wassname/simpeg
1
0
Fork 0
mirror of https://github.com/wassname/simpeg.git synced 2026-06-27 19:32:36 +08:00
Code Issues Packages Projects Releases Wiki Activity
Files
maps/feat-parametrizedBlock
simpeg/SimPEG/Maps.py
T
Lindsey Heagy e7e497a06d don't use Zero() in mapping derivs)
2016-06-29 08:45:45 -07:00

1753 lines
64 KiB
Python
Raw Permalink Blame History

from __future__ import division
import Utils, numpy as np, scipy.sparse as sp
from scipy.sparse.linalg import LinearOperator
from Tests import checkDerivative
from PropMaps import PropMap, Property
from numpy.polynomial import polynomial
from scipy.interpolate import UnivariateSpline
import warnings
from SimPEG.Utils import Zero
class IdentityMap(object):
"""
SimPEG Map
"""
__metaclass__ = Utils.SimPEGMetaClass
def __init__(self, mesh=None, nP=None, **kwargs):
Utils.setKwargs(self, **kwargs)
if nP is not None:
assert type(nP) in [int, long, np.int64], ' Number of parameters must be an integer.'
self.mesh = mesh
self._nP = nP
@property
def nP(self):
"""
:rtype: int
:return: number of parameters that the mapping accepts
"""
if self._nP is not None:
return self._nP
if self.mesh is None:
return '*'
return self.mesh.nC
@property
def shape(self):
"""
The default shape is (mesh.nC, nP) if the mesh is defined.
If this is a meshless mapping (i.e. nP is defined independently)
the shape will be the the shape (nP,nP).
:rtype: (int,int)
:return: shape of the operator as a tuple
"""
if self._nP is not None:
return (self.nP, self.nP)
if self.mesh is None:
return ('*', self.nP)
return (self.mesh.nC, self.nP)
def _transform(self, m):
"""
Changes the model into the physical property.
.. note::
This can be called by the __mul__ property against a numpy.ndarray.
:param numpy.array m: model
:rtype: numpy.array
:return: transformed model
"""
return m
def inverse(self, D):
"""
Changes the physical property into the model.
.. note::
The *transformInverse* may not be easy to create in general.
:param numpy.array D: physical property
:rtype: numpy.array
:return: model
"""
raise NotImplementedError('The transformInverse is not implemented.')
def deriv(self, m):
"""
The derivative of the transformation.
:param numpy.array m: model
:rtype: scipy.csr_matrix
:return: derivative of transformed model
"""
return sp.identity(self.nP)
def test(self, m=None, **kwargs):
"""Test the derivative of the mapping.
:param numpy.array m: model
:param kwargs: key word arguments of :meth:`SimPEG.Tests.checkDerivative`
:rtype: bool
:return: passed the test?
"""
print 'Testing %s' % str(self)
if m is None:
m = abs(np.random.rand(self.nP))
if 'plotIt' not in kwargs:
kwargs['plotIt'] = False
return checkDerivative(lambda m : [self * m, self.deriv(m)], m, num=4, **kwargs)
def _assertMatchesPair(self, pair):
assert (isinstance(self, pair) or
isinstance(self, ComboMap) and isinstance(self.maps[0], pair)
), "Mapping object must be an instance of a %s class."%(pair.__name__)
def __mul__(self, val):
if isinstance(val, IdentityMap):
if not (self.shape[1] == '*' or val.shape[0] == '*') and not self.shape[1] == val.shape[0]:
raise ValueError('Dimension mismatch in %s and %s.' % (str(self), str(val)))
return ComboMap([self, val])
elif isinstance(val, np.ndarray):
if not self.shape[1] == '*' and not self.shape[1] == val.shape[0]:
raise ValueError('Dimension mismatch in %s and np.ndarray%s.' % (str(self), str(val.shape)))
return self._transform(val)
raise Exception('Unrecognized data type to multiply. Try a map or a numpy.ndarray!')
def __str__(self):
return "%s(%s,%s)" % (self.__class__.__name__, self.shape[0], self.shape[1])
class ComboMap(IdentityMap):
"""
Combination of various maps.
The ComboMap holds the information for multiplying and combining
maps. It also uses the chain rule to create the derivative.
Remember, any time that you make your own combination of mappings
be sure to test that the derivative is correct.
"""
def __init__(self, maps, **kwargs):
IdentityMap.__init__(self, None, **kwargs)
self.maps = []
for ii, m in enumerate(maps):
assert isinstance(m, IdentityMap), 'Unrecognized data type, inherit from an IdentityMap or ComboMap!'
if ii > 0 and not (self.shape[1] == '*' or m.shape[0] == '*') and not self.shape[1] == m.shape[0]:
prev = self.maps[-1]
errArgs = (prev.__class__.__name__, prev.shape[0], prev.shape[1], m.__class__.__name__, m.shape[0], m.shape[1])
raise ValueError('Dimension mismatch in map[%s] (%s, %s) and map[%s] (%s, %s).' % errArgs)
if isinstance(m, ComboMap):
self.maps += m.maps
elif isinstance(m, IdentityMap):
self.maps += [m]
@property
def shape(self):
return (self.maps[0].shape[0], self.maps[-1].shape[1])
@property
def nP(self):
"""Number of model properties.
The number of cells in the
last dimension of the mesh."""
return self.maps[-1].nP
def _transform(self, m):
for map_i in reversed(self.maps):
m = map_i * m
return m
def deriv(self, m):
deriv = 1
mi = m
for map_i in reversed(self.maps):
deriv = map_i.deriv(mi) * deriv
mi = map_i * mi
return deriv
def __str__(self):
return 'ComboMap[%s](%s,%s)' % (' * '.join([m.__str__() for m in self.maps]), self.shape[0], self.shape[1])
class ExpMap(IdentityMap):
"""
Electrical conductivity varies over many orders of magnitude, so it is a common
technique when solving the inverse problem to parameterize and optimize in terms
of log conductivity. This makes sense not only because it ensures all conductivities
will be positive, but because this is fundamentally the space where conductivity
lives (i.e. it varies logarithmically).
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
"""
def __init__(self, mesh, **kwargs):
IdentityMap.__init__(self, mesh, **kwargs)
def _transform(self, m):
return np.exp(Utils.mkvc(m))
def inverse(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 deriv(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 ReciprocalMap(IdentityMap):
"""
Reciprocal mapping. For example, electrical resistivity and conductivity.
.. math::
\\rho = \\frac{1}{\sigma}
"""
def _transform(self, m):
return 1.0 / Utils.mkvc(m)
def inverse(self, D):
return 1.0 / Utils.mkvc(m)
def deriv(self, m):
# TODO: if this is a tensor, you might have a problem.
return Utils.sdiag( - Utils.mkvc(m)**(-2) )
class LogMap(IdentityMap):
"""
Changes the model into the physical property.
If \\(p\\) is the physical property and \\(m\\) is the model, then
..math::
p = \\log(m)
and
..math::
m = \\exp(p)
NOTE: If you have a model which is log conductivity (ie. \\(m = \\log(\\sigma)\\)),
you should be using an ExpMap
"""
def __init__(self, mesh, **kwargs):
IdentityMap.__init__(self, mesh, **kwargs)
def _transform(self, m):
return np.log(Utils.mkvc(m))
def deriv(self, m):
mod = Utils.mkvc(m)
deriv = np.zeros(mod.shape)
tol = 1e-16 # zero
ind = np.greater_equal(np.abs(mod),tol)
deriv[ind] = 1.0/mod[ind]
return Utils.sdiag(deriv)
def inverse(self, m):
return np.exp(Utils.mkvc(m))
class SurjectFull(IdentityMap):
"""
SurjectFull
Given a scalar, the SurjectFull maps the value to the
full model space.
