The BornAgain minimizer interface was developed with the following ideas in mind:
Particularly, we have been inspired by the lmfit Python package, so the BornAgain setup looks very similar. In the code snippet below we give an example of finding the minimum of the Rosenbrock function using the BornAgain minimizer with default settings.
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The rest of the page gives additional details on
The BornAgain Parameters class allows to define a collection of fit parameters which will be varied during the fit.
Each fit parameter should have a unique name, starting value and possible bounds on its value.
params = ba.Parameters()
params.add("a", value=-1.2)
params.add("b", value=-1.2, min=0.0)
params.add("c", value=-1.2, min=-5.0, max=5.0, step=0.01)
params.add("d", value=1.0, vary=False)It is not possible to use mathematical expressions to constrain these value, as it is done
in the more advanced
parameter machinery
of lmfit package.
The BornAgain minimizer is a wrapper around a variety of minimization engines
from ROOT and GSL libraries.
They are listed in the table below. By default, Minuit2/Migrad will be used and no additional configuration needs to be done.
| Minimizer name | Algorithm | Description |
|---|---|---|
| Minuit2 | Migrad | Variable-metric method with inexact line search, a stable metric updating scheme, and checks for positive-definiteness. According to the Minuit users guide [ch. 5.1.1], this is the best minimizer for nearly all functions |
| Simplex | Simplex method of Nelder and Mead usually, slower than Migrad, rather robust with respect to gross fluctuations in the function value, gives no reliable information about parameter errors. |
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| Combined | Minimizes with Migrad, but switches to Simplex if Migrad fails to converge. |
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| Scan | Not intended to minimize, just scans the function, one parameter at a time, retains the best value after each scan. | |
| Fumili | Optimized method for least square and log likelihood minimizations. | |
| GSLMultiMin | ConjugateFR | Fletcher-Reeves conjugate gradient algorithm. |
| ConjugatePR | Polak-Ribiere conjugate gradient algorithm. | |
| BFGS | Broyden-Fletcher-Goldfarb-Shanno algorithm | |
| BFGS2 | Improved version of BFGS. |
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| SteepestDescent | Follows the downhill gradient of the function at each step. | |
| GSLLMA | Levenberg-Marquardt Algorithm | |
| GSLSimAn | Simulated Annealing Algorithm | |
| Genetic | Genetic Algorithm | |
| Test | Single-shot minimizer |
To change the minimize engine and its algorithm one has to use
minimizer = ba.Minimizer()
minimizer.setMinimizer("GSLMultiMin", "BFGS2")There are a number of minimizer options that can be changed. The commands below print the detailed info about the available minimizers, their options and the default option values.
# prints info about available minimizers
print(ba.MinimizerFactory().catalogueToString())
# prints detailed info about available minimizers and their options
print(ba.MinimizerFactory().catalogueDetailsToString())Click to expand command output
-------------------------------------------------------------------------------- Minuit2 | Minuit2 minimizer from ROOT library -------------------------------------------------------------------------------- Algorithm names Migrad | Variable-metric method with inexact line search, best minimizer according to ROOT. Simplex | Simplex method of Nelder and Meadh, robust against big fluctuations in objective function. Combined | Combination of Migrad and Simplex (if Migrad fails). Scan | Simple objective function scan, one parameter at a time. Fumili | Gradient descent minimizer similar to Levenberg-Margquardt, sometimes can be better than all others. Default algorithm | MigradOptions Strategy | 1 Minimization strategy (0-low, 1-medium, 2-high quality) ErrorDef | 1 Error definition factor for parameter error calculation Tolerance | 0.01 Tolerance on the function value at the minimum Precision | -1 Relative floating point arithmetic precision PrintLevel | 0 Minimizer internal print level MaxFunctionCalls | 0 Maximum number of function calls
GSLMultiMin | MultiMin minimizer from GSL library
Algorithm names SteepestDescent | Steepest descent ConjugateFR | Fletcher-Reeves conjugate gradient ConjugatePR | Polak-Ribiere conjugate gradient BFGS | BFGS conjugate gradient BFGS2 | BFGS conjugate gradient (Version 2) Default algorithm | ConjugateFR
Options PrintLevel | 0 Minimizer internal print level MaxIterations | 0 Maximum number of iterations
GSLLMA | Levenberg-Marquardt from GSL library
Algorithm names Default | Default algorithm
Options Tolerance | 0.01 Tolerance on the function value at the minimum PrintLevel | 0 Minimizer internal print level MaxIterations | 0 Maximum number of iterations
GSLSimAn | Simmulated annealing minimizer from GSL library
Algorithm names Default | Default algorithm
Options PrintLevel | 0 Minimizer internal print level MaxIterations | 100 Number of points to try for each step IterationsAtTemp | 10 Number of iterations at each temperature StepSize | 1 Max step size used in random walk k | 1 Boltzmann k t_init | 50 Boltzmann initial temperature mu | 1.05 Boltzmann mu t_min | 0.1 Boltzmann minimal temperature
Genetic | Genetic minimizer from TMVA library
Algorithm names Default | Default algorithm
Options Tolerance | 0.01 Tolerance on the function value at the minimum PrintLevel | 0 Minimizer internal print level MaxIterations | 3 Maximum number of iterations PopSize | 300 Population size RandomSeed | 0 Random seed
Test | One-shot minimizer to test whole chain
Algorithm names Default | Default algorithm
For example, to run the Minuit minimizer with the Migrad algorithm, limit the maximum number of objective function calls and set the minimizer strategy parameter to a certain value
one can use
minimizer.setMinimizer("Minuit2", "Migrad", "MaxFunctionCalls=50;Strategy=2")BornAgain fitting can also be done using other minimization packages. A short list of some of them is given below:
In this example we demonstrate how to use the lmfit minimizer for a typical fit of GISAS data.