["BayesicFitting"]

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class ScipyFitter( MaxLikelihoodFitter )	Source

Unified interface to the Scipy minimization module minimize, to fit data to a model.

For documentation see scipy.org->Docs->Reference Guide->optimization and root finding. scipy.optimize.minimize

Examples

# assume x and y are Double1d data arrays.
x = numpy.arange( 100, dtype=float ) / 10
y = numpy.arange( 100, dtype=float ) / 122          # make slope
y += 0.3 * numpy.random.randn( 100 )                # add noise
y[9:12] += numpy.asarray( [5,10,7], dtype=float )   # make some peak
gauss = GaussModel( )                               # Gaussian
gauss += PolynomialModel( 1 )                       # add linear background
print( gauss.npchain )
cgfit = ConjugateGradientFitter( x, gauss )
param = cgfit.fit( y )
print( len( param ) )
5
stdev = cgfit.stdevs
chisq = cgfit.chisq
scale = cgfit.scale                                 # noise scale
yfit  = cgfit.getResult( )                          # fitted values
yband = cgfit.monteCarloEoor( )                         # 1 sigma confidence region

Notes

CGF is not guaranteed to find the global minimum.
CGF does not work with fixed parameters or limits

Attributes

gradient : callable gradient( par )
     User provided method to calculate the gradient of chisq.
     It can be used to speed up the dotproduct calculation, maybe
     because of the sparseness of the partial.
     default dotproduct of the partial with the residuals
tol : float (1.0e-5)
Stop when the norm of the gradient is less than tol.
norm : float (inf)
Order to use for the norm of the gradient (-np.Inf is min, np.Inf is max).
maxIter : int (200*len(par))
Maximum number of iterations
verbose : bool (False)
if True print status at convergence
debug : bool (False)
return the result of each iteration in vectors
yfit : ndarray (read only)
the result of the model at the optimal parameters
ntrans : int (read only)
number of function calls
ngrad : int (read only)
number of gradient calls
vectors : list of ndarray (read only when debug=True)
list of intermediate vectors

Hidden Attributes

_Chisq : class
to calculate chisq in the method Chisq.func() and Chisq.dfunc()

Returns

pars : array_like
the parameters at the minimum of the function (chisq).

ScipyFitter( xdata, model, method=None, gradient=True, hessp=None, **kwargs )

Constructor. Create a class, providing inputs and model.

Parameters

xdata : array_like
array of independent input values
model : Model
a model function to be fitted (linear or nonlinear)
method : None | 'CG' | 'NELDER-MEAD' | 'POWELL' | 'BFGS' | 'NEWTON-CG' | 'L-BFGS-B' |
           'TNC' | 'COBYLA' | 'SLSQP' | 'DOGLEG' | 'TRUST-NCG'
     the method name is case invariant.
     None Automatic selection of the method.
                     'SLSQP' when the problem has constraints
                     'L-BFGS-B' when the problem has limits
                     'BFGS' otherwise
     'CG' Conjugate Gradient Method of Polak and Ribiere
                     encapsulates scipy.optimize.minimize-cg
     'NELDER-MEAD' Nelder Mead downhill simplex
                     encapsulates scipy.optimize.minimize-neldermead
     'POWELL' Powell's conjugate direction method
                     encapsulates scipy.optimize.minimize-powell
     'BFGS' Quasi-Newton method of Broyden, Fletcher, Goldfarb, and Shannon
                     encapsulates scipy.optimize.minimize-bfgs
     'NEWTON-CG' Truncated Newton method
                     encapsulates scipy.optimize.minimize-newtoncg
     'L-BFGS-B' Limited Memory Algorithm for Bound Constrained Optimization
                     encapsulates scipy.optimize.minimize-lbfgsb
     'TNC' Truncated Newton method with limits
                     encapsulates scipy.optimize.minimize-tnc
     'COBYLA' Constrained Optimization BY Linear Approximation
                     encapsulates scipy.optimize.minimize-cobyla
     'SLSQP' Sequential Least Squares
                     encapsulates scipy.optimize.minimize-slsqp
     'DOGLEG' Dog-leg trust-region algorithm
                     encapsulates scipy.optimize.minimize-dogleg
     'TRUST-NCG' Newton conjugate gradient trust-region algorithm
                     encapsulates scipy.optimize.minimize-trustncg
gradient : bool or None or callable gradient( par )
     if True use gradient calculated from model. It is the default.
     if False/None dont use gradient (use numeric approximation in stead)
     if callable use the method as gradient
hessp : callable hessp(x, p, *args) or None
Function which computes the Hessian times an arbitrary vector, p.
The hessian itself is always provided.
kwargs : dict
     Possibly includes keywords from
         MaxLikelihoodFitter : errdis, scale, power
         IterativeFitter : maxIter, tolerance, verbose
         BaseFitter : map, keep, fixedScale

fit( data, weights=None, par0=None, keep=None, limits=None, maxiter=None, tolerance=None, constraints=(), verbose=0, accuracy=None, plot=False, callback=None, **options )

Return parameters for the model fitted to the data array.

Parameters

ydata : array_like
the data vector to be fitted
weights : array_like
weights pertaining to the data
accuracy : float or array_like
accuracy of (individual) data
par0 : array_like
initial values of the function. Default from Model.
keep : dict of {int:float}
     dictionary of indices (int) to be kept at a fixed value (float)
     The values of keep are only valid for this fit
     See also ScipyFitter( ..., keep=dict )
limits : None or list of 2 floats or list of 2 array_like
     None : no limits applied
     [lo,hi] : low and high limits for all values
     [la,ha] : low array and high array limits for the values
constraints : list of callables
constraint functions cf. All are subject to cf(par) > 0.
maxiter : int
max number of iterations
tolerance : float
stops when ( |hi-lo| / (|hi|+|lo|) ) < tolerance
verbose : int
0 : silent
>0 : print output if iter % verbose == 0
plot : bool
Plot the results
callback : callable
     is called each iteration as
     val = callback( val )
     where val is the minimizable array
options : dict
options to be passed to the method

Raises

ConvergenceError if it stops when the tolerance has not yet been reached.

collectVectors( par )

Methods inherited from MaxLikelihoodFitter

Methods inherited from IterativeFitter

Methods inherited from BaseFitter