""" Interface between the models and the fitters. :class:`Fitness` defines the interface that model evaluators can follow. These models can be bundled together into a :func:`FitProblem` and sent to :class:`bumps.fitters.FitDriver` for optimization and uncertainty analysis. Summary of problem attributes:: # Used by fitters nllf(p: Optional[Vector]) -> float # main calculation bounds() -> Tuple(Vector, Vector) # or equivalent sequence setp(p: Vector) -> None getp() -> Vector residuals() -> Vector # for LM, MPFit parameter_residuals() -> Vector # for LM, MPFit constraints_nllf() -> float # for LM, MPFit; constraint cost is spread across the individual residuals randomize() -> None # for multistart resynth_data() -> None # for Monte Carlo resampling of maximum likelihood restore_data() -> None # for Monte Carlo resampling of maximum likelihood name: str # DREAM uses this chisq() -> float chisq_str() -> str labels() -> List[str] summarize() -> str show() -> None load(input_path: str) -> None save(output_path: str) -> None plot(figfile: str, view: str) -> None # Set/used by bumps.cli model_reset() -> None # called by load_model path: str # set by load_model name: str # set by load_model title: str = filename # set by load_moel options: List[str] # from sys.argv[1:] undefined:List[int] # when loading a save .par file, these parameters weren't defined store: str # set by make_store output_path: str # set by make_store simulate_data(noise: float) -> None # for --simulate in opts cov() -> Matrix # for --cov in opts """ # Don't include print_function in imports; since the model coded is exec'd # in the __future__ context of this file, it would force the models to use the # new print function syntax. load_problem() should be moved to its own file # to avoid this issue. from __future__ import division, with_statement __all__ = ['Fitness', 'FitProblem', 'load_problem', 'BaseFitProblem', 'MultiFitProblem'] import sys import os import traceback import logging import warnings import numpy as np from numpy import inf, isnan, NaN from . import parameter, bounds as mbounds from .parameter import to_dict from .formatnum import format_uncertainty from . import util # Abstract base class class Fitness(object): """ Manage parameters, data, and theory function evaluation. See :ref:`fitness` for a detailed explanation. """ def parameters(self): """ return the parameters in the model. model parameters are a hierarchical structure of lists and dictionaries. """ raise NotImplementedError() def to_dict(self): raise NotImplementedError() def update(self): """ Called when parameters have been updated. Any cached values will need to be cleared and the model reevaluated. """ raise NotImplementedError() def numpoints(self): """ Return the number of data points. """ raise NotImplementedError() def nllf(self): """ Return the negative log likelihood value of the current parameter set. """ raise NotImplementedError() def resynth_data(self): """ Generate fake data based on uncertainties in the real data. For Monte Carlo resynth-refit uncertainty analysis. Bootstrapping? """ raise NotImplementedError() def restore_data(self): """ Restore the original data in the model (after resynth). """ raise NotImplementedError() def residuals(self): """ Return residuals for current theory minus data. Used for Levenburg-Marquardt, and for plotting. """ raise NotImplementedError() def save(self, basename): """ Save the model to a file based on basename+extension. This will point to a path to a directory on a remote machine; don't make any assumptions about information stored on the server. Return the set of files saved so that the monitor software can make a pretty web page. """ pass def plot(self, view='linear'): """ Plot the model to the current figure. You only get one figure, but you can make it as complex as you want. This will be saved as a png on the server, and composed onto a results web page. """ pass def no_constraints(): """default constraints function for FitProblem""" return 0 # TODO: refactor FitProblem definition # deprecate the direct use of MultiFitProblem def FitProblem(*args, **kw): """ Return a fit problem instance for the fitness function(s). For an individual model: *fitness* is a :class:`Fitness` instance. For a set of models: *models* is a sequence of :class:`Fitness` instances. *weights* is an optional scale factor for each model *freevars* is :class:`.parameter.FreeVariables` instance defining the per-model parameter assignments. See :ref:`freevariables` for details. Additional parameters: *name* name of the problem *constraints* is a function which returns the negative log likelihood of seeing the parameters independent from the fitness function. Use this for example to check for feasible regions of the search