scipy Routines

Fitter

lsqfit uses routines from the open-source scipy Python module provided it is installed. These routines are used in place of GSL routines if the latter are not installed. There is one fitter available for use by lsqfit.nonlinear_fit.

class lsqfit.scipy_least_squares(x0, n, f, tol=(1e-08, 1e-08, 1e-08), maxit=1000, **extra_args)

scipy fitter for nonlinear least-squares multidimensional fits.

scipy_least_squares is a function-class whose constructor does a least-squares fit by minimizing sum_i f_i(x)**2 as a function of vector x.

scipy_least_squares is a wrapper for the scipy.optimize.least_squares.

Parameters:

  • x0 (array of floats) – Starting point for minimization.

  • n (positive int) – Length of vector returned by the fit function f(x).

  • f (array-valued function) – sum_i f_i(x)**2 is minimized by varying parameters x. The parameters are a 1-d numpy array of either numbers or gvar.GVars.

  • tol (float or tuple) –

    Assigning tol=(xtol, gtol, ftol) causes the fit to stop searching for a minimum when any of

    xtol >= relative change in parameters between iterations

    gtol >= relative size of gradient of chi**2

    ftol >= relative change in chi**2 between iterations

    is statisfied. See the scipy.optimize.least_squares documentation detailed definitions of the stopping conditions. Typically one sets xtol=1/10**d where d is the number of digits of precision desired in the result, while gtol<<1 and ftol<<1. Setting tol=eps where eps is a number is equivalent to setting tol=(eps,1e-10,1e-10). Setting tol=(eps1,eps2) is equivlent to setting tol=(eps1,eps2,1e-10). Default is tol=1e-5.

  • method (str or None) –

    Minimization algorithm. Options include:

    'trf'

    Trusted Region Reflective algorithm (default). Best choice with bounded parameters.

    'dogbox'

    dogleg algorithm adapted for bounded parameters.

    'lm'

    Levenberg-Marquardt algorithm as implemented in MINPACK. Best for smaller problems. Does not work with bounded parameters (bounds are ignored).

    Setting method=None implies the default 'trf'.

  • maxit (int) – Maximum number of function evaluations in search for minimum; default is 1000.

Other arguments include: x_jac, loss, tr_solver, f_scale, tr_options, bounds. See the documentation for scipy.optimize.least_squares for information about these and other options.

lsqfit.scipy_least_squares objects have the following attributes.

x

Location of the most recently computed (best) fit point.

Type:

array

cov

Covariance matrix at the minimum point.

Type:

array

description

Short description of internal fitter settings.

Type:

str

f

Fit function value f(x) at the minimum in the most recent fit.

Type:

array

J

Gradient J_ij = df_i/dx[j] for most recent fit.

Type:

array

nit

Number of function evaluations used in last fit to find the minimum.

Type:

int

stopping_criterion

Criterion used to stop fit:

  1. didn’t converge

  2. xtol >= relative change in parameters between iterations

  3. gtol >= relative size of gradient of chi**2

  4. ftol >= relative change in chi**2 between iterations

Type:

int

error

None if fit successful; an error message otherwise.

Type:

str or None

results

Results returned by scipy.optimize.least_squares.

Type:

dict

Minimizer

The lsqfit.empbayes_fit() uses a minimizer from the scipy module to minimize logGBF.

class lsqfit.scipy_multiminex(x0, f, tol=1e-4, maxit=1000, step=1, alg='nmsimplex2', analyzer=None)

scipy minimizer for multidimensional functions.

scipy_multiminex is a function-class whose constructor minimizes a multidimensional function f(x) by varying vector x. This routine does not use user-supplied information about the gradient of f(x).

scipy_multiminex is a wrapper for the minimize scipy function. It gives access to only part of that function.

Parameters:

  • x0 (array of floats) – Starting point for minimization search.

  • f – Function f(x) to be minimized by varying vector x.

  • tol (float) – Minimization stops when x has converged to with tolerance tol; default is 1e-4.

  • maxit (positive int) – Maximum number of iterations in search for minimum; default is 1000.

  • analyzer (function) – Optional function of the current x. This can be used to inspect intermediate steps in the minimization, if needed.

  • step (bool) – Included for consistency with GSL routines but ignored in scipy routine.

lsqfit.scipy_multiminex objects have the following attributes.

x

Location of the minimum.

Type:

array

f

Value of function f(x) at the minimum.

Type:

float

nit

Number of iterations required to find the minimum.

Type:

int

error

None if fit successful; an error message otherwise.

Type:

Noe or str