"""
def __init__(self,mesh,**kwargs):
IdentityMap.__init__(self, mesh,**kwargs)
@property
def nP(self):
return 1
def _transform(self, m):
"""
:param m: model (scalar)
:rtype: numpy.array
:return: transformed model
"""
return np.ones(self.mesh.nC)*m
def deriv(self, m):
"""
:param numpy.array m: model
:rtype: numpy.array
:return: derivative of transformed model
"""
return np.ones([self.mesh.nC,1])
class FullMap(SurjectFull):
def __init__(self,mesh,**kwargs):
warnings.warn(
"`FullMap` is deprecated and will be removed in future versions. Use `SurjectFull` instead",
FutureWarning)
SurjectFull.__init__(self,mesh,**kwargs)
class SurjectVertical1D(IdentityMap):
"""SurjectVertical1DMap
Given a 1D vector through the last dimension
of the mesh, this will extend to the full
model space.
"""
def __init__(self, mesh, **kwargs):
IdentityMap.__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 deriv(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 Vertical1DMap(SurjectVertical1D):
def __init__(self,mesh,**kwargs):
warnings.warn(
"`Vertical1DMap` is deprecated and will be removed in future versions. Use `SurjectVertical1D` instead",
FutureWarning)
SurjectVertical1D.__init__(self,mesh,**kwargs)
class Surject2Dto3D(IdentityMap):
"""Map2Dto3D
Given a 2D vector, this will extend to the full
3D model space.
"""
normal = 'Y' #: The normal
def __init__(self, mesh, **kwargs):
assert mesh.dim == 3, 'Only works for a 3D Mesh'
IdentityMap.__init__(self, mesh, **kwargs)
assert self.normal in ['X','Y','Z'], 'For now, only "Y" normal is supported'
@property
def nP(self):
"""Number of model properties.
The number of cells in the
last dimension of the mesh."""
if self.normal == 'Z':
return self.mesh.nCx * self.mesh.nCy
elif self.normal == 'Y':
return self.mesh.nCx * self.mesh.nCz
elif self.normal == 'X':
return self.mesh.nCy * self.mesh.nCz
def _transform(self, m):
"""
:param numpy.array m: model
:rtype: numpy.array
:return: transformed model
"""
m = Utils.mkvc(m)
if self.normal == 'Z':
return Utils.mkvc(m.reshape(self.mesh.vnC[[0,1]], order='F')[:,:,np.newaxis].repeat(self.mesh.nCz,axis=2))
elif self.normal == 'Y':
return Utils.mkvc(m.reshape(self.mesh.vnC[[0,2]], order='F')[:,np.newaxis,:].repeat(self.mesh.nCy,axis=1))
elif self.normal == 'X':
return Utils.mkvc(m.reshape(self.mesh.vnC[[1,2]], order='F')[np.newaxis,:,:].repeat(self.mesh.nCx,axis=0))
def deriv(self, m):
"""
:param numpy.array m: model
:rtype: scipy.csr_matrix
:return: derivative of transformed model
"""
inds = self * np.arange(self.nP)
nC, nP = self.mesh.nC, self.nP
P = sp.csr_matrix(
(np.ones(nC),
(range(nC), inds)
), shape=(nC, nP))
return P
class Map2Dto3D(Surject2Dto3D):
def __init__(self,mesh,**kwargs):
warnings.warn(
"`Map2Dto3D` is deprecated and will be removed in future versions. Use `Surject2Dto3D` instead",
FutureWarning)
Surject2Dto3D.__init__(self,mesh,**kwargs)
class Mesh2Mesh(IdentityMap):
"""
Takes a model on one mesh are translates it to another mesh.
.. plot::
from SimPEG import *
import matplotlib.pyplot as plt
M = Mesh.TensorMesh([100,100])
h1 = Utils.meshTensor([(6,7,-1.5),(6,10),(6,7,1.5)])
h1 = h1/h1.sum()
M2 = Mesh.TensorMesh([h1,h1])
V = Utils.ModelBuilder.randomModel(M.vnC, seed=79, its=50)
v = Utils.mkvc(V)
modh = Maps.Mesh2Mesh([M,M2])
modH = Maps.Mesh2Mesh([M2,M])
H = modH * v
h = modh * 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)')
plt.show()
"""
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 shape(self):
"""Number of parameters in the model."""
return (self.mesh.nC, self.mesh2.nC)
@property
def nP(self):
"""Number of parameters in the model."""
return self.mesh2.nC
def _transform(self, m):
return self.P*m
def deriv(self, m):
return self.P
class InjectActiveCells(IdentityMap):
"""
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 Utils.isScalar(valInactive):
self.valInactive = np.ones(self.nC)*float(valInactive)
self.valInactive[self.indActive] = 0.
else:
if len(valInactive) == sum(self.indInactive):
self.valInactive = np.zeros(nC)
self.valInactive[self.indInactive] = valInactive.copy()
else:
assert len(self.valInactive) == self.nC, 'valInactive must be the size of nC or nInactive'
self.valInactive = valInactive.copy()
if any(self.valInactive[self.indActive] != 0.):
warnings.warn('the inactive has non-zero values in the active set.')
inds = np.nonzero(self.indActive)[0]
# inds[self.indActive]
self.P = sp.csr_matrix((np.ones(inds.size),(inds, range(inds.size))), shape=(self.nC, self.nP))
@property
def shape(self):
return (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 inverse(self, D):
return self.P.T*D
def deriv(self, m):
return self.P
class ActiveCells(InjectActiveCells):
def __init__(self, mesh, indActive, valInactive, nC=None):
warnings.warn(
"`ActiveCells` is deprecated and will be removed in future versions. Use `InjectActiveCells` instead",
FutureWarning)
InjectActiveCells.__init__(self, mesh, indActive, valInactive, nC)
class Weighting(IdentityMap):
"""
Model weight parameters.
"""
weights = None #: Active Cells
nC = None #: Number of cells in the full model
def __init__(self, mesh, weights=None, nC=None):
self.mesh = mesh
self.nC = nC or mesh.nC
if weights is None:
weights = np.ones(self.nC)
self.weights = np.array(weights, dtype=float)
self.P = Utils.sdiag(self.weights)
@property
def shape(self):
return (self.nC, self.nP)
@property
def nP(self):
"""Number of parameters in the model."""
return self.nC
def _transform(self, m):
return self.P*m
def inverse(self, D):
Pinv = Utils.sdiag(self.weights**(-1.))
return Pinv*D
def deriv(self, m):
return self.P
class Projection(IdentityMap):
"""
A map to rearrange parameters
"""
def __init__(self, indTo, indFrom, shape, mesh=None, **kwargs):
assert len(indTo) == len(indFrom)
self.P = sp.csr_matrix((np.ones(len(indTo)), (indTo, indFrom)), shape=shape)
self._shape = shape
super(Projection, self).__init__(mesh, **kwargs)
@property
def shape(self):
return self._shape
@property
def nP(self):
"""Number of parameters in the model."""
return self.shape[1]
def _transform(self, m):
return self.P*m
def deriv(self, m):
return self.P
class ComplexMap(IdentityMap):
"""ComplexMap
default nP is nC in the mesh times 2 [real, imag]
"""
def __init__(self, mesh, nP=None):
IdentityMap.__init__(self, mesh)
if nP is not None:
assert nP%2 == 0, 'nP must be even.'
self._nP = nP or (self.mesh.nC * 2)
@property
def nP(self):
return self._nP
@property
def shape(self):
return (self.nP/2,self.nP)
def _transform(self, m):
nC = self.mesh.nC
return m[:nC] + m[nC:]*1j
def deriv(self, m):
nC = self.nP/2
shp = (nC, nC*2)
def fwd(v):
return v[:nC] + v[nC:]*1j
def adj(v):
return np.r_[v.real,v.imag]
return LinearOperator(shp,matvec=fwd,rmatvec=adj)
inverse = deriv
class CircleMap(IdentityMap):
"""CircleMap
Parameterize the model space using a circle in a wholespace.
