Common fitting models

Several often needed models are shipped with funcFit.

Common fitting model available

The use of these models is demonstrated in the tutorial.

Single Gaussian with linear continuum

class PyAstronomy.funcFit.GaussFit1d(prm=('A', 'sig'))

A one-dimensional Gaussian

The functional form is:

\[\frac{A}{\sqrt{2\pi\sigma^2}}e^{-(x-\mu)^2/(2\sigma^2)} + x \times lin + off\]

Here, lin and off denote the linear and the offset term.

Fit parameters:

  • A - Area of the Gaussian (formerly called Amplitude)

  • mu - Center of the Gaussian

  • sig - Standard deviation

  • off - Offset

  • lin - Linear term

Note

Other parameterizations using FWHM and ‘height’ of the curve can be used.

Parameters
prmoptional tuple of two strings, {(“A”, “sig”), (“h”, “sig”), (“A”, “FWHM”), (“h”, “FWHM”)}

Can be used to adapt the parameterization of the Gaussian. By default, the curve is parameterized by Area (A) and standard deviation (sig). Alternatively, also the height (h) of the curve (h = A/sqrt(2*pi*sig**2)) and the Full Width at Half Maximum (FWHM) can be used. The naming of the fit parameters is updated accordingly.

Methods

MCMCautoParameters(ranges[, picky, ...])

Convenience function to generate parameters for MCMC fit.

addConditionalRestriction(*args)

Define a conditional restriction.

assignValue(specval)

Assign new values to variables.

assignValues(specval)

Assign new values to variables.

autoFitMCMC(x, y, ranges[, picky, stepsize, ...])

Convenience function to using auto-generated sampling parameters in MCMC.

availableParameters()

Provides a list of existing parameters.

delRestriction(parName)

Delete restriction

description([parenthesis])

Returns a description of the model based on the names of the individual components.

errorConfInterval(par[, dstat, statTol, ...])

Calculate confidence interval for a parameter.

evaluate_h_sig(x, h, sig)

Evaluates the model for given height and standard deviation (sig)-

fit(x, y[, yerr, X0, minAlgo, mAA, ...])

Carries out a fit.

fitEMCEE([x, y, yerr, nwalker, priors, ...])

MCMC sampling using emcee package.

fitMCMC(x, y, X0, Lims, Steps[, yerr, ...])

Carry out MCMC fit/error estimation.

freeParamNames()

Get the names of the free parameters.

freeParameters()

Get names and values of free parameters.

freeze(specifiers)

Consider variables free to float.

frozenParameters()

Get names and values of frozen parameters.

getRelationsOf(specifier)

Return relations of a variable.

getRestrictions()

Get all restrictions.

hasVariable(specifier)

Determine whether the variable exists.

numberOfFreeParams()

Get number of free parameters.

parameterSummary([toScreen, prefix, sorting])

Writes a summary of the parameters in text form.

parameters()

Obtain parameter names and values.

relate(dependentVar, independentVars[, func])

Define a relation.

removeConditionalRestriction(*args)

Remove an existing conditional constraint.

renameVariable(oldName, newName)

Change name of variable.

restoreState(resource)

Restores parameter values from file or dictionary.

saveState(*args, **kwargs)

Save the state of the fitting object.

setObjectiveFunction([miniFunc])

Define the objective function.

setPenaltyFactor(penalFac)

Change the penalty factor.

setRestriction(restricts)

Define restrictions.

setRootName(root[, rename])

Define the root name of the model.

showConditionalRestrictions(**kwargs)

Show conditional restrictions.

steppar(pars, ranges[, extractFctVal, quiet])

Allows to step a parameter through a specified range.

thaw(specifiers)

Consider variables fixed.

untie(parName[, forceFree])

Remove all relations of parameter parName, i.e., the parameter is not dependend on other parameters.

updateModel()

Recalculate the model using current settings.

evaluate

Multicomponent Gaussian with linear continuum

class PyAstronomy.funcFit.MultiGauss1d(n)

A multicomponent Gaussian with a single linear continuum component.

The parameters are the same as for the GaussFit1d, except that all receive a number specifying the Gaussian component to which they belong. Therefore, they are, e.g., named A1, mu2, and so on, only off and lin remain unnumbered.

Parameters
nint

The number if Gaussian components.

Methods

MCMCautoParameters(ranges[, picky, ...])

Convenience function to generate parameters for MCMC fit.

addConditionalRestriction(*args)

Define a conditional restriction.

assignValue(specval)

Assign new values to variables.

assignValues(specval)

Assign new values to variables.

autoFitMCMC(x, y, ranges[, picky, stepsize, ...])

Convenience function to using auto-generated sampling parameters in MCMC.

availableParameters()

Provides a list of existing parameters.

delRestriction(parName)

Delete restriction

description([parenthesis])

Returns a description of the model based on the names of the individual components.

errorConfInterval(par[, dstat, statTol, ...])

Calculate confidence interval for a parameter.

evalComponent(x, p)

Evaluate the model considering only a single component.

evaluate(x)

Evaluates the model for current parameter values.

fit(x, y[, yerr, X0, minAlgo, mAA, ...])

Carries out a fit.

fitEMCEE([x, y, yerr, nwalker, priors, ...])

