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https://github.com/wassname/simpeg.git
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modularizing regularization
This commit is contained in:
Lindsey Heagy
+269
-135
@@ -403,7 +403,203 @@ class BaseRegularization(object):
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return mD.T * ( self.W.T * ( self.W * ( mD * v) ) )
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class Tikhonov(BaseRegularization):
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class Simple(BaseRegularization):
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"""
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Simple regularization that does not include length scales in the derivatives.
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"""
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mrefInSmooth = False #: SMOOTH and SMOOTH_MOD_DIF options
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alpha_s = Utils.dependentProperty('_alpha_s', 1e-6, ['_W', '_Wsmall'], "Smallness weight")
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alpha_x = Utils.dependentProperty('_alpha_x', 1.0, ['_W', '_Wx'], "Weight for the first derivative in the x direction")
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alpha_y = Utils.dependentProperty('_alpha_y', 1.0, ['_W', '_Wy'], "Weight for the first derivative in the y direction")
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alpha_z = Utils.dependentProperty('_alpha_z', 1.0, ['_W', '_Wz'], "Weight for the first derivative in the z direction")
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wght = 1.
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def __init__(self, mesh, mapping=None, indActive=None, **kwargs):
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BaseRegularization.__init__(self, mesh, mapping=mapping, indActive=indActive, **kwargs)
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if isinstance(self.wght,float):
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self.wght = np.ones(self.regmesh.nC) * self.wght
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@property
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def Wsmall(self):
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"""Regularization matrix Wsmall"""
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if getattr(self,'_Wsmall', None) is None:
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self._Wsmall = Utils.sdiag((self.regmesh.vol*self.alpha_s*self.wght)**0.5)
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return self._Wsmall
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@property
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def Wx(self):
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"""Regularization matrix Wx"""
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if getattr(self, '_Wx', None) is None:
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self._Wx = Utils.sdiag((self.regmesh.aveCC2Fx * self.regmesh.vol*self.alpha_x*(self.regmesh.aveCC2Fx*self.wght))**0.5)*self.regmesh.cellDiffxStencil
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return self._Wx
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@property
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def Wy(self):
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"""Regularization matrix Wy"""
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if getattr(self, '_Wy', None) is None:
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self._Wy = Utils.sdiag((self.regmesh.aveCC2Fy * self.regmesh.vol * self.alpha_y*(self.regmesh.aveCC2Fy*self.wght))**0.5)*self.regmesh.cellDiffyStencil
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return self._Wy
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@property
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def Wz(self):
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"""Regularization matrix Wz"""
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if getattr(self, '_Wz', None) is None:
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self._Wz = Utils.sdiag((self.regmesh.aveCC2Fz * self.regmesh.vol*self.alpha_z*(self.regmesh.aveCC2Fz*self.wght))**0.5)*self.regmesh.cellDiffzStencil
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return self._Wz
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@property
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def Wsmooth(self):
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"""Full smoothness regularization matrix W"""
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if getattr(self, '_Wsmooth', None) is None:
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wlist = (self.Wx,)
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if self.regmesh.dim > 1:
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wlist += (self.Wy,)
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if self.regmesh.dim > 2:
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wlist += (self.Wz,)
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self._Wsmooth = sp.vstack(wlist)
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return self._Wsmooth
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@property
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def W(self):
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"""Full regularization matrix W"""
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if getattr(self, '_W', None) is None:
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wlist = (self.Wsmall, self.Wsmooth)
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self._W = sp.vstack(wlist)
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return self._W
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@Utils.timeIt
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def _evalSmall(self, m):
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r = self.Wsmall * ( self.mapping * (m - self.mref) )
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return 0.5 * r.dot(r)
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@property
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def W(self):
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"""Full regularization matrix W"""
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if getattr(self, '_W', None) is None:
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wlist = (self.Wsmall, self.Wsmooth)
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self._W = sp.vstack(wlist)
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return self._W
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@property
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def Wsmooth(self):
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"""Full smoothness regularization matrix W"""
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if getattr(self, '_Wsmooth', None) is None:
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wlist = (self.Wx,)
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if self.regmesh.dim > 1:
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wlist += (self.Wy,)
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if self.regmesh.dim > 2:
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wlist += (self.Wz,)
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self._Wsmooth = sp.vstack(wlist)
