|
"""
|
|
|
|
def __init__(self, mesh, **kwargs):
|
|
BaseModel.__init__(self, mesh, **kwargs)
|
|
|
|
@property
|
|
def nP(self):
|
|
"""Number of model properties.
|
|
|
|
The number of cells in the
|
|
last dimension of the mesh."""
|
|
return self.mesh.vnC[self.mesh.dim-1]
|
|
|
|
def transform(self, m):
|
|
"""
|
|
:param numpy.array m: model
|
|
:rtype: numpy.array
|
|
:return: transformed model
|
|
"""
|
|
repNum = self.mesh.vnC[:self.mesh.dim-1].prod()
|
|
return Utils.mkvc(m).repeat(repNum)
|
|
|
|
def transformDeriv(self, m):
|
|
"""
|
|
:param numpy.array m: model
|
|
:rtype: scipy.csr_matrix
|
|
:return: derivative of transformed model
|
|
"""
|
|
repNum = self.mesh.vnC[:self.mesh.dim-1].prod()
|
|
repVec = sp.csr_matrix(
|
|
(np.ones(repNum),
|
|
(range(repNum), np.zeros(repNum))
|
|
), shape=(repNum, 1))
|
|
return sp.kron(sp.identity(self.nP), repVec)
|
|
|
|
class Mesh2Mesh(BaseModel):
|
|
"""
|
|
Takes a model on one mesh are translates it to another mesh.
|
|
|
|
.. plot::
|
|
|
|
from SimPEG import *
|
|
M = Mesh.TensorMesh([100,100])
|
|
h1 = Utils.meshTensors(((7,6,1.5),(10,6),(7,6,1.5)))
|
|
h1 = h1/h1.sum()
|
|
M2 = Mesh.TensorMesh([h1,h1])
|
|
V = Utils.ModelBuilder.randomModel(M.vnC, seed=79, its=50)
|
|
v = Utils.mkvc(V)
|
|
modh = Model.Mesh2Mesh([M,M2])
|
|
modH = Model.Mesh2Mesh([M2,M])
|
|
H = modH.transform(v)
|
|
h = modh.transform(H)
|
|
ax = plt.subplot(131)
|
|
M.plotImage(v, ax=ax)
|
|
ax.set_title('Fine Mesh (Original)')
|
|
ax = plt.subplot(132)
|
|
M2.plotImage(H,clim=[0,1],ax=ax)
|
|
ax.set_title('Course Mesh')
|
|
ax = plt.subplot(133)
|
|
M.plotImage(h,clim=[0,1],ax=ax)
|
|
ax.set_title('Fine Mesh (Interpolated)')
|
|
|
|
"""
|
|
|
|
def __init__(self, meshes, **kwargs):
|
|
Utils.setKwargs(self, **kwargs)
|
|
|
|
assert type(meshes) is list, "meshes must be a list of two meshes"
|
|
assert len(meshes) == 2, "meshes must be a list of two meshes"
|
|
assert meshes[0].dim == meshes[1].dim, """The two meshes must be the same dimension"""
|
|
|
|
self.mesh = meshes[0]
|
|
self.mesh2 = meshes[1]
|
|
|
|
self.P = self.mesh2.getInterpolationMat(self.mesh.gridCC,'CC',zerosOutside=True)
|
|
|
|
@property
|
|
def nP(self):
|
|
"""Number of parameters in the model."""
|
|
return self.mesh2.nC
|
|
def transform(self, m):
|
|
return self.P*m
|
|
def transformDeriv(self, m):
|
|
return self.P
|
|
|
|
|
|
class ActiveModel(BaseModel):
|
|
"""
|
|
Active model parameters.
|
|
|
|
"""
|
|
|
|
indActive = None #: Active Cells
|
|
valInactive = None #: Values of inactive Cells
|
|
nC = None #: Number of cells in the full model
|
|
|
|
def __init__(self, mesh, indActive, valInactive, nC=None):
|
|
self.mesh = mesh
|
|
|
|
self.nC = nC or mesh.nC
|
|
|
|
if indActive.dtype is not bool:
|
|
z = np.zeros(self.nC,dtype=bool)
|
|
z[indActive] = True
|
|
indActive = z
|
|
self.indActive = indActive
|
|
self.indInactive = np.logical_not(indActive)
|
|
if type(valInactive) in [float, int, long]:
|
|
valInactive = np.ones(self.nC)*float(valInactive)
|
|
|
|
valInactive[self.indActive] = 0
|
|
self.valInactive = valInactive
|
|
|
|
inds = np.nonzero(self.indActive)[0]
|
|
self.P = sp.csr_matrix((np.ones(inds.size),(inds, range(inds.size))), shape=(self.nC, self.nP))
|
|
|
|
@property
|
|
def nP(self):
|
|
"""Number of parameters in the model."""
|
|
return self.indActive.sum()
|
|
|
|
def transform(self, m):
|
|
return self.P*m + self.valInactive
|
|
def transformDeriv(self, m):
|
|
return self.P
|
|
|
|
class ComboModel(BaseModel):
|
|
"""Combination of various models."""
|
|
|
|
def __init__(self, mesh, models, **kwargs):
|
|
BaseModel.__init__(self, mesh, **kwargs)
|
|
|
|
self.models = []
|
|
for m in models:
|
|
if not isinstance(m, BaseModel):
|
|
self.models += [m(mesh, **kwargs)]
|
|
else:
|
|
self.models += [m]
|
|
|
|
@property
|
|
def nP(self):
|
|
"""Number of model properties.
|
|
|
|
The number of cells in the
|
|
last dimension of the mesh."""
|
|
return self.models[-1].nP
|
|
|
|
def transform(self, m):
|
|
for model in reversed(self.models):
|
|
m = model.transform(m)
|
|
return m
|
|
|
|
def transformDeriv(self, m):
|
|
deriv = 1
|
|
mi = m
|
|
for model in reversed(self.models):
|
|
deriv = model.transformDeriv(mi) * deriv
|
|
mi = model.transform(mi)
|
|
return deriv
|
|
|
|
if __name__ == '__main__':
|
|
from SimPEG import *
|
|
mesh = Mesh.TensorMesh([10,8])
|
|
combo = ComboModel(mesh, [LogModel, Vertical1DModel])
|
|
m = combo.example()
|
|
print m.shape
|
|
print combo.test(np.arange(8))
|