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rowanc1
440 lines
12 KiB
Python
440 lines
12 KiB
Python
import Utils, numpy as np, scipy.sparse as sp
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from Tests import checkDerivative
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class IdentityMap(object):
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"""
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SimPEG Map
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"""
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__metaclass__ = Utils.SimPEGMetaClass
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counter = None #: A SimPEG.Utils.Counter object
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mesh = None #: A SimPEG Mesh
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def __init__(self, mesh):
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self.mesh = mesh
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def transform(self, m):
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"""
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:param numpy.array m: model
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:rtype: numpy.array
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:return: transformed model
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The *transform* changes the model into the physical property.
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"""
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return m
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def transformInverse(self, D):
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"""
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:param numpy.array D: physical property
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:rtype: numpy.array
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:return: model
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The *transformInverse* changes the physical property into the model.
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.. note:: The *transformInverse* may not be easy to create in general.
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"""
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raise NotImplementedError('The transformInverse is not implemented.')
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def transformDeriv(self, m):
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"""
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:param numpy.array m: model
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:rtype: scipy.csr_matrix
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:return: derivative of transformed model
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The *transform* changes the model into the physical property.
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The *transformDeriv* provides the derivative of the *transform*.
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"""
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return sp.identity(m.size)
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@property
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def nP(self):
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"""Number of parameters in the model."""
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return self.mesh.nC
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def example(self):
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return np.random.rand(self.nP)
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def test(self, m=None, **kwargs):
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print 'Testing the %s Class!' % self.__class__.__name__
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if m is None:
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m = self.example()
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if 'plotIt' not in kwargs:
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kwargs['plotIt'] = False
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return checkDerivative(lambda m : [self.transform(m), self.transformDeriv(m)], m, **kwargs)
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def _assertMatchesPair(self, pair):
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assert (isinstance(self, pair) or
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isinstance(self, ComboMap) and isinstance(self.maps[0], pair)
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), "Mapping object must be an instance of a %s class."%(pair.__name__)
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def __mul__(self, val):
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if isinstance(val, ComboMap):
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return ComboMap(self.mesh, [self] + val.maps)
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elif isinstance(val, IdentityMap):
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return ComboMap(self.mesh, [self, val])
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elif type(val) is np.ndarray:
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return self.transform(val)
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class NonLinearMap(object):
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"""
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SimPEG NonLinearMap
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"""
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__metaclass__ = Utils.SimPEGMetaClass
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counter = None #: A SimPEG.Utils.Counter object
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mesh = None #: A SimPEG Mesh
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def __init__(self, mesh):
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self.mesh = mesh
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def transform(self, u, m):
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"""
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:param numpy.array u: fields
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:param numpy.array m: model
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:rtype: numpy.array
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:return: transformed model
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The *transform* changes the model into the physical property.
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"""
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return m
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def transformDerivU(self, u, m):
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"""
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:param numpy.array u: fields
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:param numpy.array m: model
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:rtype: scipy.csr_matrix
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:return: derivative of transformed model
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The *transform* changes the model into the physical property.
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The *transformDerivU* provides the derivative of the *transform* with respect to the fields.
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"""
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raise NotImplementedError('The transformDerivU is not implemented.')
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def transformDerivM(self, u, m):
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"""
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:param numpy.array u: fields
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:param numpy.array m: model
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:rtype: scipy.csr_matrix
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:return: derivative of transformed model
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The *transform* changes the model into the physical property.
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The *transformDerivU* provides the derivative of the *transform* with respect to the model.
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"""
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raise NotImplementedError('The transformDerivM is not implemented.')
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@property
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def nP(self):
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"""Number of parameters in the model."""
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return self.mesh.nC
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def example(self):
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raise NotImplementedError('The example is not implemented.')
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def test(self, m=None):
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raise NotImplementedError('The test is not implemented.')
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class ExpMap(IdentityMap):
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"""SimPEG ExpMap"""
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def __init__(self, mesh, **kwargs):
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IdentityMap.__init__(self, mesh, **kwargs)
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def transform(self, m):
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"""
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:param numpy.array m: model
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:rtype: numpy.array
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:return: transformed model
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The *transform* changes the model into the physical property.
