Source code for pyspeckit.spectrum.models.model

"""
=============================
Generic SpectralModel wrapper
=============================
.. moduleauthor:: Adam Ginsburg <adam.g.ginsburg@gmail.com>

Module API
^^^^^^^^^^
"""
import numpy as np
from pyspeckit.mpfit import mpfit,mpfitException
from pyspeckit.spectrum.parinfo import ParinfoList,Parinfo
import copy
from astropy import log
import matplotlib.cbook as mpcb
from . import fitter
from . import mpfit_messages
from pyspeckit.specwarnings import warn
import itertools
import operator
import six
try:
    from collections import OrderedDict
except ImportError:
    from ordereddict import OrderedDict
except ImportError:
    warn("OrderedDict is required for modeling.  "
         "If you have python <2.7, install the ordereddict module.")

# define the allowed guess types and the order in which they are received
valid_guess_types = ('amplitude', 'center', 'width')

[docs]class SpectralModel(fitter.SimpleFitter): """ A wrapper class for a spectra model. Includes internal functions to generate multi-component models, annotations, integrals, and individual components. The declaration can be complex, since you should name individual variables, set limits on them, set the units the fit will be performed in, and set the annotations to be used. Check out some of the hyperfine codes (hcn, n2hp) for examples. """ def __init__(self, modelfunc, npars, shortvarnames=("A","\\Delta x","\\sigma"), fitunit=None, centroid_par=None, fwhm_func=None, fwhm_pars=None, integral_func=None, use_lmfit=False, guess_types=('amplitude', 'center', 'width'), **kwargs): """ Spectral Model Initialization Create a Spectral Model class for data fitting Parameters ---------- modelfunc : function the model function to be fitted. Should take an X-axis (spectroscopic axis) as an input followed by input parameters. Returns an array with the same shape as the input X-axis npars : int number of parameters required by the model parnames : list (optional) a list or tuple of the parameter names parvalues : list (optional) the initial guesses for the input parameters (defaults to ZEROS) parlimits : list (optional) the upper/lower limits for each variable (defaults to ZEROS) parfixed : list (optional) Can declare any variables to be fixed (defaults to ZEROS) parerror : list (optional) technically an output parameter. Specifying it here will have no effect. (defaults to ZEROS) partied : list (optional) not the past tense of party. Can declare, via text, that some parameters are tied to each other. Defaults to zeros like the others, but it's not clear if that's a sensible default fitunit : str (optional) convert X-axis to these units before passing to model parsteps : list (optional) minimum step size for each paremeter (defaults to ZEROS) npeaks : list (optional) default number of peaks to assume when fitting (can be overridden) shortvarnames : list (optional) TeX names of the variables to use when annotating amplitude_types : tuple A tuple listing the types of the different parameters when guessing. The valid values are 'amplitude', 'width', and 'center'. These are handled by parse_3par_guesses, which translate these into input guess lists for the fitter. For a "standard" 3-parameter Gaussian fitter, nothing changes, but for other models that have more than 3 parameters, some translation is needed. Returns ------- A tuple containing (model best-fit parameters, the model, parameter errors, chi^2 value) """ self.modelfunc = modelfunc if self.__doc__ is None: self.__doc__ = modelfunc.__doc__ elif modelfunc.__doc__ is not None: self.__doc__ += modelfunc.__doc__ self.npars = npars self.default_npars = npars self.fitunit = fitunit # this needs to be set once only self.shortvarnames = shortvarnames self.default_parinfo = None self.default_parinfo, kwargs = self._make_parinfo(**kwargs) self.parinfo = copy.copy(self.default_parinfo) self.modelfunc_kwargs = kwargs self.use_lmfit = use_lmfit # default name of parameter that represents the profile centroid self.centroid_par = centroid_par # FWHM function and parameters self.fwhm_func = fwhm_func self.fwhm_pars = fwhm_pars # analytic integral function self.integral_func = integral_func for gt in guess_types: if not isinstance(gt, float) and not any(g in gt for g in valid_guess_types): raise ValueError("Guess type must be one of {0} or a float" .format(valid_guess_types)) self.guess_types = guess_types def __copy__(self): # http://stackoverflow.com/questions/1500718/what-is-the-right-way-to-override-the-copy-deepcopy-operations-on-an-object-in-p cls = self.__class__ result = cls.__new__(cls) result.__dict__.update(self.__dict__) return result def __deepcopy__(self, memo): cls = self.