MCMC sampling using emcee package.

fitMCMC(x, y, X0, Lims, Steps[, yerr, ...])

Carry out MCMC fit/error estimation.

freeParamNames()

Get the names of the free parameters.

freeParameters()

Get names and values of free parameters.

freeze(specifiers)

Consider variables free to float.

frozenParameters()

Get names and values of frozen parameters.

getRelationsOf(specifier)

Return relations of a variable.

getRestrictions()

Get all restrictions.

hasVariable(specifier)

Determine whether the variable exists.

numberOfFreeParams()

Get number of free parameters.

parameterSummary([toScreen, prefix, sorting])

Writes a summary of the parameters in text form.

parameters()

Obtain parameter names and values.

relate(dependentVar, independentVars[, func])

Define a relation.

removeConditionalRestriction(*args)

Remove an existing conditional constraint.

renameVariable(oldName, newName)

Change name of variable.

restoreState(resource)

Restores parameter values from file or dictionary.

saveState(*args, **kwargs)

Save the state of the fitting object.

setObjectiveFunction([miniFunc])

Define the objective function.

setPenaltyFactor(penalFac)

Change the penalty factor.

setRestriction(restricts)

Define restrictions.

setRootName(root[, rename])

Define the root name of the model.

showConditionalRestrictions(**kwargs)

Show conditional restrictions.

steppar(pars, ranges[, extractFctVal, quiet])

Allows to step a parameter through a specified range.

thaw(specifiers)

Consider variables fixed.

untie(parName[, forceFree])

Remove all relations of parameter parName, i.e., the parameter is not dependend on other parameters.

updateModel()

Recalculate the model using current settings.

Cauchy-Lorentz with linear continuum

class PyAstronomy.funcFit.CauchyLorentz1d

A Cauchy-Lorentz profile

Fit parameters:

  • A - Amplitude

  • g - Scale parameter (usually gamma)

  • mu - Center

  • off - A constant offset

  • lin - A linear contribution

Methods

MCMCautoParameters(ranges[, picky, ...])

Convenience function to generate parameters for MCMC fit.

addConditionalRestriction(*args)

Define a conditional restriction.

assignValue(specval)

Assign new values to variables.

assignValues(specval)

Assign new values to variables.

autoFitMCMC(x, y, ranges[, picky, stepsize, ...])

Convenience function to using auto-generated sampling parameters in MCMC.

availableParameters()

Provides a list of existing parameters.

delRestriction(parName)

Delete restriction

description([parenthesis])

Returns a description of the model based on the names of the individual components.

errorConfInterval(par[, dstat, statTol, ...])

Calculate confidence interval for a parameter.

evaluate(x)

Evaluates the model for current parameter values.

fit(x, y[, yerr, X0, minAlgo, mAA, ...])

Carries out a fit.

fitEMCEE([x, y, yerr, nwalker, priors, ...])

MCMC sampling using emcee package.

fitMCMC(x, y, X0, Lims, Steps[, yerr, ...])

Carry out MCMC fit/error estimation.

freeParamNames()

Get the names of the free parameters.

freeParameters()

Get names and values of free parameters.

freeze(specifiers)

Consider variables free to float.

frozenParameters()

Get names and values of frozen parameters.

getRelationsOf(specifier)

Return relations of a variable.

getRestrictions()

Get all restrictions.

hasVariable(specifier)

Determine whether the variable exists.

numberOfFreeParams()

Get number of free parameters.

parameterSummary([toScreen, prefix, sorting])

Writes a summary of the parameters in text form.

parameters()

Obtain parameter names and values.

relate(dependentVar, independentVars[, func])

Define a relation.

removeConditionalRestriction(*args)

Remove an existing conditional constraint.

renameVariable(oldName, newName)

Change name of variable.

restoreState(resource)

Restores parameter values from file or dictionary.

saveState(*args, **kwargs)

Save the state of the fitting object.

setObjectiveFunction([miniFunc])

Define the objective function.

setPenaltyFactor(penalFac)

Change the penalty factor.

setRestriction(restricts)

Define restrictions.

setRootName(root[, rename])

Define the root name of the model.

showConditionalRestrictions(**kwargs)

Show conditional restrictions.

steppar(pars, ranges[, extractFctVal, quiet])

Allows to step a parameter through a specified range.

thaw(specifiers)

Consider variables fixed.

untie(parName[, forceFree])

Remove all relations of parameter parName, i.e., the parameter is not dependend on other parameters.

updateModel()

Recalculate the model using current settings.

Voigt with linear continuum

class PyAstronomy.funcFit.Voigt1d

Implements a Voigt profile (convolution of Cauchy-Lorentz and Gaussian distribution).

Note

The profile is implemented so that al is half the FWHM of the Cauchy-Lorentz distribution.

