mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-30 23:29:21 +08:00
Rowan Cockett
212 lines
6.8 KiB
Python
212 lines
6.8 KiB
Python
import numpy as np
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import scipy.sparse as sp
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import SimPEG
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from SimPEG.utils import sdiag, mkvc, setKwargs, checkStoppers
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class Inversion(object):
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"""docstring for Inversion"""
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maxIter = 10
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name = 'SimPEG Inversion'
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def __init__(self, prob, reg, opt, **kwargs):
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setKwargs(self, **kwargs)
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self.prob = prob
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self.reg = reg
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self.opt = opt
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self.opt.parent = self
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self.stoppers = [SimPEG.inverse.StoppingCriteria.iteration, SimPEG.inverse.StoppingCriteria.phi_d_target_Inversion]
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# Check if we have inserted printers into the optimization
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if not np.any([p is SimPEG.inverse.IterationPrinters.phi_d for p in self.opt.printers]):
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self.opt.printers.insert(1,SimPEG.inverse.IterationPrinters.beta)
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self.opt.printers.insert(2,SimPEG.inverse.IterationPrinters.phi_d)
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self.opt.printers.insert(3,SimPEG.inverse.IterationPrinters.phi_m)
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self.opt.stoppers.append(SimPEG.inverse.StoppingCriteria.phi_d_target_Minimize)
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@property
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def Wd(self):
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"""
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Standard deviation weighting matrix.
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"""
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if getattr(self,'_Wd',None) is None:
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eps = np.linalg.norm(mkvc(self.prob.dobs),2)*1e-5
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self._Wd = 1/(abs(self.prob.dobs)*self.prob.std+eps)
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return self._Wd
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@property
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def phi_d_target(self):
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"""
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target for phi_d
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By default this is the number of data.
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Note that we do not set the target if it is None, but we return the default value.
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"""
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if getattr(self, '_phi_d_target', None) is None:
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return self.prob.dobs.size #
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return self._phi_d_target
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@phi_d_target.setter
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def phi_d_target(self, value):
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self._phi_d_target = value
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def run(self, m0):
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m = m0
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self._iter = 0
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self._beta = None
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while True:
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self._beta = self.getBeta()
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m = self.opt.minimize(self.evalFunction,m)
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self._iter += 1
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if self.stoppingCriteria(): break
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return m
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beta0 = 1.e2
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beta_coolingFactor = 5.
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def getBeta(self):
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if self._beta is None:
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return self.beta0
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return self._beta / self.beta_coolingFactor
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def stoppingCriteria(self):
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return checkStoppers(self, self.stoppers)
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def evalFunction(self, m, return_g=True, return_H=True):
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u = self.prob.field(m)
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phi_d = self.dataObj(m, u)
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phi_m = self.reg.modelObj(m)
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self.phi_d = phi_d
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self.phi_m = phi_m
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f = phi_d + self._beta * phi_m
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out = (f,)
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if return_g:
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phi_dDeriv = self.dataObjDeriv(m, u=u)
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phi_mDeriv = self.reg.modelObjDeriv(m)
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g = phi_dDeriv + self._beta * phi_mDeriv
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out += (g,)
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if return_H:
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def H_fun(v):
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phi_d2Deriv = self.dataObj2Deriv(m, v, u=u)
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phi_m2Deriv = self.reg.modelObj2Deriv(m)*v
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return phi_d2Deriv + self._beta * phi_m2Deriv
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operator = sp.linalg.LinearOperator( (m.size, m.size), H_fun, dtype=float )
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out += (operator,)
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return out if len(out) > 1 else out[0]
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def dataObj(self, m, u=None):
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"""
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:param numpy.array m: geophysical model
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:param numpy.array u: fields
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:rtype: float
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:return: data misfit
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The data misfit using an l_2 norm is:
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.. math::
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\mu_\\text{data} = {1\over 2}\left| \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs}) \\right|_2^2
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Where P is a projection matrix that brings the field on the full domain to the data measurement locations;
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u is the field of interest; d_obs is the observed data; and W is the weighting matrix.
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"""
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# TODO: ensure that this is a data is vector and Wd is a matrix.
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R = self.Wd*self.prob.dataResidual(m, u=u)
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R = mkvc(R)
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return 0.5*np.vdot(R, R)
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def dataObjDeriv(self, m, u=None):
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"""
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:param numpy.array m: geophysical model
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:param numpy.array u: fields
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:rtype: numpy.array
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:return: data misfit derivative
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The data misfit using an l_2 norm is:
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.. math::
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\mu_\\text{data} = {1\over 2}\left| \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs}) \\right|_2^2
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If the field, u, is provided, the calculation of the data is fast:
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.. math::
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\mathbf{d}_\\text{pred} = \mathbf{Pu(m)}
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\mathbf{R} = \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs})
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Where P is a projection matrix that brings the field on the full domain to the data measurement locations;
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u is the field of interest; d_obs is the observed data; and W is the weighting matrix.
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The derivative of this, with respect to the model, is:
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.. math::
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\\frac{\partial \mu_\\text{data}}{\partial \mathbf{m}} = \mathbf{J}^\\top \mathbf{W \circ R}
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"""
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if u is None:
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u = self.prob.field(m)
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R = self.Wd*self.prob.dataResidual(m, u=u)
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dmisfit = self.prob.Jt(m, self.Wd * R, u=u)
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return dmisfit
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def dataObj2Deriv(self, m, v, u=None):
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"""
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:param numpy.array m: geophysical model
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:param numpy.array u: fields
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:rtype: numpy.array
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:return: data misfit derivative
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The data misfit using an l_2 norm is:
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.. math::
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\mu_\\text{data} = {1\over 2}\left| \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs}) \\right|_2^2
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If the field, u, is provided, the calculation of the data is fast:
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.. math::
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\mathbf{d}_\\text{pred} = \mathbf{Pu(m)}
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\mathbf{R} = \mathbf{W} \circ (\mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs})
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Where P is a projection matrix that brings the field on the full domain to the data measurement locations;
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u is the field of interest; d_obs is the observed data; and W is the weighting matrix.
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The derivative of this, with respect to the model, is:
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.. math::
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\\frac{\partial \mu_\\text{data}}{\partial \mathbf{m}} = \mathbf{J}^\\top \mathbf{W \circ R}
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\\frac{\partial^2 \mu_\\text{data}}{\partial^2 \mathbf{m}} = \mathbf{J}^\\top \mathbf{W \circ W J}
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"""
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if u is None:
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u = self.prob.field(m)
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R = self.Wd*self.prob.dataResidual(m, u=u)
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# TODO: abstract to different norms a little cleaner.
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# \/ it goes here. in l2 it is the identity.
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dmisfit = self.prob.Jt_approx(m, self.Wd * self.Wd * self.prob.J_approx(m, v, u=u), u=u)
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return dmisfit
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