testmodels {sensitivity}

Test Models for Sensitivity Analysis

Description

These functions are standard testcases for sensitivity analysis benchmarks. For a scalar output (see Saltelli et al. 2000 and https://www.sfu.ca/~ssurjano/):

• the g-function of Sobol' with 8 inputs, X ~ U[0,1];

• the function of Ishigami with 3 inputs, X ~ U[-pi,pi];

• the function of Morris with 20 inputs, X ~ U[0,1];

• the Linkletter decreasing coefficients function, X ~ U[0,1] (Linkletter et al. (2006));

• the heterdisc function with 4 inputs, X ~ U[0,20];

• the Friedman function with 5 inputs, X ~ U[0,1] (Friedman, 1991);

• the Matyas function with 2 inputs, X ~ U[0,1].

For functional output cases:

• the Arctangent temporal function with 2 inputs, X ~ U[-7,7] (Auder, 2011). The functional support is on [0,2pi];

• the Cambell1D function with 4 inputs, X ~U[-1,5] (Campbell et al. 2006). The functional support is on [-90,90].

Usage

sobol.fun(X)
ishigami.fun(X)
morris.fun(X)
atantemp.fun(X, q = 100)
campbell1D.fun(X, theta = -90:90)
linkletter.fun(X)
heterdisc.fun(X)
friedman.fun(X)
matyas.fun(X)

Arguments

X

a matrix (or data.frame) containing the input sample.

q

for the atantemp() function: the number of discretization steps of the functional output

theta

for the campbell1D() function: the discretization steps (angles in degrees)

Value

A vector of function responses.

Author(s)

Gilles Pujol and Bertrand Iooss

References

A. Saltelli, K. Chan and E. M. Scott eds, 2000, Sensitivity Analysis, Wiley.

Examples

# Examples for the functional toy fonctions

# atantemp function

y0 <- atantemp.fun(matrix(c(-7,0,7,-7,0,7),ncol=2))
plot(y0[1,],type="l")
apply(y0,1,lines)

n <- 100
X <- matrix(c(runif(2*n,-7,7)),ncol=2)
y <- atantemp.fun(X)
plot(y0[2,],ylim=c(-2,2),type="l")
apply(y,1,lines)

# campbell1D function

N1=100         # nombre de simulations pour courbes 1D
min=-1 ; max=5
nominal=(max+min)/2

X1 = NULL ; y1 = NULL
Xnom=matrix(nominal,nr=1,nc=4)
ynom=campbell1D.fun(Xnom,theta=-90:90)
plot(ynom,ylim=c(8,30),type="l",col="red")
for (i in 1:N1){
  X=matrix(runif(4,min=min,max=max),nr=1,nc=4)
  rbind(X1,X)
  y=campbell1D.fun(X,theta=-90:90)
  rbind(y1,y)
  lines(y)
}