Fit parameters:

  • A - Area under the curve

  • al - Scale parameter of the Cauchy-Lorentz distribution (half its FWHM)

  • ad - The width (standard deviation) of the Gaussian (usually called sigma)

  • mu - Center

  • off - Constant offset

  • lin - Linear contribution

Notes

The Voigt profile V is defined as the convolution

\[V(x) = A\int G(x')L(x-x')dx'\]

of a Gaussian distribution

\[G=1/(\sqrt{2 \pi} \ ad)\exp(-(x-mu)^2/(2 \ ad^2))\]

and a Cauchy-Lorentz distribution

\[L=al/(\pi ((x-mu)^2+al^2)) .\]

We here take into account an additional offset and linear term so that

\[V'(x) = V(x) + (lin \ x + off) .\]

The Voigt profile is calculated via the real part of the Faddeeva function. For details, see http://en.wikipedia.org/wiki/Voigt_profile and http://en.wikipedia.org/wiki/Error_function.

Methods

FWHM()

Calculates an approximation of the FWHM.

MCMCautoParameters(ranges[, picky, ...])

Convenience function to generate parameters for MCMC fit.

addConditionalRestriction(*args)

Define a conditional restriction.

assignValue(specval)

Assign new values to variables.

assignValues(specval)

Assign new values to variables.

autoFitMCMC(x, y, ranges[, picky, stepsize, ...])

Convenience function to using auto-generated sampling parameters in MCMC.

availableParameters()

Provides a list of existing parameters.

delRestriction(parName)

Delete restriction

description([parenthesis])

Returns a description of the model based on the names of the individual components.

errorConfInterval(par[, dstat, statTol, ...])

Calculate confidence interval for a parameter.

evaluate(x)

Evaluates the model for current parameter values.

fit(x, y[, yerr, X0, minAlgo, mAA, ...])

Carries out a fit.

fitEMCEE([x, y, yerr, nwalker, priors, ...])

MCMC sampling using emcee package.

fitMCMC(x, y, X0, Lims, Steps[, yerr, ...])

Carry out MCMC fit/error estimation.

freeParamNames()

Get the names of the free parameters.

freeParameters()

Get names and values of free parameters.

freeze(specifiers)

Consider variables free to float.

frozenParameters()

Get names and values of frozen parameters.

getRelationsOf(specifier)

Return relations of a variable.

getRestrictions()

Get all restrictions.

hasVariable(specifier)

Determine whether the variable exists.

numberOfFreeParams()

Get number of free parameters.

parameterSummary([toScreen, prefix, sorting])

Writes a summary of the parameters in text form.

parameters()

Obtain parameter names and values.

relate(dependentVar, independentVars[, func])

Define a relation.

removeConditionalRestriction(*args)

Remove an existing conditional constraint.

renameVariable(oldName, newName)

Change name of variable.

restoreState(resource)

Restores parameter values from file or dictionary.

saveState(*args, **kwargs)

Save the state of the fitting object.

setObjectiveFunction([miniFunc])

Define the objective function.

setPenaltyFactor(penalFac)

Change the penalty factor.

setRestriction(restricts)

Define restrictions.

setRootName(root[, rename])

Define the root name of the model.

showConditionalRestrictions(**kwargs)

Show conditional restrictions.

steppar(pars, ranges[, extractFctVal, quiet])

Allows to step a parameter through a specified range.

thaw(specifiers)

Consider variables fixed.

untie(parName[, forceFree])

Remove all relations of parameter parName, i.e., the parameter is not dependend on other parameters.

updateModel()

Recalculate the model using current settings.

Multicomponent Voigt profile with linear continuum

class PyAstronomy.funcFit.MultiVoigt1d(n)

Multicomponent Voigt with a single linear continuum component.

The parameters are the same as for Voigt1d, except that all are extended by a number specifying the component to which they belong. Therefore, they read, e.g., A1, mu2, and so on; only off and lin remain unnumbered.

Parameters
nint

The number of Voigt components.

Methods

MCMCautoParameters(ranges[, picky, ...])

Convenience function to generate parameters for MCMC fit.

addConditionalRestriction(*args)

Define a conditional restriction.

assignValue(specval)

Assign new values to variables.

assignValues(specval)

Assign new values to variables.

autoFitMCMC(x, y, ranges[, picky, stepsize, ...])

Convenience function to using auto-generated sampling parameters in MCMC.

availableParameters()

Provides a list of existing parameters.

delRestriction(parName)

Delete restriction

description([parenthesis])

Returns a description of the model based on the names of the individual components.

errorConfInterval(par[, dstat, statTol, ...])

Calculate confidence interval for a parameter.

evalComponent(x, p)

Evaluate the model considering only a single component.

evaluate(x)

Evaluates the model for current parameter values.

fit(x, y[, yerr, X0, minAlgo, mAA, ...])

Carries out a fit.

fitEMCEE([x, y, yerr, nwalker, priors, ...])

MCMC sampling using emcee package.

fitMCMC(x, y, X0, Lims, Steps[, yerr, ...])