.. math::
\sigma(m) = \sigma_1 + (\sigma_2 - \sigma_1)\left(\\arctan\left(100*\sqrt{(\\vec{x}-x_0)^2 + (\\vec{y}-y_0)}-r\\right) \pi^{-1} + 0.5\\right)
Define the model as:
.. math::
m = [\sigma_1, \sigma_2, x_0, y_0, r]
"""
def __init__(self, mesh, logSigma=True):
assert mesh.dim == 2, "Working for a 2D mesh only right now. But it isn't that hard to change.. :)"
IdentityMap.__init__(self, mesh)
self.logSigma = logSigma
slope = 1e-1
@property
def nP(self):
return 5
def _transform(self, m):
a = self.slope
sig1,sig2,x,y,r = m[0],m[1],m[2],m[3],m[4]
if self.logSigma:
sig1, sig2 = np.exp(sig1), np.exp(sig2)
X = self.mesh.gridCC[:,0]
Y = self.mesh.gridCC[:,1]
return sig1 + (sig2 - sig1)*(np.arctan(a*(np.sqrt((X-x)**2 + (Y-y)**2) - r))/np.pi + 0.5)
def deriv(self, m):
a = self.slope
sig1,sig2,x,y,r = m[0],m[1],m[2],m[3],m[4]
if self.logSigma:
sig1, sig2 = np.exp(sig1), np.exp(sig2)
X = self.mesh.gridCC[:,0]
Y = self.mesh.gridCC[:,1]
if self.logSigma:
g1 = -(np.arctan(a*(-r + np.sqrt((X - x)**2 + (Y - y)**2)))/np.pi + 0.5)*sig1 + sig1
g2 = (np.arctan(a*(-r + np.sqrt((X - x)**2 + (Y - y)**2)))/np.pi + 0.5)*sig2
else:
g1 = -(np.arctan(a*(-r + np.sqrt((X - x)**2 + (Y - y)**2)))/np.pi + 0.5) + 1.0
g2 = (np.arctan(a*(-r + np.sqrt((X - x)**2 + (Y - y)**2)))/np.pi + 0.5)
g3 = a*(-X + x)*(-sig1 + sig2)/(np.pi*(a**2*(-r + np.sqrt((X - x)**2 + (Y - y)**2))**2 + 1)*np.sqrt((X - x)**2 + (Y - y)**2))
g4 = a*(-Y + y)*(-sig1 + sig2)/(np.pi*(a**2*(-r + np.sqrt((X - x)**2 + (Y - y)**2))**2 + 1)*np.sqrt((X - x)**2 + (Y - y)**2))
g5 = -a*(-sig1 + sig2)/(np.pi*(a**2*(-r + np.sqrt((X - x)**2 + (Y - y)**2))**2 + 1))
return sp.csr_matrix(np.c_[g1,g2,g3,g4,g5])
class PolyMap(IdentityMap):
"""PolyMap
Parameterize the model space using a polynomials in a wholespace.
..math::
y = \mathbf{V} c
Define the model as:
..math::
m = [\sigma_1, \sigma_2, c]
Can take in an actInd vector to account for topography.
"""
def __init__(self, mesh, order, logSigma=True, normal='X', actInd = None):
IdentityMap.__init__(self, mesh)
self.logSigma = logSigma
self.order = order
self.normal = normal
self.actInd = actInd
if getattr(self, 'actInd', None) is None:
self.actInd = range(self.mesh.nC)
self.nC = self.mesh.nC
else:
self.nC = len(self.actInd)
slope = 1e4
@property
def shape(self):
return (self.nC, self.nP)
@property
def nP(self):
if np.isscalar(self.order):
nP = self.order+3
else:
nP =(self.order[0]+1)*(self.order[1]+1)+2
return nP
def _transform(self, m):
# Set model parameters
alpha = self.slope
sig1,sig2 = m[0],m[1]
c = m[2:]
if self.logSigma:
sig1, sig2 = np.exp(sig1), np.exp(sig2)
#2D
if self.mesh.dim == 2:
X = self.mesh.gridCC[self.actInd,0]
Y = self.mesh.gridCC[self.actInd,1]
if self.normal =='X':
f = polynomial.polyval(Y, c) - X
elif self.normal =='Y':
f = polynomial.polyval(X, c) - Y
else:
raise(Exception("Input for normal = X or Y or Z"))
#3D
elif self.mesh.dim == 3:
X = self.mesh.gridCC[self.actInd,0]
Y = self.mesh.gridCC[self.actInd,1]
Z = self.mesh.gridCC[self.actInd,2]
if self.normal =='X':
f = polynomial.polyval2d(Y, Z, c.reshape((self.order[0]+1,self.order[1]+1))) - X
elif self.normal =='Y':
f = polynomial.polyval2d(X, Z, c.reshape((self.order[0]+1,self.order[1]+1))) - Y
elif self.normal =='Z':
f = polynomial.polyval2d(X, Y, c.reshape((self.order[0]+1,self.order[1]+1))) - Z
else:
raise(Exception("Input for normal = X or Y or Z"))
else:
raise(Exception("Only supports 2D"))
return sig1+(sig2-sig1)*(np.arctan(alpha*f)/np.pi+0.5)
def deriv(self, m):
alpha = self.slope
sig1,sig2, c = m[0],m[1],m[2:]
if self.logSigma:
sig1, sig2 = np.exp(sig1), np.exp(sig2)
#2D
if self.mesh.dim == 2:
X = self.mesh.gridCC[self.actInd,0]
Y = self.mesh.gridCC[self.actInd,1]
if self.normal =='X':
f = polynomial.polyval(Y, c) - X
V = polynomial.polyvander(Y, len(c)-1)
elif self.normal =='Y':
f = polynomial.polyval(X, c) - Y
V = polynomial.polyvander(X, len(c)-1)
else:
raise(Exception("Input for normal = X or Y or Z"))
#3D
elif self.mesh.dim == 3:
X = self.mesh.gridCC[self.actInd,0]
Y = self.mesh.gridCC[self.actInd,1]
Z = self.mesh.gridCC[self.actInd,2]
if self.normal =='X':
f = polynomial.polyval2d(Y, Z, c.reshape((self.order[0]+1,self.order[1]+1))) - X
V = polynomial.polyvander2d(Y, Z, self.order)
elif self.normal =='Y':
f = polynomial.polyval2d(X, Z, c.reshape((self.order[0]+1,self.order[1]+1))) - Y
V = polynomial.polyvander2d(X, Z, self.order)
elif self.normal =='Z':
f = polynomial.polyval2d(X, Y, c.reshape((self.order[0]+1,self.order[1]+1))) - Z
V = polynomial.polyvander2d(X, Y, self.order)
else:
raise(Exception("Input for normal = X or Y or Z"))
if self.logSigma:
g1 = -(np.arctan(alpha*f)/np.pi + 0.5)*sig1 + sig1
g2 = (np.arctan(alpha*f)/np.pi + 0.5)*sig2
else:
g1 = -(np.arctan(alpha*f)/np.pi + 0.5) + 1.0
g2 = (np.arctan(alpha*f)/np.pi + 0.5)
g3 = Utils.sdiag(alpha*(sig2-sig1)/(1.+(alpha*f)**2)/np.pi)*V
return sp.csr_matrix(np.c_[g1,g2,g3])
class SplineMap(IdentityMap):
"""SplineMap
Parameterize the boundary of two geological units using a spline interpolation
..math::
g = f(x)-y
Define the model as:
..math::
m = [\sigma_1, \sigma_2, y]
"""
def __init__(self, mesh, pts, ptsv=None,order=3, logSigma=True, normal='X'):
IdentityMap.__init__(self, mesh)
self.logSigma = logSigma
self.order = order
self.normal = normal
self.pts= pts
self.npts = np.size(pts)
self.ptsv = ptsv
self.spl = None
slope = 1e4
@property
def nP(self):
if self.mesh.dim == 2:
return np.size(self.pts)+2
elif self.mesh.dim == 3:
return np.size(self.pts)*2+2
else:
raise(Exception("Only supports 2D and 3D"))
def _transform(self, m):
# Set model parameters
alpha = self.slope
sig1,sig2 = m[0],m[1]
c = m[2:]
if self.logSigma:
sig1, sig2 = np.exp(sig1), np.exp(sig2)
#2D
if self.mesh.dim == 2:
X = self.mesh.gridCC[:,0]
Y = self.mesh.gridCC[:,1]
self.spl = UnivariateSpline(self.pts, c, k=self.order, s=0)
if self.normal =='X':
f = self.spl(Y) - X
elif self.normal =='Y':
f = self.spl(X) - Y
else:
raise(Exception("Input for normal = X or Y or Z"))
# 3D:
# Comments:
# Make two spline functions and link them using linear interpolation.
# This is not quite direct extension of 2D to 3D case
# Using 2D interpolation is possible
elif self.mesh.dim == 3:
X = self.mesh.gridCC[:,0]
Y = self.mesh.gridCC[:,1]
Z = self.mesh.gridCC[:,2]
npts = np.size(self.pts)
if np.mod(c.size, 2):
raise(Exception("Put even points!"))
