OptimizerOptions

class nexus.OptimizerOptions

OptimizerOptions for the used algorithms in the Optimizer and Fit classes.

For more information on the different solvers and their algorithms see:

method

Method used by the Optimizer or Fit module. All methods take boundary constraints except the LineSearch method. Default is LevMar.

Gradient-based LOCAL fitting - Ceres solver.

  • LevMar - Levenberg-Marquardt algorithm.

  • Dogleg - Dogleg algorithm.

  • SubDogleg - Subspace Dogleg algorithm.

  • LineSearch - Linear search algorithm. No boundary constraints.

Gradient-free LOCAL fitting - NLopt or Pagmo solver.

  • Subplex - Nelder-Mead algorithm on a sequence of subspaces (NLopt).

  • Newuoa - New Unconstrained Optimization with quadratic Approximation algorithm (NLopt).

  • CompassSearch - Compass Search algorithm (Pagmo).

Gradient-free GLOBAL fitting - Pagmo solver.

  • PagmoDiffEvol - Self-adaptive Differential Evolution 1220 algorithm.

  • AdaptiveDiffEvol - Self-adaptive Differential Evolution algorithm.

  • DiffEvol - Differential Evolution algorithm.

  • BeeColony - Artificial Bee Colony algorithm.

  • CMA-ES - Covariance Matrix Adaptation Evolutionary Strategy algorithm.

  • AntColony - Extended Ant Colony Optimization algorithm.

  • GreyWolf - Grey Wolf Optimizer algorithm.

  • ParticleSwarm - Particle Swarm Optimization algorithm.

  • ParticleSwarmGen - Particle Swarm Optimization Generational algorithm.

  • SimpleEvol - (N+1)-ES Simple Evolutionary Algorithm.

  • Genetic - Simple Genetic Algorithm.

  • Annealing - Simulated Annealing algorithm.

  • NaturalEvol - Exponential Natural Evolution Strategies algorithm.

  • BasinHopping - Monotonic Basin Hopping with local algorithm.

Type:

string

local

A subsequent local solver following the method. If it is the same as method no second fit is performed. Default is LevMar.

Type:

string

population

Initial population for global fit methods. When value is zero the population is set by the fit method. Default is 0.

Type:

int

iterations

Maximum of iterations of a solver. If set to zero the solver method will set a reasonable value. Default is 0.

Type:

int

max_time

Maximum run time of the ceres solver or the Nlopt solver (seconds). Default is 300.

Type:

float

output

Set output during fitting. Default is True.

Type:

bool

report

Output of the ceres solver. None, Brief or Full. Default Brief.

Type:

string

function_tolerance

Tolerance of change of the cost value for termination of the solver \(|(\Delta cost) / cost|\). Only for methods that support this option. Default is 1.0e-10.

Type:

float

gradient_tolerance

Tolerance of change of the gradient for termination of the solver. Only for methods that support this option. Default is 1.0e-10.

Type:

float

parameter_tolerance

Tolerance of change of the parameter for termination of the solver. Only for methods that support this option. Default is 1.0e-4.

Type:

float

cost_relative_step_size

Relative step size for the numerical derivatives in the ceres solver. Default is 1e-6.

Changed in version 1.1.0: - Default changed from 0.01 to 1e-6.

Type:

float

file_output

Determines if an output file with the fit results is generated. The file is named after the id and each time a fit is run the filename is automatically increased in numbers.

New in version 1.1.0.

Type:

bool

error_method

Set the method of error calculations of the fit parameters.

  • Gradient: Based on the gradient-based local algorithms from the ceres solver. The ceres solver will be called as last fit instance to determine the error estimates. Default.

  • Bootstrap: Bootstrap method for error analysis. A resampling strategy to determine errors of unknown distributions. This method is computationally expensive and might take quite long. See BootstrapOptions for options on this method.

  • None: No error analysis.

New in version 1.1.0.

Type:

string

LineSearch

Options for the LineSearch method of the ceres solver.

Type:

LineSearchOptions

DiffEvol

Options for all Differential Evolution algorithms.

Type:

DiffEvolOptions

CompassSearch

Options for the Compass Search algorithm.

Type:

CompassSearchOptions

BasinHopping

Options for the Basin Hopping algorithm.

Type:

BasinHoppingOptions

Bootstrap

Options for the Bootstrap error analysis.

New in version 1.1.0.

Type:

BootstrapOptions

class nexus.LineSearchOptions

LineSearchOptions for the Line Search method. The LineSearch method does not support boundaries on the fit parameters.

See also

https://en.wikipedia.org/wiki/Line_search

line_search_type

Linear search type for the “LineSearch” method. Default is LBFGS.

  • LBFGS: Limited-memory Broyden Fletcher Goldfarb Shanno method.

  • BFGS: Broyden Fletcher Goldfarb Shanno method.

  • SteepDes: Steepest descent method.

  • NonConGrag: Non-linear conjugate gradient method.

Type:

string

max_num_line_search_step_size_iterations

Default is 20.

