mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-29 20:17:38 +08:00
Rowan Cockett
222 lines
7.0 KiB
Python
222 lines
7.0 KiB
Python
import numpy as np
|
|
import scipy.sparse as sp
|
|
from SimPEG.utils import sdiag, mkvc
|
|
|
|
class Inversion(object):
|
|
"""docstring for Inversion"""
|
|
|
|
maxIter = 10
|
|
name = 'SimPEG Inversion'
|
|
|
|
def __init__(self, prob, reg, opt, **kwargs):
|
|
self.prob = prob
|
|
self.reg = reg
|
|
self.opt = opt
|
|
self.opt.parent = self
|
|
self.setKwargs(**kwargs)
|
|
|
|
def setKwargs(self, **kwargs):
|
|
"""Sets key word arguments (kwargs) that are present in the object, throw an error if they don't exist."""
|
|
for attr in kwargs:
|
|
if hasattr(self, attr):
|
|
setattr(self, attr, kwargs[attr])
|
|
else:
|
|
raise Exception('%s attr is not recognized' % attr)
|
|
|
|
def printInit(self):
|
|
print "%s %s %s" % ('='*22, self.name, '='*22)
|
|
print " # beta phi_d phi_m f norm(dJ) #LS"
|
|
print "%s" % '-'*62
|
|
|
|
def printIter(self):
|
|
print "%3d %1.2e %1.2e %1.2e %1.2e %1.2e %3d" % (self.opt._iter, self._beta, self._phi_d_last, self._phi_m_last, self.opt.f, np.linalg.norm(self.opt.g), self.opt._iterLS)
|
|
|
|
@property
|
|
def Wd(self):
|
|
"""
|
|
Standard deviation weighting matrix.
|
|
"""
|
|
if getattr(self,'_Wd',None) is None:
|
|
eps = np.linalg.norm(mkvc(self.prob.dobs),2)*1e-5
|
|
self._Wd = 1/(abs(self.prob.dobs)*self.prob.std+eps)
|
|
return self._Wd
|
|
|
|
@property
|
|
def phi_d_target(self):
|
|
"""
|
|
target for phi_d
|
|
|
|
By default this is the number of data.
|
|
|
|
Note that we do not set the target if it is None, but we return the default value.
|
|
"""
|
|
if getattr(self, '_phi_d_target', None) is None:
|
|
return self.prob.dobs.size #
|
|
return self._phi_d_target
|
|
@phi_d_target.setter
|
|
def phi_d_target(self, value):
|
|
self._phi_d_target = value
|
|
|
|
def run(self, m0):
|
|
m = m0
|
|
self._iter = 0
|
|
self._beta = None
|
|
while True:
|
|
self._beta = self.getBeta()
|
|
m = self.opt.minimize(self.evalFunction,m)
|
|
if self.stoppingCriteria(): break
|
|
self._iter += 1
|
|
return m
|
|
|
|
beta0 = 1.e2
|
|
beta_coolingFactor = 5.
|
|
|
|
def getBeta(self):
|
|
if self._beta is None:
|
|
return self.beta0
|
|
return self._beta / self.beta_coolingFactor
|
|
|
|
def stoppingCriteria(self):
|
|
self._STOP = np.zeros(2,dtype=bool)
|
|
self._STOP[0] = self._iter >= self.maxIter
|
|
self._STOP[1] = self._phi_d_last <= self.phi_d_target
|
|
return np.any(self._STOP)
|
|
|
|
|
|
def evalFunction(self, m, return_g=True, return_H=True):
|
|
|
|
u = self.prob.field(m)
|
|
phi_d = self.dataObj(m, u)
|
|
phi_m = self.reg.modelObj(m)
|
|
|
|
self._phi_d_last = phi_d
|
|
self._phi_m_last = phi_m
|
|
|
|
f = phi_d + self._beta * phi_m
|
|
|
|
out = (f,)
|
|
if return_g:
|
|
phi_dDeriv = self.dataObjDeriv(m, u=u)
|
|
phi_mDeriv = self.reg.modelObjDeriv(m)
|
|
|
|
g = phi_dDeriv + self._beta * phi_mDeriv
|
|
out += (g,)
|
|
|
|
if return_H:
|
|
def H_fun(v):
|
|
phi_d2Deriv = self.dataObj2Deriv(m, v, u=u)
|
|
phi_m2Deriv = self.reg.modelObj2Deriv(m)*v
|
|
|
|
return phi_d2Deriv + self._beta * phi_m2Deriv
|
|
|
|
operator = sp.linalg.LinearOperator( (m.size, m.size), H_fun, dtype=float )
|
|
out += (operator,)
|
|
return out
|
|
|
|
|
|
def dataObj(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.
|
|
"""
|
|
# TODO: ensure that this is a data is vector and Wd is a matrix.
|
|
R = self.Wd*self.prob.dataResidual(m, u=u)
|
|
R = mkvc(R)
|
|
return 0.5*np.vdot(R, R)
|
|
|
|
def dataObjDeriv(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.prob.field(m)
|
|
|
|
R = self.Wd*self.prob.dataResidual(m, u=u)
|
|
|
|
dmisfit = self.prob.Jt(m, self.Wd * R, u=u)
|
|
|
|
return dmisfit
|
|
|
|
def dataObj2Deriv(self, m, v, 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.prob.field(m)
|
|
|
|
R = self.Wd*self.prob.dataResidual(m, u=u)
|
|
|
|
# TODO: abstract to different norms a little cleaner.
|
|
# \/ it goes here. in l2 it is the identity.
|
|
dmisfit = self.prob.Jt_approx(m, self.Wd * self.Wd * self.prob.J_approx(m, v, u=u), u=u)
|
|
|
|
return dmisfit
|
|
|