self.spl = {"splb":UnivariateSpline(self.pts, c[:npts], k=self.order, s=0),
"splt":UnivariateSpline(self.pts, c[npts:], k=self.order, s=0)}
if self.normal =='X':
zb = self.ptsv[0]
zt = self.ptsv[1]
flines = (self.spl["splt"](Y)-self.spl["splb"](Y))*(Z-zb)/(zt-zb) + self.spl["splb"](Y)
f = flines - X
# elif self.normal =='Y':
# elif self.normal =='Z':
else:
raise(Exception("Input for normal = X or Y or Z"))
else:
raise(Exception("Only supports 2D and 3D"))
return sig1+(sig2-sig1)*(np.arctan(alpha*f)/np.pi+0.5)
def deriv(self, m):
alpha = self.slope
sig1,sig2, c = m[0],m[1],m[2:]
if self.logSigma:
sig1, sig2 = np.exp(sig1), np.exp(sig2)
#2D
if self.mesh.dim == 2:
X = self.mesh.gridCC[:,0]
Y = self.mesh.gridCC[:,1]
if self.normal =='X':
f = self.spl(Y) - X
elif self.normal =='Y':
f = self.spl(X) - Y
else:
raise(Exception("Input for normal = X or Y or Z"))
#3D
elif self.mesh.dim == 3:
X = self.mesh.gridCC[:,0]
Y = self.mesh.gridCC[:,1]
Z = self.mesh.gridCC[:,2]
if self.normal =='X':
zb = self.ptsv[0]
zt = self.ptsv[1]
flines = (self.spl["splt"](Y)-self.spl["splb"](Y))*(Z-zb)/(zt-zb) + self.spl["splb"](Y)
f = flines - X
# elif self.normal =='Y':
# elif self.normal =='Z':
else:
raise(Exception("Not Implemented for Y and Z, your turn :)"))
if self.logSigma:
g1 = -(np.arctan(alpha*f)/np.pi + 0.5)*sig1 + sig1
g2 = (np.arctan(alpha*f)/np.pi + 0.5)*sig2
else:
g1 = -(np.arctan(alpha*f)/np.pi + 0.5) + 1.0
g2 = (np.arctan(alpha*f)/np.pi + 0.5)
if self.mesh.dim ==2:
g3 = np.zeros((self.mesh.nC, self.npts))
if self.normal =='Y':
# Here we use perturbation to compute sensitivity
# TODO: bit more generalization of this ...
# Modfications for X and Z directions ...
for i in range(np.size(self.pts)):
ctemp = c[i]
ind = np.argmin(abs(self.mesh.vectorCCy-ctemp))
ca = c.copy()
cb = c.copy()
dy = self.mesh.hy[ind]*1.5
ca[i] = ctemp+dy
cb[i] = ctemp-dy
spla = UnivariateSpline(self.pts, ca, k=self.order, s=0)
splb = UnivariateSpline(self.pts, cb, k=self.order, s=0)
fderiv = (spla(X)-splb(X))/(2*dy)
g3[:,i] = Utils.sdiag(alpha*(sig2-sig1)/(1.+(alpha*f)**2)/np.pi)*fderiv
elif self.mesh.dim==3:
g3 = np.zeros((self.mesh.nC, self.npts*2))
if self.normal =='X':
# Here we use perturbation to compute sensitivity
for i in range(self.npts*2):
ctemp = c[i]
ind = np.argmin(abs(self.mesh.vectorCCy-ctemp))
ca = c.copy()
cb = c.copy()
dy = self.mesh.hy[ind]*1.5
ca[i] = ctemp+dy
cb[i] = ctemp-dy
#treat bottom boundary
if i< self.npts:
splba = UnivariateSpline(self.pts, ca[:self.npts], k=self.order, s=0)
splbb = UnivariateSpline(self.pts, cb[:self.npts], k=self.order, s=0)
flinesa = (self.spl["splt"](Y)-splba(Y))*(Z-zb)/(zt-zb) + splba(Y) - X
flinesb = (self.spl["splt"](Y)-splbb(Y))*(Z-zb)/(zt-zb) + splbb(Y) - X
#treat top boundary
else:
splta = UnivariateSpline(self.pts, ca[self.npts:], k=self.order, s=0)
spltb = UnivariateSpline(self.pts, ca[self.npts:], k=self.order, s=0)
flinesa = (self.spl["splt"](Y)-splta(Y))*(Z-zb)/(zt-zb) + splta(Y) - X
flinesb = (self.spl["splt"](Y)-spltb(Y))*(Z-zb)/(zt-zb) + spltb(Y) - X
fderiv = (flinesa-flinesb)/(2*dy)
g3[:,i] = Utils.sdiag(alpha*(sig2-sig1)/(1.+(alpha*f)**2)/np.pi)*fderiv
else :
raise(Exception("Not Implemented for Y and Z, your turn :)"))
return sp.csr_matrix(np.c_[g1,g2,g3])
class ParametrizedLayer(IdentityMap):
"""
Parametrized Layer Space
m = [val_background, val_layer, layer_center, layer_thickness]
.. plot::
:include-source:
from SimPEG import Mesh, Maps, np
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1,1,figsize=(2,3))
mesh = Mesh.TensorMesh([50,50],x0='CC')
mapping = Maps.ParametrizedLayer(mesh)
m = np.hstack(np.r_[1., 2., -0.1, 0.2])
rho = mapping._transform(m)
mesh.plotImage(rho, ax=ax)
**Required**
:param Mesh mesh: SimPEG Mesh, 2D or 3D
**Optional**
:param float slopeFact: arctan slope factor - divided by the minimum h spacing to give the slope of the arctan functions
:param float slope: slope of the arctan function
:param numpy.ndarray indActive: bool vector with
"""
slopeFact = 1e2 # will be scaled by the mesh.
slope = None
indActive = None
def __init__(self, mesh, **kwargs):
super(ParametrizedLayer, self).__init__(mesh, **kwargs)
if self.slope is None:
self.slope = self.slopeFact / np.hstack(self.mesh.h).min()
self.x = [self.mesh.gridCC[:,0] if self.indActive is None else self.mesh.gridCC[self.indActive,0]][0]
if self.mesh.dim > 1:
self.y = [self.mesh.gridCC[:,1] if self.indActive is None else self.mesh.gridCC[self.indActive,1]][0]
if self.mesh.dim > 2:
self.z = [self.mesh.gridCC[:,2] if self.indActive is None else self.mesh.gridCC[self.indActive,2]][0]
@property
def nP(self):
return 4
@property
def shape(self):
if self.indActive is not None:
return (sum(self.indActive), self.nP)
return (self.mesh.nC, self.nP)
def mDict(self, m):
return {
'val_background': m[0],
'val_layer': m[1],
'layer_center': m[2],
'layer_thickness': m[3],
}
def _atanfct(self, xyz, xyzi, slope):
return np.arctan(slope * (xyz - xyzi))/np.pi + 0.5
def _atanfctDeriv(self, xyz, xyzi, slope):
# d/dx(atan(x)) = 1/(1+x**2)
x = slope * (xyz - xyzi)
dx = - slope
return (1./(1 + x**2))/np.pi * dx
def _atanLayer(self, mDict):
if self.mesh.dim == 2:
z = self.y
elif self.mesh.dim == 3:
z = self.z
layer_bottom = mDict['layer_center'] - mDict['layer_thickness'] / 2.