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return self._Wsmooth
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@Utils.timeIt
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def _evalSmall(self, m):
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r = self.Wsmall * ( self.mapping * (m - self.mref) )
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return 0.5 * r.dot(r)
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@Utils.timeIt
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def _evalSmallDeriv(self,m):
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r = self.Wsmall * ( self.mapping * (m - self.mref) )
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return r.T * ( self.Wsmall * self.mapping.deriv(m - self.mref) )
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@Utils.timeIt
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def _evalSmoothx(self, m):
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if self.mrefInSmooth == True:
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r = self.Wx * ( self.mapping * (m - self.mref) )
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elif self.mrefInSmooth == False:
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r = self.Wx * ( self.mapping * (m) )
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return 0.5 * r.dot(r)
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@Utils.timeIt
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def _evalSmoothy(self, m):
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if self.mrefInSmooth == True:
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r = self.Wy * ( self.mapping * (m - self.mref) )
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elif self.mrefInSmooth == False:
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r = self.Wy * ( self.mapping * (m) )
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return 0.5 * r.dot(r)
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@Utils.timeIt
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def _evalSmoothz(self, m):
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if self.mrefInSmooth == True:
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r = self.Wz * ( self.mapping * (m - self.mref) )
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elif self.mrefInSmooth == False:
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r = self.Wz * ( self.mapping * (m) )
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return 0.5 * r.dot(r)
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@Utils.timeIt
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def _evalSmooth(self, m):
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phiSmooth = self._evalSmoothx(m)
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if self.regmesh.dim > 1:
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phiSmooth += self._evalSmoothy(m)
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if self.regmesh.dim > 2:
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phiSmooth += self._evalSmoothz(m)
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return phiSmooth
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@Utils.timeIt
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def _evalSmoothxDeriv(self,m):
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if self.mrefInSmooth == True:
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r = self.Wx * ( self.mapping * ( m - self.mref ) )
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return r.T * ( self.Wx * self.mapping.deriv(m - self.mref) )
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elif self.mrefInSmooth == False:
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r = self.Wx * ( self.mapping * m )
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return r.T * ( self.Wx * self.mapping.deriv(m) )
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@Utils.timeIt
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def _evalSmoothyDeriv(self,m):
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if self.mrefInSmooth == True:
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r = self.Wy * ( self.mapping * ( m - self.mref ) )
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return r.T * ( self.Wy * self.mapping.deriv(m - self.mref) )
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elif self.mrefInSmooth == False:
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r = self.Wy * ( self.mapping * m )
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return r.T * ( self.Wy * self.mapping.deriv(m) )
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@Utils.timeIt
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def _evalSmoothzDeriv(self,m):
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if self.mrefInSmooth == True:
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r = self.Wz * ( self.mapping * ( m - self.mref ) )
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return r.T * ( self.Wz * self.mapping.deriv(m - self.mref) )
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elif self.mrefInSmooth == False:
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r = self.Wz * ( self.mapping * m )
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return r.T * ( self.Wz * self.mapping.deriv(m) )
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@Utils.timeIt
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def _evalSmoothDeriv(self,m):
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deriv = self._evalSmoothxDeriv(m)
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if self.regmesh.dim > 1:
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deriv += self._evalSmoothyDeriv(m)
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if self.regmesh.dim > 2:
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deriv += self._evalSmoothzDeriv(m)
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return deriv
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@Utils.timeIt
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def eval(self, m):
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return self._evalSmall(m) + self._evalSmooth(m)
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@Utils.timeIt
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def evalDeriv(self, m):
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"""
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The regularization is:
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.. math::
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R(m) = \\frac{1}{2}\mathbf{(m-m_\\text{ref})^\\top W^\\top W(m-m_\\text{ref})}
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So the derivative is straight forward:
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.. math::
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R(m) = \mathbf{W^\\top W (m-m_\\text{ref})}
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"""
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return self._evalSmallDeriv(m) + self._evalSmoothDeriv(m)
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class Tikhonov(Simple):
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"""
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L2 Tikhonov regularization with both smallness and smoothness (first order
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derivative) contributions.
