# Bumps 1.0.0a13 documentation

## bumps.fitters

# Source code for bumps.fitters

    """
    Interfaces to various optimizers.
    """

    import sys
    import warnings

    # CRUFT: time.clock() removed from python 3.8
    try:
        from time import perf_counter
    except ImportError:
        from time import clock as perf_counter

    import numpy as np

    from . import monitor
    from . import initpop
    from . import lsqerror

    from .history import History
    from .formatnum import format_uncertainty
    from .fitproblem import nllf_scale

    from .dream import MCMCModel

    class ConsoleMonitor(monitor.TimedUpdate):
        """
        Display fit progress on the console
        """

        def __init__(self, problem, progress=1, improvement=30):
            monitor.TimedUpdate.__init__(self, progress=progress, improvement=improvement)
            self.problem = problem

        def show_progress(self, history):
            scale, err = nllf_scale(self.problem)
            chisq = format_uncertainty(scale * history.value[0], err)
            print("step", history.step[0], "cost", chisq)
            sys.stdout.flush()

        def show_improvement(self, history):
            # print("step",history.step[0],"chisq",history.value[0])
            p = self.problem.getp()
            try:
                self.problem.setp(history.point[0])
                print(self.problem.summarize())
            finally:
                self.problem.setp(p)
            sys.stdout.flush()

    class CheckpointMonitor(monitor.TimedUpdate):
        """
        Periodically save fit state so that it can be resumed later.
        """

        #: Function to call at each checkpoint.
        checkpoint = None  # type: Callable[None, None]

        def __init__(self, checkpoint, progress=60 * 30):
            monitor.TimedUpdate.__init__(self, progress=progress, improvement=np.inf)
            self.checkpoint = checkpoint
            self._first = True

        def show_progress(self, history):
            # Skip the first checkpoint since it only contains the
            # start/resume state
            if self._first:
                self._first = False
            else:
                self.checkpoint(history)

        def show_improvement(self, history):
            pass

    class StepMonitor(monitor.Monitor):
        """
        Collect information at every step of the fit and save it to a file.

        *fid* is the file to save the information to
        *fields* is the list of "step|time|value|point" fields to save

        The point field should be last in the list.
        """

        FIELDS = ["step", "time", "value", "point"]

        def __init__(self, problem, fid, fields=FIELDS):
            if any(f not in self.FIELDS for f in fields):
                raise ValueError("invalid monitor field")
            self.fid = fid
            self.fields = fields
            self.problem = problem
            self._pattern = "%%(%s)s\n" % (")s %(".join(fields))
            fid.write("# " + " ".join(fields) + "\n")

        def config_history(self, history):
            history.requires(time=1, value=1, point=1, step=1)

        def __call__(self, history):
            point = " ".join("%.15g" % v for v in history.point[0])
            time = "%g" % history.time[0]
            step = "%d" % history.step[0]
            scale, _ = nllf_scale(self.problem)
            value = "%.15g" % (scale * history.value[0])
            out = self._pattern % dict(point=point, time=time, value=value, step=step)
            self.fid.write(out)

    class MonitorRunner(object):
        """
        Adaptor which allows solvers to accept progress monitors.
        """

        def __init__(self, monitors, problem):
            if monitors is None:
                monitors = [ConsoleMonitor(problem)]
            self.monitors = monitors
            self.history = History(time=1, step=1, point=1, value=1, population_points=1, population_values=1)
            for M in self.monitors:
                M.config_history(self.history)
            self._start = perf_counter()

        def __call__(self, step, point, value, population_points=None, population_values=None):
            self.history.update(
                time=perf_counter() - self._start,
                step=step,
                point=point,
                value=value,
                population_points=population_points,
                population_values=population_values,
            )
            for M in self.monitors:
                M(self.history)

    class FitBase(object):
        """
        FitBase defines the interface from bumps models to the various fitting
        engines available within bumps.

        Each engine is defined in its own class with a specific set of attributes
        and methods.

        The *name* attribute is the name of the optimizer.  This is just a simple
        string.

        The *settings* attribute is a list of pairs (name, default), where the
        names are defined as fields in FitOptions.  A best attempt should be
        made to map the fit options for the optimizer to the standard fit options,
        since each of these becomes a new command line option when running
        bumps.  If that is not possible, then a new option should be added
        to FitOptions.  A plugin architecture might be appropriate here, if
        there are reasons why specific problem domains might need custom fitters,
        but this is not yet supported.

        Each engine takes a fit problem in its constructor.

        The :meth:`solve` method runs the fit.  It accepts a
        monitor to track updates, a mapper to distribute work and
        key-value pairs defining the settings.

        There are a number of optional methods for the fitting engines.  Basically,
        all the methods in :class:`FitDriver` first check if they are specialized
        in the fit engine before performing a default action.

        The *load*/*save* methods load and save the fitter state in a given
        directory with a specific base file name.  The fitter can choose a file
        extension to add to the base name.  Some care is needed to be sure that
        the extension doesn't collide with other extensions such as .mon for
        the fit monitor.

        The *plot* method shows any plots to help understand the performance of
        the fitter, such as a convergence plot showing the the range of values
        in the population over time, as well as plots of the parameter uncertainty
        if available.  The plot should work within  is given a figure canvas to work with

        The *stderr*/*cov* methods should provide summary statistics for the
        parameter uncertainties.  Some fitters, such as MCMC, will compute these
        directly from the population.  Others, such as BFGS, will produce an
        estimate of the uncertainty as they go along.  If the fitter does not
        provide these estimates, then they will be computed from numerical
        derivatives at the minimum in the FitDriver method.
        """

        def __init__(self, problem):
            """Fit the models and show the results"""
            self.problem = problem

        def solve(self, monitors=None, mapper=None, **options):
            raise NotImplementedError()

    class MultiStart(FitBase):
        """
        Multi-start monte carlo fitter.

