fast (version 0.64)

fast-package: Implementation of the Fourier Amplitute Sensitivity Test (FAST)

Description

The Fourier Amplitute Sensitivity Test (FAST) is a method to deterimine global sensitivities of a model on parameter changes with relavtively few model runs. This package implements this sensitivity analysis method.

Details

Package:

fast

Type:

Package

Version:

0.5

Date:

2007-12-15

License:

GPL2

Generate a set of parameter sets with the function fast_parameters. Run your model with each parameter set. sensitivity then evaluates the sensitivities of the model results on each of the parameters.

References

Reusser, Dominik E., Wouter Buytaert, and Erwin Zehe. "Temporal dynamics of model parameter sensitivity for computationally expensive models with FAST (Fourier Amplitude Sensitivity Test)." Water Resources Research 47 (2011): W07551.

CUKIER, R. I.; LEVINE, H. B. & SHULER, K. E. Non-Linear Sensitivity Analysis Of Multi-Parameter Model Systems Journal Of Computational Physics, 1978 , 26 , 1-42

CUKIER, R. I.; FORTUIN, C. M.; SHULER, K. E.; PETSCHEK, A. G. & SCHAIBLY, J. H. Study Of Sensitivity Of Coupled Reaction Systems To Uncertainties In Rate Coefficients .1. Theory Journal Of Chemical Physics, 1973 , 59 , 3873-3878

SCHAIBLY, J. H. & SHULER, K. E. Study Of Sensitivity Of Coupled Reaction Systems To Uncertainties In Rate Coefficients .2. Applications Journal Of Chemical Physics, 1973 , 59 , 3879-3888

CUKIER, R. I.; SCHAIBLY, J. H. & SHULER, K. E. Study Of Sensitivity Of Coupled Reaction Systems To Uncertainties In Rate Coefficients .3. Analysis Of Approximations Journal Of Chemical Physics, 1975 , 63 , 1140-1149

Examples

#A simple model depending on two
#parameters and an additional
#"hyperparameter" x. Depending on
#x the model is sensitive to p[1] only (x=1) 
#or p[2] only (x=0) or both (0<x<1)

example_model1<-function(p,x){
   return(p[1]*x+p[2]*(1-x))
}
paras<-fast_parameters(minimum=c(0,0,0),maximum=c(1,1,1))
paras
model_results <- apply(paras, 1, example_model1, x=0.5)
plot(model_results)
sensitivity <- sensitivity(x=model_results, numberf=3, make.plot=TRUE)
sensitivity


#In the second example, sensitivities are calculated for
#200 model results (which might be a time series).
#
#The model depends on 4 parameters
#
#It produces a weighted sum of the 4 parameters and returns this sum
#
#The weights depend on an additional parameter x=1:200 

example_model2(p=c(1,3,1,1),fig=TRUE)
example_model2(p=c(1,2,2,3),fig=TRUE)
paras<-fast_parameters(min=c(0,0,0,0),max=c(1,2,2,3))
paras
model_results <- apply(paras, 1, example_model2)
plot(model_results)
dev.new()
sensitivity <- sensitivity_rep(data = model_results, xval=1:200, direction = 1, order=4 , numberf=4)
p.sensitivity(sen=sensitivity, xval=1:200, legend=names(paras))