space, or to add constraints that cannot be easily calculated per parameter. Ideally, the constraints nllf will increase as you go farther from the feasible region so that the fit will be directed toward feasible values. *soft_limit* is the constraints function cutoff, beyond which the *penalty_nllf* will be used and *fitness* nllf will not be calculated. *penalty_nllf* is the nllf to use for *fitness* when *constraints* is greater than *soft_limit*. Total nllf is the sum of the parameter nllf, the constraints nllf and the depending on whether constraints is greater than soft_limit, either the fitness nllf or the penalty nllf. """ if len(args) > 0: if isinstance(args[0], (list, tuple)): return MultiFitProblem(args[0], *args[1:], **kw) else: return BaseFitProblem(*args, **kw) else: if 'fitness' in kw: return BaseFitProblem(*args, **kw) else: return MultiFitProblem(*args, **kw) class BaseFitProblem(object): """ See :func:`FitProblem` """ def __init__(self, fitness, name=None, constraints=None, penalty_nllf=np.inf, soft_limit=np.inf, partial=False): self.constraints = constraints self.fitness = fitness self.partial = partial if name is not None: self.name = name else: try: self.name = fitness.name except AttributeError: self.name = 'FitProblem' self.soft_limit = soft_limit self.penalty_nllf = penalty_nllf self.model_reset() # noinspection PyAttributeOutsideInit def model_reset(self): """ Prepare for the fit. This sets the parameters and the bounds properties that the solver is expecting from the fittable object. We also compute the degrees of freedom so that we can return a normalized fit likelihood. If the set of fit parameters changes, then model_reset must be called. """ # print self.model_parameters() all_parameters = parameter.unique(self.model_parameters()) # print "all_parameters",all_parameters self._parameters = parameter.varying(all_parameters) # print "varying",self._parameters self.bounded = [p for p in all_parameters if not isinstance(p.bounds, mbounds.Unbounded)] self.dof = self.model_points() if not self.partial: self.dof -= len(self._parameters) if self.dof <= 0: raise ValueError("Need more data points than fitting parameters") #self.constraints = pars.constraints() def model_parameters(self): """ Parameters associated with the model. """ return self.fitness.parameters() def to_dict(self): return { 'type': type(self).__name__, 'name': self.name, 'fitness': to_dict(self.fitness), 'partial': self.partial, 'soft_limit': self.soft_limit, 'penalty_nllf': self.penalty_nllf, # TODO: constraints may be a function. 'constraints': to_dict(self.constraints), } def model_points(self): """ Number of data points associated with the model. """ return self.fitness.numpoints() def model_update(self): """ Update the model according to the changed parameters. """ if hasattr(self.fitness, 'update'): self.fitness.update() def model_nllf(self): """ Negative log likelihood of seeing data given model. """ return self.fitness.nllf() def simulate_data(self, noise=None): """Simulate data with added noise""" self.fitness.simulate_data(noise=noise) def resynth_data(self): """Resynthesize data with noise from the uncertainty estimates.""" self.fitness.resynth_data() def restore_data(self): """Restore original data after resynthesis.""" self.fitness.restore_data() def valid(self, pvec): """Return true if the point is in the feasible region""" return all(v in p.bounds for p, v in zip(self._parameters, pvec)) def setp(self, pvec): """ Set a new value for the parameters into the model. If the model is valid, calls model_update to signal that the model should be recalculated. Returns True if the value is valid and the parameters were set, otherwise returns False. """ # TODO: do we have to leave the model in an invalid state? # WARNING: don't try to conditionally update the model # depending on whether any model parameters have changed. # For one thing, the model_update below probably calls # the subclass MultiFitProblem.model_update, which signals # the individual models. Furthermore, some parameters may # related to others via expressions, and so a dependency # tree needs to be generated. Whether this is better than # clicker() from SrFit I do not know. for v, p in zip(pvec, self._parameters): p.value = v # TODO: setp_hook is a hack to support parameter expressions in sasview # Don't depend on this existing long term. setp_hook = getattr(self, 'setp_hook', no_constraints) setp_hook() self.model_update() def getp(self): """ Returns the current value of the parameter vector. """ return np.array([p.value for p in self._parameters], 'd') def bounds(self): """Return the bounds fore each parameter a 2 x N array""" limits = [p.bounds.limits for p in self._parameters] return np.array(limits, 'd').T if limits