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@@ -493,56 +689,92 @@ class Tikhonov(BaseRegularization):
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self._Wzz = Utils.sdiag((self.regmesh.vol*self.alpha_zz)**0.5)*self.regmesh.faceDiffz*self.regmesh.cellDiffz
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return self._Wzz
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@property
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def Wsmooth(self):
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def Wsmooth2(self):
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"""Full smoothness regularization matrix W"""
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if getattr(self, '_Wsmooth', None) is None:
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wlist = (self.Wx, self.Wxx)
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wlist = (self.Wxx)
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if self.regmesh.dim > 1:
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wlist += (self.Wy, self.Wyy)
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wlist += (self.Wyy)
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if self.regmesh.dim > 2:
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wlist += (self.Wz, self.Wzz)
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wlist += (self.Wzz)
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self._Wsmooth = sp.vstack(wlist)
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return self._Wsmooth
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@property
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def W(self):
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"""Full regularization matrix W"""
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if getattr(self, '_W', None) is None:
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wlist = (self.Wsmall, self.Wsmooth)
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self._W = sp.vstack(wlist)
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return self._W
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@Utils.timeIt
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def _evalSmall(self, m):
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r = self.Wsmall * ( self.mapping * (m - self.mref) )
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return 0.5 * r.dot(r)
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@Utils.timeIt
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def _evalSmooth(self, m):
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def _evalSmoothxx(self, m):
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if self.mrefInSmooth == True:
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r = self.Wsmooth * ( self.mapping * (m - self.mref) )
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r = self.Wxx * ( self.mapping * (m - self.mref) )
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elif self.mrefInSmooth == False:
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r = self.Wsmooth * ( self.mapping * (m) )
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r = self.Wxx * ( self.mapping * (m) )
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return 0.5 * r.dot(r)
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@Utils.timeIt
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def _evalSmoothyy(self, m):
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if self.mrefInSmooth == True:
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r = self.Wyy * ( self.mapping * (m - self.mref) )
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elif self.mrefInSmooth == False:
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r = self.Wyy * ( self.mapping * (m) )
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return 0.5 * r.dot(r)
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@Utils.timeIt
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def _evalSmoothzz(self, m):
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if self.mrefInSmooth == True:
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r = self.Wzz * ( self.mapping * (m - self.mref) )
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elif self.mrefInSmooth == False:
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r = self.Wzz * ( self.mapping * (m) )
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return 0.5 * r.dot(r)
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@Utils.timeIt
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def _evalSmooth2(self, m):
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phiSmooth2 = self._evalSmoothxx(m)
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if self.regmesh.dim > 1:
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phiSmooth2 += self._evalSmoothyy(m)
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if self.regmesh.dim > 2:
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phiSmooth2 += self._evalSmoothzz(m)
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return phiSmooth2
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@Utils.timeIt
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def _evalSmoothxxDeriv(self,m):
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if self.mrefInSmooth == True:
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r = self.Wxx * ( self.mapping * ( m - self.mref ) )
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return r.T * ( self.Wxx * self.mapping.deriv(m - self.mref) )
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elif self.mrefInSmooth == False:
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r = self.Wxx * ( self.mapping * m )
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return r.T * ( self.Wxx * self.mapping.deriv(m) )
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@Utils.timeIt
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def _evalSmoothyyDeriv(self,m):
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if self.mrefInSmooth == True:
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r = self.Wyy * ( self.mapping * ( m - self.mref ) )
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return r.T * ( self.Wyy * self.mapping.deriv(m - self.mref) )
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elif self.mrefInSmooth == False:
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r = self.Wyy * ( self.mapping * m )
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return r.T * ( self.Wyy * self.mapping.deriv(m) )
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@Utils.timeIt
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def _evalSmoothzzDeriv(self,m):
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if self.mrefInSmooth == True:
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r = self.Wzz * ( self.mapping * ( m - self.mref ) )
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return r.T * ( self.Wzz * self.mapping.deriv(m - self.mref) )
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elif self.mrefInSmooth == False:
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r = self.Wzz * ( self.mapping * m )
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return r.T * ( self.Wzz * self.mapping.deriv(m) )
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@Utils.timeIt
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def _evalSmooth2Deriv(self,m):
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deriv = self._evalSmoothxxDeriv(m)
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if self.regmesh.dim > 1:
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deriv += self._evalSmoothyyDeriv(m)
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if self.regmesh.dim > 2:
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deriv += self._evalSmoothzzDeriv(m)
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return deriv
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@Utils.timeIt
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def eval(self, m):
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return self._evalSmall(m) + self._evalSmooth(m)
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@Utils.timeIt
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def _evalSmallDeriv(self,m):
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r = self.Wsmall * ( self.mapping * (m - self.mref) )
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return r.T * ( self.Wsmall * self.mapping.deriv(m - self.mref) )
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@Utils.timeIt
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def _evalSmoothDeriv(self,m):
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if self.mrefInSmooth == True:
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r = self.Wsmooth * ( self.mapping * ( m - self.mref ) )
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return r.T * ( self.Wsmooth * self.mapping.deriv(m - self.mref) )
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elif self.mrefInSmooth == False:
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r = self.Wsmooth * ( self.mapping * m )
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return r.T * ( self.Wsmooth * self.mapping.deriv(m) )
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return self._evalSmall(m) + self._evalSmooth(m) + self._evalSmooth2(m)
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@Utils.timeIt
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def evalDeriv(self, m):
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@@ -560,88 +792,9 @@ class Tikhonov(BaseRegularization):
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R(m) = \mathbf{W^\\top W (m-m_\\text{ref})}
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"""
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return self._evalSmallDeriv(m) + self._evalSmoothDeriv(m)
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return self._evalSmallDeriv(m) + self._evalSmoothDeriv(m) + self._evalSmooth2Deriv(m)
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class Simple(Tikhonov):
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"""
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Simple regularization that does not include length scales in the derivatives.
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"""
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mrefInSmooth = False #: SMOOTH and SMOOTH_MOD_DIF options
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alpha_s = Utils.dependentProperty('_alpha_s', 1.0, ['_W', '_Wsmall'], "Smallness weight")
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alpha_x = Utils.dependentProperty('_alpha_x', 1.0, ['_W', '_Wx'], "Weight for the first derivative in the x direction")
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alpha_y = Utils.dependentProperty('_alpha_y', 1.0, ['_W', '_Wy'], "Weight for the first derivative in the y direction")
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alpha_z = Utils.dependentProperty('_alpha_z', 1.0, ['_W', '_Wz'], "Weight for the first derivative in the z direction")
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wght = 1.