Carry out MCMC fit/error estimation.

freeParamNames()

Get the names of the free parameters.

freeParameters()

Get names and values of free parameters.

freeze(specifiers)

Consider variables free to float.

frozenParameters()

Get names and values of frozen parameters.

getRelationsOf(specifier)

Return relations of a variable.

getRestrictions()

Get all restrictions.

hasVariable(specifier)

Determine whether the variable exists.

numberOfFreeParams()

Get number of free parameters.

parameterSummary([toScreen, prefix, sorting])

Writes a summary of the parameters in text form.

parameters()

Obtain parameter names and values.

relate(dependentVar, independentVars[, func])

Define a relation.

removeConditionalRestriction(*args)

Remove an existing conditional constraint.

renameVariable(oldName, newName)

Change name of variable.

restoreState(resource)

Restores parameter values from file or dictionary.

saveState(*args, **kwargs)

Save the state of the fitting object.

setObjectiveFunction([miniFunc])

Define the objective function.

setPenaltyFactor(penalFac)

Change the penalty factor.

setRestriction(restricts)

Define restrictions.

setRootName(root[, rename])

Define the root name of the model.

showConditionalRestrictions(**kwargs)

Show conditional restrictions.

steppar(pars, ranges[, extractFctVal, quiet])

Allows to step a parameter through a specified range.

thaw(specifiers)

Consider variables fixed.

untie(parName[, forceFree])

Remove all relations of parameter parName, i.e., the parameter is not dependend on other parameters.

updateModel()

Recalculate the model using current settings.
evalComponent(x, p)

Evaluate the model considering only a single component.

Parameters
xarray

The abscissa.

pint

Component number (starts with one).

Returns
Single component modelarray

The model considering a single component. Note that the linear continuum is included.

evaluate(x)

Evaluates the model for current parameter values.

Parameters
xarray

Specifies the points at which to evaluate the model.

Sine fit

class PyAstronomy.funcFit.SinusFit1d
Implements a sinusoidal function of the form:

A * sin[ 2*pi * (nu * t + phi) ] + off.

Fit parameters:

  • A - Amplitude

  • nu - Frequency (= 1/Period)

  • phi - Phase

  • off - Offset

Methods

MCMCautoParameters(ranges[, picky, ...])

Convenience function to generate parameters for MCMC fit.

addConditionalRestriction(*args)

Define a conditional restriction.

assignValue(specval)

Assign new values to variables.

assignValues(specval)

Assign new values to variables.

autoFitMCMC(x, y, ranges[, picky, stepsize, ...])

Convenience function to using auto-generated sampling parameters in MCMC.

availableParameters()

Provides a list of existing parameters.

delRestriction(parName)

Delete restriction

description([parenthesis])

Returns a description of the model based on the names of the individual components.

errorConfInterval(par[, dstat, statTol, ...])

Calculate confidence interval for a parameter.

evaluate(x)

Evaluates the model for current parameter values.

fit(x, y[, yerr, X0, minAlgo, mAA, ...])

Carries out a fit.

fitEMCEE([x, y, yerr, nwalker, priors, ...])

MCMC sampling using emcee package.

fitMCMC(x, y, X0, Lims, Steps[, yerr, ...])

Carry out MCMC fit/error estimation.

freeParamNames()

Get the names of the free parameters.

freeParameters()

Get names and values of free parameters.

freeze(specifiers)

Consider variables free to float.

frozenParameters()

Get names and values of frozen parameters.

getRelationsOf(specifier)

Return relations of a variable.

getRestrictions()

Get all restrictions.

hasVariable(specifier)

Determine whether the variable exists.

numberOfFreeParams()

Get number of free parameters.

parameterSummary([toScreen, prefix, sorting])

Writes a summary of the parameters in text form.

parameters()

Obtain parameter names and values.

relate(dependentVar, independentVars[, func])

Define a relation.

removeConditionalRestriction(*args)

Remove an existing conditional constraint.

renameVariable(oldName, newName)

Change name of variable.

restoreState(resource)

Restores parameter values from file or dictionary.

saveState(*args, **kwargs)

Save the state of the fitting object.

setObjectiveFunction([miniFunc])

Define the objective function.

setPenaltyFactor(penalFac)

Change the penalty factor.

setRestriction(restricts)

Define restrictions.

setRootName(root[, rename])

Define the root name of the model.

showConditionalRestrictions(**kwargs)

Show conditional restrictions.

steppar(pars, ranges[, extractFctVal, quiet])

Allows to step a parameter through a specified range.

thaw(specifiers)

Consider variables fixed.

untie(parName[, forceFree])

Remove all relations of parameter parName, i.e., the parameter is not dependend on other parameters.

updateModel()

Recalculate the model using current settings.

Exponential decay

class PyAstronomy.funcFit.ExpDecayFit1d
Implements an exponential decay function of the form

A * exp[ - (t-t0)/tau] + off.

Fit parameters:

  • A - Amplitude

  • tau - Mean lifetime (=1/decay rate)

  • t0 - Onset time

  • off - Continuum offset

Methods

MCMCautoParameters(ranges[, picky, ...])

Convenience function to generate parameters for MCMC fit.

addConditionalRestriction(*args)

Define a conditional restriction.

assignValue(specval)

Assign new values to variables.

assignValues(specval)

Assign new values to variables.

autoFitMCMC(x, y, ranges[, picky, stepsize, ...])

Convenience function to using auto-generated sampling parameters in MCMC.

availableParameters()

Provides a list of existing parameters.

delRestriction(parName)

Delete restriction

description([parenthesis])

Returns a description of the model based on the names of the individual components.

errorConfInterval(par[, dstat, statTol, ...])