else np.empty((2, 0)) def randomize(self, n=None): """ Generates a random model. *randomize()* sets the model to a random value. *randomize(n)* returns a population of *n* random models. For indefinite bounds, the random population distribution is centered on initial value of the parameter, or 1. if the initial parameter is not finite. """ # TODO: split into two: randomize and random_pop if n is None: self.setp(self.randomize(n=1)[0]) return # Not returning anything since no n is requested target = self.getp() target[~np.isfinite(target)] = 1. pop = [p.bounds.random(n, target=v) for p, v in zip(self._parameters, target)] return np.array(pop).T def parameter_nllf(self): """ Returns negative log likelihood of seeing parameters p. """ s = sum(p.nllf() for p in self.bounded) # print "; ".join("%s %g %g"%(p,p.value,p.nllf()) for p in # self.bounded) return s def constraints_nllf(self): """ Returns the cost of all constraints. """ return self.constraints() if self.constraints else 0. def parameter_residuals(self): """ Returns negative log likelihood of seeing parameters p. """ return [p.residual() for p in self.bounded] @property def has_residuals(self): """ True if the underlying fitness function defines residuals. """ return hasattr(self.fitness, 'residuals') def residuals(self): r""" Return the model residuals. If the model is defined by $y = f(x) + \epsilon$ for normally distributed error in the measurement $y$ equal to $\epsilon \sim N(0, \sigma^2)$, then residuals will be defined by $R = (y - f(x))/\sigma$. If the measurement uncertainty is not normal, then the normal equivalent residuals should be defined so that the Levenberg-Marquardt fit behaves reasonably, and the plot of residuals gives an indication of which points are driving the fit. """ if not hasattr(self.fitness, 'residuals'): ## Fake residuals by using single nllf value as residual #return np.asarray([np.sqrt(self.nllf())]) raise NotImplementedError("model does not define residuals") return self.fitness.residuals() def chisq(self): """ Return sum squared residuals normalized by the degrees of freedom. In the context of a composite fit, the reduced chisq on the individual models only considers the points and the fitted parameters within the individual model. Note that this does not include cost factors due to constraints on the parameters, such as sample_offset ~ N(0,0.01). """ if hasattr(self.fitness, 'chisq'): return self.fitness.chisq() return np.sum(self.residuals() ** 2) / self.dof # return 2*self.nllf()/self.dof def chisq_str(self): """ Return a string representing the chisq equivalent of the nllf. If the model has strictly gaussian independent uncertainties then the negative log likelihood function will return 0.5*sum(residuals**2), which is 1/2*chisq. Since we are printing normalized chisq, we multiply the model nllf by 2/DOF before displaying the value. This is different from the problem nllf function, which includes the cost of the prior parameters and the cost of the penalty constraints in the total nllf. The constraint value is displayed separately. """ pparameter, pconstraints, pmodel = self._nllf_components() chisq_norm, chisq_err = nllf_scale(self) chisq = pmodel * chisq_norm text = format_uncertainty(chisq, chisq_err) constraints = pparameter + pconstraints if constraints > 0.: text += " constraints=%g" % constraints return text def nllf(self, pvec=None): """ compute the cost function for a new parameter set p. this is not simply the sum-squared residuals, but instead is the negative log likelihood of seeing the data given the model parameters plus the negative log likelihood of seeing the model parameters. the value is used for a likelihood ratio test so normalization constants can be ignored. there is an additional penalty value provided by the model which can be used to implement inequality constraints. any penalty should be large enough that it is effectively excluded from the parameter space returned from uncertainty analysis. the model is not actually calculated if the parameter nllf plus the constraint nllf are bigger than *soft_limit*, but instead it is assigned a value of *penalty_nllf*. this will prevent expensive models from spending time computing values in the unfeasible region. """ if pvec is not None: if self.valid(pvec): self.setp(pvec) else: return inf pparameter, pconstraints, pmodel = self._nllf_components() cost = pparameter + pconstraints + pmodel # print(pvec, "cost=",pparameter,"+",pconstraints,"+",pmodel,"=",cost) if isnan(cost): # TODO: make sure errors get back to the user # print "point evaluates to nan" # print parameter.summarize(self._parameters) return inf return cost def _nllf_components(self): try: pparameter = self.parameter_nllf() if isnan(pparameter): # TODO: make