layer_top = mDict['layer_center'] + mDict['layer_thickness'] / 2.
return self._atanfct(z, layer_bottom, self.slope)*self._atanfct(z, layer_top, -self.slope)
def _atanLayerDeriv_layer_center(self, mDict):
if self.mesh.dim == 2:
z = self.y
elif self.mesh.dim == 3:
z = self.z
layer_bottom = mDict['layer_center'] - mDict['layer_thickness'] / 2.
layer_top = mDict['layer_center'] + mDict['layer_thickness'] / 2.
return (self._atanfctDeriv(z, layer_bottom, self.slope)*self._atanfct(z, layer_top, -self.slope)
+ self._atanfct(z, layer_bottom, self.slope)*self._atanfctDeriv(z, layer_top, -self.slope))
def _atanLayerDeriv_layer_thickness(self, mDict):
if self.mesh.dim == 2:
z = self.y
elif self.mesh.dim == 3:
z = self.z
layer_bottom = mDict['layer_center'] - mDict['layer_thickness'] / 2.
layer_top = mDict['layer_center'] + mDict['layer_thickness'] / 2.
return (-0.5*self._atanfctDeriv(z, layer_bottom, self.slope)*self._atanfct(z, layer_top, -self.slope)
+ 0.5*self._atanfct(z, layer_bottom, self.slope)*self._atanfctDeriv(z, layer_top, -self.slope))
def layer_cont(self, mDict):
return mDict['val_background'] + (mDict['val_layer'] - mDict['val_background'])*self._atanLayer(mDict)
def _transform(self, m):
mDict = self.mDict(m)
return self.layer_cont(mDict)
def _deriv_val_background(self, mDict):
return np.ones_like(self.x) - self._atanLayer(mDict)
def _deriv_val_layer(self, mDict):
return self._atanLayer(mDict)
def _deriv_layer_center(self, mDict):
return (mDict['val_layer']-mDict['val_background'])*self._atanLayerDeriv_layer_center(mDict)
def _deriv_layer_thickness(self, mDict):
return (mDict['val_layer']-mDict['val_background'])*self._atanLayerDeriv_layer_thickness(mDict)
def deriv(self, m):
mDict = self.mDict(m)
return sp.csr_matrix(np.vstack([
self._deriv_val_background(mDict),
self._deriv_val_layer(mDict),
self._deriv_layer_center(mDict),
self._deriv_layer_thickness(mDict),
]).T)
class ParametrizedCasingAndLayer(ParametrizedLayer):
"""
Parametrized layered space with casing.
m = [val_background, val_layer, val_casing, val_insideCasing, layer_center, layer_thickness, casing_radius, casing_thickness, casing_bottom, casing_top]
"""
def __init__(self, mesh, **kwargs):
assert mesh._meshType == 'CYL', 'Parametrized Casing in a layer map only works for a cyl mesh.'
super(ParametrizedCasingAndLayer, self).__init__(mesh, **kwargs)
@property
def nP(self):
return 10
@property
def shape(self):
if self.indActive is not None:
return (sum(self.indActive), self.nP)
return (self.mesh.nC, self.nP)
def mDict(self, m):
#m = [val_background, val_layer, val_casing, val_insideCasing, layer_center, layer_thickness, casing_radius, casing_thickness, casing_bottom, casing_top]
return {
'val_background': m[0],
'val_layer': m[1],
'val_casing': m[2],
'val_insideCasing': m[3],
'layer_center': m[4],
'layer_thickness': m[5],
'casing_radius': m[6],
'casing_thickness': m[7],
'casing_bottom': m[8],
'casing_top': m[9]
}
def _atanCasingLength(self, mDict):
return (self._atanfct(self.z, mDict['casing_top'], -self.slope)
* self._atanfct(self.z, mDict['casing_bottom'], self.slope))
def _atanCasingLengthDeriv_casing_top(self, mDict):
return (self._atanfctDeriv(self.z, mDict['casing_top'], -self.slope)
* self._atanfct(self.z, mDict['casing_bottom'], self.slope))
def _atanCasingLengthDeriv_casing_bottom(self, mDict):
return (self._atanfct(self.z, mDict['casing_top'], -self.slope)
* self._atanfctDeriv(self.z, mDict['casing_bottom'], self.slope))
def _atanInsideCasing(self, mDict):
casing_a = mDict['casing_radius'] - 0.5*mDict['casing_thickness']
return (self._atanCasingLength(mDict)
* self._atanfct(self.x, casing_a, -self.slope))
def _atanInsideCasingDeriv_casing_radius(self, mDict):
casing_a = mDict['casing_radius'] - 0.5*mDict['casing_thickness']
return (self._atanCasingLength(mDict)
* self._atanfctDeriv(self.x, casing_a, -self.slope))
def _atanInsideCasingDeriv_casing_thickness(self, mDict):
casing_a = mDict['casing_radius'] - 0.5*mDict['casing_thickness']
return (self._atanCasingLength(mDict)
* - 0.5*self._atanfctDeriv(self.x, casing_a, -self.slope))
def _atanInsideCasingDeriv_casing_top(self, mDict):
casing_a = mDict['casing_radius'] - 0.5*mDict['casing_thickness']
return (self._atanCasingLengthDeriv_casing_top(mDict)
* self._atanfct(self.x, casing_a, -self.slope))
def _atanInsideCasingDeriv_casing_bottom(self, mDict):
casing_a = mDict['casing_radius'] - 0.5*mDict['casing_thickness']
return (self._atanCasingLengthDeriv_casing_bottom(mDict)
* self._atanfct(self.x, casing_a, -self.slope))
def _atanCasing(self, mDict):
casing_a, casing_b = mDict['casing_radius'] - 0.5*mDict['casing_thickness'], mDict['casing_radius'] + 0.5*mDict['casing_thickness']
return (self._atanCasingLength(mDict)
* self._atanfct(self.x, casing_a, self.slope)
* self._atanfct(self.x, casing_b, -self.slope))
def _atanCasingDeriv_casing_radius(self, mDict):
casing_a, casing_b = mDict['casing_radius'] - 0.5*mDict['casing_thickness'], mDict['casing_radius'] + 0.5*mDict['casing_thickness']
return (self._atanCasingLength(mDict) * (
self._atanfctDeriv(self.x, casing_a, self.slope)
* self._atanfct(self.x, casing_b, -self.slope)
+
self._atanfct(self.x, casing_a, self.slope)
* self._atanfctDeriv(self.x, casing_b, -self.slope)
))
def _atanCasingDeriv_casing_thickness(self, mDict):
casing_a, casing_b = mDict['casing_radius'] - 0.5*mDict['casing_thickness'], mDict['casing_radius'] + 0.5*mDict['casing_thickness']
return (self._atanCasingLength(mDict) * (
- 0.5*self._atanfctDeriv(self.x, casing_a, self.slope)
* 0.5*self._atanfct(self.x, casing_b, -self.slope)
+
- 0.5*self._atanfct(self.x, casing_a, self.slope)
* 0.5*self._atanfctDeriv(self.x, casing_b, -self.slope)
))
def _atanCasingDeriv_casing_bottom(self, mDict):
casing_a, casing_b = mDict['casing_radius'] - 0.5*mDict['casing_thickness'], mDict['casing_radius'] + 0.5*mDict['casing_thickness']
return (self._atanCasingLengthDeriv_casing_bottom(mDict)
* self._atanfct(self.x, casing_a, self.slope)
* self._atanfct(self.x, casing_b, -self.slope))
def _atanCasingDeriv_casing_top(self, mDict):
casing_a, casing_b = mDict['casing_radius'] - 0.5*mDict['casing_thickness'], mDict['casing_radius'] + 0.5*mDict['casing_thickness']
return (self._atanCasingLengthDeriv_casing_top(mDict)
* self._atanfct(self.x, casing_a, self.slope)
* self._atanfct(self.x, casing_b, -self.slope))
def layer_cont(self, mDict):
return mDict['val_background'] + (mDict['val_layer']-mDict['val_background']) * self._atanLayer(mDict) # contribution from the layered background
def _transform(self, m):
mDict = self.mDict(m)
# assemble the model
layer = self.layer_cont(mDict)
casing = (mDict['val_casing'] - layer) * self._atanCasing(mDict)
insideCasing = (mDict['val_insideCasing'] - layer) * self._atanInsideCasing(mDict)
return layer + casing + insideCasing
def _deriv_val_background(self, mDict):
d_layer_cont_dval_background = 1. - self._atanLayer(mDict) # contribution from the layered background
d_casing_cont_dval_background = -1. * d_layer_cont_dval_background * self._atanCasing(mDict)
d_insideCasing_cont_dval_background = -1. * d_layer_cont_dval_background * self._atanInsideCasing(mDict)
return d_layer_cont_dval_background + d_casing_cont_dval_background + d_insideCasing_cont_dval_background
def _deriv_val_layer(self, mDict):
d_layer_cont_dval_layer = self._atanLayer(mDict)
d_casing_cont_dval_layer = -1. * d_layer_cont_dval_layer * self._atanCasing(mDict)
d_insideCasing_cont_dval_layer = -1. * d_layer_cont_dval_layer * self._atanInsideCasing(mDict)
return d_layer_cont_dval_layer + d_casing_cont_dval_layer + d_insideCasing_cont_dval_layer
def _deriv_val_casing(self, mDict):
d_layer_cont_dval_casing = 0.