__class__ result = cls.__new__(cls) memo[id(self)] = result for k, v in self.__dict__.items(): setattr(result, k, copy.deepcopy(v, memo)) return result def __call__(self, *args, **kwargs): log.debug("Fitter called with args={0} and kwargs={1}".format(args, kwargs)) use_lmfit = kwargs.pop('use_lmfit') if 'use_lmfit' in kwargs else self.use_lmfit if use_lmfit: return self.lmfitter(*args,**kwargs) return self.fitter(*args,**kwargs) @property def npeaks(self): return int(self._npeaks) @npeaks.setter def npeaks(self, value): if int(value) != value: raise ValueError("npeaks must be an integer") self._npeaks = int(value) def make_parinfo(self, **kwargs): return self._make_parinfo(**kwargs)[0] def _make_parinfo(self, params=None, parnames=None, parvalues=None, parlimits=None, parlimited=None, parfixed=None, parerror=None, partied=None, fitunit=None, parsteps=None, npeaks=1, parinfo=None, names=None, values=None, limits=None, limited=None, fixed=None, error=None, tied=None, steps=None, negamp=None, limitedmin=None, limitedmax=None, minpars=None, maxpars=None, vheight=False, debug=False, **kwargs): """ Generate a `ParinfoList` that matches the inputs This code is complicated - it can take inputs in a variety of different forms with different priority. It will return a `ParinfoList` (and therefore must have values within parameter ranges) """ log.debug("BEGIN _make_parinfo") # for backwards compatibility - partied = tied, etc. locals_dict = locals() for varname in str.split("parnames,parvalues,parsteps,parlimits,parlimited,parfixed,parerror,partied",","): shortvarname = varname.replace("par","") if locals_dict.get(shortvarname) is not None and locals_dict.get(varname) is not None: raise ValueError("Cannot specify both {0} and {1}".format(varname, shortvarname)) input_pardict = {k: locals_dict.get(k) for k in str.split("parnames,parvalues,parsteps,parlimits,parlimited,parfixed,parerror,partied",",")} _tip = {'par'+k: locals_dict.get(k) for k in str.split("names,values,steps,limits,limited,fixed,error,tied",",") if locals_dict.get(k) } input_pardict.update(_tip) if params is not None and parvalues is not None: raise ValueError("parvalues and params both specified; they're redundant so that's not allowed.") elif params is not None and parvalues is None: input_pardict['parvalues'] = params log.debug("Parvalues = {0}, npeaks = {1}".format(input_pardict['parvalues'], npeaks)) # this is used too many damned times to keep referencing a dict. parnames = input_pardict['parnames'] parlimited = input_pardict['parlimited'] parlimits = input_pardict['parlimits'] parvalues = input_pardict['parvalues'] if parnames is not None: self.parnames = parnames elif parnames is None and hasattr(self,'parnames') and self.parnames is not None: parnames = self.parnames elif self.default_parinfo is not None and parnames is None: parnames = [p['parname'] for p in self.default_parinfo] input_pardict['parnames'] = parnames assert input_pardict['parnames'] is not None if limitedmin is not None: if limitedmax is not None: parlimited = list(zip(limitedmin,limitedmax)) else: parlimited = list(zip(limitedmin,(False,)*len(parnames))) elif limitedmax is not None: parlimited = list(zip((False,)*len(parnames),limitedmax)) elif self.default_parinfo is not None and parlimited is None: parlimited = [p['limited'] for p in self.default_parinfo] input_pardict['parlimited'] = parlimited if minpars is not None: if maxpars is not None: parlimits = list(zip(minpars,maxpars)) else: parlimits = list(zip(minpars,(False,)*len(parnames))) elif maxpars is not None: parlimits = list(zip((False,)*len(parnames),maxpars)) elif limits is not None: parlimits = limits elif self.default_parinfo is not None and parlimits is None: parlimits = [p['limits'] for p in self.default_parinfo] input_pardict['parlimits'] = parlimits self.npeaks = int(npeaks) # the height / parvalue popping needs to be done before the temp_pardict is set in order to make sure # that the height guess isn't assigned to the amplitude self.vheight = vheight if ((vheight and len(self.parinfo) == self.default_npars and len(parvalues) == self.default_npars + 1)): # if the right number of parameters are passed, the first is the height self.parinfo = [{'n':0, 'value':parvalues.pop(0), 'limits':(0,0), 'limited': (False,False), 'fixed':False, 'parname':'HEIGHT', 'error': 0, 'tied':""}] elif vheight and len(self.parinfo) == self.default_npars and len(parvalues) == self.default_npars: # if you're one par short, guess zero self.parinfo = [{ 'n':0, 'value': 0, 'limits':(0,0), 'limited': (False,False), 'fixed':False, 'parname':'HEIGHT', 'error': 0, 'tied':"" }] elif vheight and len(self.parinfo) == self.default_npars+1 and len(parvalues) == self.default_npars+1: # the right numbers are passed *AND* there is already a height param self.parinfo = [{ 'n':0, 'value':parvalues.pop(0), 'limits':(0,0), 'limited': (False,False), 'fixed': False, 'parname':'HEIGHT', 'error': 0, 'tied':"" }] #heightparnum = (i for i,s in self.parinfo if 'HEIGHT' in s['parname']) #for hpn in heightparnum: # self.parinfo[hpn]['value'] = parvalues[0] elif vheight: raise ValueError('VHEIGHT is specified but a case was found that did not allow it to be included.') else: self.parinfo = [] log.debug("After VHEIGHT parse len(parinfo): %i vheight: %s" % (len(self.parinfo), vheight)) # this is a clever way to turn the parameter lists into a dict of lists # clever = hard to read temp_pardict = OrderedDict([(varname, np.zeros(self.npars*self.npeaks, dtype='bool')) if input_pardict.get(varname) is None else (varname, list(input_pardict.get(varname))) for varname in str.split("parnames,parvalues,parsteps,parlimits,parlimited,parfixed,parerror,partied",",")]) temp_pardict['parlimits'] = parlimits if parlimits is not None else [(0,0)] * (self.npars*self.npeaks) temp_pardict['parlimited'] = parlimited if parlimited is not None else [(False,False)] * (self.npars*self.npeaks) for k,v in temp_pardict.items(): if (self.npars*self.npeaks) / len(v) > 1: n_components = ((self.npars*self.npeaks) / len(v)) if n_components != int(n_components): raise ValueError("The number of parameter values is not a " "multiple of the number of allowed " "parameters.") temp_pardict[k] = list(v) * int(n_components) # generate the parinfo dict # note that 'tied' must be a blank string (i.e. ""), not False, if it is not set # parlimited, parfixed, and parlimits are all two-element items (tuples or lists) self.parinfo += [{'n':ii+self.npars*jj+vheight, 'value':float(temp_pardict['parvalues'][ii+self.npars*jj]), 'step':temp_pardict['parsteps'][ii+self.npars*jj], 'limits':temp_pardict['parlimits'][ii+self.npars*jj], 'limited':temp_pardict['parlimited'][ii+self.npars*jj], 'fixed':temp_pardict['parfixed'][ii+self.npars*jj], 'parname':temp_pardict['parnames'][ii].upper()+"%0i" % int(jj), 'error':float(temp_pardict['parerror'][ii+self.npars*jj]), 'tied':temp_pardict['partied'][ii+self.npars*jj] if temp_pardict['partied'][ii+self.npars*jj] else ""} for jj in range(self.npeaks) for ii in range(self.npars) ] # order matters! log.debug("After Generation step len(parinfo): %i vheight: %s " "parinfo: %s" % (len(self.parinfo), vheight, self.parinfo)) if debug > True: import pdb; pdb.set_trace() # special keyword to specify emission/absorption lines if negamp is not None: if negamp: for p in self.parinfo: if 'AMP' in p['parname']: p['limited'] = (p['limited'][0], True) p['limits'] = (p['limits'][0], 0) else: for p in self.parinfo: if 'AMP' in p['parname']: p['limited'] = (True, p['limited'][1]) p['limits'] = (0, p['limits'][1]) # This is effectively an override of all that junk above (3/11/2012) # Much of it is probably unnecessary, but it was easier to do this than # rewrite the above self.parinfo = ParinfoList([Parinfo(p) for p in self.parinfo]) # New feature: scaleability for par in self.parinfo: if par.parname.lower().strip('0123456789') in ('amplitude','amp'): par.scaleable = True log.debug("Parinfo has been set: {0}".format(self.parinfo)) log.debug("kwargs {0} were passed.".format(kwargs)) assert self.parinfo != [] return self.parinfo, kwargs
[docs] def n_modelfunc(self, pars=None, debug=False, **kwargs): """ Simple wrapper to deal with N independent peaks for a given spectral model """ if pars is None: pars = self.parinfo elif not isinstance(pars, ParinfoList): try: partemp = copy.copy(self.parinfo) partemp._from_Parameters(pars) pars = partemp except AttributeError: log.log(5, "Reading pars {0} as LMPar failed.".format(pars)) if debug > 1: import pdb; pdb.set_trace() if hasattr(pars,'values'): # important to treat as Dictionary, since lmfit params & parinfo both have .items parnames,parvals = list(zip(*list(pars.items()))) parnames = [p.lower() for p in parnames] parvals = [p.value for p in parvals] else: parvals = list(pars) if np.any(np.isnan(parvals)): raise ValueError("A parameter is NaN. Unless you gave a NaN " "value directly, this is a bug and should be " "reported. If you specified a NaN parameter, " "don't do that.") log.debug("pars to n_modelfunc: {0}, parvals:{1}".format(pars, parvals)) def L(x): v = np.zeros(len(x)) if self.vheight: v += parvals[0] # use len(pars) instead of self.npeaks because we want this to work # independent of the current best fit for jj in range(int((len(parvals)-self.vheight)/self.npars)): lower_parind = jj*self.npars+self.vheight upper_parind = (jj+1)*self.npars+self.vheight v += self.modelfunc(x, *parvals[lower_parind:upper_parind], **kwargs) return v return L