sure errors get back to the user info = ["Parameter nllf is wrong"] info += ["%s %g"%(p, p.nllf()) for p in self.bounded] logging.error("\n ".join(info)) pconstraints = self.constraints_nllf() # Note: for hard constraints (which return inf) avoid computing # model even if soft_limit is inf by using strict comparison # since inf <= inf is True but inf < inf is False. pmodel = (self.model_nllf() if pparameter + pconstraints < self.soft_limit else self.penalty_nllf) return pparameter, pconstraints, pmodel except Exception: # TODO: make sure errors get back to the user info = (traceback.format_exc(), parameter.summarize(self._parameters)) logging.error("\n".join(info)) return NaN, NaN, NaN def __call__(self, pvec=None): """ Problem cost function. Returns the negative log likelihood scaled by DOF so that the result looks like the familiar normalized chi-squared. These scale factors will not affect the value of the minimum, though some care will be required when interpreting the uncertainty. """ return 2 * self.nllf(pvec) / self.dof def show(self, _subs={}): """Print the available parameters to the console as a tree.""" print(parameter.format(self.model_parameters(), freevars=_subs)) print("[chisq=%s, nllf=%g]" % (self.chisq_str(), self.nllf())) #print(self.summarize()) def summarize(self): """Return a table of current parameter values with range bars.""" return parameter.summarize(self._parameters) def labels(self): """Return the list of labels, one per fitted parameter.""" return [p.name for p in self._parameters] def save(self, basename): """ Save the problem state for the current parameter set. The underlying Fitness object *save* method is called, if it exists, so that theory values can be saved in a format suitable to the problem. Uses *basename* as the base of any files that are created. """ if hasattr(self.fitness, 'save'): self.fitness.save(basename) def plot(self, p=None, fignum=None, figfile=None, view=None): """ Plot the problem state for the current parameter set. The underlying Fitness object *plot* method is called with *view*. It should produce its plot on the current matplotlib figure. This method will add chisq to the plot and save it to a file. """ if not hasattr(self.fitness, 'plot'): return import pylab if fignum is not None: pylab.figure(fignum) if p is not None: self.setp(p) self.fitness.plot(view=view) pylab.text(0.01, 0.01, 'chisq=%s' % self.chisq_str(), transform=pylab.gca().transAxes) if figfile is not None: pylab.savefig(figfile + "-model.png", format='png') def cov(self): """ Return the covariance matrix as computed by numdifftools from the Hessian matrix for the problem at the current parameter values. """ # TODO: remove from model warnings.warn("use cov and stderr from FitDriver, not problem.", DeprecationWarning) from . import lsqerror H = lsqerror.hessian(self) H, L = lsqerror.perturbed_hessian(H) return lsqerror.chol_cov(L) def stderr(self): """ Return the 1-sigma uncertainty estimate for each parameter and the correlation matrix *R* as computed from the covariance returned by *cov*. """ # TODO: remove from model warnings.warn("use cov and stderr from FitDriver, not problem.", DeprecationWarning) from . import lsqerror c = self.cov() return lsqerror.stderr(c), lsqerror.corr(c) def __getstate__(self): return (self.fitness, self.partial, self.name, self.penalty_nllf, self.soft_limit, self.constraints) def __setstate__(self, state): self.fitness, self.partial, self.name, self.penalty_nllf, \ self.soft_limit, self.constraints = state self.model_reset() class MultiFitProblem(BaseFitProblem): """ Weighted fits for multiple models. """ def __init__(self, models, weights=None, name=None, constraints=None, soft_limit=np.inf, penalty_nllf=1e6, freevars=None): self.partial = False self.constraints = constraints if freevars is None: names = ["M%d" % i for i, _ in enumerate(models)] freevars = parameter.FreeVariables(names=names) self.freevars = freevars self._models = [BaseFitProblem(m, partial=True) for m in models] if weights is None: weights = [1 for _ in models] self.weights = weights self.penalty_nllf = penalty_nllf self.soft_limit = soft_limit self.set_active_model(0) # Set the active model to model 0 self.model_reset() self.name = name @property def models(self): """Iterate over models, with free parameters set from model values""" for i, f in enumerate(self._models): self.freevars.set_model(i) yield f # Restore the active model after cycling self.freevars.set_model(self._active_model_index) # noinspection PyAttributeOutsideInit def set_active_model(self, i): """Use free parameters from model *i*""" self._active_model_index = i self.active_model = self._models[i] self.freevars.set_model(i) def model_parameters(self): """Return parameters from all models""" pars = {'models': [f.model_parameters() for f in self.models]} free = self.freevars.parameters() if free: pars['freevars'] = free return pars def to_dict(self): return { 'type': type(self).