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A common example of this is to invert for electrical conductivity
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in log space. In this case, your model will be log(sigma) and to
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get back to sigma, you can take the exponential:
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.. math::
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m = \log{\sigma}
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\exp{m} = \exp{\log{\sigma}} = \sigma
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"""
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return np.exp(Utils.mkvc(m))
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def transformInverse(self, D):
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"""
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:param numpy.array D: physical property
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:rtype: numpy.array
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:return: model
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The *transformInverse* changes the physical property into the model.
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.. math::
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m = \log{\sigma}
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"""
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return np.log(Utils.mkvc(D))
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def transformDeriv(self, m):
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"""
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:param numpy.array m: model
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:rtype: scipy.csr_matrix
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:return: derivative of transformed model
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The *transform* changes the model into the physical property.
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The *transformDeriv* provides the derivative of the *transform*.
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If the model *transform* is:
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.. math::
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m = \log{\sigma}
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\exp{m} = \exp{\log{\sigma}} = \sigma
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Then the derivative is:
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.. math::
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\\frac{\partial \exp{m}}{\partial m} = \\text{sdiag}(\exp{m})
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"""
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return Utils.sdiag(np.exp(Utils.mkvc(m)))
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class Vertical1DMap(IdentityMap):
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"""Vertical1DMap
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Given a 1D vector through the last dimension
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of the mesh, this will extend to the full
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model space.
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"""
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def __init__(self, mesh, **kwargs):
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IdentityMap.__init__(self, mesh, **kwargs)
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@property
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def nP(self):
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"""Number of model properties.
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The number of cells in the
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last dimension of the mesh."""
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return self.mesh.vnC[self.mesh.dim-1]
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def transform(self, m):
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"""
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:param numpy.array m: model
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:rtype: numpy.array
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:return: transformed model
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"""
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repNum = self.mesh.vnC[:self.mesh.dim-1].prod()
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return Utils.mkvc(m).repeat(repNum)
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def transformDeriv(self, m):
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"""
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:param numpy.array m: model
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:rtype: scipy.csr_matrix
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:return: derivative of transformed model
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"""
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repNum = self.mesh.vnC[:self.mesh.dim-1].prod()
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repVec = sp.csr_matrix(
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(np.ones(repNum),
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(range(repNum), np.zeros(repNum))
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), shape=(repNum, 1))
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return sp.kron(sp.identity(self.nP), repVec)
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class Mesh2Mesh(IdentityMap):
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"""
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Takes a model on one mesh are translates it to another mesh.
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.. plot::
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from SimPEG import *
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M = Mesh.TensorMesh([100,100])
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h1 = Utils.meshTensor([(6,7,-1.5),(6,10),(6,7,1.5)])
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h1 = h1/h1.sum()
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M2 = Mesh.TensorMesh([h1,h1])
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V = Utils.ModelBuilder.randomModel(M.vnC, seed=79, its=50)
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v = Utils.mkvc(V)
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modh = Maps.Mesh2Mesh([M,M2])
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modH = Maps.Mesh2Mesh([M2,M])
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H = modH.transform(v)
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h = modh.transform(H)
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ax = plt.subplot(131)
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M.plotImage(v, ax=ax)
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ax.set_title('Fine Mesh (Original)')
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ax = plt.subplot(132)
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M2.plotImage(H,clim=[0,1],ax=ax)
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ax.set_title('Course Mesh')
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ax = plt.subplot(133)
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M.plotImage(h,clim=[0,1],ax=ax)
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ax.set_title('Fine Mesh (Interpolated)')
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"""
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def __init__(self, meshes, **kwargs):
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Utils.setKwargs(self, **kwargs)
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assert type(meshes) is list, "meshes must be a list of two meshes"
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assert len(meshes) == 2, "meshes must be a list of two meshes"
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assert meshes[0].dim == meshes[1].dim, """The two meshes must be the same dimension"""
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self.mesh = meshes[0]
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self.mesh2 = meshes[1]
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self.P = self.mesh2.getInterpolationMat(self.mesh.gridCC,'CC',zerosOutside=True)
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@property
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def nP(self):
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"""Number of parameters in the model."""