d_casing_cont_dval_casing = self._atanCasing(mDict)
d_insideCasing_cont_dval_casing = 0.
return d_layer_cont_dval_casing + d_casing_cont_dval_casing + d_insideCasing_cont_dval_casing
def _deriv_val_insideCasing(self, mDict):
d_layer_cont_dval_insideCasing = 0.
d_casing_cont_dval_insideCasing = 0.
d_insideCasing_cont_dval_insideCasing = self._atanInsideCasing(mDict)
return d_layer_cont_dval_insideCasing + d_casing_cont_dval_insideCasing + d_insideCasing_cont_dval_insideCasing
def _deriv_layer_center(self, mDict):
d_layer_cont_dlayer_center = (mDict['val_layer'] - mDict['val_background']) * self._atanLayerDeriv_layer_center(mDict)
d_casing_cont_dlayer_center = - d_layer_cont_dlayer_center * self._atanCasing(mDict)
d_insideCasing_cont_dlayer_center = - d_layer_cont_dlayer_center * self._atanInsideCasing(mDict)
return d_layer_cont_dlayer_center + d_casing_cont_dlayer_center + d_insideCasing_cont_dlayer_center
def _deriv_layer_thickness(self, mDict):
d_layer_cont_dlayer_thickness = (mDict['val_layer']-mDict['val_background']) * self._atanLayerDeriv_layer_thickness(mDict)
d_casing_cont_dlayer_thickness = - d_layer_cont_dlayer_thickness * self._atanCasing(mDict)
d_insideCasing_cont_dlayer_thickness = - d_layer_cont_dlayer_thickness * self._atanInsideCasing(mDict)
return d_layer_cont_dlayer_thickness + d_casing_cont_dlayer_thickness + d_insideCasing_cont_dlayer_thickness
def _deriv_casing_radius(self, mDict):
layer = self.layer_cont(mDict)
d_layer_cont_dcasing_radius = 0.
d_casing_cont_dcasing_radius = (mDict['val_casing'] - layer) * self._atanCasingDeriv_casing_radius(mDict)
d_insideCasing_cont_dcasing_radius = (mDict['val_insideCasing'] - layer) * self._atanInsideCasingDeriv_casing_radius(mDict)
return d_layer_cont_dcasing_radius + d_casing_cont_dcasing_radius + d_insideCasing_cont_dcasing_radius
def _deriv_casing_thickness(self, mDict):
d_layer_cont_dcasing_thickness = 0.
d_casing_cont_dcasing_thickness = (mDict['val_casing'] - self.layer_cont(mDict)) * self._atanCasingDeriv_casing_thickness(mDict)
d_insideCasing_cont_dcasing_thickness = (mDict['val_insideCasing'] - self.layer_cont(mDict)) * self._atanInsideCasingDeriv_casing_thickness(mDict)
return d_layer_cont_dcasing_thickness + d_casing_cont_dcasing_thickness + d_insideCasing_cont_dcasing_thickness
def _deriv_casing_bottom(self, mDict):
d_layer_cont_dcasing_bottom = 0.
d_casing_cont_dcasing_bottom = (mDict['val_casing'] - self.layer_cont(mDict)) * self._atanCasingDeriv_casing_bottom(mDict)
d_insideCasing_cont_dcasing_bottom = (mDict['val_insideCasing'] - self.layer_cont(mDict)) * self._atanInsideCasingDeriv_casing_bottom(mDict)
return d_layer_cont_dcasing_bottom + d_casing_cont_dcasing_bottom + d_insideCasing_cont_dcasing_bottom
def _deriv_casing_top(self, mDict):
d_layer_cont_dcasing_top = 0.