        This fitter wraps a local optimizer, restarting it a number of times
        to give it a chance to find a different local minimum.  If the keep_best
        option is True, then restart near the best fit, otherwise restart at
        random.
        """

        name = "Multistart Monte Carlo"
        settings = [("starts", 100)]

        def __init__(self, fitter):
            FitBase.__init__(self, fitter.problem)
            self.fitter = fitter

        def solve(self, monitors=None, mapper=None, **options):
            # TODO: need better way of tracking progress
            import logging

            starts = options.pop("starts", 1)
            reset = not options.pop("keep_best", True)
            f_best = np.inf
            x_best = self.problem.getp()
            for _ in range(max(starts, 1)):
                logging.info("multistart round %d", _)
                x, fx = self.fitter.solve(monitors=monitors, mapper=mapper, **options)
                if fx < f_best:
                    x_best, f_best = x, fx
                    logging.info("multistart f(x),x: %s %s", str(fx), str(x_best))
                if reset:
                    self.problem.randomize()
                else:
                    # Jitter
                    self.problem.setp(x_best)
                    pop = initpop.eps_init(1, self.problem.getp(), self.problem.bounds(), use_point=False, eps=1e-3)
                    self.problem.setp(pop[0])
            return x_best, f_best

    class DEFit(FitBase):
        """
        Classic Storn and Price differential evolution optimizer.
        """

        name = "Differential Evolution"
        id = "de"
        settings = [
            ("steps", 1000),
            ("pop", 10),
            ("CR", 0.9),
            ("F", 2.0),
            ("ftol", 1e-8),
            ("xtol", 1e-6),  # ('stop', ''),
        ]

        def solve(self, monitors=None, abort_test=None, mapper=None, **options):
            if abort_test is None:
                abort_test = lambda: False
            options = _fill_defaults(options, self.settings)
            from .mystic.optimizer import de
            from .mystic.solver import Minimizer
            from .mystic import stop

            if monitors is None:
                monitors = [ConsoleMonitor(self.problem)]
            if mapper is not None:
                _mapper = lambda p, v: mapper(v)
            else:
                _mapper = lambda p, v: list(map(self.problem.nllf, v))
            resume = hasattr(self, "state")
            steps = options["steps"] + (self.state["step"][-1] if resume else 0)
            strategy = de.DifferentialEvolution(
                npop=options["pop"], CR=options["CR"], F=options["F"], crossover=de.c_bin, mutate=de.rand1u
            )
            success = parse_tolerance(options)
            failure = stop.Steps(steps)
            self.history = History()
            # Step adds to current step number if resume
            minimize = Minimizer(
                strategy=strategy,
                problem=self.problem,
                history=self.history,
                monitors=monitors,
                success=success,
                failure=failure,
            )
            if resume:
                self.history.restore(self.state)
            x = minimize(mapper=_mapper, abort_test=abort_test, resume=resume)
            # print(minimize.termination_condition())
            # with open("/tmp/evals","a") as fid:
            #   print >>fid,minimize.history.value[0],minimize.history.step[0],\
            #       minimize.history.step[0]*options['pop']*len(self.problem.getp())
            return x, self.history.value[0]

        def load(self, input_path):
            self.state = load_history(input_path)

        def save(self, output_path):
            save_history(output_path, self.history.snapshot())

    def parse_tolerance(options):
        from .mystic import stop

        if options.get("stop", ""):
            return stop.parse_condition(options["stop"])

        xtol, ftol = options["xtol"], options["ftol"]
        if xtol == 0:
            if ftol == 0:
                return None
            if ftol < 0:
                return stop.Rf(-ftol, scaled=True)
            return stop.Rf(ftol, scaled=False)
        else:
            if xtol == 0:
                return None
            if xtol < 0:
                return stop.Rx(-xtol, scaled=True)
            return stop.Rx(xtol, scaled=False)

    def _history_file(path):
        return path + "-history.json"

    def load_history(path):
        """
        Load fitter details from a history file.
        """
        import json

        with open(_history_file(path), "r") as fid:
            return json.load(fid)

    def save_history(path, state):
        """
        Save fitter details to a history file as JSON.

        The content of the details are fitter specific.
        """
        import json

        with open(_history_file(path), "w") as fid:
            json.dump(state, fid)

    class BFGSFit(FitBase):
        """
        BFGS quasi-newton optimizer.

        BFGS estimates Hessian and its Cholesky decomposition, but initial
        tests give uncertainties quite different from the directly computed
        Jacobian in Levenburg-Marquardt or the Hessian estimated at the
        minimum by numerical differentiation.