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return self.mesh2.nC
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def transform(self, m):
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return self.P*m
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def transformDeriv(self, m):
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return self.P
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class ActiveCells(IdentityMap):
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"""
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Active model parameters.
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"""
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indActive = None #: Active Cells
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valInactive = None #: Values of inactive Cells
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nC = None #: Number of cells in the full model
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def __init__(self, mesh, indActive, valInactive, nC=None):
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self.mesh = mesh
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self.nC = nC or mesh.nC
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if indActive.dtype is not bool:
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z = np.zeros(self.nC,dtype=bool)
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z[indActive] = True
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indActive = z
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self.indActive = indActive
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self.indInactive = np.logical_not(indActive)
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if Utils.isScalar(valInactive):
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valInactive = np.ones(self.nC)*float(valInactive)
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valInactive[self.indActive] = 0
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self.valInactive = valInactive
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inds = np.nonzero(self.indActive)[0]
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self.P = sp.csr_matrix((np.ones(inds.size),(inds, range(inds.size))), shape=(self.nC, self.nP))
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@property
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def nP(self):
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"""Number of parameters in the model."""
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return self.indActive.sum()
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def transform(self, m):
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return self.P*m + self.valInactive
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def transformDeriv(self, m):
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return self.P
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class ComboMap(IdentityMap):
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"""Combination of various maps."""
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def __init__(self, mesh, maps, **kwargs):
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IdentityMap.__init__(self, mesh, **kwargs)
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self.maps = []
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for m in maps:
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if not isinstance(m, IdentityMap):
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self.maps += [m(mesh, **kwargs)]
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else:
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self.maps += [m]
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@property
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def nP(self):
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"""Number of model properties.
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The number of cells in the
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last dimension of the mesh."""
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return self.maps[-1].nP
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def transform(self, m):
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for map_i in reversed(self.maps):
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m = map_i.transform(m)
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return m
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def transformDeriv(self, m):
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deriv = 1
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mi = m
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for map_i in reversed(self.maps):
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deriv = map_i.transformDeriv(mi) * deriv
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mi = map_i.transform(mi)
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return deriv
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def __mul__(self, val):
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if isinstance(val, ComboMap):
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return ComboMap(self.mesh, self.maps + val.maps)
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elif isinstance(val, IdentityMap):
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return ComboMap(self.mesh, self.maps + [val])
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elif type(val) is np.ndarray:
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return self.transform(val)
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class ComplexMap(IdentityMap):
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"""docstring for ComplexMap
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default nP is nC in the mesh times 2 [real, imag]
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"""
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def __init__(self, mesh, nP=None):
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IdentityMap.__init__(self, mesh)
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if nP is not None:
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assert nP%2 == 0, 'nP must be even.'
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self._nP = nP or (self.mesh.nC * 2)
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@property
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def nP(self):
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return self._nP
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def transform(self, m):
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nC = self.mesh.nC
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return m[:nC] + m[nC:]*1j
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def transformDeriv(self, m):
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nC = self.nP/2
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shp = (nC, nC*2)
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def fwd(v):
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return v[:nC] + v[nC:]*1j
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def adj(v):
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return np.r_[v.real,v.imag]
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return Utils.SimPEGLinearOperator(shp,fwd,adj)
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transformInverse = transformDeriv
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if __name__ == '__main__':
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from SimPEG import *
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mesh = Mesh.TensorMesh([10,8])
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emap = ExpMap(mesh)
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vmap = Vertical1DMap(mesh)
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combo = emap*vmap
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print combo
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print combo.maps
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# combo = ComboMap(mesh, [ExpMap, Vertical1DMap])
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# combo = ComboMap(mesh, [ExpMap, Vertical1DMap])
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# m = combo.example()
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# print m.shape
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# print combo.test(np.arange(8))
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mesh = Mesh.TensorMesh([10,8])
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mapping = ComplexMap(mesh)
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m = mapping.example()
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print m.shape
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# print mapping.test(m)
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