text: """
  Basic Fitting Models for 1-D data, simplifying fits to many standard line shapes.
  
    usage:
    ------
    param_group = fit_peak(x, y, model, dy=None,
                           background='linear', form='linear')
  
    arguments:
    ---------
    x           array of values at which to calculate model
    y           array of values for model to try to match
    dy          array of values for uncertainty in y data to be matched.
    model       name of model to use.  One of (case insensitive)
                   'linear', 'quadratic', 'step', 'rectangle',
                   'exponential', 'gaussian', 'lorentzian', 'voigt'
  
    background  name of background model to use. One of (case insensitive)
                   None, 'constant', 'linear', or 'quadratic'
                this is ignored when model is 'linear' or 'quadratic'
    form        name of form to use for 'step' and 'rectangle' models.
                One of (case insensitive):
                   'linear', 'erf', or 'atan'
    output:
    -------
    param_group   Group with fit parameters, and
  """
  
  import numpy as np
  from scipy.special import gamma, gammaln, beta, betaln, erf, erfc, wofz
  from lmfit import Parameter, Minimizer
  from lmfit.model import Model
  
  from lmfit.models import (update_param_vals, LinearModel, ConstantModel,
                            QuadraticModel, PolynomialModel, GaussianModel,
                            LorentzianModel, VoigtModel, PseudoVoigtModel,
                            MoffatModel, Pearson7Model, StudentsTModel,
                            BreitWignerModel, LognormalModel,
                            DampedOscillatorModel,
                            DampedHarmonicOscillatorModel,
                            ExponentialGaussianModel, SkewedGaussianModel,
                            DoniachModel, PowerLawModel, ExponentialModel,
                            StepModel, RectangleModel, ExpressionModel,
                            update_param_vals)
  
  
  from .. import Group
  from .utils import index_nearest, index_of, savitzky_golay
  
  VALID_BKGS = ('constant', 'linear', 'quadratic')
  
  
  MODELS = {'constant': ConstantModel,
            'linear': LinearModel,
            'quadratic': QuadraticModel,
            'step': StepModel,
            'rectangle': RectangleModel,
            'exponential': ExponentialModel,
            'gaussian': GaussianModel,
            'lorentzian': LorentzianModel,
            'voigt': VoigtModel,
            'pseudovoigt': PseudoVoigtModel,
            'pearson7': Pearson7Model,
            'dho': DampedHarmonicOscillatorModel,
            'expgaussian': ExponentialGaussianModel,
            'skewedgaussian': SkewedGaussianModel,
            'exponential': ExponentialModel,
            }
  
  # a better guess for step and rectangle models
  def step_guess(self, data, x=None, **kwargs):
      if x is None:
          return
      ymin, ymax = min(data), max(data)
      xmin, xmax = min(x), max(x)
      ntest = min(2, len(data)/5)
      step_up =  (data[:ntest].mean() > data[-ntest:].mean())
  
      dydx = savitzky_golay(np.gradient(data)/np.gradient(x), 5, 2)
      if step_up:
          cen = x[np.where(dydx==dydx.max())][0]
      else:
          cen = x[np.where(dydx==dydx.min())][0]
  
      pars = self.make_params(amplitude=(ymax-ymin), center=cen)
      pars['%ssigma' % self.prefix].set(value=(xmax-xmin)/5.0, min=0.0)
      return update_param_vals(pars, self.prefix, **kwargs)
  
  def rect_guess(self, data, x=None, **kwargs):
      if x is None:
          return
      ymin, ymax = min(data), max(data)
      xmin, xmax = min(x), max(x)
  
      ntest = min(2, len(data)/5)
      step_up =  (data[:ntest].mean() > data[-ntest:].mean())
  
  
      dydx = savitzky_golay(np.gradient(data)/np.gradient(x), 5, 2)
      cen1 = x[np.where(dydx==dydx.max())][0]
      cen2 = x[np.where(dydx==dydx.min())][0]
      if step_up:
          center1 = cen1 # + (xmax+xmin)/4.0)/2.
          center2 = cen2 # + 3*(xmax+xmin)/4.0)/2.
      else:
          center1 = cen2 # + (xmax+xmin)/4.0)/2.0
          center2 = cen1 # + 3*(xmax+xmin)/4.0)/2.0
  
      pars = self.make_params(amplitude=(ymax-ymin),
                              center1=center1, center2=center2)
  
      pars['%ssigma1' % self.prefix].set(value=(xmax-xmin)/5.0, min=0.0)
      pars['%ssigma2' % self.prefix].set(value=(xmax-xmin)/5.0, min=0.0)
      return update_param_vals(pars, self.prefix, **kwargs)
  
  StepModel.guess = step_guess
  RectangleModel.guess = rect_guess
  
  def fit_peak(x, y, model, dy=None, background=None, form=None, step=None,
               negative=False, use_gamma=False):
      """fit peak to one a selection of simple 1d models
  
      out = fit_peak(x, y, model, dy=None,
                     background='linear', form='linear')
  
      arguments:
      ---------
      x           array of values at which to calculate model
      y           array of values for model to try to match
      dy          array of values for uncertainty in y data to be matched.
      model       name of model to use.  One of (case insensitive)
                       'linear', 'quadratic', 'step', 'rectangle',
                        'gaussian', 'lorentzian', 'voigt', 'exponential'
      background  name of background model to use. One of (case insensitive)
                       None, 'constant', 'linear', or 'quadratic'
                  this is ignored when model is 'linear' or 'quadratic'
      form        name of form to use for 'step' and 'rectangle' models.
                  One of (case insensitive):
                      'linear', 'erf', or 'atan'
      negative    True/False for whether peak or steps are expected to go down.
      use_gamma   True/False for whether to use separate gamma parameter for
                  voigt model.
      output:
      -------
      Group with fit parameters, and more...
      """
      if form is None and step is not None:
          form = step
      out = Group(name='fit_peak result', x=x*1.0, y=y*1.0, dy=1.0,
                  model=model, background=background, form=form)
  
      weight = None
      if dy is not None:
          out.dy = 1.0*dy
          weight = 1.0/max(1.e-16, abs(dy))
  
      if model.lower() not in MODELS:
          raise ValueError('Unknown fit model: %s ' % model)
  
      kwargs = dict(negative=negative, background=background,
                    form=form, weight=weight)
  
      fitclass = MODELS[model.lower()]
      if fitclass == VoigtModel:
          kwargs['use_gamma'] = use_gamma
  
      mod = fitclass(**kwargs)
      pars = mod.guess(out.y, out.x)
  
      if background is not None:
          bkg = MODELS[background.lower()](prefix='bkg_')
          bpars = bkg.guess(out.y, x=out.x)
          for p, par  in bpars.items():
              par.value = 0.
              par.vary = True
          pars += bpars
          mod += bkg
  
      out.init_params = pars
  
      result = mod.fit(out.y, params=pars, x=out.x) # , dy=out.dy)
      out.fit = mod.eval(result.params, x=out.x)
      out.fit_init = mod.eval(pars, x=out.x)
  
      out.fit_details = result
      out.chi_square  = result.chisqr
      out.chi_reduced = result.redchi
  
      for attr in ('aic', 'bic', 'covar', 'rfactor', 'params', 'nvarys',
                   'nfree', 'ndata', 'var_names', 'nfev', 'success',
                   'errorbars', 'message', 'lmdif_message', 'residual'):
          setattr(out, attr, getattr(result, attr, None))
  
      if background is not None:
          comps = mod.eval_components(x=out.x)
          out.bkg = comps['bkg_']
      return out
  