wassname/simpeg
1
0
Fork 0
mirror of https://github.com/wassname/simpeg.git synced 2026-07-09 12:19:05 +08:00
Code Issues Packages Projects Releases Wiki Activity

Inversion Framework - a start..

Browse Source
This commit is contained in:
Rowan Cockett
2013-10-22 19:42:38 -07:00
parent 0cb9fa210a
commit 2a8f43aa10
5 changed files with 341 additions and 154 deletions
Download Patch File Download Diff File Expand all files Collapse all files
SimPEG/forward/Problem.py
+16 -123
View File
@@ -49,16 +49,6 @@ class Problem(object):
def RHS(self, value):
self._RHS = value
@property
def W(self):
"""
Standard deviation weighting matrix.
"""
return self._W
@W.setter
def W(self, value):
self._W = value
@property
def P(self):
"""
@@ -83,16 +73,24 @@ class Problem(object):
def dobs(self, value):
self._dobs = value
def evalFunction(self, m, doDerivative=True):
def misfit(self, m, u=None):
"""
:param numpy.array m: model
:param bool doDerivative: do you want to compute the derivative?
:rtype: numpy.array
:return: Jv
"""
f = self.misfit(m)
:param numpy.array m: geophysical model
:param numpy.array u: fields
:rtype: float
:return: data misfit
return f, g, H
The data misfit:
.. math::
\mu_\\text{data} = \mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs}
Where P is a projection matrix that brings the field on the full domain to the data measurement locations;
u is the field of interest; d_obs is the observed data.
"""
return self.dpred(m, u=u) - self.dobs
def J(self, m, v, u=None):
"""
@@ -201,112 +199,7 @@ class Problem(object):
"""
return sdiag(np.exp(mkvc(m)))
def misfit(self, m, u=None):
"""
:param numpy.array m: geophysical model
:param numpy.array u: fields
:rtype: float
:return: data misfit
The data misfit using an l_2 norm is:
.. math::
\mu_\\text{data} = {1\over 2}\left| \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs}) \\right|_2^2
Where P is a projection matrix that brings the field on the full domain to the data measurement locations;
u is the field of interest; d_obs is the observed data; and W is the weighting matrix.
"""
R = self.W*(self.dpred(m, u=u) - self.dobs)
R = mkvc(R)
return 0.5*R.dot(R)
def misfitDeriv(self, m, u=None):
"""
:param numpy.array m: geophysical model
:param numpy.array u: fields
:rtype: numpy.array
:return: data misfit derivative
The data misfit using an l_2 norm is:
.. math::
\mu_\\text{data} = {1\over 2}\left| \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs}) \\right|_2^2
If the field, u, is provided, the calculation of the data is fast:
.. math::
\mathbf{d}_\\text{pred} = \mathbf{Pu(m)}
\mathbf{R} = \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs})
Where P is a projection matrix that brings the field on the full domain to the data measurement locations;
u is the field of interest; d_obs is the observed data; and W is the weighting matrix.
The derivative of this, with respect to the model, is:
.. math::
\\frac{\partial \mu_\\text{data}}{\partial \mathbf{m}} = \mathbf{J}^\\top \mathbf{W \circ R}
"""
if u is None:
u = self.field(m)
R = self.W*(self.dpred(m, u=u) - self.dobs)
dmisfit = 0
for i in range(self.RHS.shape[1]): # Loop over each right hand side
dmisfit += self.Jt(m, self.W[:,i]*R[:,i], u=u[:,i])
return dmisfit
def misfitDerivDeriv(self, m, u=None):
"""
:param numpy.array m: geophysical model
:param numpy.array u: fields
:rtype: numpy.array
:return: data misfit derivative
The data misfit using an l_2 norm is:
.. math::
\mu_\\text{data} = {1\over 2}\left| \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs}) \\right|_2^2
If the field, u, is provided, the calculation of the data is fast:
.. math::
\mathbf{d}_\\text{pred} = \mathbf{Pu(m)}
\mathbf{R} = \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs})
Where P is a projection matrix that brings the field on the full domain to the data measurement locations;
u is the field of interest; d_obs is the observed data; and W is the weighting matrix.
The derivative of this, with respect to the model, is:
.. math::
\\frac{\partial \mu_\\text{data}}{\partial \mathbf{m}} = \mathbf{J}^\\top \mathbf{W \circ R}
\\frac{\partial^2 \mu_\\text{data}}{\partial^2 \mathbf{m}} = \mathbf{J}^\\top \mathbf{W \circ W J}
"""
if u is None:
u = self.field(m)
R = self.W*(self.dpred(m, u=u) - self.dobs)
dmisfit = 0
for i in range(self.RHS.shape[1]): # Loop over each right hand side
dmisfit += self.Jt(m, self.W[:,i]*R[:,i], u=u[:,i])
return dmisfit
class SyntheticProblem(object):