[docs] def mpfitfun(self,x,y,err=None): """ Wrapper function to compute the fit residuals in an mpfit-friendly format """ if err is None: def f(p,fjac=None): residuals = (y-self.n_modelfunc(p, **self.modelfunc_kwargs)(x)) return [0,residuals] else: def f(p,fjac=None): residuals = (y-self.n_modelfunc(p, **self.modelfunc_kwargs)(x))/err return [0,residuals] return f
[docs] def lmfitfun(self,x,y,err=None,debug=False): """ Wrapper function to compute the fit residuals in an lmfit-friendly format """ def f(p): #pars = [par.value for par in p.values()] kwargs = {} kwargs.update(self.modelfunc_kwargs) log.debug("Pars, kwarg keys: {0},{1}".format(p,list(kwargs.keys()))) if err is None: return (y-self.n_modelfunc(p,**kwargs)(x)) else: return (y-self.n_modelfunc(p,**kwargs)(x))/err return f
[docs] def lmfitter(self, xax, data, err=None, parinfo=None, quiet=True, debug=False, **kwargs): """ Use lmfit instead of mpfit to do the fitting Parameters ---------- xax : SpectroscopicAxis The X-axis of the spectrum data : ndarray The data to fit err : ndarray (optional) The error on the data. If unspecified, will be uniform unity parinfo : ParinfoList The guesses, parameter limits, etc. See `pyspeckit.spectrum.parinfo` for details quiet : bool If false, print out some messages about the fitting """ try: import lmfit except ImportError as e: raise ImportError("Could not import lmfit, try using mpfit instead.") log.debug("lmfit called with parinfo=\n{0}".format(parinfo)) self.xax = xax # the 'stored' xax is just a link to the original if hasattr(xax,'convert_to_unit') and self.fitunit is not None: # some models will depend on the input units. For these, pass in an X-axis in those units # (gaussian, voigt, lorentz profiles should not depend on units. Ammonia, formaldehyde, # H-alpha, etc. should) xax = copy.copy(xax) xax.convert_to_unit(self.fitunit, quiet=quiet) elif self.fitunit is not None: raise TypeError("X axis does not have a convert method") if np.any(np.isnan(data)) or np.any(np.isinf(data)): err[np.isnan(data) + np.isinf(data)] = np.inf data[np.isnan(data) + np.isinf(data)] = 0 if np.any(np.isnan(err)): raise ValueError("One or more of the error values is NaN." " This is not allowed. Errors can be infinite " "(which is equivalent to giving zero weight to " "a data point), but otherwise they must be positive " "floats.") elif np.any(err<0): raise ValueError("At least one error value is negative, which is " "not allowed as negative errors are not " "meaningful in the optimization process.") if parinfo is None: parinfo, kwargs = self._make_parinfo(debug=debug, **kwargs) log.debug("Parinfo created from _make_parinfo: {0}".format(parinfo)) LMParams = parinfo.as_Parameters() log.debug("LMParams: "+"\n".join([repr(p) for p in list(LMParams.values())])) log.debug("parinfo: {0}".format(parinfo)) log.debug("BEGIN MINIMIZER") minimizer = lmfit.minimize(self.lmfitfun(xax,np.array(data),err,debug=debug),LMParams,**kwargs) log.debug("END MINIMIZER") if not quiet: log.info("There were %i function evaluations" % (minimizer.nfev)) #modelpars = [p.value for p in parinfo.values()] #modelerrs = [p.stderr for p in parinfo.values() if p.stderr is not None else 0] self.LMParams = minimizer.params # Force consistency w/earlier versions of lmfit: if error == 0 exactly, # change it to None for par in self.LMParams: if hasattr(par, 'stderr') and par.stderr == 0: #assert minimizer.ier == 4 par.stderr = None self.parinfo._from_Parameters(self.LMParams) log.debug("LMParams: {0}".format(self.LMParams)) log.debug("parinfo: {0}".format(parinfo)) self.mp = minimizer self.mpp = self.parinfo.values self.mpperr = self.parinfo.errors self.mppnames = self.parinfo.names modelkwargs = {} modelkwargs.update(self.modelfunc_kwargs) self.model = self.n_modelfunc(self.parinfo, **modelkwargs)(xax) if hasattr(minimizer,'chisqr'): chi2 = minimizer.chisqr else: try: chi2 = (((data-self.model)/err)**2).sum() except TypeError: chi2 = ((data-self.model)**2).sum() if np.isnan(chi2): warn("Warning: chi^2 is nan") if hasattr(self.mp,'ier') and self.mp.ier not in [1,2,3,4]: log.warning("Fitter failed: %s, %s" % (self.mp.message, self.mp.lmdif_message)) return self.mpp,self.model,self.mpperr,chi2