        To use the internal 'H' and 'L' and save some computation time, then
        use::

            C = lsqerror.chol_cov(fit.result['L'])
            stderr = lsqerror.stderr(C)
        """

        name = "Quasi-Newton BFGS"
        id = "newton"
        settings = [("steps", 3000), ("starts", 1), ("ftol", 1e-6), ("xtol", 1e-12)]

        def solve(self, monitors=None, abort_test=None, mapper=None, **options):
            if abort_test is None:
                abort_test = lambda: False
            options = _fill_defaults(options, self.settings)
            from .quasinewton import quasinewton

            self._update = MonitorRunner(problem=self.problem, monitors=monitors)
            result = quasinewton(
                fn=self.problem.nllf,
                x0=self.problem.getp(),
                monitor=self._monitor,
                abort_test=abort_test,
                itnlimit=options["steps"],
                gradtol=options["ftol"],
                steptol=1e-12,
                macheps=1e-8,
                eta=1e-8,
            )
            self.result = result
            # code = result['status']
            # from .quasinewton import STATUS
            # print("%d: %s, x=%s, fx=%s"
            #      % (code, STATUS[code], result['x'], result['fx']))
            return result["x"], result["fx"]

        def _monitor(self, step, x, fx):
            self._update(step=step, point=x, value=fx, population_points=[x], population_values=[fx])
            return True

    class PSFit(FitBase):
        """
        Particle swarm optimizer.
        """

        name = "Particle Swarm"
        id = "ps"
        settings = [("steps", 3000), ("pop", 1)]

        def solve(self, monitors=None, mapper=None, **options):
            options = _fill_defaults(options, self.settings)
            if mapper is None:
                mapper = lambda x: list(map(self.problem.nllf, x))
            from .random_lines import particle_swarm

            self._update = MonitorRunner(problem=self.problem, monitors=monitors)
            low, high = self.problem.bounds()
            cfo = dict(
                parallel_cost=mapper, n=len(low), x0=self.problem.getp(), x1=low, x2=high, f_opt=0, monitor=self._monitor
            )
            npop = int(cfo["n"] * options["pop"])

            result = particle_swarm(cfo, npop, maxiter=options["steps"])
            satisfied_sc, n_feval, f_best, x_best = result

            return x_best, f_best

        def _monitor(self, step, x, fx, k):
            self._update(step=step, point=x[:, k], value=fx[k], population_points=x.T, population_values=fx)
            return True

    class RLFit(FitBase):
        """
        Random lines optimizer.
        """

        name = "Random Lines"
        id = "rl"
        settings = [("steps", 3000), ("starts", 20), ("pop", 0.5), ("CR", 0.9)]

        def solve(self, monitors=None, abort_test=None, mapper=None, **options):
            if abort_test is None:
                abort_test = lambda: False
            options = _fill_defaults(options, self.settings)
            if mapper is None:
                mapper = lambda x: list(map(self.problem.nllf, x))
            from .random_lines import random_lines

            self._update = MonitorRunner(problem=self.problem, monitors=monitors)
            low, high = self.problem.bounds()
            cfo = dict(
                parallel_cost=mapper, n=len(low), x0=self.problem.getp(), x1=low, x2=high, f_opt=0, monitor=self._monitor
            )
            npop = max(int(cfo["n"] * options["pop"]), 3)

            result = random_lines(cfo, npop, abort_test=abort_test, maxiter=options["steps"], CR=options["CR"])
            satisfied_sc, n_feval, f_best, x_best = result

            return x_best, f_best

        def _monitor(self, step, x, fx, k):
            # print "rl best",k, x.shape,fx.shape
            self._update(step=step, point=x[:, k], value=fx[k], population_points=x.T, population_values=fx)
            return True

    class PTFit(FitBase):
        """
        Parallel tempering optimizer.
        """

        name = "Parallel Tempering"
        id = "pt"
        settings = [("steps", 400), ("nT", 24), ("CR", 0.9), ("burn", 100), ("Tmin", 0.1), ("Tmax", 10)]

        def solve(self, monitors=None, mapper=None, **options):
            options = _fill_defaults(options, self.settings)
            # TODO: no mapper??
            from .partemp import parallel_tempering

            self._update = MonitorRunner(problem=self.problem, monitors=monitors)
            t = np.logspace(np.log10(options["Tmin"]), np.log10(options["Tmax"]), options["nT"])
            history = parallel_tempering(
                nllf=self.problem.nllf,
                p=self.problem.getp(),
                bounds=self.problem.bounds(),
                # logfile="partemp.dat",
                T=t,
                CR=options["CR"],
                steps=options["steps"],
                burn=options["burn"],
                monitor=self._monitor,
            )
            return history.best_point, history.best

        def _monitor(self, step, x, fx, P, E):
            self._update(step=step, point=x, value=fx, population_points=P, population_values=E)
            return True

    class SimplexFit(FitBase):
        """
        Nelder-Mead simplex optimizer.
        """

        name = "Nelder-Mead Simplex"
        id = "amoeba"
        settings = [("steps", 1000), ("starts", 1), ("radius", 0.15), ("xtol", 1e-6), ("ftol", 1e-8)]

        def solve(self, monitors=None, abort_test=None, mapper=None, **options):
            from .simplex import simplex

            if abort_test is None:
                abort_test = lambda: False
            options = _fill_defaults(options, self.settings)
            # TODO: no mapper??
            self._update = MonitorRunner(problem=self.problem, monitors=monitors)
            # print("bounds", self.problem.bounds())
            result = simplex(
                f=self.problem.nllf,
                x0=self.problem.getp(),
                bounds=self.problem.bounds(),
                abort_test=abort_test,
                update_handler=self._monitor,
                maxiter=options["steps"],
                radius=options["radius"],
                xtol=options["xtol"],
                ftol=options["ftol"],
            )
            # Let simplex propose the starting point for the next amoeba
            # fit in a multistart amoeba context.  If the best is always
            # used, the fit can get stuck in a local minimum.
            self.problem.setp(result.next_start)
            # print("amoeba %s %s"%(result.x,result.fx))
            return result.x, result.fx

        def _monitor(self, k, n, x, fx):
            self._update(step=k, point=x[0], value=fx[0], population_points=x, population_values=fx)
            return True

