FMINUIT is a multidimensional nonlinear minimization by means of the MINUIT engine. Usage is similar (but not identical) to that of Matlab Fmins. For a description of the MINUIT commands, read the MINUIT writeup or type HELP during the interactive execution of Fminuit.
This document consists of the following parts:

• Basic FMINUIT Usage
• Optional Arguments
• Return Values
• Unsupported

Basic FMINUIT Usage

[BestPars, Errs, Chi2, ErrMatrix] = fminuit(FunName, InitGuess, ...)

This version minimizes a scalar user function named FunName, using InitGuess as initial values of the variational parameters. Here FunName is a string and InitGuess a vector.
Dots "..." stand for a variable number of optional extra-arguments. The user function depends on one or two variables: a vector of variational parameters (same dimension as InitGuess) and, optionally, on arbitrary structure of constant data (any data type except a string), respectively. Functions of more than 2 variables are not supported.

Note: If the user function would need to be passed many matrices of constant data, such matrices should rather be arranged into a cell array or a struct (Matlab, Octave) or a list (Scilab), and passed as a single argument to the user function.

[BestPars, Errs, Chi2, ErrMatrix] = fminuit(FunName, AuxFunName, InitGuess, ...)

(where AuxFunName is a string) behaves as in the previous case. In addition, an auxiliary function named AuxFunName is called whenever a 'CALL 5' Minuit command is issued. Such a function is passed the following argument list:

• (BestPars, FunName, ErrMatrix), or
• (BestPars, Data, FunName, ErrMatrix) if the argument Data (constant data, see below) is defined.

Values of BestPars and ErrMatrix are those currently returned by Minuit. Return arguments of the auxiliary function are ignored.
The interface to AuxFunName is mainly intended for logging, or to draw a run-time plot during the minimization process.

Optional Arguments

Everything following the InitGuess, in any order. Possible optional arguments are given below:

Data

constant data: any data type supported by Matlab (Octave, Scilab), except a string. If this argument is supplied to Fminuit, it is passed to the user function FunName as its second argument. In the case of chi-square fitting, Data usually consists of a 3-column (or 3-row) matrix of experimental data: the independent variable, measured values of the dependent variable and error bars.
Note: (for the case of a scalar Data) The first occurrence of a scalar argument is interpreted as ConstError (see below). Therefore, in the case that a scalar Data is required by the user function to be minimized, ConstError has to be specified as well, and Data must follow in the argument list.

 

ConstError

a scalar parameter. The value returned by the user function to Fminuit is internally divided by ConstError². In the case of chi-square fitting, ConstError has the meaning of a uniform error bar assigned to the experimental points. Default value is ConstError = 1.

 

'-a' or 'a'

option switch. Interactive mode. If the string constant '-a' or 'a' is supplied, Fminuit prompts for Minuit commands interactively, until 'EXIT', or 'RETURN' is issued. This is the default behaviour.

 

'-b' or 'b'

option switch. Batch mode. If the string constant '-b' or 'b' is supplied, Fminuit runs a sequence of Minuit commands in batch mode without user control. The command sequence can be defined by the (...,'-c', MinuitCommands, ...) option, or by creating a global string variable named 'commands' in the caller workspace (see below).
The default sequence is 'MINIMIZE; IMPROVE'.

 

..., '-c', MinuitCommands, ...

option switch followed by a string argument. Flow control. If the string constant '-c' followed by a string argument MinuitCommands is passed, Fminuit executes the Minuit commands defined in MinuitCommands when in batch mode. Defining a global non-empty string variable named 'commands' in the caller workspace controls the program flow in the same way. The latter feature is kept in Fminuit for backward compatibility, and might be removed in future releases. Controlling the program flow via the command line should be preferred.
If both the '-c' option and the global variable 'commands' are present, the latter is overridden.
Minuit commands are separated by one of the characters: ';', '\', '|', '/' '@'; for instance,
fminuit(... ,'-c', 'set par 1 3; fix 1; mini; rel 1; mini', ...).
Note: The '-c' option switch implicitly implies '-b' and is always effective; the global variable 'commands' is only effective when batch mode is explicitly set via the '-b' (or 'b') option switch.

 

..., '-n', ParameterNames, ...

option switch followed by a string argument. Parameters Names. If the string constant '-n' followed by a string argument ParameterNames is passed, within Minuit, the variational parameters are given the names specified in ParameterNames, instead of the default values 'par #1', 'par #2', ... . Defining a global non-empty string variable named 'parnames' in the caller workspace controls the parameter names in the same way (backward compatibility; setting name via the command line should be preferred).
If both the '-n' option and the global variable parnames are present, the latter is overridden.
Parameter names are separated by commas or blanks, and must be as many as the variational parameters. If the number of names does not match the number of parameters, this option is neglected.

 

..., '-s', StepBounds, ...

option switch followed by a matrix. Definition of parameter steps and limits. A string constant '-s' in the argument list, followed by a 2-, 3-, or 4-column matrix, defines new parameter steps and/or parameter limits. Defining a global non-empty matrix variable named 'stepbounds' in the caller workspace controls parameter steps and/or limits in the same way (backward compatibility).
The '-c' switch always overrides the global variable StepBounds. Format of StepBounds is the following:
Each line is referred to a variational parameter.
The first column contains indices of the parameters whose steps and/or limits are to be modified.

• If StepBounds is a two- or four-column matrix, the second column is interpreted as the new steps, i.e. StepBounds(k,2) is the step of the StepBounds(k,1)-th parameter;
• If StepBounds is a three-column matrix, columns 2 and 3 are interpreted as upper and lower limits, i.e. the StepBounds(k,1)-th parameter is constrained between StepBounds(k,2) and StepBounds(k,3);
• If StepBounds is a four-column matrix, columns 2 is interpreted as new steps, column 3 and 4 as parameter limits.

Note: Step = 0 means that the parameter is kept fixed; a negative step signifies usage of the default step definition.