[docs] def fitter(self, xax, data, err=None, quiet=True, veryverbose=False, debug=False, parinfo=None, **kwargs): """ Run the fitter using mpfit. kwargs will be passed to _make_parinfo and mpfit. Parameters ---------- xax : SpectroscopicAxis The X-axis of the spectrum data : ndarray The data to fit err : ndarray (optional) The error on the data. If unspecified, will be uniform unity parinfo : ParinfoList The guesses, parameter limits, etc. See `pyspeckit.spectrum.parinfo` for details quiet : bool pass to mpfit. If False, will print out the parameter values for each iteration of the fitter veryverbose : bool print out a variety of mpfit output parameters debug : bool raise an exception (rather than a warning) if chi^2 is nan """ if parinfo is None: parinfo, kwargs = self._make_parinfo(debug=debug, **kwargs) else: log.debug("Using user-specified parinfo dict") # clean out disallowed kwargs (don't want to pass them to mpfit) #throwaway, kwargs = self._make_parinfo(debug=debug, **kwargs) self.xax = xax # the 'stored' xax is just a link to the original if hasattr(xax,'as_unit') and self.fitunit is not None: # some models will depend on the input units. For these, pass in an X-axis in those units # (gaussian, voigt, lorentz profiles should not depend on units. Ammonia, formaldehyde, # H-alpha, etc. should) xax = copy.copy(xax) # xax.convert_to_unit(self.fitunit, quiet=quiet) xax = xax.as_unit(self.fitunit, quiet=quiet, **kwargs) elif self.fitunit is not None: raise TypeError("X axis does not have a convert method") if np.any(np.isnan(data)) or np.any(np.isinf(data)): err[np.isnan(data) + np.isinf(data)] = np.inf data[np.isnan(data) + np.isinf(data)] = 0 if np.any(np.isnan(err)): raise ValueError("One or more of the error values is NaN." " This is not allowed. Errors can be infinite " "(which is equivalent to giving zero weight to " "a data point), but otherwise they must be positive " "floats.") elif np.any(err<0): raise ValueError("At least one error value is negative, which is " "not allowed as negative errors are not " "meaningful in the optimization process.") for p in parinfo: log.debug( p ) log.debug( "\n".join(["%s %i: tied: %s value: %s" % (p['parname'],p['n'],p['tied'],p['value']) for p in parinfo]) ) mp = mpfit(self.mpfitfun(xax,data,err),parinfo=parinfo,quiet=quiet,debug=debug,**kwargs) mpp = mp.params if mp.perror is not None: mpperr = mp.perror else: mpperr = mpp*0 chi2 = mp.fnorm if mp.status == 0: if "parameters are not within PARINFO limits" in mp.errmsg: log.warning(parinfo) raise mpfitException(mp.errmsg) for i,(p,e) in enumerate(zip(mpp,mpperr)): self.parinfo[i]['value'] = p # for consistency w/lmfit, and because it makes more sense, errors # of 0 will instead be None self.parinfo[i]['error'] = e if (e != 0 or mp.status != 4) else None # sanity check: if status==4, errors could not be computed # Apparently some parameters can have errors estimated even if all can't? #if mp.status == 4: # assert all([self.parinfo[ii]['error'] is None # for ii in range(len(mpp))]) if veryverbose: log.info("Fit status: {0}".format(mp.status)) log.info("Fit error message: {0}".format(mp.errmsg)) log.info("Fit message: {0}".format(mpfit_messages[mp.status])) for i,p in enumerate(mpp): log.info("{0}: {1} +/- {2}".format(self.parinfo[i]['parname'], p,mpperr[i])) log.info("Chi2: {0} Reduced Chi2: {1} DOF:{2}".format(mp.fnorm, mp.fnorm/(len(data)-len(mpp)), len(data)-len(mpp))) self.mp = mp self.mpp = self.parinfo.values self.mpperr = self.parinfo.errors self.mppnames = self.parinfo.names self.model = self.n_modelfunc(self.parinfo,**self.modelfunc_kwargs)(xax) log.debug("Modelpars: {0}".format(self.mpp)) if np.isnan(chi2): if debug: raise ValueError("Error: chi^2 is nan") else: log.warning("Warning: chi^2 is nan") return mpp,self.model,mpperr,chi2
[docs] def slope(self, xinp): """ Find the local slope of the model at location x (x must be in xax's units) """ if hasattr(self, 'model'): dm = np.diff(self.model) # convert requested x to pixels xpix = self.xax.x_to_pix(xinp) dmx = np.average(dm[xpix-1:xpix+1]) if np.isfinite(dmx): return dmx else: return 0
[docs] def annotations(self, shortvarnames=None, debug=False): """ Return a list of TeX-formatted labels The values and errors are formatted so that only the significant digits are displayed. Rounding is performed using the decimal package. Parameters ---------- shortvarnames : list A list of variable names (tex is allowed) to include in the annotations. Defaults to self.shortvarnames Examples -------- >>> # Annotate a Gaussian >>> sp.specfit.annotate(shortvarnames=['A','\\Delta x','\\sigma']) """ from decimal import Decimal # for formatting svn = self.shortvarnames if shortvarnames is None else shortvarnames # if pars need to be replicated.... if len(svn) < self.npeaks*self.npars: svn = svn * self.npeaks parvals = self.parinfo.values parerrs = self.parinfo.errors loop_list = [(parvals[ii+jj*self.npars+self.vheight], parerrs[ii+jj*self.npars+self.vheight], svn[ii+jj*self.npars], self.parinfo.fixed[ii+jj*self.npars+self.vheight], jj) for jj in range(self.npeaks) for ii in range(self.npars)] label_list = [] for (value, error, varname, fixed, varnumber) in loop_list: log.debug(", ".join([str(x) for x in (value, error, varname, fixed, varnumber)])) if None in (value, error): label = "{0}({1})=None".format(varname, varnumber) elif fixed or error==0: label = ("$%s(%i)$=%8s" % (varname, varnumber, Decimal("%g" % value).quantize(Decimal("%0.6g" % (value))))) else: label = ("$%s(%i)$=%8s $\\pm$ %8s" % (varname, varnumber, Decimal("%g" % value).quantize(Decimal("%0.2g" % (min(np.abs([value,error]))))), Decimal("%g" % error).quantize(Decimal("%0.2g" % (error))),)) label_list.append(label) labels = tuple(mpcb.flatten(label_list)) return labels