Calculate confidence interval for a parameter.

evaluate(x)

Evaluates the model for current parameter values.

fit(x, y[, yerr, X0, minAlgo, mAA, ...])

Carries out a fit.

fitEMCEE([x, y, yerr, nwalker, priors, ...])

MCMC sampling using emcee package.

fitMCMC(x, y, X0, Lims, Steps[, yerr, ...])

Carry out MCMC fit/error estimation.

freeParamNames()

Get the names of the free parameters.

freeParameters()

Get names and values of free parameters.

freeze(specifiers)

Consider variables free to float.

frozenParameters()

Get names and values of frozen parameters.

getRelationsOf(specifier)

Return relations of a variable.

getRestrictions()

Get all restrictions.

hasVariable(specifier)

Determine whether the variable exists.

numberOfFreeParams()

Get number of free parameters.

parameterSummary([toScreen, prefix, sorting])

Writes a summary of the parameters in text form.

parameters()

Obtain parameter names and values.

relate(dependentVar, independentVars[, func])

Define a relation.

removeConditionalRestriction(*args)

Remove an existing conditional constraint.

renameVariable(oldName, newName)

Change name of variable.

restoreState(resource)

Restores parameter values from file or dictionary.

saveState(*args, **kwargs)

Save the state of the fitting object.

setObjectiveFunction([miniFunc])

Define the objective function.

setPenaltyFactor(penalFac)

Change the penalty factor.

setRestriction(restricts)

Define restrictions.

setRootName(root[, rename])

Define the root name of the model.

showConditionalRestrictions(**kwargs)

Show conditional restrictions.

steppar(pars, ranges[, extractFctVal, quiet])

Allows to step a parameter through a specified range.

thaw(specifiers)

Consider variables fixed.

untie(parName[, forceFree])

Remove all relations of parameter parName, i.e., the parameter is not dependend on other parameters.

updateModel()

Recalculate the model using current settings.

Polynomial of degree n

class PyAstronomy.funcFit.PolyFit1d(degree, xoff=0.0)

Implements a polynomial fit.

Fit parameters:
  • cn - Here n is a number indicating degree

    (e.g., c0 + c1*x + c2*x**2 …)

If xoff is specified, the polynomial will be evaluated at the points x-xoff. This can be useful to suppress correlation.

Methods

MCMCautoParameters(ranges[, picky, ...])

Convenience function to generate parameters for MCMC fit.

addConditionalRestriction(*args)

Define a conditional restriction.

asNPPoly()

Construct a numpy.poly1d object from the coefficients.

assignValue(specval)

Assign new values to variables.

assignValues(specval)

Assign new values to variables.

autoFitMCMC(x, y, ranges[, picky, stepsize, ...])

Convenience function to using auto-generated sampling parameters in MCMC.

availableParameters()

Provides a list of existing parameters.

delRestriction(parName)

Delete restriction

description([parenthesis])

Returns a description of the model based on the names of the individual components.

errorConfInterval(par[, dstat, statTol, ...])

Calculate confidence interval for a parameter.

evaluate(x)

Evaluates the model for current parameter values.

fit(x, y[, yerr, X0, minAlgo, mAA, ...])

Carries out a fit.

fitEMCEE([x, y, yerr, nwalker, priors, ...])

MCMC sampling using emcee package.

fitMCMC(x, y, X0, Lims, Steps[, yerr, ...])

Carry out MCMC fit/error estimation.

freeParamNames()

Get the names of the free parameters.

freeParameters()

Get names and values of free parameters.

freeze(specifiers)

Consider variables free to float.

frozenParameters()

Get names and values of frozen parameters.

getRelationsOf(specifier)

Return relations of a variable.

getRestrictions()

Get all restrictions.

hasVariable(specifier)

Determine whether the variable exists.

numberOfFreeParams()

Get number of free parameters.

parameterSummary([toScreen, prefix, sorting])

Writes a summary of the parameters in text form.

parameters()

Obtain parameter names and values.

relate(dependentVar, independentVars[, func])

Define a relation.

removeConditionalRestriction(*args)

Remove an existing conditional constraint.

renameVariable(oldName, newName)

Change name of variable.

restoreState(resource)

Restores parameter values from file or dictionary.

saveState(*args, **kwargs)

Save the state of the fitting object.

setObjectiveFunction([miniFunc])

Define the objective function.

setPenaltyFactor(penalFac)

Change the penalty factor.

setRestriction(restricts)

Define restrictions.

setRootName(root[, rename])

Define the root name of the model.

showConditionalRestrictions(**kwargs)

Show conditional restrictions.

steppar(pars, ranges[, extractFctVal, quiet])

Allows to step a parameter through a specified range.

thaw(specifiers)

Consider variables fixed.

untie(parName[, forceFree])

Remove all relations of parameter parName, i.e., the parameter is not dependend on other parameters.

updateModel()

Recalculate the model using current settings.

Hyperbolic secant

class PyAstronomy.funcFit.Sech1d

Implements a one dimensional hyperbolic secant

The functional form is:

\[\frac{2 A}{e^{(x-mu)/w} + e^{-(x-mu)/w} } + x \times lin + off\]

Here, lin and off denote the linear and the offset term.