    class MPFit(FitBase):
        """
        MPFit optimizer.
        """

        name = "Levenberg-Marquardt"
        id = "lm"
        settings = [("steps", 200), ("ftol", 1e-10), ("xtol", 1e-10)]

        def solve(self, monitors=None, abort_test=None, mapper=None, **options):
            from .mpfit import mpfit

            if abort_test is None:
                abort_test = lambda: False
            options = _fill_defaults(options, self.settings)
            self._low, self._high = self.problem.bounds()
            self._update = MonitorRunner(problem=self.problem, monitors=monitors)
            self._abort = abort_test
            x0 = self.problem.getp()
            parinfo = []
            for low, high in zip(*self.problem.bounds()):
                parinfo.append(
                    {
                        #'value': None,  # passed in by xall instead
                        #'fixed': False,  # everything is varying
                        "limited": (np.isfinite(low), np.isfinite(high)),
                        "limits": (low, high),
                        #'parname': '',  # could probably ask problem for this...
                        # From the code, default step size is sqrt(eps)*abs(value)
                        # or eps if value is 0.  This seems okay.  The other
                        # other alternative is to limit it by bounds.
                        #'step': 0,  # compute step automatically
                        #'mpside': 0,  # 1, -1 or 2 for right-, left- or 2-sided deriv
                        #'mpmaxstep': 0.,  # max step for this parameter
                        #'tied': '',  # parameter expressions tying fit parameters
                        #'mpprint': 1,  # print the parameter value when iterating
                    }
                )

            result = mpfit(
                fcn=self._residuals,
                xall=x0,
                parinfo=parinfo,
                autoderivative=True,
                fastnorm=True,
                double=0,  # use single precision machine epsilon for derivative step
                # damp=0,  # no damping when damp=0
                # Stopping conditions
                ftol=options["ftol"],
                xtol=options["xtol"],
                # gtol=1e-100, # exclude gtol test
                maxiter=options["steps"],
                # Progress monitor
                iterfunct=self._monitor,
                nprint=1,  # call monitor each iteration
                quiet=True,  # leave it to monitor to print any info
                # Returns values
                nocovar=True,  # use our own covar calculation for consistency
            )

            if result.status > 0:
                x, fx = result.params, result.fnorm
            else:
                x, fx = None, None

            return x, fx

        def _monitor(self, fcn, p, k, fnorm, functkw=None, parinfo=None, quiet=0, dof=None, **extra):
            self._update(k, p, fnorm)

        def _residuals(self, p, fjac=None):
            if self._abort():
                return -1, None

            self.problem.setp(p)
            # treat prior probabilities on the parameters as additional
            # measurements
            residuals = np.hstack((self.problem.residuals().flat, self.problem.parameter_residuals()))
            # Tally costs for broken constraints
            extra_cost, failing_constraints = self.problem.constraints_nllf()
            # Spread the cost over the residuals.  Since we are smoothly increasing
            # residuals as we leave the boundary, this should push us back into the
            # boundary (within tolerance) during the lm fit.
            residuals += np.sign(residuals) * (extra_cost / len(residuals))
            return 0, residuals

    class LevenbergMarquardtFit(FitBase):
        """
        Levenberg-Marquardt optimizer.
        """

        name = "Levenberg-Marquardt (scipy.leastsq)"
        id = "scipy.leastsq"
        settings = [("steps", 200), ("ftol", 1.5e-8), ("xtol", 1.5e-8)]
        # LM also has
        #    gtol: orthoganality between jacobian columns
        #    epsfcn: numerical derivative step size
        #    factor: initial radius
        #    diag: variable scale factors to bring them near 1

        def solve(self, monitors=None, abort_test=None, mapper=None, **options):
            from scipy import optimize

            if abort_test is None:
                abort_test = lambda: False
            options = _fill_defaults(options, self.settings)
            self._low, self._high = self.problem.bounds()
            self._update = MonitorRunner(problem=self.problem, monitors=monitors)
            x0 = self.problem.getp()
            maxfev = options["steps"] * (len(x0) + 1)
            result = optimize.leastsq(
                self._bounded_residuals,
                x0,
                ftol=options["ftol"],
                xtol=options["xtol"],
                maxfev=maxfev,
                epsfcn=1e-8,
                full_output=True,
            )
            x, cov_x, info, mesg, success = result
            if not 1 <= success <= 4:
                # don't treat "reached maxfev" as a true failure
                if "reached maxfev" in mesg:
                    # unless the x values are bad
                    if not np.all(np.isfinite(x)):
                        x = None
                        mesg = "Levenberg-Marquardt fit failed with bad values"
                else:
                    x = None
            self._cov = cov_x if x is not None else None
            # compute one last time with x forced inside the boundary, and using
            # problem.nllf as returned by other optimizers.  We will ignore the
            # covariance output and calculate it again ourselves.  Not ideal if
            # f is expensive, but it will be consistent with other optimizers.
            if x is not None:
                x += self._stray_delta(x)
                self.problem.setp(x)
                fx = self.problem.nllf()
            else:
                fx = None
            return x, fx

        def _bounded_residuals(self, p):
            # Force the fit point into the valid region
            stray = self._stray_delta(p)
            stray_cost = np.sum(stray**2)
            if stray_cost > 0:
                stray_cost += 1e6
            self.problem.setp(p + stray)
            # treat prior probabilities on the parameters as additional
            # measurements
            residuals = np.hstack((self.problem.residuals().flat, self.problem.parameter_residuals()))
            # Tally costs for straying outside the boundaries plus other costs
            constraints_cost, failing_constraints = self.problem.constraints_nllf()
            extra_cost = stray_cost + constraints_cost
            # Spread the cost over the residuals.  Since we are smoothly increasing
            # residuals as we leave the boundary, this should push us back into the
            # boundary (within tolerance) during the lm fit.
            residuals += np.sign(residuals) * (extra_cost / len(residuals))
            return residuals

