rgn {RGN}

Robust Gauss Newton optimization

Description

rgn performs optimization of weighted-sum-of-squares (WSS) objective function using the Robust Gauss Newton algorithm

Usage

rgn(
  simFunc,
  simTarget = 0,
  weights = NULL,
  par,
  lower,
  upper,
  control = NULL,
  ...
)

Arguments

simFunc

is a function that simulates a (vector) response, with first argument the vector of parameters over which optimization is performed

simTarget

is the target vector that simFunc is trying to match

weights

is a vector of weights used in the WSS objective function. Defaults to equal weights.

par

is the vector of initial parameters

lower

is the lower bounds on parameters

upper

is the upper bounds on parameters

control

list of RGN settings

• control$n.multi is number of multi-starts (i.e. invocations of optimization with different initial parameter estimates). Default is 1.

• control$iterMax is maximum iterations. Default is 100.

• control$dump is level of diagnostic outputs between 0 (none) and 3 (highest). Default is 0.

• control$keep.multi (TRUE/FALSE) controls whether diagnostic output from each multi-start is recorded. Default is FALSE.

• control$logFile is log file name

...

other arguments to simFunc()

Details

rgn minimizes the objective function sum((weights*(simFunc-simTarget)^2)), which is a sum of squared weighted residuals (residuals=weights*(simFunc-simTarget)). Note simFunc corresponds to the vector of residuals when default arguments for simTarget and weights are used.

Value

List with

• par, the optimal parameters

• value, the optimal objective function value

• sim, the simulated vector using optimal parameters

• residuals, the vector of residuals using optimal parameters

• counts, the total number of function calls

• convergence, an integer code indicating reason for completion. 1 maximum iterations reached, 2 relative reduction in function value small. 3 absolute reduction in function value small 4 relative change in parameters small

Examples

# Example 1: Rosenbrock
simFunc_rosenbrock=function(x) c(1.0-x[1],10.0*(x[2]-x[1]**2))
rgnOut = rgn(simFunc=simFunc_rosenbrock,
             par=c(-1.0,  0.0), lower=c(-1.5, -1.0), upper=c( 1.5,  3.0),
             simTarget=c(0,0))
rgnOut$par #optimal parameters
rgnOut$value #optimal objective function value

# Example 2: Hymod

data("BassRiver") # load Bass River hydrological data
rgnOut = rgn(simFunc=simFunc_hymod,
             par=c(400.,0.5,0.1,0.2,0.1),
             lower=c(1.,0.1,0.05,0.000001,0.000001),
             upper=c(1000.,2.,0.95,0.99999,0.99999),
             simTarget=BassRiverData$Runoff.mm.day[365:length(BassRiverData$Date)],
             stateVal=c(100.0,30.0,27.0,25.0,30.0,0.0,0.0,0.0), # initial states for hymod
             nWarmUp=365,                                       # warmup period
             rain=BassRiverData$Rain.mm,                        # precip input
             pet=BassRiverData$ET.mm)                           # PET input
rgnOut$par #optimal parameters
rgnOut$value #optimal objective function value