Note

The area under the curve is given by \(\pi \times A\)

Fit parameters:

  • A - Amplitude (maximum/minimum of the curve, not area)

  • mu - Center of the hyperbolic secant

  • w - Width parameter

  • off - Offset

  • lin - Linear term

Methods

MCMCautoParameters(ranges[, picky, ...])

Convenience function to generate parameters for MCMC fit.

addConditionalRestriction(*args)

Define a conditional restriction.

assignValue(specval)

Assign new values to variables.

assignValues(specval)

Assign new values to variables.

autoFitMCMC(x, y, ranges[, picky, stepsize, ...])

Convenience function to using auto-generated sampling parameters in MCMC.

availableParameters()

Provides a list of existing parameters.

delRestriction(parName)

Delete restriction

description([parenthesis])

Returns a description of the model based on the names of the individual components.

errorConfInterval(par[, dstat, statTol, ...])

Calculate confidence interval for a parameter.

evaluate(x)

Evaluates the model for current parameter values.

fit(x, y[, yerr, X0, minAlgo, mAA, ...])

Carries out a fit.

fitEMCEE([x, y, yerr, nwalker, priors, ...])

MCMC sampling using emcee package.

fitMCMC(x, y, X0, Lims, Steps[, yerr, ...])

Carry out MCMC fit/error estimation.

freeParamNames()

Get the names of the free parameters.

freeParameters()

Get names and values of free parameters.

freeze(specifiers)

Consider variables free to float.

frozenParameters()

Get names and values of frozen parameters.

getRelationsOf(specifier)

Return relations of a variable.

getRestrictions()

Get all restrictions.

hasVariable(specifier)

Determine whether the variable exists.

numberOfFreeParams()

Get number of free parameters.

parameterSummary([toScreen, prefix, sorting])

Writes a summary of the parameters in text form.

parameters()

Obtain parameter names and values.

relate(dependentVar, independentVars[, func])

Define a relation.

removeConditionalRestriction(*args)

Remove an existing conditional constraint.

renameVariable(oldName, newName)

Change name of variable.

restoreState(resource)

Restores parameter values from file or dictionary.

saveState(*args, **kwargs)

Save the state of the fitting object.

setObjectiveFunction([miniFunc])

Define the objective function.

setPenaltyFactor(penalFac)

Change the penalty factor.

setRestriction(restricts)

Define restrictions.

setRootName(root[, rename])

Define the root name of the model.

showConditionalRestrictions(**kwargs)

Show conditional restrictions.

steppar(pars, ranges[, extractFctVal, quiet])

Allows to step a parameter through a specified range.

thaw(specifiers)

Consider variables fixed.

untie(parName[, forceFree])

Remove all relations of parameter parName, i.e., the parameter is not dependend on other parameters.

updateModel()

Recalculate the model using current settings.

Constant

class PyAstronomy.funcFit.ConstantFit1d

Implements a constant model.

Fit parameters:

  • c - The constant.

Methods

MCMCautoParameters(ranges[, picky, ...])

Convenience function to generate parameters for MCMC fit.

addConditionalRestriction(*args)

Define a conditional restriction.

assignValue(specval)

Assign new values to variables.

assignValues(specval)

Assign new values to variables.

autoFitMCMC(x, y, ranges[, picky, stepsize, ...])

Convenience function to using auto-generated sampling parameters in MCMC.

availableParameters()

Provides a list of existing parameters.

delRestriction(parName)

Delete restriction

description([parenthesis])

Returns a description of the model based on the names of the individual components.

errorConfInterval(par[, dstat, statTol, ...])

Calculate confidence interval for a parameter.

evaluate(x)

Evaluates the model for current parameter values.

fit(x, y[, yerr, X0, minAlgo, mAA, ...])

Carries out a fit.

fitEMCEE([x, y, yerr, nwalker, priors, ...])

MCMC sampling using emcee package.

fitMCMC(x, y, X0, Lims, Steps[, yerr, ...])

Carry out MCMC fit/error estimation.

freeParamNames()

Get the names of the free parameters.

freeParameters()

Get names and values of free parameters.

freeze(specifiers)

Consider variables free to float.

frozenParameters()

Get names and values of frozen parameters.

getRelationsOf(specifier)

Return relations of a variable.

getRestrictions()

Get all restrictions.

hasVariable(specifier)

Determine whether the variable exists.

numberOfFreeParams()

Get number of free parameters.

parameterSummary([toScreen, prefix, sorting])

Writes a summary of the parameters in text form.

parameters()

Obtain parameter names and values.

relate(dependentVar, independentVars[, func])

Define a relation.

removeConditionalRestriction(*args)

Remove an existing conditional constraint.

renameVariable(oldName, newName)

Change name of variable.

restoreState(resource)

Restores parameter values from file or dictionary.

saveState(*args, **kwargs)

Save the state of the fitting object.

setObjectiveFunction([miniFunc])

Define the objective function.

setPenaltyFactor(penalFac)

Change the penalty factor.

setRestriction(restricts)

Define restrictions.

setRootName(root[, rename])

Define the root name of the model.

showConditionalRestrictions(**kwargs)

Show conditional restrictions.

steppar(pars, ranges[, extractFctVal, quiet])

Allows to step a parameter through a specified range.

thaw(specifiers)

Consider variables fixed.

untie(parName[, forceFree])

Remove all relations of parameter parName, i.e., the parameter is not dependend on other parameters.

updateModel()

Recalculate the model using current settings.