__name__, 'name': self.name, 'models': to_dict(self._models), 'weights': self.weights, 'partial': self.partial, 'soft_limit': self.soft_limit, 'penalty_nllf': self.penalty_nllf, # TODO: constraints may be a function. 'constraints': to_dict(self.constraints), 'freevars': to_dict(self.freevars), } def model_points(self): """Return number of points in all models""" return sum(f.model_points() for f in self.models) def model_update(self): """Let all models know they need to be recalculated""" # TODO: consider an "on changed" signal for model updates. # The update function would be associated with model parameters # rather than always recalculating everything. This # allows us to set up fits with 'fast' and 'slow' parameters, # where the fit can quickly explore a subspace where the # computation is cheap before jumping to a more expensive # subspace. SrFit does this. for f in self.models: f.model_update() def model_nllf(self): """Return cost function for all data sets""" return sum(f.model_nllf() for f in self.models) def constraints_nllf(self): """Return the cost function for all constraints""" return (sum(f.constraints_nllf() for f in self.models) + BaseFitProblem.constraints_nllf(self)) def simulate_data(self, noise=None): """Simulate data with added noise""" for f in self.models: f.simulate_data(noise=noise) def resynth_data(self): """Resynthesize data with noise from the uncertainty estimates.""" for f in self.models: f.resynth_data() def restore_data(self): """Restore original data after resynthesis.""" for f in self.models: f.restore_data() @property def has_residuals(self): """ True if all underlying fitness functions define residuals. """ return all(f.has_residuals for f in self.models) def residuals(self): resid = np.hstack([w * f.residuals() for w, f in zip(self.weights, self.models)]) return resid def save(self, basename): for i, f in enumerate(self.models): f.save(basename + "-%d" % (i + 1)) def show(self): for i, f in enumerate(self.models): print("-- Model %d %s" % (i, f.name)) subs = self.freevars.get_model(i) if self.freevars else {} f.show(_subs=subs) print("[overall chisq=%s, nllf=%g]" % (self.chisq_str(), self.nllf())) def plot(self, p=None, fignum=1, figfile=None, view=None): import pylab if p is not None: self.setp(p) for i, f in enumerate(self.models): f.plot(fignum=i + fignum, view=view) pylab.suptitle('Model %d - %s' % (i, f.name)) if figfile is not None: pylab.savefig(figfile + "-model%d.png" % i, format='png') # Note: restore default behaviour of getstate/setstate rather than # inheriting from BaseFitProblem def __getstate__(self): return self.__dict__ def __setstate__(self, state): self.__dict__ = state # TODO: consider adding nllf_scale to FitProblem. ONE_SIGMA = 0.68268949213708585 def nllf_scale(problem): r""" Return the scale factor for reporting the problem nllf as an approximate normalized chisq, along with an associated "uncertainty". The uncertainty is the amount that chisq must change in order for the fit to be significantly better. From Numerical Recipes 15.6: *Confidence Limits on Estimated Model Parameters*, the $1-\sigma$ contour in parameter space corresponds to $\Delta\chi^2 = \text{invCDF}(1-\sigma,k)$ where $1-\sigma \approx 0.6827$ and $k$ is the number of fitting parameters. Since we are reporting the normalized $\chi^2$, this needs to be scaled by the problem degrees of freedom, $n-k$, where $n$ is the number of measurements. To first approximation, the uncertainty in $\chi^2_N$ is $k/(n-k)$ """ dof = getattr(problem, 'dof', np.NaN) if dof <= 0 or np.isnan(dof) or np.isinf(dof): return 1., 0. else: #return 2./dof, 1./dof from scipy.stats import chi2 npars = max(len(problem.getp()), 1) return 2./dof, chi2.ppf(ONE_SIGMA, npars)/dof def load_problem(filename, options=None): """ Load a problem definition from a python script file. sys.argv is set to ``[file] + options`` within the context of the script. The user must define ``problem=FitProblem(...)`` within the script. Raises ValueError if the script does not define problem. """ # Allow relative imports from the bumps model package = util.relative_import(filename) module = os.path.splitext(os.path.basename(filename))[0] ctx = dict(__file__=filename, __package__=package, __name__=module) old_argv = sys.argv sys.argv = [filename] + options if options else [filename] source = open(filename).read() code = compile(source, filename, 'exec') exec(code, ctx) sys.argv = old_argv problem = ctx.get("problem", None) if problem is None: raise ValueError(filename + " requires 'problem = FitProblem(...)'") return problem