d_casing_cont_dcasing_top = (mDict['val_casing'] - self.layer_cont(mDict)) * self._atanCasingDeriv_casing_top(mDict)
d_insideCasing_cont_dcasing_top = (mDict['val_insideCasing'] - self.layer_cont(mDict)) * self._atanInsideCasingDeriv_casing_top(mDict)
return d_layer_cont_dcasing_top + d_casing_cont_dcasing_top + d_insideCasing_cont_dcasing_top
def deriv(self, m):
mDict = self.mDict(m)
return sp.csr_matrix(np.vstack([
self._deriv_val_background(mDict),
self._deriv_val_layer(mDict),
self._deriv_val_casing(mDict),
self._deriv_val_insideCasing(mDict),
self._deriv_layer_center(mDict),
self._deriv_layer_thickness(mDict),
self._deriv_casing_radius(mDict),
self._deriv_casing_thickness(mDict),
self._deriv_casing_bottom(mDict),
self._deriv_casing_top(mDict),
]).T)
class ParametrizedBlockInLayer(ParametrizedLayer):
"""
Parametrized Block in a Layered Space
For 2D:
m = [val_background, val_layer, val_block, layer_center, layer_thickness, block_x0, block_dx]
For 3D:
m = [val_background, val_layer, val_block, layer_center, layer_thickness, block_x0, block_y0, block_dx, block_dy]
.. plot::
:include-source:
from SimPEG import Mesh, Maps, np
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1,1,figsize=(2,3))
mesh = Mesh.TensorMesh([50,50],x0='CC')
mapping = Maps.ParametrizedBlockInLayer(mesh)
m = np.hstack(np.r_[1., 2., 3., -0.1, 0.2, 0.3, 0.2])
rho = mapping._transform(m)
mesh.plotImage(rho, ax=ax)
**Required**
:param Mesh mesh: SimPEG Mesh, 2D or 3D
**Optional**
:param float slopeFact: arctan slope factor - divided by the minimum h spacing to give the slope of the arctan functions
:param float slope: slope of the arctan function
:param numpy.ndarray indActive: bool vector with
"""
def __init__(self, mesh, **kwargs):
super(ParametrizedBlockInLayer, self).__init__(mesh, **kwargs)
@property
def nP(self):
if self.mesh.dim == 2:
return 7
elif self.mesh.dim == 3:
return 9
@property
def shape(self):
if self.indActive is not None:
return (sum(self.indActive), self.nP)
return (self.mesh.nC, self.nP)
def _mDict2d(self, m):
return{
'val_background': m[0],
'val_layer': m[1],
'val_block': m[2],
'layer_center': m[3],
'layer_thickness': m[4],
'x0_block': m[5],
'dx_block': m[6]
}
def _mDict3d(self, m):
return{
'val_background': m[0],
'val_layer': m[1],
'val_block': m[2],
'layer_center': m[3],
'layer_thickness': m[4],
'x0_block': m[5],
'y0_block': m[6],
'dx_block': m[7],
'dy_block': m[8]
}
def mDict(self, m):
if self.mesh.dim == 2:
return self._mDict2d(m)
elif self.mesh.dim == 3:
return self._mDict3d(m)
def _atanBlock2d(self, mDict):
return (self._atanLayer(mDict)
* self._atanfct(self.x, mDict['x0_block'] - 0.5*mDict['dx_block'], self.slope)
* self._atanfct(self.x, mDict['x0_block'] + 0.5*mDict['dx_block'], -self.slope))
def _atanBlock2dDeriv_layer_center(self, mDict):
return (self._atanLayerDeriv_layer_center(mDict)
* self._atanfct(self.x, mDict['x0_block'] - 0.5*mDict['dx_block'], self.slope)
* self._atanfct(self.x, mDict['x0_block'] + 0.5*mDict['dx_block'], -self.slope))
def _atanBlock2dDeriv_layer_thickness(self, mDict):
return (self._atanLayerDeriv_layer_thickness(mDict)
* self._atanfct(self.x, mDict['x0_block'] - 0.5*mDict['dx_block'], self.slope)
* self._atanfct(self.x, mDict['x0_block'] + 0.5*mDict['dx_block'], -self.slope))
def _atanBlock2dDeriv_x0(self, mDict):
return self._atanLayer(mDict) * (
(self._atanfctDeriv(self.x, mDict['x0_block'] - 0.5*mDict['dx_block'], self.slope)
* self._atanfct(self.x, mDict['x0_block'] + 0.5*mDict['dx_block'], -self.slope))
+
(self._atanfct(self.x, mDict['x0_block'] - 0.5*mDict['dx_block'], self.slope)
* self._atanfctDeriv(self.x, mDict['x0_block'] + 0.5*mDict['dx_block'], -self.slope))
)
def _atanBlock2dDeriv_dx(self, mDict):
return self._atanLayer(mDict) * (
(self._atanfctDeriv(self.x, mDict['x0_block'] - 0.5*mDict['dx_block'], self.slope) * -0.5
* self._atanfct(self.x, mDict['x0_block'] + 0.5*mDict['dx_block'], -self.slope))
+
(self._atanfct(self.x, mDict['x0_block'] - 0.5*mDict['dx_block'], self.slope)
* self._atanfctDeriv(self.x, mDict['x0_block'] + 0.5*mDict['dx_block'], -self.slope) * 0.5)
)
def _atanBlock3d(self, mDict):
return (self._atanLayer(mDict)
* self._atanfct(self.x, mDict['x0_block'] - 0.5*mDict['dx_block'], self.slope)
* self._atanfct(self.x, mDict['x0_block'] + 0.5*mDict['dx_block'], -self.slope)
* self._atanfct(self.y, mDict['y0_block'] - 0.5*mDict['dy_block'], self.slope)
* self._atanfct(self.y, mDict['y0_block'] + 0.5*mDict['dy_block'], -self.slope))
def _atanBlock3dDeriv_layer_center(self, mDict):
return (self._atanLayerDeriv_layer_center(mDict)
* self._atanfct(self.x, mDict['x0_block'] - 0.5*mDict['dx_block'], self.slope)
* self._atanfct(self.x, mDict['x0_block'] + 0.5*mDict['dx_block'], -self.slope)
* self._atanfct(self.y, mDict['y0_block'] - 0.5*mDict['dy_block'], self.slope)
* self._atanfct(self.y, mDict['y0_block'] + 0.5*mDict['dy_block'], -self.slope))
def _atanBlock3dDeriv_layer_thickness(self, mDict):
return (self._atanLayerDeriv_layer_thickness(mDict)
* self._atanfct(self.x, mDict['x0_block'] - 0.5*mDict['dx_block'], self.slope)
* self._atanfct(self.x, mDict['x0_block'] + 0.5*mDict['dx_block'], -self.slope)
* self._atanfct(self.y, mDict['y0_block'] - 0.5*mDict['dy_block'], self.slope)
* self._atanfct(self.y, mDict['y0_block'] + 0.5*mDict['dy_block'], -self.slope))
def _atanBlock3dDeriv_x0(self, mDict):
return self._atanLayer(mDict) * (
(self._atanfctDeriv(self.x, mDict['x0_block'] - 0.5*mDict['dx_block'], self.slope)
* self._atanfct(self.x, mDict['x0_block'] + 0.5*mDict['dx_block'], -self.slope)
* self._atanfct(self.y, mDict['y0_block'] - 0.5*mDict['dy_block'], self.slope)
* self._atanfct(self.y, mDict['y0_block'] + 0.5*mDict['dy_block'], -self.slope))
+
(self._atanfct(self.x, mDict['x0_block'] - 0.5*mDict['dx_block'], self.slope)
* self._atanfctDeriv(self.x, mDict['x0_block'] + 0.5*mDict['dx_block'], -self.slope)
* self._atanfct(self.y, mDict['y0_block'] - 0.5*mDict['dy_block'], self.slope)
* self._atanfct(self.y, mDict['y0_block'] + 0.5*mDict['dy_block'], -self.slope))
)
def _atanBlock3dDeriv_y0(self, mDict):
return self._atanLayer(mDict) * (
(self._atanfct(self.x, mDict['x0_block'] - 0.5*mDict['dx_block'], self.slope)
* self._atanfct(self.x, mDict['x0_block'] + 0.5*mDict['dx_block'], -self.slope)
* self._atanfctDeriv(self.y, mDict['y0_block'] - 0.5*mDict['dy_block'], self.slope)
* self._atanfct(self.y, mDict['y0_block'] + 0.5*mDict['dy_block'], -self.slope))
+
(self._atanfct(self.x, mDict['x0_block'] - 0.5*mDict['dx_block'], self.slope)
* self._atanfct(self.x, mDict['x0_block'] + 0.5*mDict['dx_block'], -self.slope)
* self._atanfct(self.y, mDict['y0_block'] - 0.5*mDict['dy_block'], self.slope)
* self._atanfctDeriv(self.y, mDict['y0_block'] + 0.5*mDict['dy_block'], -self.slope))
)
def _atanBlock3dDeriv_dx(self, mDict):
return self._atanLayer(mDict) * (
(self._atanfctDeriv(self.x, mDict['x0_block'] - 0.5*mDict['dx_block'], self.slope) * -0.5
* self._atanfct(self.x, mDict['x0_block'] + 0.5*mDict['dx_block'], -self.slope)
* self._atanfct(self.y, mDict['y0_block'] - 0.5*mDict['dy_block'], self.slope)
* self._atanfct(self.y, mDict['y0_block'] + 0.5*mDict['dy_block'], -self.slope))
+
(self._atanfct(self.x, mDict['x0_block'] - 0.5*mDict['dx_block'], self.slope)
* self._atanfctDeriv(self.x, mDict['x0_block'] + 0.5*mDict['dx_block'], -self.slope) * 0.5
* self._atanfct(self.y, mDict['y0_block'] - 0.5*mDict['dy_block'], self.slope)
* self._atanfct(self.y, mDict['y0_block'] + 0.5*mDict['dy_block'], -self.slope))
)
def _atanBlock3dDeriv_dy(self, mDict):
return self._atanLayer(mDict) * (
(self._atanfct(self.x, mDict['x0_block'] - 0.5*mDict['dx_block'], self.slope)
* self._atanfct(self.x, mDict['x0_block'] + 0.5*mDict['dx_block'], -self.slope)
* self._atanfctDeriv(self.y, mDict['y0_block'] - 0.5*mDict['dy_block'], self.slope) * -0.5
* self._atanfct(self.y, mDict['y0_block'] + 0.5*mDict['dy_block'], -self.slope))
+
(self._atanfct(self.x, mDict['x0_block'] - 0.5*mDict['dx_block'], self.slope)
* self._atanfct(self.x, mDict['x0_block'] + 0.5*mDict['dx_block'], -self.slope)
* self._atanfct(self.y, mDict['y0_block'] - 0.5*mDict['dy_block'], self.slope)
* self._atanfctDeriv(self.y, mDict['y0_block'] + 0.5*mDict['dy_block'], -self.slope) * 0.5)
)
def _transform2d(self, m):
mDict = self.mDict(m)
# assemble the model
layer_cont = mDict['val_background'] + (mDict['val_layer']-mDict['val_background'])*self._atanLayer(mDict) # contribution from the layered background
block_cont = (mDict['val_block']-layer_cont)*self._atanBlock2d(mDict) # perturbation due to the block
return layer_cont + block_cont
def _deriv2d_val_background(self, mDict):
d_layer_dval_background = np.ones_like(self.x) - self._atanLayer(mDict)
d_block_dval_background = (-d_layer_dval_background)*self._atanBlock2d(mDict)
return d_layer_dval_background + d_block_dval_background
def _deriv2d_val_layer(self, mDict):
d_layer_dval_layer = self._atanLayer(mDict)
d_block_dval_layer = (-d_layer_dval_layer)*self._atanBlock2d(mDict)
return d_layer_dval_layer + d_block_dval_layer
def _deriv2d_val_block(self, mDict):
d_layer_dval_block = 0.
