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https://github.com/wassname/simpeg.git
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rowanc1
282 lines
8.8 KiB
Python
282 lines
8.8 KiB
Python
from SimPEG import Utils, np, sp
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class BaseObjFunction(object):
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"""docstring for BaseObjFunction"""
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__metaclass__ = Utils.Save.Savable
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beta = Utils.ParameterProperty('beta', default=None, doc='Regularization trade-off parameter')
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debug = False #: Print debugging information
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counter = None #: Set this to a SimPEG.Utils.Counter() if you want to count things
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name = 'BaseObjFunction' #: Name of the objective function
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u_current = None #: The most current evaluated field
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m_current = None #: The most current model
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@property
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def parent(self):
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"""This is the parent of the objective function."""
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return getattr(self,'_parent',None)
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@parent.setter
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def parent(self, p):
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if getattr(self,'_parent',None) is not None:
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print 'Objective function has switched to a new parent!'
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self._parent = p
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def __init__(self, data, reg, **kwargs):
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Utils.setKwargs(self, **kwargs)
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self.data = data
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self.reg = reg
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@Utils.callHooks('startup')
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def startup(self, m0):
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"""startup(m0)
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Called when inversion is first starting.
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"""
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if self.debug: print 'Calling ObjFunction.startup'
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if not hasattr(self.reg, '_mref'):
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print 'Regularization has not set mref. SimPEG will set it to m0.'
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self.reg.mref = m0
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self.phi_d = np.nan
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self.phi_m = np.nan
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self.m_current = m0
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@Utils.timeIt
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def evalFunction(self, m, return_g=True, return_H=True):
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"""evalFunction(m, return_g=True, return_H=True)
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"""
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self.u_current = None
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self.m_current = m
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u = self.data.prob.field(m)
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self.u_current = u
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phi_d = self.dataObj(m, u=u)
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phi_m = self.reg.modelObj(m)
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self.dpred = self.data.dpred(m, u=u) # This is a cheap matrix vector calculation.
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self.phi_d, self.phi_d_last = phi_d, self.phi_d
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self.phi_m, self.phi_m_last = phi_m, self.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()*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=m.dtype )
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out += (operator,)
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return out if len(out) > 1 else out[0]
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@Utils.timeIt
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def dataObj(self, m, u=None):
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"""dataObj(m, u=None)
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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.data.residualWeighted(m, u=u)
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return 0.5*np.vdot(R, R)
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@Utils.timeIt
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def dataObjDeriv(self, m, u=None):
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"""dataObjDeriv(m, u=None)
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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: u = self.data.prob.field(m)
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R = self.data.residualWeighted(m, u=u)
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dmisfit = self.data.prob.Jt(m, self.data.Wd * R, u=u)
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return dmisfit
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@Utils.timeIt
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def dataObj2Deriv(self, m, v, u=None):
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"""dataObj2Deriv(m, v, u=None)
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:param numpy.array m: geophysical model
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:param numpy.array v: vector to multiply
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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: u = self.data.prob.field(m)
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R = self.data.residualWeighted(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.data.prob.Jt_approx(m, self.data.Wd * self.data.Wd * self.data.prob.J_approx(m, v, u=u), u=u)
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return dmisfit
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class BetaSchedule(Utils.Parameter):
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"""BetaSchedule"""
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beta0 = 'guess' #: The initial Beta (regularization parameter)
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beta0_ratio = 0.1 #: When beta0 is set to 'guess', estimateBeta0 is used with this ratio
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coolingFactor = 2.
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coolingRate = 3
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beta = None #: Beta parameter
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def __init__(self, *args, **kwargs):
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Utils.Parameter.__init__(self, *args, **kwargs)
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Utils.setKwargs(self, **kwargs)
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def initialize(self):
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self.beta = self.beta0
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@Utils.requires('parent')
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def nextIter(self):
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if self.beta is 'guess':
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if self.debug: print 'BetaSchedule is estimating Beta0.'
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self.beta = self.estimateBeta0()
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opt = self.parent.parent.opt
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if opt._iter > 0 and opt._iter % self.coolingRate == 0:
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if self.debug: print 'BetaSchedule is cooling Beta. Iteration: %d' % opt._iter
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self.beta /= self.coolingFactor
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return self.beta
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@Utils.requires('parent')
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def estimateBeta0(self):
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"""estimateBeta0(u=None)
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The initial beta is calculated by comparing the estimated
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eigenvalues of JtJ and WtW.
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To estimate the eigenvector of **A**, we will use one iteration
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of the *Power Method*:
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.. math::
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\mathbf{x_1 = A x_0}
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Given this (very course) approximation of the eigenvector,
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we can use the *Rayleigh quotient* to approximate the largest eigenvalue.
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.. math::
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\lambda_0 = \\frac{\mathbf{x^\\top A x}}{\mathbf{x^\\top x}}
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We will approximate the largest eigenvalue for both JtJ and WtW, and
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use some ratio of the quotient to estimate beta0.
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.. math::
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\\beta_0 = \gamma \\frac{\mathbf{x^\\top J^\\top J x}}{\mathbf{x^\\top W^\\top W x}}
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:param numpy.array u: fields
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:param float ratio: desired ratio of the eigenvalues, default is 0.1
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:rtype: float
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:return: beta0
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"""
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objFunc = self.parent
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data = objFunc.data
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m = objFunc.m_current
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u = objFunc.u_current
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if u is None:
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u = data.prob.field(m)
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x0 = np.random.rand(*m.shape)
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t = x0.dot(objFunc.dataObj2Deriv(m,x0,u=u))
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b = x0.dot(objFunc.reg.modelObj2Deriv()*x0)
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return self.beta0_ratio*(t/b)
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