[docs] def components(self, xarr, pars, **kwargs): """ Return a numpy ndarray of shape [npeaks x modelshape] of the independent components of the fits """ modelcomponents = np.array( [self.modelfunc(xarr, *pars[i*self.npars:(i+1)*self.npars], **dict(list(self.modelfunc_kwargs.items())+list(kwargs.items()))) for i in range(self.npeaks)]) if len(modelcomponents.shape) == 3: newshape = [modelcomponents.shape[0]*modelcomponents.shape[1], modelcomponents.shape[2]] modelcomponents = np.reshape(modelcomponents, newshape) return modelcomponents
[docs] def integral(self, modelpars, dx=None, **kwargs): """ Extremely simple integrator: IGNORES modelpars; just sums self.model """ if not hasattr(self,'model'): raise ValueError("Must fit (or compute) a model before computing" " its integral.") if dx is not None: return (self.model*dx).sum() else: return self.model.sum()
[docs] def analytic_integral(self, modelpars=None, npeaks=None, npars=None): """ Placeholder for analyic integrals; these must be defined for individual models """ if self.integral_func is None: raise NotImplementedError("Analytic integrals must be implemented independently for each model type") # all of these parameters are allowed to be overwritten if modelpars is None: modelpars = self.parinfo.values if npeaks is None: npeaks = self.npeaks if npars is None: npars = self.npars return np.sum([ self.integral_func(modelpars[npars*ii:npars*(1+ii)]) for ii in range(npeaks)])
[docs] def component_integrals(self, xarr, dx=None): """ Compute the integrals of each component """ components = self.components(xarr, self.parinfo.values) if dx is None: dx = 1 integrals = [com.sum()*dx for com in components] return integrals
[docs] def analytic_fwhm(self, parinfo=None): """ Return the FWHMa of the model components *if* a fwhm_func has been defined Done with incomprehensible list comprehensions instead of nested for loops... readability sacrificed for speed and simplicity. This is unpythonic. """ if self.fwhm_func is None and self.fwhm_pars is None: raise TypeError("fwhm_func not implemented for model %s" % self.__name__) if parinfo is None: parinfo = self.parinfo fwhm = [self.fwhm_func( *[self.parinfo[str.upper(p+'%i' % n)] for p in self.fwhm_pars] ) for n in range(self.npeaks)] return fwhm
[docs] def analytic_centroids(self, centroidpar=None): """ Return the *analytic* centroids of the model components Parameters ---------- centroidpar : None or string The name of the parameter in the fit that represents the centroid *some models have default centroid parameters - these will be used if centroidpar is unspecified* Returns ------- List of the centroid values (even if there's only 1) """ if centroidpar is None: centroidpar = self.centroid_par centr = [par.value for par in self.parinfo if str.upper(centroidpar) in par.parname] return centr
[docs] def computed_centroid(self, xarr=None): """ Return the *computed* centroid of the model Parameters ---------- xarr : None or np.ndarray The X coordinates of the model over which the centroid should be computed. If unspecified, the centroid will be in pixel units """ if not hasattr(self, 'model'): raise ValueError("Must fit (or compute) a model before measuring " "its centroid") if xarr is None: xarr = np.arange(self.model.size) centr = (self.model*xarr).sum() / self.model.sum() return centr
[docs] def logp(self, xarr, data, error, pars=None): """ Return the log probability of the model. If the parameter is out of range, return -inf """ if pars is None: pars = self.parinfo else: parinfo = copy.copy(self.parinfo) for value,parameter in zip(pars,parinfo): try: parameter.value = value except ValueError: return -np.inf model = self.n_modelfunc(pars, **self.modelfunc_kwargs)(xarr) difference = np.abs(data-model) # prob = 1/(2*np.pi)**0.5/error * exp(-difference**2/(2.*error**2)) #logprob = np.log(1./(2.*np.pi)**0.5/error) * (-difference**2/(2.*error**2)) logprob = (-difference**2/(2.*error**2)) totallogprob = np.sum(logprob) return totallogprob
