linear_fit

Tools for linear least square fitting also called linear regression.

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class LT_Fit.linear_fit.linefit(x, y, yerr=None, quiet=False, plot_fit=True)

simple line fit for a set of data. Example:

>>> R = linefit(x,y, [yerr = errors])      # do the fit
>>> print(R.res['parameters'])             # print the parameters
>>> R.plot()                               # plot the fitted line
>>> R(x)                                   # evaluate the fitted function at x 

x and y are arrays (numpy.array()) R is an object containing the results of the fit with the following additional useful members:

Member	Meaning
offset	offset of the line
slope	slope of the line
sigma_o	error in offset
sigma_s	error in slope
chi_red	reduce chi square
CL	probability to find a chi square larger than the fit result (ideal 50%)
cov	covariance matrix (2D numpy.array())
res	dictionary with all fit information
line(x)	evaluate the fitted function at x

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class LT_Fit.linear_fit.polyfit(x, y, yerr=None, order=2, np_scale=5, parameters=None, quiet=False, plot_fit=True)

Polynomial fit of order n, example:

>>> R = polyfit(x,y, order, [yerr = errors]) # perform the fit 
>>> print(R['parameters'])                    # R is a dictionary containing the results of the fit
>>> R.plot()                                  # plot the fitted curve

x and y are arrays (numpy.array()) If you want to use predefined parameters to store the results:

>>> import LT_Fit.parameters as P                                                           # get the parameter module
>>> C0 = P.Parameter(0., 'const'); C1 = P.Parameter(0., 'lin'); C2 = P.Parameter(0.,'quad') # create Parameter objects
>>> R = polyfit(x,y, order, parameters=[C0,C1,C2])                                          # perform the fit
>>> R.show_parameters()                                                                     # will show the fit result
>>> R(x)                                                                                    # evaluate the fitted function at x

Member	Meaning
chi_red	reduce chi square
CL	probability to find a chi square larger than the fit result (ideal 50%)
par	parameters (numpy.array())
parameters	parameter (list of Parameter objects)
sig_par	parameter errors (variances)
cov	covarance matric (2D numpy.array())
res	dictionary with all fit information
poly(x)	evaluate the fitted function at x

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class LT_Fit.linear_fit.gen_linfit(functions, x, y, parameters=None, yerr=None, np_scale=5, quiet=False, plot_fit=True)

general linear fit of:

f(x) = a0*f0(x) + a1*f1(x) + ...

where:

f = [f0, f1, f2, ..]

is a list of functions provided by the user.

An example of making a list of function and using it in a fit

>>> import LT_Fit.parameters as P                                                     # get the parameter module
>>> f0 = lambda x: sin(x)                                                             # define lambda functions
>>> f1 = lambda x: sin(2.*x)
>>> f2 = lambda x: sin(4.*x)
>>> a0 = P.Parameter(0.,'ax'); a1 = P.Parameter(0.,'a2x'); a2 = P.Parameter(0.,'a4x') # define Parameter objects (optional)
>>> R = gen_linfit([f0, f1, f2], x, y, parameters = [a0, a1, a2], yerr = sig_y)       # do the fit
>>> R.plot()                                                                          # plot the fit
>>> R.show_parameters()                                                               # print the parameters
>>> R(x)                                                                              # evaluate the fitted function at x

R is a gen_linfit object containing the fit results and the fitted function

Member	Meaning
chi_red	reduce chi square
CL	probability to find a chi square larger than the fit result (ideal 50%)
par	parameters (numpy array)
parameters	parameter (list of Parameter objects)
sig_par	parameter errors (variances)
cov	covariance matrix (2D numpy.array())
res	dictionary with all fit information
func(x)	evaluate the fitted function at x