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renaming to ensure capitals
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rowanc1
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import SimPEG
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from SimPEG import Utils, sp, np
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from Optimize import Remember
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from BetaSchedule import Cooling
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from SimPEG.Inverse import IterationPrinters, StoppingCriteria
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class BaseInversion(object):
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"""BaseInversion(prob, reg, opt, data, **kwargs)
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"""
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__metaclass__ = Utils.Save.Savable
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maxIter = 1 #: Maximum number of iterations
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name = 'BaseInversion'
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debug = False #: Print debugging information
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comment = '' #: Used by some functions to indicate what is going on in the algorithm
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counter = None #: Set this to a SimPEG.Utils.Counter() if you want to count things
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beta0 = None #: The initial Beta (regularization parameter)
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beta0_ratio = 0.1 #: When beta0 is set to None, estimateBeta0 is used with this ratio
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def __init__(self, prob, reg, opt, data, **kwargs):
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Utils.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.data = data
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self.opt.parent = self
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self.stoppers = [StoppingCriteria.iteration]
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# Check if we have inserted printers into the optimization
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if IterationPrinters.phi_d not in self.opt.printers:
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self.opt.printers.insert(1,IterationPrinters.beta)
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self.opt.printers.insert(2,IterationPrinters.phi_d)
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self.opt.printers.insert(3,IterationPrinters.phi_m)
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if not hasattr(opt, '_bfgsH0') and hasattr(opt, 'bfgsH0'): # Check if it has been set by the user and the default is not being used.
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print 'Setting bfgsH0 to the inverse of the modelObj2Deriv. Done using direct methods.'
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opt.bfgsH0 = SimPEG.Solver(reg.modelObj2Deriv())
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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.data.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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@Utils.timeIt
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def run(self, m0):
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"""run(m0)
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Runs the inversion!
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"""
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self.startup(m0)
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while True:
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self.doStartIteration()
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self.m = self.opt.minimize(self.evalFunction, self.m)
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self.doEndIteration()
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if self.stoppingCriteria(): break
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self.printDone()
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self.finish()
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return self.m
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@Utils.callHooks('startup')
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def startup(self, m0):
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"""
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**startup** is called at the start of any new run call.
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:param numpy.ndarray x0: initial x
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:rtype: None
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:return: None
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"""
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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.m = m0
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self._iter = 0
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self._beta = None
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self.phi_d_last = np.nan
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self.phi_m_last = np.nan
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@Utils.callHooks('doStartIteration')
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def doStartIteration(self):
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"""
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**doStartIteration** is called at the end of each run iteration.
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:rtype: None
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:return: None
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"""
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self._beta = self.getBeta()
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@Utils.callHooks('doEndIteration')
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def doEndIteration(self):
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"""
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**doEndIteration** is called at the end of each run iteration.
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:rtype: None
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:return: None
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"""
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# store old values
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self.phi_d_last = self.phi_d
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self.phi_m_last = self.phi_m
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self._iter += 1
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def getBeta(self):
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return self.beta0
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def estimateBeta0(self, u=None, ratio=0.1):
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"""estimateBeta0(u=None, ratio=0.1)
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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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if u is None:
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u = self.prob.field(self.m)
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x0 = np.random.rand(*self.m.shape)
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t = x0.dot(self.dataObj2Deriv(self.m,x0,u=u))
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b = x0.dot(self.reg.modelObj2Deriv()*x0)
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return ratio*(t/b)
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def stoppingCriteria(self):
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if self.debug: print 'checking stoppingCriteria'
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return Utils.checkStoppers(self, self.stoppers)
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def printDone(self):
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"""
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**printDone** is called at the end of the inversion routine.
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"""
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Utils.printStoppers(self, self.stoppers)
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@Utils.callHooks('finish')
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def finish(self):
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"""finish()
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**finish** is called at the end of the optimization.
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"""
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pass
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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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u = self.prob.field(m)
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if self._iter is 0 and self._beta is None:
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self._beta = self.beta0 = self.estimateBeta0(u=u,ratio=self.beta0_ratio)
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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.dpred = self.prob.dpred(m, u=u) # This is a cheap matrix vector calculation.
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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()*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.Wd*self.prob.dataResidual(m, self.data, u=u)
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R = Utils.mkvc(R)
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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:
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u = self.prob.field(m)
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R = self.Wd*self.prob.dataResidual(m, self.data, 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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@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:
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u = self.prob.field(m)
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R = self.Wd*self.prob.dataResidual(m, self.data, 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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def save(self, group):
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group.attrs['phi_d'] = self.phi_d
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group.attrs['phi_m'] = self.phi_m
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group.setArray('m', self.m)
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group.setArray('dpred', self.dpred)
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class Inversion(Cooling, Remember, BaseInversion):
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maxIter = 10
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name = "SimPEG Inversion"
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def __init__(self, prob, reg, opt, data, **kwargs):
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BaseInversion.__init__(self, prob, reg, opt, data, **kwargs)
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self.stoppers.append(StoppingCriteria.phi_d_target_Inversion)
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if StoppingCriteria.phi_d_target_Minimize not in self.opt.stoppers:
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self.opt.stoppers.append(StoppingCriteria.phi_d_target_Minimize)
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class TimeSteppingInversion(Remember, BaseInversion):
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"""
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A slightly different view on regularization parameters,
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let Beta be viewed as 1/dt, and timestep by updating the
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reference model every optimization iteration.
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"""
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maxIter = 1
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name = "Time-Stepping SimPEG Inversion"
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def __init__(self, prob, reg, opt, data, **kwargs):
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BaseInversion.__init__(self, prob, reg, opt, data, **kwargs)
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self.stoppers.append(StoppingCriteria.phi_d_target_Inversion)
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if StoppingCriteria.phi_d_target_Minimize not in self.opt.stoppers:
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self.opt.stoppers.append(StoppingCriteria.phi_d_target_Minimize)
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def _startup_TimeSteppingInversion(self, m0):
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def _doEndIteration_updateMref(self, xt):
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if self.debug: 'Updating the reference model.'
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self.parent.reg.mref = self.xc
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self.opt.hook(_doEndIteration_updateMref, overwrite=True)
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