rminuit2: Function Minimization and model fitting with Minuit2

In alusiani/rminuit2: Function Minimization with Minuit2

Function Minimization and model fitting with Minuit2

Description

Performs function minimization using Minuit2

Usage

rminuit2(
  mll,
  start = formals(mll),
  err = NULL,
  lower = NULL,
  upper = NULL,
  fix = NULL,
  opt = "h",
  maxcalls = 0L,
  nsigma = 1,
  ...
)

Arguments

mll	The function to be minimized. The full potential of this package is attained when the function corresponds to the negative logarithm of a likelihood or minus-log-likelihood (MLL).
start	numeric vector, initial values of the function parameters
err	numeric vector, expected uncertainty of function parameters
lower	numeric vector, lower bounds for the parameters (default none)
upper	numeric vector, upper bounds for the parameters (default none)
fix	boolean vector, each TRUE element fixes the corresponding parameter
opt	string, pass fit options, default "h" (compute HESSE errors) v: Verbose mode (not yet implemented) h: Run Hesse to estimate errors m: Get Minos errors 0: Run Migrad with strategy 0 1: Run Migrad with strategy 1 2: Run Migrad with strategy 2 neither 1, 2, 3: Run Migrad with strategy 1, and if it fails run with strategy 2
maxcalls	integer, maximum number of calls, defaults to 0 (no limit).
nsigma	numeric, number of standard deviations for Minos errors
...	extra arguments for the mll function.

Value

A list with the following components:

fval:

Value of function at found minimum (1/2 * chi square if the function is the negative log-likelihood of a Gaussian likelihood.

Edm:

Estimated distance from the value of the function true minimum

par:

Fitted parameters

err:

Estimated uncertainties of fitted parameters

cov:

Covariance matrix of the fitted parameters

cor:

Correlation matrix of the fitted parameters

err_minos_pos:

Minos-estimated positive parameters' uncertainties (if Minos errors were requested)

err_minos_neg:

Minos-estimated negative parameters' uncertainties (if Minos errors requested)

err_minos_pos_valid:

boolean vector, TRUE if Minos positive uncertainties are valid (if Minos errors were requested)

err_minos_neg_valid:

boolean vector, TRUE if Minos negative uncertainties are valid (if Minos errors were requested)

allOK:

TRUE if the fit converged and the parameters and their covariance are OK

MinosErrorsValid:

TRUE if the MINOS errors are all valid

IsValid:

TRUE if the fit minimization converged

IsValidFirstInvocation:

TRUE if Minuit strategy 1 succeeded (if it failed Minuit2 strategy 2 is performed)

IsAboveMaxEdm:

TRUE if the estimated distance from the true minimum is above the tolerance

HasReachedCallLimit:

TRUE if the maximum call limit was exceeded

HasValidParameters:

TRUE if the fitted parameters are considered valid

HasCovariance:

TRUE if a covariance matrix is returned

HasValidCovariance:

TRUE if the estimated covariance matrix is considered valid

HasAccurateCovar:

TRUE if the accuracy of the estimated covariance matrix is considered valid

HasPosDefCovar:

TRUE if the numerically computed covariance matrix is positive definite

HasMadePosDefCovar:

TRUE if the covariance matrix has been adjusted to make it positive definite

HesseFailed:

TRUE if the numeric computation of the HESSE matrix failed

Author(s)

Alberto Lusiani, [e-mail]

See Also

rminuit2_par

Examples

#
# Rosenbrock Banana function, to be minimized vs. x, y
#
rosenbrock <- function(x, y, a, b) {
  (a-x)^2 + b*(y-x^2)^2
}

# minimize Rosenbrock Banana function, also setting parameters a, b
fit.rc <- rminuit2(rosenbrock, c(x=0.7, y=1.2), a=1, b=100)
fit.rc$par

#
# simulate model y = a*exp(-x/b)
#
x = seq(0, 1, length.out=31)
y.func = function(x, norm, tau) norm*exp(-x/tau)

# simulate data with Gaussian errors for specific model
model.par = c(norm=2.3, tau=0.47)
y.err = 0.01
y = do.call(y.func, c(list(x), model.par)) + rnorm(sd=y.err, n=length(x))

# negative log-likelihood for model
halfchisq = function(norm, tau, x, y, y.err) {
  sum( (y - y.func(x, norm, tau))^2 / (2 * y.err^2) )
}

# fit model on data, ask to compute Minos errors too
fit.rc = rminuit2(halfchisq, c(norm=1, tau=10), opt="hm", x=x, y=y, y.err=y.err)

# chi square / number of degrees of freedom
cbind(chisq=2*fit.rc$fval, ndof=length(x) - length(model.par))

# fitted parameters and their estimated uncertainties
cbind(model.value=model.par, value=fit.rc$par, error=fit.rc$err,
      minos_pos=fit.rc$err_minos_pos, minos_neg=fit.rc$err_minos_neg)

# parameters' correlation matrix
fit.rc$cor

alusiani/rminuit2 documentation built on Aug. 7, 2024, 8:38 a.m.