Two-dimensional Gaussian

class PyAstronomy.funcFit.GaussFit2d

Implements a two dimensional Gaussian.

Expects a coordinate array to evaluate model.

The functional form is:

\[\frac{A}{2\pi\sigma_x\sigma_y\sqrt{1-\rho^2}} exp\left(-\frac{1}{2(1-\rho^2)}\left( \frac{(x-\mu_x)^2}{\sigma_x^2} + \frac{(y-\mu_y)^2}{\sigma_y^2} - \frac{2\rho(x-\mu_x)(y-\mu_y)}{\sigma_x\sigma_y} \right)\right)\]

Here, lin and off denote the linear and the offset term.

Fit parameters:

  • A - Amplitude (the area of the Gaussian)

  • mux - Center of the Gaussian (x-axis)

  • muy - Center of the Gaussian (y-axis)

  • sigx - Standard deviation (x-axis)

  • sigy - Standard deviation (y-axis)

  • rho - Correlation

Methods

MCMCautoParameters(ranges[, picky, ...])

Convenience function to generate parameters for MCMC fit.

addConditionalRestriction(*args)

Define a conditional restriction.

assignValue(specval)

Assign new values to variables.

assignValues(specval)

Assign new values to variables.

autoFitMCMC(x, y, ranges[, picky, stepsize, ...])

Convenience function to using auto-generated sampling parameters in MCMC.

availableParameters()

Provides a list of existing parameters.

delRestriction(parName)

Delete restriction

description([parenthesis])

Returns a description of the model based on the names of the individual components.

errorConfInterval(par[, dstat, statTol, ...])

Calculate confidence interval for a parameter.

evaluate(co)

Evaluates the model for current parameter values.

fit(x, y[, yerr, X0, minAlgo, mAA, ...])

Carries out a fit.

fitEMCEE([x, y, yerr, nwalker, priors, ...])

MCMC sampling using emcee package.

fitMCMC(x, y, X0, Lims, Steps[, yerr, ...])

Carry out MCMC fit/error estimation.

freeParamNames()

Get the names of the free parameters.

freeParameters()

Get names and values of free parameters.

freeze(specifiers)

Consider variables free to float.

frozenParameters()

Get names and values of frozen parameters.

getRelationsOf(specifier)

Return relations of a variable.

getRestrictions()

Get all restrictions.

hasVariable(specifier)

Determine whether the variable exists.

numberOfFreeParams()

Get number of free parameters.

parameterSummary([toScreen, prefix, sorting])

Writes a summary of the parameters in text form.

parameters()

Obtain parameter names and values.

relate(dependentVar, independentVars[, func])

Define a relation.

removeConditionalRestriction(*args)

Remove an existing conditional constraint.

renameVariable(oldName, newName)

Change name of variable.

restoreState(resource)

Restores parameter values from file or dictionary.

saveState(*args, **kwargs)

Save the state of the fitting object.

setObjectiveFunction([miniFunc])

Define the objective function.

setPenaltyFactor(penalFac)

Change the penalty factor.

setRestriction(restricts)

Define restrictions.

setRootName(root[, rename])

Define the root name of the model.

showConditionalRestrictions(**kwargs)

Show conditional restrictions.

steppar(pars, ranges[, extractFctVal, quiet])

Allows to step a parameter through a specified range.

thaw(specifiers)

Consider variables fixed.

untie(parName[, forceFree])

Remove all relations of parameter parName, i.e., the parameter is not dependend on other parameters.

updateModel()

Recalculate the model using current settings.

Multicomponent two-dimensional Gaussian

class PyAstronomy.funcFit.MultiGauss2d(n)

Implements a multicomponent, two dimensional Gaussian.

Expects a coordinate array to evaluate model.

The functional form is:

\[\frac{A}{2\pi\sigma_x\sigma_y\sqrt{1-\rho^2}} exp\left(-\frac{1}{2(1-\rho^2)}\left( \frac{(x-\mu_x)^2}{\sigma_x^2} + \frac{(y-\mu_y)^2}{\sigma_y^2} - \frac{2\rho(x-\mu_x)(y-\mu_y)}{\sigma_x\sigma_y} \right)\right)\]
Parameters
nint

The number of Gaussian components.

*Fit parameters*:

  • A - Amplitude (the area of the Gaussian)

  • mux - Center of the Gaussian (x-axis)

  • muy - Center of the Gaussian (y-axis)

  • sigx - Standard deviation (x-axis)

  • sigy - Standard deviation (y-axis)

  • rho - Correlation

  • off - Constant offset

Methods

MCMCautoParameters(ranges[, picky, ...])

Convenience function to generate parameters for MCMC fit.

addConditionalRestriction(*args)

Define a conditional restriction.

assignValue(specval)

Assign new values to variables.

assignValues(specval)

Assign new values to variables.

autoFitMCMC(x, y, ranges[, picky, stepsize, ...])