        def _stray_delta(self, p):
            """calculate how far point is outside the boundary"""
            return np.where(p < self._low, self._low - p, 0) + np.where(p > self._high, self._high - p, 0)

        def cov(self):
            return self._cov

    class SnobFit(FitBase):
        name = "SNOBFIT"
        id = "snobfit"
        settings = [("steps", 200)]

        def solve(self, monitors=None, mapper=None, **options):
            options = _fill_defaults(options, self.settings)
            # TODO: no mapper??
            from snobfit.snobfit import snobfit

            self._update = MonitorRunner(problem=self.problem, monitors=monitors)
            x, fx, _ = snobfit(self.problem, self.problem.getp(), self.problem.bounds(), fglob=0, callback=self._monitor)
            return x, fx

        def _monitor(self, k, x, fx, improved):
            # TODO: snobfit does have a population...
            self._update(step=k, point=x, value=fx, population_points=[x], population_values=[fx])

    class DreamModel(MCMCModel):
        """
        DREAM wrapper for fit problems.
        """

        def __init__(self, problem=None, mapper=None):
            """
            Create a sampling from the multidimensional likelihood function
            represented by the problem set using dream.
            """
            # print "dream"
            self.problem = problem
            self.bounds = self.problem.bounds()
            self.labels = self.problem.labels()

            self.mapper = mapper if mapper else lambda p: list(map(self.nllf, p))

        def log_density(self, x):
            return -self.nllf(x)

        def nllf(self, x):
            """Negative log likelihood of seeing models given *x*"""
            # Note: usually we will be going through the provided mapper, and
            # this function will never be called.
            # print "eval",x; sys.stdout.flush()
            return self.problem.nllf(x)

        def map(self, pop):
            # print "calling mapper",self.mapper
            return -np.array(self.mapper(pop))

    class DreamFit(FitBase):
        name = "DREAM"
        id = "dream"
        settings = [
            ("samples", int(1e4)),
            ("burn", 100),
            ("pop", 10),
            ("init", "eps"),
            ("thin", 1),
            ("alpha", 0.01),
            ("outliers", "none"),
            ("trim", False),
            ("steps", 0),  # deprecated: use --samples instead
        ]

        def __init__(self, problem):
            FitBase.__init__(self, problem)
            self.dream_model = DreamModel(problem)
            self.state = None

        def solve(self, monitors=None, abort_test=None, mapper=None, **options):
            from .dream import Dream

            if abort_test is None:
                abort_test = lambda: False
            options = _fill_defaults(options, self.settings)

            if mapper:
                self.dream_model.mapper = mapper
            self._update = MonitorRunner(problem=self.dream_model.problem, monitors=monitors)

            population = initpop.generate(self.dream_model.problem, **options)
            pop_size = population.shape[0]
            draws, steps = int(options["samples"]), options["steps"]
            if steps == 0:
                steps = (draws + pop_size - 1) // pop_size
            # TODO: need a better way to announce number of steps
            # maybe somehow print iteration # of # iters in the monitor?
            print("# steps: %d, # draws: %d" % (steps, pop_size * steps))
            population = population[None, :, :]
            sampler = Dream(
                model=self.dream_model,
                population=population,
                draws=pop_size * steps,
                burn=pop_size * options["burn"],
                thinning=options["thin"],
                monitor=self._monitor,
                alpha=options["alpha"],
                outlier_test=options["outliers"],
                DE_noise=1e-6,
            )

            self.state = sampler.sample(state=self.state, abort_test=abort_test)

            self._trimmed = self.state.trim_portion() if options["trim"] else 1.0
            # print("trimming", options['trim'], self._trimmed)
            self.state.mark_outliers(portion=self._trimmed)
            self.state.keep_best()
            self.state.title = self.dream_model.problem.name

            # TODO: Temporary hack to apply a post-mcmc action to the state vector
            # The problem is that if we manipulate the state vector before saving
            # it then we will not be able to use the --resume feature.  We can
            # get around this by just not writing state for the derived variables,
            # at which point we can remove this notice.
            # TODO: Add derived/visible variable support to other optimizers
            fn, labels = getattr(self.problem, "derive_vars", (None, None))
            if fn is not None:
                self.state.derive_vars(fn, labels=labels)
            visible_vars = getattr(self.problem, "visible_vars", None)
            if visible_vars is not None:
                self.state.set_visible_vars(visible_vars)
            integer_vars = getattr(self.problem, "integer_vars", None)
            if integer_vars is not None:
                self.state.set_integer_vars(integer_vars)

            x, fx = self.state.best()

            # Check that the last point is the best point
            # points, logp = self.state.sample()
            # assert logp[-1] == fx
            # print(points[-1], x)
            # assert all(points[-1, i] == xi for i, xi in enumerate(x))
            return x, -fx

        def entropy(self, **kw):
            return self.state.entropy(portion=self._trimmed, **kw)

        def _monitor(self, state, pop, logp):
            # Get an early copy of the state
            self.state = self._update.history.uncertainty_state = state
            step = state.generation
            x, fx = state.best()
            self._update(step=step, point=x, value=-fx, population_points=pop, population_values=-logp)
            return True

        def stderr(self):
            """
            Approximate standard error as 1/2 the 68% interval fo the sample,
            which is a more robust measure than the mean of the sample for
            non-normal distributions.
            """
            from .dream.stats import var_stats

            vstats = var_stats(self.state.draw(portion=self._trimmed))
            return np.array([(v.p68[1] - v.p68[0]) / 2 for v in vstats], "d")