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def __init__(self, mesh, mapping=None, indActive=None, **kwargs):
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BaseRegularization.__init__(self, mesh, mapping=mapping, indActive=indActive, **kwargs)
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if isinstance(self.wght,float):
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self.wght = np.ones(self.regmesh.nC) * self.wght
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@property
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def Wsmall(self):
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"""Regularization matrix Wsmall"""
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if getattr(self,'_Wsmall', None) is None:
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self._Wsmall = Utils.sdiag((self.regmesh.vol*self.alpha_s*self.wght)**0.5)
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return self._Wsmall
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@property
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def Wx(self):
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"""Regularization matrix Wx"""
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if getattr(self, '_Wx', None) is None:
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self._Wx = Utils.sdiag((self.regmesh.aveCC2Fx * self.regmesh.vol*self.alpha_x*(self.regmesh.aveCC2Fx*self.wght))**0.5)*self.regmesh.cellDiffxStencil
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return self._Wx
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@property
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def Wy(self):
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"""Regularization matrix Wy"""
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if getattr(self, '_Wy', None) is None:
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self._Wy = Utils.sdiag((self.regmesh.aveCC2Fy * self.regmesh.vol * self.alpha_y*(self.regmesh.aveCC2Fy*self.wght))**0.5)*self.regmesh.cellDiffyStencil
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return self._Wy
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@property
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def Wz(self):
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"""Regularization matrix Wz"""
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if getattr(self, '_Wz', None) is None:
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self._Wz = Utils.sdiag((self.regmesh.aveCC2Fz * self.regmesh.vol*self.alpha_z*(self.regmesh.aveCC2Fz*self.wght))**0.5)*self.regmesh.cellDiffzStencil
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return self._Wz
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@property
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def Wsmooth(self):
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"""Full smoothness regularization matrix W"""
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if getattr(self, '_Wsmooth', None) is None:
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wlist = (self.Wx,)
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if self.regmesh.dim > 1:
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wlist += (self.Wy,)
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if self.regmesh.dim > 2:
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wlist += (self.Wz,)
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self._Wsmooth = sp.vstack(wlist)
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return self._Wsmooth
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@property
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def W(self):
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"""Full regularization matrix W"""
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if getattr(self, '_W', None) is None:
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wlist = (self.Wsmall, self.Wsmooth)
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self._W = sp.vstack(wlist)
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return self._W
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@Utils.timeIt
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def _evalSmall(self, m):
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r = self.Wsmall * ( self.mapping * (m - self.mref) )
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return 0.5 * r.dot(r)
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@Utils.timeIt
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def _evalSmooth(self, m):
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if self.mrefInSmooth == True:
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r = self.Wsmooth * ( self.mapping * (m - self.mref) )
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elif self.mrefInSmooth == False:
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r = self.Wsmooth * ( self.mapping * m)
|
||||
return 0.5 * r.dot(r)
|
||||
|
||||
|
||||
class Sparse(Simple):
|
||||
|
||||
@@ -716,25 +869,6 @@ class Sparse(Simple):
|
||||
|
||||
return Utils.sdiag(((self.regmesh.aveCC2Fz * self.regmesh.vol)*self.alpha_z*self.gamma*(self.regmesh.aveCC2Fz*self.wght))**0.5)*self.Rz*self.regmesh.cellDiffzStencil
|
||||
|
||||
@property
|
||||
def Wsmooth(self):
|
||||
"""Full smoothness regularization matrix W"""
|
||||
#if getattr(self, '_Wsmooth', None) is None:
|
||||
wlist = (self.Wx,)
|
||||
if self.regmesh.dim > 1:
|
||||
wlist += (self.Wy,)
|
||||
if self.regmesh.dim > 2:
|
||||
wlist += (self.Wz,)
|
||||
#self._Wsmooth = sp.vstack(wlist)
|
||||
return sp.vstack(wlist)
|
||||
|
||||
@property
|
||||
def W(self):
|
||||
"""Full regularization matrix W"""
|
||||
if getattr(self, '_W', None) is None:
|
||||
wlist = (self.Wsmall, self.Wsmooth)
|
||||
self._W = sp.vstack(wlist)
|
||||
return self._W
|
||||
|
||||
def R(self, f_m , eps, exponent):
|
||||
|
||||
|
||||
Reference in New Issue
Block a user