d_block_dval_block = (1.-d_layer_dval_block)*self._atanBlock2d(mDict)
return d_layer_dval_block + d_block_dval_block
def _deriv2d_layer_center(self, mDict):
d_layer_dlayer_center = (mDict['val_layer']-mDict['val_background'])*self._atanLayerDeriv_layer_center(mDict)
d_block_dlayer_center = ((mDict['val_block']-self.layer_cont(mDict))*self._atanBlock2dDeriv_layer_center(mDict)
- d_layer_dlayer_center*self._atanBlock2d(mDict))
return d_layer_dlayer_center + d_block_dlayer_center
def _deriv2d_layer_thickness(self, mDict):
d_layer_dlayer_thickness = (mDict['val_layer']-mDict['val_background'])*self._atanLayerDeriv_layer_thickness(mDict)
d_block_dlayer_thickness = ((mDict['val_block']-self.layer_cont(mDict))*self._atanBlock2dDeriv_layer_thickness(mDict)
- d_layer_dlayer_thickness*self._atanBlock2d(mDict))
return d_layer_dlayer_thickness + d_block_dlayer_thickness
def _deriv2d_x0_block(self, mDict):
d_layer_dx0 = 0.
d_block_dx0 = (mDict['val_block']-self.layer_cont(mDict))*self._atanBlock2dDeriv_x0(mDict)
return d_layer_dx0 + d_block_dx0
def _deriv2d_dx_block(self, mDict):
d_layer_ddx = 0.
d_block_ddx = (mDict['val_block']-self.layer_cont(mDict))*self._atanBlock2dDeriv_dx(mDict)
return d_layer_ddx + d_block_ddx
def _deriv2d(self, m):
mDict = self.mDict(m)
return np.vstack([
self._deriv2d_val_background(mDict),
self._deriv2d_val_layer(mDict),
self._deriv2d_val_block(mDict),
self._deriv2d_layer_center(mDict),
self._deriv2d_layer_thickness(mDict),
self._deriv2d_x0_block(mDict),
self._deriv2d_dx_block(mDict)
]).T
def _transform3d(self, m):
# parse model
mDict = self.mDict(m)
# assemble the model
layer_cont = mDict['val_background'] + (mDict['val_layer']-mDict['val_background'])*self._atanLayer(mDict) # contribution from the layered background
block_cont = (mDict['val_block']-layer_cont)*self._atanBlock3d(mDict) # perturbation due to the block
return layer_cont + block_cont
def _deriv3d_val_background(self, mDict):
d_layer_dval_background = np.ones_like(self.x) - self._atanLayer(mDict)
d_block_dval_background = (-d_layer_dval_background)*self._atanBlock3d(mDict)
return d_layer_dval_background + d_block_dval_background
def _deriv3d_val_layer(self, mDict):
d_layer_dval_layer = self._atanLayer(mDict)
d_block_dval_layer = (-d_layer_dval_layer)*self._atanBlock3d(mDict)
return d_layer_dval_layer + d_block_dval_layer
def _deriv3d_val_block(self, mDict):
d_layer_dval_block = 0.
d_block_dval_block = (1.-d_layer_dval_block)*self._atanBlock3d(mDict)
return d_layer_dval_block + d_block_dval_block
def _deriv3d_layer_center(self, mDict):
d_layer_dlayer_center = (mDict['val_layer']-mDict['val_background'])*self._atanLayerDeriv_layer_center(mDict)
d_block_dlayer_center = ((mDict['val_block']-self.layer_cont(mDict))*self._atanBlock3dDeriv_layer_center(mDict)
- d_layer_dlayer_center*self._atanBlock3d(mDict))
return d_layer_dlayer_center + d_block_dlayer_center
def _deriv3d_layer_thickness(self, mDict):
d_layer_dlayer_thickness = (mDict['val_layer']-mDict['val_background'])*self._atanLayerDeriv_layer_thickness(mDict)
d_block_dlayer_thickness = ((mDict['val_block']-self.layer_cont(mDict))*self._atanBlock3dDeriv_layer_thickness(mDict)
- d_layer_dlayer_thickness*self._atanBlock3d(mDict))
return d_layer_dlayer_thickness + d_block_dlayer_thickness
def _deriv3d_x0_block(self, mDict):
d_layer_dx0 = 0.
d_block_dx0 = (mDict['val_block']-self.layer_cont(mDict))*self._atanBlock3dDeriv_x0(mDict)
return d_layer_dx0 + d_block_dx0
def _deriv3d_y0_block(self, mDict):
d_layer_dy0 = 0.
d_block_dy0 = (mDict['val_block']-self.layer_cont(mDict))*self._atanBlock3dDeriv_y0(mDict)
return d_layer_dy0 + d_block_dy0
def _deriv3d_dx_block(self, mDict):
d_layer_ddx = 0.
d_block_ddx = (mDict['val_block']-self.layer_cont(mDict))*self._atanBlock3dDeriv_dx(mDict)
return d_layer_ddx + d_block_ddx
def _deriv3d_dy_block(self, mDict):
d_layer_ddy = 0.
d_block_ddy = (mDict['val_block']-self.layer_cont(mDict))*self._atanBlock3dDeriv_dy(mDict)
return d_layer_ddy + d_block_ddy
def _deriv3d(self, m):
mDict = self.mDict(m)
return np.vstack([
self._deriv3d_val_background(mDict),
self._deriv3d_val_layer(mDict),
self._deriv3d_val_block(mDict),
self._deriv3d_layer_center(mDict),
self._deriv3d_layer_thickness(mDict),
self._deriv3d_x0_block(mDict),
self._deriv3d_y0_block(mDict),
self._deriv3d_dx_block(mDict),
self._deriv3d_dy_block(mDict),
]).T
def _transform(self, m):
if self.mesh.dim == 2:
return self._transform2d(m)
elif self.mesh.dim == 3:
return self._transform3d(m)
def deriv(self, m):
if self.mesh.dim == 2:
return sp.csr_matrix(self._deriv2d(m))
elif self.mesh.dim == 3:
return sp.csr_matrix(self._deriv3d(m))
Reference in New Issue View Git Blame Copy Permalink