        # def cov(self):
        #    # Covariance estimate from final 1000 points
        #    return np.cov(self.state.draw().points[-1000:])

        def load(self, input_path):
            from .dream.state import load_state, path_contains_saved_state

            if path_contains_saved_state(input_path):
                print("loading saved state from %s (this might take awhile) ..." % (input_path,))
                fn, labels = getattr(self.problem, "derive_vars", (None, []))
                self.state = load_state(input_path, report=100, derived_vars=len(labels))
            else:
                # Warn if mc files are not found on --resume path
                warnings.warn("No mcmc found; ignoring --resume=%r" % input_path)

        def save(self, output_path):
            self.state.save(output_path)

        def plot(self, output_path):
            self.state.show(figfile=output_path, portion=self._trimmed)
            self.error_plot(figfile=output_path)

        def show(self):
            pass

        def error_plot(self, figfile):
            # Produce error plot
            import pylab
            from . import errplot

            # TODO: shouldn't mix calc and display!
            res = errplot.calc_errors_from_state(problem=self.dream_model.problem, state=self.state, portion=self._trimmed)
            if res is not None:
                pylab.figure()
                errplot.show_errors(res)
                pylab.savefig(figfile + "-errors.png", format="png")

    class Resampler(FitBase):
        # TODO: why isn't cli.resynth using this?

        def __init__(self, fitter):
            self.fitter = fitter
            raise NotImplementedError()

        def solve(self, **options):
            starts = options.pop("starts", 1)
            restart = options.pop("restart", False)
            x, fx = self.fitter.solve(**options)
            points = _resampler(self.fitter, x, samples=starts, restart=restart, **options)
            self.points = points  # save points for later plotting
            return x, fx

    def _resampler(fitter, xinit, samples=100, restart=False, **options):
        """
        Refit the result multiple times with resynthesized data, building
        up an array in Result.samples which contains the best fit to the
        resynthesized data.  *samples* is the number of samples to generate.
        *fitter* is the (local) optimizer to use. **kw are the parameters
        for the optimizer.
        """
        x = xinit
        points = []
        try:  # TODO: some solvers already catch KeyboardInterrupt
            for _ in range(samples):
                # print "== resynth %d of %d" % (i, samples)
                fitter.problem.resynth_data()
                if restart:
                    fitter.problem.randomize()
                else:
                    fitter.problem.setp(x)
                x, fx = fitter.solve(**options)
                points.append(np.hstack((fx, x)))
                # print self.problem.summarize()
                # print "[chisq=%g]" % (nllf*2/self.problem.dof)
        except KeyboardInterrupt:
            # On keyboard interrupt we can declare that we are finished sampling
            # without it being an error condition, so let this exception pass.
            pass
        finally:
            # Restore the state of the problem
            fitter.problem.restore_data()
            fitter.problem.setp(xinit)
            # fitter.problem.model_update()  # setp does model update
        return points

    class FitDriver(object):
        def __init__(self, fitclass=None, problem=None, monitors=None, abort_test=None, mapper=None, **options):
            self.fitclass = fitclass
            self.problem = problem
            self.options = options
            self.monitors = monitors
            self.abort_test = abort_test
            self.mapper = mapper if mapper else lambda p: list(map(problem.nllf, p))
            self.fitter = None
            self.result = None

        def fit(self, resume=None):
            if hasattr(self, "_cov"):
                del self._cov
            if hasattr(self, "_stderr"):
                del self._stderr
            fitter = self.fitclass(self.problem)
            if resume:
                fitter.load(resume)
            starts = self.options.get("starts", 1)
            if starts > 1:
                fitter = MultiStart(fitter)
            t0 = perf_counter()
            self.fitter = fitter
            x, fx = fitter.solve(monitors=self.monitors, abort_test=self.abort_test, mapper=self.mapper, **self.options)
            self.time = perf_counter() - t0
            self.result = x, fx
            if x is not None:
                self.problem.setp(x)
            return x, fx

        def clip(self):
            """
            Force parameters within bounds so constraints are finite.

            The problem is updated with the new parameter values.

            Returns a list of parameter names that were clipped.
            """
            labels = self.problem.labels()
            values = self.problem.getp()
            bounds = self.problem.bounds()
            new_values = np.clip(values, bounds[0], bounds[1])
            clipped = [name for name, old, new in zip(labels, values, new_values) if old != new]
            self.problem.setp(new_values)
            return clipped

        def entropy(self, method=None):
            if hasattr(self.fitter, "entropy"):
                return self.fitter.entropy(method=method)
            else:
                from .dream import entropy

                return entropy.cov_entropy(self.cov()), 0

        def chisq(self):
            if not hasattr(self, "_chisq"):
                self._chisq = self.problem.chisq()
            return self._chisq

        def cov(self):
            r"""
            Return an estimate of the covariance of the fit.

            Depending on the fitter and the problem, this may be computed from
            existing evaluations within the fitter, or from numerical
            differentiation around the minimum.