Convenience function to using auto-generated sampling parameters in MCMC.

availableParameters()

Provides a list of existing parameters.

delRestriction(parName)

Delete restriction

description([parenthesis])

Returns a description of the model based on the names of the individual components.

errorConfInterval(par[, dstat, statTol, ...])

Calculate confidence interval for a parameter.

evaluate(co)

Evaluates the model for current parameter values.

fit(x, y[, yerr, X0, minAlgo, mAA, ...])

Carries out a fit.

fitEMCEE([x, y, yerr, nwalker, priors, ...])

MCMC sampling using emcee package.

fitMCMC(x, y, X0, Lims, Steps[, yerr, ...])

Carry out MCMC fit/error estimation.

freeParamNames()

Get the names of the free parameters.

freeParameters()

Get names and values of free parameters.

freeze(specifiers)

Consider variables free to float.

frozenParameters()

Get names and values of frozen parameters.

getRelationsOf(specifier)

Return relations of a variable.

getRestrictions()

Get all restrictions.

hasVariable(specifier)

Determine whether the variable exists.

numberOfFreeParams()

Get number of free parameters.

parameterSummary([toScreen, prefix, sorting])

Writes a summary of the parameters in text form.

parameters()

Obtain parameter names and values.

relate(dependentVar, independentVars[, func])

Define a relation.

removeConditionalRestriction(*args)

Remove an existing conditional constraint.

renameVariable(oldName, newName)

Change name of variable.

restoreState(resource)

Restores parameter values from file or dictionary.

saveState(*args, **kwargs)

Save the state of the fitting object.

setObjectiveFunction([miniFunc])

Define the objective function.

setPenaltyFactor(penalFac)

Change the penalty factor.

setRestriction(restricts)

Define restrictions.

setRootName(root[, rename])

Define the root name of the model.

showConditionalRestrictions(**kwargs)

Show conditional restrictions.

steppar(pars, ranges[, extractFctVal, quiet])

Allows to step a parameter through a specified range.

thaw(specifiers)

Consider variables fixed.

untie(parName[, forceFree])

Remove all relations of parameter parName, i.e., the parameter is not dependend on other parameters.

updateModel()

Recalculate the model using current settings.

Demonstration models

Models mainly used for demonstration purposes.

Simple circular orbit

class PyAstronomy.funcFit.Circle2d

Implements a simple, two-dimensional circular orbit.

The functional form is:

\[(x,y) = (r \cos(\omega (t-t_0)), r \sin(\omega (t-t_0)))\]

where \(\omega\) is \(2\pi/Period\).

Fit parameters:

  • r - Radius of the circle

  • per - Period of orbit

  • t0 - Starting time of orbit

Methods

MCMCautoParameters(ranges[, picky, ...])

Convenience function to generate parameters for MCMC fit.

addConditionalRestriction(*args)

Define a conditional restriction.

assignValue(specval)

Assign new values to variables.

assignValues(specval)

Assign new values to variables.

autoFitMCMC(x, y, ranges[, picky, stepsize, ...])

Convenience function to using auto-generated sampling parameters in MCMC.

availableParameters()

Provides a list of existing parameters.

delRestriction(parName)

Delete restriction

description([parenthesis])

Returns a description of the model based on the names of the individual components.

errorConfInterval(par[, dstat, statTol, ...])

Calculate confidence interval for a parameter.

evaluate(t)

Evaluates the model for current parameter values.

fit(x, y[, yerr, X0, minAlgo, mAA, ...])

Carries out a fit.

fitEMCEE([x, y, yerr, nwalker, priors, ...])

MCMC sampling using emcee package.

fitMCMC(x, y, X0, Lims, Steps[, yerr, ...])

Carry out MCMC fit/error estimation.

freeParamNames()

Get the names of the free parameters.

freeParameters()

Get names and values of free parameters.

freeze(specifiers)

Consider variables free to float.

frozenParameters()

Get names and values of frozen parameters.

getRelationsOf(specifier)

Return relations of a variable.

getRestrictions()

Get all restrictions.

hasVariable(specifier)

Determine whether the variable exists.

numberOfFreeParams()

Get number of free parameters.

parameterSummary([toScreen, prefix, sorting])

Writes a summary of the parameters in text form.

parameters()

Obtain parameter names and values.

relate(dependentVar, independentVars[, func])

Define a relation.

removeConditionalRestriction(*args)

Remove an existing conditional constraint.

renameVariable(oldName, newName)

Change name of variable.

restoreState(resource)

Restores parameter values from file or dictionary.

saveState(*args, **kwargs)

Save the state of the fitting object.

setObjectiveFunction([miniFunc])

Define the objective function.

setPenaltyFactor(penalFac)

Change the penalty factor.

setRestriction(restricts)

Define restrictions.

setRootName(root[, rename])

Define the root name of the model.

showConditionalRestrictions(**kwargs)

Show conditional restrictions.

steppar(pars, ranges[, extractFctVal, quiet])

Allows to step a parameter through a specified range.

thaw(specifiers)

Consider variables fixed.

untie(parName[, forceFree])

Remove all relations of parameter parName, i.e., the parameter is not dependend on other parameters.

updateModel()

Recalculate the model using current settings.