GOFit Algorithms

The GOFit module contains the following three optimization algorithms for parameter fitting nonlinear least-squares problems. The first two are global optimization algorithms and the third is an interface to the local optimization algorithm that is used within the global algorithms. Note that all algorithms expect numpy arrays for vector and matrix inputs.

Multistart Algorithm

gofit.multistart(m, n, xl, xu, res [, jac=None, samples=100, maxit=200, eps_r=1e-05, eps_g=1e-04, eps_s=1e-08, scaling=True]) -> (x, status)

Multistart global optimization algorithm. Starts multiple regularisation local optimization algorithms from a given number of randomly generated Latin Hypercube starting points.

Parameters:

  • m (int) – number of residuals (number of data points)

  • n (int) – number of parameters (dimension of the problem)

  • xl (numpy.ndarray) – lower bounds of the parameters to optimize

  • xu (numpy.ndarray) – upper bounds of the parameters to optimize

  • res (callable) – function that evaluates the residual, must have the signature r = res(x) where r is the residual (a numpy.ndarray of size m) evaluated at x (a numpy.ndarray of size n)

  • jac (None or callable, optional) – optional function that evaluates the Jacobian, must have the signature J = jac(x) where J is the Jacobian (a numpy.ndarray of size (m,n)) of the residual evaluated at x (a numpy.ndarray of size n). If not given computes the Jacobian using finite-differences

  • samples (int, optional) – number of Latin Hypercube starting points for the local solver

  • maxit (int, optional) – maximum number of iterations for each local solver run

  • eps_r (float, optional) – residual stopping tolerance

  • eps_g (float, optional) – norm of gradient stopping tolerance

  • eps_s (float, optional) – norm of step stopping tolerance

  • scaling (bool, optional) – whether to scale the optimization parameters (recommended)

Returns:

optimal parameters, status code

Return type:

(numpy.ndarray,int)

Alternating Algorithm

gofit.alternating(m, n, n_split, x0, xl, xu, res [, samples=100, maxit=200, eps_r=1e-05, eps_g=1e-04, eps_s=1e-08]) -> (x, status)

Alternating multistart global optimization algorithm. Assumes the parameters split into n_split model parameters and n-n_split shape parameters. Then proceeds as follows: 1. fix initial shape params, globally optimize model params; 2. fix model params, locally optimize shape params; 3. locally optimize over model params again; 4. locally optimize over shape params again. Please note that the optimization parameters are scaled by default.

Parameters:

  • m (int) – number of residuals (number of data points)

  • n (int) – number of parameters (dimension of the problem)

  • n_split (int) – parameter split point for alternating optimization (<n)

  • x0 (numpy.ndarray) – initial guess for the parameters

  • xl (numpy.ndarray) – lower bounds of the parameters to optimize

  • xu (numpy.ndarray) – upper bounds of the parameters to optimize

  • res (callable) – function that evaluates the residual, must have the signature r = res(x) where r is the residual (a numpy.ndarray of size m) evaluated at x (a numpy.ndarray of size n)

  • samples (int, optional) – number of Latin Hypercube starting points for the local solver

  • maxit (int, optional) – maximum number of iterations for each local solver run

  • eps_r (float, optional) – residual stopping tolerance

  • eps_g (float, optional) – norm of gradient stopping tolerance

  • eps_s (float, optional) – norm of step stopping tolerance

Returns:

optimal parameters, status code

Return type:

(numpy.ndarray,int)

Regularisation Algorithm

gofit.regularisation(m, n, x, res [, jac=None, maxit=200, eps_g=1e-04, eps_s=1e-08]) -> (x, status)

Adaptive quadratic regularisation local optimization algorithm. Included for completeness.

Parameters:

  • m (int) – number of residuals (number of data points)

  • n (int) – number of parameters (dimension of the problem)

  • x0 (numpy.ndarray) – initial guess for the parameters

  • res (callable) – function that evaluates the residual, must have the signature r = res(x) where r is the residual (a numpy.ndarray of size m) evaluated at x (a numpy.ndarray of size n)

  • jac (None or callable, optional) – optional function that evaluates the Jacobian, must have the signature J = jac(x) where J is the Jacobian (a numpy.ndarray of size (m,n)) of the residual evaluated at x (a numpy.ndarray of size n). If not given computes the Jacobian using finite-differences

  • maxit (int, optional) – maximum number of iterations for each local solver run

  • eps_g (float, optional) – norm of gradient stopping tolerance

  • eps_s (float, optional) – norm of step stopping tolerance

Returns:

optimal parameters, status code

Return type:

(numpy.ndarray,int)