            If the problem uses $\chi^2/2$ as its nllf, then the covariance
            is derived from the Jacobian::

                x = fit.problem.getp()
                J = bumps.lsqerror.jacobian(fit.problem, x)
                cov = bumps.lsqerror.jacobian_cov(J)

            Otherwise, the numerical differentiation will use the Hessian
            estimated from nllf::

                x = fit.problem.getp()
                H = bumps.lsqerror.hessian(fit.problem, x)
                cov = bumps.lsqerror.hessian_cov(H)
            """
            # Note: if fit() has not been run then self.fitter is None and in
            # particular, self.fitter will not have a covariance matrix.  In
            # this case, the code will fall through to computing the covariance
            # matrix directly from the problem.  It will use the initial value
            # stored in the problem parameters because results will also be None.
            if not hasattr(self, "_cov"):
                self._cov = None
                if hasattr(self.fitter, "cov"):
                    self._cov = self.fitter.cov()
                    # print("fitter cov", self._cov)
            if self._cov is None:
                # Use Jacobian if residuals are available because it is faster
                # to compute.  Otherwise punt and use Hessian.  The has_residuals
                # attribute should be True if present.  It may be false if
                # the problem defines a residuals method but doesn't really
                # have residuals (e.g. to allow levenberg-marquardt to run even
                # though it is not fitting a sum-square problem).
                if hasattr(self.problem, "has_residuals"):
                    has_residuals = self.problem.has_residuals
                else:
                    has_residuals = hasattr(self.problem, "residuals")
                x = self.problem.getp() if self.result is None else self.result[0]
                if has_residuals:
                    J = lsqerror.jacobian(self.problem, x)
                    # print("Jacobian", J)
                    self._cov = lsqerror.jacobian_cov(J)
                else:
                    H = lsqerror.hessian(self.problem, x)
                    # print("Hessian", H)
                    self._cov = lsqerror.hessian_cov(H)
            return self._cov

        def stderr(self):
            """
            Return an estimate of the standard error of the fit.

            Depending on the fitter and the problem, this may be computed from
            existing evaluations within the fitter, or from numerical
            differentiation around the minimum.
            """
            # Note: if fit() has not been run then self.fitter is None and in
            # particular, self.fitter will not have a stderr method defined so
            # it will compute stderr from covariance.
            if not hasattr(self, "_stderr"):
                self._stderr = None
                if hasattr(self.fitter, "stderr"):
                    self._stderr = self.fitter.stderr()
            if self._stderr is None:
                # If no stderr from the fitter then compute it from the covariance
                self._stderr = self.stderr_from_cov()
            return self._stderr

        def stderr_from_cov(self):
            """
            Return an estimate of standard error of the fit from covariance matrix.

            Unlike stderr, which uses the estimate from the underlying
            fitter (DREAM uses the MCMC sample for this), *stderr_from_cov*
            estimates the error from the diagonal of the covariance matrix.
            Here, the covariance matrix may have been estimated by the fitter
            instead of the Hessian.
            """
            if not hasattr(self, "_stderr_from_cov"):
                self._stderr_from_cov = lsqerror.stderr(self.cov())
            return self._stderr_from_cov

        def show(self):
            if hasattr(self.fitter, "show"):
                self.fitter.show()
            if hasattr(self.problem, "show"):
                self.problem.show()

        # TODO: reenable the "implied variance" calculation
        def _unused_show_err(self):
            """
            Display the error approximation from the numerical derivative.

            Warning: cost grows as the cube of the number of parameters.
            """
            # TODO: need cheaper uncertainty estimate
            # Note: error estimated from hessian diagonal is insufficient.
            err = self.stderr_from_cov()
            # TODO: citation needed
            # The "implied variance" column is obtained by scaling the covariance
            # matrix so that chisq = DOF. Any excess chisq implies increased
            # variance in the measurements, so increased variance in the parameters.
            # This is well defined for linear systems with equal but unknown
            # variance in each measurement, and assumed to be approximately true
            # for nonlinear systems, with the unexplained variance distributed
            # proportionately amongst the measurement uncertainties.
            norm = np.sqrt(self.chisq())
            print("=== Uncertainty from curvature:     name value(unc.)     value(unc./chi)) ===")
            for k, v, dv in zip(self.problem.labels(), self.problem.getp(), err):
                print("%40s %-15s %-15s" % (k, format_uncertainty(v, dv), format_uncertainty(v, dv / norm)))
            print("=" * 75)

        def show_err(self):
            """
            Display the error approximation from the numerical derivative.

            Warning: cost grows as the cube of the number of parameters.
            """
            # TODO: need cheaper uncertainty estimate
            # Note: error estimated from hessian diagonal is insufficient.
            err = self.stderr_from_cov()
            print("=== Uncertainty from curvature:     name   value(unc.) ===")
            for k, v, dv in zip(self.problem.labels(), self.problem.getp(), err):
                print(f"{k:>40s}   {format_uncertainty(v, dv):<15s}")
            print("=" * 58)

        def show_cov(self):
            cov = self.cov()
            maxn = 1000  # max array dims to print
            cov_str = np.array2string(
                cov,
                max_line_width=20 * maxn,
                threshold=maxn * maxn,
                precision=6,  # suppress_small=True,
                separator=", ",
            )
            print("=== Covariance matrix ===")
            print(cov_str)
            print("=========================")

        def show_entropy(self, method=None):
            print("Calculating entropy...")
            S, dS = self.entropy(method=method)
            print("Entropy: %s bits" % format_uncertainty(S, dS))

        def save(self, output_path):
            # print "calling driver save"
            if hasattr(self.fitter, "save"):
                self.fitter.save(output_path)
            if hasattr(self.problem, "save"):
                self.problem.save(output_path)