[docs] def get_emcee_sampler(self, xarr, data, error, **kwargs): """ Get an emcee walker for the data & model Parameters ---------- xarr : pyspeckit.units.SpectroscopicAxis data : np.ndarray error : np.ndarray Examples -------- >>> import pyspeckit >>> x = pyspeckit.units.SpectroscopicAxis(np.linspace(-10,10,50), unit='km/s') >>> e = np.random.randn(50) >>> d = np.exp(-np.asarray(x)**2/2.)*5 + e >>> sp = pyspeckit.Spectrum(data=d, xarr=x, error=np.ones(50)*e.std()) >>> sp.specfit(fittype='gaussian') >>> emcee_sampler = sp.specfit.fitter.get_emcee_sampler(sp.xarr, sp.data, sp.error) >>> p0 = sp.specfit.parinfo >>> emcee_sampler.run_mcmc(p0,100) """ try: import emcee except ImportError: return def probfunc(pars): return self.logp(xarr, data, error, pars=pars) raise NotImplementedError("emcee's metropolis-hastings sampler is not implemented; use pymc") sampler = emcee.MHSampler(self.npars*self.npeaks+self.vheight, probfunc, **kwargs) return sampler
[docs] def get_emcee_ensemblesampler(self, xarr, data, error, nwalkers, **kwargs): """ Get an emcee walker ensemble for the data & model Parameters ---------- data : np.ndarray error : np.ndarray nwalkers : int Number of walkers to use Examples -------- >>> import pyspeckit >>> x = pyspeckit.units.SpectroscopicAxis(np.linspace(-10,10,50), unit='km/s') >>> e = np.random.randn(50) >>> d = np.exp(-np.asarray(x)**2/2.)*5 + e >>> sp = pyspeckit.Spectrum(data=d, xarr=x, error=np.ones(50)*e.std()) >>> sp.specfit(fittype='gaussian') >>> nwalkers = sp.specfit.fitter.npars * 2 >>> emcee_ensemble = sp.specfit.fitter.get_emcee_ensemblesampler(sp.xarr, sp.data, sp.error, nwalkers) >>> p0 = np.array([sp.specfit.parinfo.values] * nwalkers) >>> p0 *= np.random.randn(*p0.shape) / 10. + 1.0 >>> pos,logprob,state = emcee_ensemble.run_mcmc(p0,100) """ try: import emcee except ImportError: return def probfunc(pars): return self.logp(xarr, data, error, pars=pars) sampler = emcee.EnsembleSampler(nwalkers, self.npars*self.npeaks+self.vheight, probfunc, **kwargs) return sampler
[docs] def get_pymc(self, xarr, data, error, use_fitted_values=False, inf=np.inf, use_adaptive=False, return_dict=False, **kwargs): """ Create a pymc MCMC sampler. Defaults to 'uninformative' priors Parameters ---------- data : np.ndarray error : np.ndarray use_fitted_values : bool Each parameter with a measured error will have a prior defined by the Normal distribution with sigma = par.error and mean = par.value use_adaptive : bool Use the Adaptive Metropolis-Hastings sampler? Examples -------- >>> x = pyspeckit.units.SpectroscopicAxis(np.linspace(-10,10,50), unit='km/s') >>> e = np.random.randn(50) >>> d = np.exp(-np.asarray(x)**2/2.)*5 + e >>> sp = pyspeckit.Spectrum(data=d, xarr=x, error=np.ones(50)*e.std()) >>> sp.specfit(fittype='gaussian') >>> MCuninformed = sp.specfit.fitter.get_pymc(sp.xarr, sp.data, sp.error) >>> MCwithpriors = sp.specfit.fitter.get_pymc(sp.xarr, sp.data, sp.error, use_fitted_values=True) >>> MCuninformed.sample(1000) >>> MCuninformed.stats()['AMPLITUDE0'] >>> # WARNING: This will fail because width cannot be set <0, but it may randomly reach that... >>> # How do you define a likelihood distribution with a lower limit?! >>> MCwithpriors.sample(1000) >>> MCwithpriors.stats()['AMPLITUDE0'] """ old_errsettings = np.geterr() try: import pymc finally: # pymc breaks error settings np.seterr(**old_errsettings) #def lowerlimit_like(x,lolim): # "lower limit (log likelihood - set very positive for unacceptable values)" # return (x>=lolim) / 1e10 #def upperlimit_like(x,uplim): # "upper limit" # return (x<=uplim) / 1e10 #LoLim = pymc.distributions.stochastic_from_dist('lolim', logp=lowerlimit_like, dtype=np.float, mv=False) #UpLim = pymc.distributions.stochastic_from_dist('uplim', logp=upperlimit_like, dtype=np.float, mv=False) funcdict = {} # very, very worrisome: pymc changes the values of parinfo parcopy = copy.deepcopy(self.parinfo) for par in parcopy: lolim = par.limits[0] if par.limited[0] else -inf uplim = par.limits[1] if par.limited[1] else inf if par.fixed: funcdict[par.parname] = pymc.distributions.Uniform(par.parname, par.value, par.value, value=par.value) elif use_fitted_values: if par.error > 0: if any(par.limited): try: funcdict[par.parname] = pymc.distributions.TruncatedNormal(par.parname, par.value, 1./par.error**2, lolim, uplim) except AttributeError: # old versions used this? funcdict[par.parname] = pymc.distributions.TruncNorm(par.parname, par.value, 1./par.error**2, lolim, uplim) else: funcdict[par.parname] = pymc.distributions.Normal(par.parname, par.value, 1./par.error**2) else: if any(par.limited): funcdict[par.parname] = pymc.distributions.Uniform(par.parname, lolim, uplim, value=par.value) else: funcdict[par.parname] = pymc.distributions.Uninformative(par.parname, value=par.value) elif any(par.limited): lolim = par.limits[0] if par.limited[0] else -1e10 uplim = par.limits[1] if par.limited[1] else 1e10 funcdict[par.parname] = pymc.distributions.Uniform(par.parname, lower=lolim, upper=uplim, value=par.value) else: funcdict[par.parname] = pymc.distributions.Uninformative(par.parname, value=par.value) d = dict(funcdict) def modelfunc(xarr, pars=parcopy, **kwargs): for k,v in kwargs.items(): if k in list(pars.keys()): pars[k].value = v return self.n_modelfunc(pars, **self.modelfunc_kwargs)(xarr) funcdict['xarr'] = xarr funcdet=pymc.Deterministic(name='f',eval=modelfunc,parents=funcdict,doc="The model function") d['f'] = funcdet datamodel = pymc.distributions.Normal('data', mu=funcdet, tau=1/np.asarray(error)**2, observed=True, value=np.asarray(data)) d['data']=datamodel if return_dict: return d mc = pymc.MCMC(d) if use_adaptive: mc.use_step_method(pymc.AdaptiveMetropolis,[d[p] for p in self.parinfo.names]) return mc
[docs] def parse_3par_guesses(self, guesses): """ Try to convert a set of interactive guesses (peak, center, width) into guesses appropriate to the model. """ if len(guesses) % 3 != 0: raise ValueError("Guesses passed to parse_3par_guesses must have " "length % 3 == 0") npeaks_guessed = len(guesses) // 3 gtypes = [parse_offset_guess(gtype, gval)[0] for gtype, gval in zip(itertools.cycle(self.guess_types), [0]*len(self.guess_types))] guess_dict = {(valid_guess_types[ii % 3], ii // 3): gval for ii, gval in enumerate(guesses)} new_guesses = [guess_dict[(gtype, ii)] if isinstance(gtype, str) else gtype for ii in range(npeaks_guessed) for gtype in gtypes ] new_guesses = [parse_offset_guess(gtype, gval)[1] for gtype, gval in zip(itertools.cycle(self.guess_types), new_guesses)] assert len(new_guesses) % len(self.guess_types) == 0 return new_guesses
[docs]class AstropyModel(SpectralModel): def __init__(self, model, shortvarnames=None, **kwargs): """ Override the SpectralModel initialization """ if hasattr(self,__doc__): # how do you extend a docstring really? self.__doc__ += SpectralModel.__doc__ if shortvarnames is None: shortvarnames = model.param_names super(AstropyModel,self).__init__(model, len(model.parameters), shortvarnames=shortvarnames, model=model, **kwargs) self.mp = None self.vheight = False self.npeaks = 1 def _make_parinfo(self, model=None): self.parinfo = ParinfoList([ Parinfo(parname=name,value=value) for name,value in zip(model.param_names,model.parameters)]) return self.parinfo, {} def _parse_parinfo(self, parinfo): """ Parse a ParinfoList into astropy.models parameters """ if len(parinfo) > self.npars: if len(parinfo) % self.npars != 0: raise ValueError("Need to have an integer number of models") else: self.modelfunc.param_names = parinfo.names self.modelfunc.parameters = parinfo.values else: self.modelfunc.param_names = parinfo.names self.modelfunc.parameters = parinfo.values
[docs] def fitter(self, xax, data, err=None, quiet=True, veryverbose=False, debug=False, parinfo=None, params=None, npeaks=None, **kwargs): import astropy.models as models if npeaks is not None and npeaks > 1: raise NotImplementedError("Astropy models cannot be used to fit multiple peaks yet") if parinfo is not None: self._parse_parinfo(parinfo) if params is not None: self.modelfunc.parameters = params self.astropy_fitter = models.fitting.NonLinearLSQFitter(self.modelfunc) if err is None: self.astropy_fitter(xax, data, **kwargs) else: self.astropy_fitter(xax, data, weights=1./err**2, **kwargs) mpp = self.astropy_fitter.fitpars cov = self.astropy_fitter.covar if cov is None: mpperr = np.zeros(len(mpp)) else: mpperr = cov.diagonal() self.model = self.astropy_fitter.model(xax) if err is None: chi2 = ((data-self.model)**2).sum() else: chi2 = ((data-self.model)**2/err**2).sum() # update object paramters self.modelfunc.parameters = mpp self._make_parinfo(self.modelfunc) return mpp,self.model,mpperr,chi2
[docs] def n_modelfunc(self, pars=None, debug=False, **kwargs): """ Only deals with single-peak functions """ try: self._parse_parinfo(pars) except AttributeError: self.modelfunc.parameters = pars return self.modelfunc
[docs]def parse_offset_guess(gname, gval): """ Utility function for handling guesses. Allows guess types to be specified as 'amplitude*2' or 'width+3'. """ operators = '+-*/' if not isinstance(gname, six.string_types): return gname, gval ops = [x for x in operators if x in gname] if len(ops)>1: raise ValueError("Invalid offset guess") elif len(ops) == 0: return gname,gval else: opmap = {"+": operator.add, "-": operator.sub, "*": operator.mul, "/": operator.truediv, } op = ops[0] pars = gname.split(op) gname = [p for p in gname.split(op) if p in valid_guess_types][0] pars = [gval if p in valid_guess_types else float(p) for p in pars] gval = opmap[op](*pars) return gname, gval