Type:

int

class nexus.CompassSearchOptions

CompassSearchOptions for the Compass Search algorithm.

  • If options.iterations = 0, the number of iterations is set to 500.

start_range

In range (0,1]. Default is 0.1.

Type:

double

stop_range

In range (0,start_range]. Default is 0.05.

Type:

double

reduction_coeff

In range (0,1). Default is 0.5.

Type:

double

class nexus.DiffEvolOptions

DiffEvolOptions for the Differential Evolution algorithms.

The Adaptive Differential Evolution takes the variant and the adaptive_variant into account. For the Pagmo Differential Evolution only the adaptive_variant is used. For the classical Differential Evolution take the following into consideration:

“The mutation factor F is a positive control parameter for scaling and controlling the amplification of the difference vector. Small values of F will lead to smaller mutation step sizes and as a result it will take longer for the algorithm to converge. Large values of F facilitate exploration, but can lead to the algorithm overshooting good optima. Thus, the value has to be small enough to enhance local exploration but also large enough to maintain diversity. The crossover probability CR has an influence on the diversity of DE, as it controls the number of elements that will change. Larger values of CR will lead to introducing more variation in the new population, therefore increasing it increases exploration.” from Manolis S. Georgioudakis and Vagelis Plevris, A Comparative Study of Differential Evolution Variants in Constrained Structural Optimization.

  • If options.population = 0, the population is set to \(10 (n+1)\), where \(n\) is the number of fit parameters. Default is 0. When you increase the population you should also decrease the weight F but typically not lower than 0.5.

  • If options.iterations = 0, the number of iterations is set to 100.

See also

https://en.wikipedia.org/wiki/Differential_evolution

F

Differential weight F in the range [0,1]. Default is 0.8.

Type:

double

CR

Crossover probability CR in the range [0,1]. Default is 0.9.

Type:

double

variant

Variants of the mutation scheme, value is 1, 2, …, 10. Default is 2. Labeling: vector decision / number difference vectors / crossover strategy (binominal or exponential)

  • 1 - best/1/exp

  • 2 - rand/1/exp

  • 3 - rand-to-best/1/exp

  • 4 - best/2/exp

  • 5 - rand/2/exp

  • 6 - best/1/bin

  • 7 - rand/1/bin

  • 8 - rand-to-best/1/bin

  • 9 - best/2/bin

  • 10 - rand/2/bin

Type:

int

adaptive_variant

Self-adaptation variants, value is 1 or 2. Default is 1.

  • 1 - jDE (Brest et al.)

  • 2 - iDE (Elsayed at al.)

Type:

int

class nexus.BasinHoppingOptions

BasinHoppingOptions for the Basin Hopping algorithm. This is a meta algorithm that uses another inner algorithm. CompassSearch or Subplex method can be used as inner algorithm.

See also

https://en.wikipedia.org/wiki/Basin-hopping

inner

Inner algorithm. Either Subplex or Compass. Default is Compass.

Type:

string

stop

Runs of the inner algorithm without improvement. Default is 5.

Type:

int

perturbation

Perturbation to be applied to each component of the decision vector of the best population. Default is 0.01.

Type:

double

class nexus.BootstrapOptions

BootstrapOptions for the Bootstrap error analysis.

See also

https://en.wikipedia.org/wiki/Bootstrapping_(statistics)

New in version 1.1.0.

method

Bootstrap method. Default is “Wild”.

  • Poisson: Parametric bootstrap with Poisson statistics. The data points are resampled at each point from a Poisson distribution with an expectation value of the measured intensity.

  • Gaussian: Parametric bootstrap with Gaussian statistics. The data points are resampled at each point from a Gaussian distribution with a mean value of the measured intensity and a with of the square root of the intensity.

  • Wild: The residuals of the initial fit are reweighted by a Gaussian distribution with a variance of one to generate a new data set. This method should be applied for heteroscedastic data sets (varying variance of all data points, like Time spectra). Can also be used for homoscedastic data sets.

  • Residuals: The residuals of the initial fit are randomly redistributed over the fit curve to generate a new data set. This method should only be applied for homoscedastic data sets (same variance of all data, like typical Moessbauer spectra).

  • Smoothed: For each data point random noise is added from a Gaussian distribution kernel with variance of one scaled by h. The smoothing parameter is the scaling factor of the data point, so h = smooting_parameter * data_point.

  • Smoothed_Uniform: For each data point random noise is added from a uniform distribution kernel [-h, h]. The smoothing parameter is the scaling factor of the data point, so h = smooting_parameter * data_point

See also

https://en.wikipedia.org/wiki/Homoscedasticity_and_heteroscedasticity

Type:

string

num_bootstrap

Number of evaluations for bootstrap error method. Default is 50.

Type:

int

smoothing_parameter

The smoothing parameter is the scaling factor of the data point. So, the distribution is scaled by h = smooting_parameter * data_point. The value determines how much noise is added to the data. Default is 0.01.

Type:

float