Minuit

Wolfram Language interface to the MINUIT2 C++ package via the Python module iminuit

Minuit can be used for general robust function minimization, as well as for likelihood fits of models to data and to get model parameter error estimates from likelihood profile analyses.

Code: github.com/statius/minuit

Installation

• Download the latest release and unpack it or clone the repository somewhere on the Wolfram Language $Path (e.g. the Applications folder in $UserBaseDirectory for Mathematica).

• Make sure that your system has an installation of Python accessible to the Wolfram Language (see FindExternalEvaluators[]) and that iminuit is installed.

  • Note that a Python executable or version can be specified after Minuit is loaded either in a local session as

    StartPythonSession[<|"Executable" -> "<path>", "Version" -> "<version>"|>]

    or on a persistant basis as

    ConfigureMinuit[
      "PythonExecutable" -> "<path>",
      "PythonVersion" -> "<version>"
    ];
    
    StartPythonSession[] (* restart Python session *)

• Load Minuit as

  Needs @ "Minuit`"

Usage

First, define an objective function in Minuit's Python session (taking the example from iminuit's tutorial):

PythonEvaluate[
  "
def line(x, a, b):
    return a + x * b

data_x = linspace(0, 1, 10)
# precomputed random numbers from a normal distribution
offsets = array([-0.49783783, -0.33041722, -1.71800806,  1.60229399,  1.36682387,
                 -1.15424221, -0.91425267, -0.03395604, -1.27611719, -0.7004073 ])
data_y = line(data_x, 1, 2) + 0.1 * offsets # generate some data points with random offsets

def least_squares(a, b):
    yvar = 0.01
    return sum((data_y - line(data_x, a, b)) ** 2 / yvar)
"
]

Next, initialize an instance of the Minuit class

m = InitializeMinuit[
  "least_squares",
  <|"a" -> 5, "b" -> 5|>, 
  "ParameterErrors" -> <|"a" -> 0.1, "b" -> 0.1|>, 
  "ErrorDefinition" -> 1
]

This will return MinuitMinimiztionObject[...] (I tried to parallel the builtin BayesianMinimizationObject). Minimize with Migrad:

Migrad[m, "MaxIterations" -> 10^5, "Subcalculations" -> 5]

Extract the minimum information

m @ "CurrentState"

and the paramter states

m @ "ParameterStates"

Minos errors can also be calculated:

Minos @ m

and returned

m @ "MinosErrors"

---

Many (but not all) properties of the Python Minuit object have been translated into Wolfram-flavored syntax and incorporated into the definition of MinuitMinimizationObject. The available properties and methods are given by

m @ "Properties"
m @ "Methods"

However, all Minuit properties can be extracted directly by passing their names (and arguments, if applicable) as

m @ "is_valid"
m["set_print_level", 0]
m["matrix", "correlation" -> True, "skip_fixed" -> False]

For more information on the available methods, see the iminuit documentation. Please be warned that not all Python output may be successfully returned to the Wolfram Language. More functionality may be translated into the Wolfram Language in future versions.

Project Information

Licensing

This project is released under the MIT license.

Contributions

This package is maintained by Andrew Miller (and primarily created for my own needs). Pull requests and suggestions are always welcomed.

iminuit citation: github.com/scikit-hep/iminuit/blob/master/CITATION.