        def load(self, input_path):
            # print "calling driver save"
            if hasattr(self.fitter, "load"):
                self.fitter.load(input_path)
            if hasattr(self.problem, "load"):
                self.problem.load(input_path)

        def plot(self, output_path, view=None):
            # print "calling fitter.plot"
            if hasattr(self.problem, "plot"):
                self.problem.plot(figfile=output_path, view=view)
            if hasattr(self.fitter, "plot"):
                self.fitter.plot(output_path=output_path)

        def _save_fit_cov(self, output_path):
            model = getattr(self.problem, "name", self.problem.__class__.__name__)
            fitter = self.fitclass.id
            cov = self.cov()
            err = self.stderr_from_cov()
            chisq = self.chisq()

            state = {
                "model": model,
                "fitter": fitter,
            }

    def _fill_defaults(options, settings):
        """
        Returns options dict with missing values filled from settings.
        """
        result = dict(settings)  # settings is a list of (key,value) pairs
        result.update(options)
        return result

    FITTERS = []
    FIT_AVAILABLE_IDS = []
    FIT_ACTIVE_IDS = []

    def register(fitter, active=True):
        """
        Register a new fitter with bumps, if it is not already there.

        *active* is False if you don't want it showing up in the GUI selector.
        """
        # Check if already registered.
        if fitter in FITTERS:
            return

        # Check that there is no other fitter of that name
        if fitter.id in FIT_AVAILABLE_IDS:
            raise ValueError("There is already a fitter registered as %r" % fitter.id)

        # Register the fitter.
        FITTERS.append(fitter)
        FIT_AVAILABLE_IDS.append(fitter.id)

        # Make it "active" by listing it in the help menu.
        if active:
            FIT_ACTIVE_IDS.append(fitter.id)

    # Register the fitters
    register(SimplexFit, active=True)
    register(DEFit, active=True)
    register(DreamFit, active=True)
    register(BFGSFit, active=True)
    register(LevenbergMarquardtFit, active=True)
    register(MPFit, active=True)
    # register(PSFit, active=False)
    register(PTFit, active=False)
    # register(RLFit, active=False)
    # register(SnobFit, active=False)

    FIT_DEFAULT_ID = SimplexFit.id

    assert FIT_DEFAULT_ID in FIT_ACTIVE_IDS
    assert all(f in FIT_AVAILABLE_IDS for f in FIT_ACTIVE_IDS)

    def fit(problem, method=FIT_DEFAULT_ID, verbose=False, **options):
        """
        Simplified fit interface.

        Given a fit problem, the name of a fitter and the fitter options,
        it will run the fit and return the best value and standard error of
        the parameters.  If *verbose* is true, then the console monitor will
        be enabled, showing progress through the fit and showing the parameter
        standard error at the end of the fit, otherwise it is completely
        silent.

        Returns an *OptimizeResult* object containing "x" and "dx".  The
        dream fitter also includes the "state" object, allowing for more
        detailed uncertainty analysis.  Optimizer information such as the
        stopping condition and the number of function evaluations are not
        yet included.

        To run in parallel (with multiprocessing and dream)::

            from bumps.mapper import MPMapper
            mapper = MPMapper.start_mapper(problem, None, cpu=0) #cpu=0 for all CPUs
            result = fit(problem, method="dream", mapper=mapper)

        """
        from scipy.optimize import OptimizeResult

        # verbose = True
        if method not in FIT_AVAILABLE_IDS:
            raise ValueError("unknown method %r not one of %s" % (method, ", ".join(sorted(FIT_ACTIVE_IDS))))
        for fitclass in FITTERS:
            if fitclass.id == method:
                break
        monitors = None if verbose else []  # default is step monitor
        driver = FitDriver(fitclass=fitclass, problem=problem, monitors=monitors, **options)
        driver.clip()  # make sure fit starts within domain
        x0 = problem.getp()
        x, fx = driver.fit()
        problem.setp(x)
        dx = driver.stderr()
        if verbose:
            print("final chisq", problem.chisq_str())
            driver.show_err()
        result = OptimizeResult(
            x=x,
            dx=driver.stderr(),
            fun=fx,
            success=True,
            status=0,
            message="successful termination",
            # nit=0, # number of iterations
            # nfev=0, # number of function evaluations
            # njev, nhev # jacobian and hessian evaluations
            # maxcv=0, # max constraint violation
        )
        if hasattr(driver.fitter, "state"):
            result.state = driver.fitter.state
        return result

    def test_fitters():
        """
        Run the fit tests to make sure they work.
        """
        from .curve import Curve
        from .fitproblem import FitProblem

        x = [1, 2, 3, 4, 5, 6]
        y = [2.1, 4.0, 6.3, 8.03, 9.6, 11.9]
        dy = [0.05, 0.05, 0.2, 0.05, 0.2, 0.2]

        def line(x, m, b=0):
            return m * x + b

        M = Curve(line, x, y, dy, m=2, b=2)
        M.m.range(0, 4)
        M.b.range(-5, 5)

        problem = FitProblem(M)

        # Set the tolerance for the tests (relative)
        fit_value_tol = 1e-3
        fit_error_tol = 1e-3
        expected_value = [1.106e-1, 1.970]
        expected_error = [5.799e-2, 2.055e-2]

        for fitter_name in FIT_ACTIVE_IDS:
            result = fit(problem, method=fitter_name, verbose=False)
            assert np.allclose(result.x, expected_value, rtol=fit_value_tol)
            if fitter_name != "dream":
                # dream error bars vary too much to test
                assert np.allclose(result.dx, expected_error, rtol=fit_error_tol)