\Sexpr[results=rd,stage=build]{tools:::Rd_package_title("polychaosbasics")}

Description

\Sexpr[results=rd,stage=build]{tools:::Rd_package_description("polychaosbasics")}

Details

Legendre chaos polynomials are calculated on a provided dataset by function polyLeg or on a simulated LHS by function analyticsPolyLeg.

Then, from the object returned by these functions, the PCESI function calculates sensitivity indexes, metamodel coefficients and some other results.

Author(s)

\Sexpr[results=rd,stage=build]{tools:::Rd_package_author("polychaosbasics")}

Maintainer: \Sexpr[results=rd,stage=build]{tools:::Rd_package_maintainer("polychaosbasics")}

References

  • Metamodeling and global sensitivity analysis for computer models with correlated inputs: a practical approach tested with a 3D light interception computer model. J.-P. Gauchi et all. In Environmental Modelling \& Software, 2016, submitted.

  • Global sensitivity analysis using polynomial chaos expansions. Bruno Sudret. In Reliability Engineering and System Safety, Vol. 93, Issue 7, July 2008, pages 964-979.

Examples

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# First example:
# the dataset is simulated by using the Ishigami function 
nlhs <- 200 # number of rows
degree <- 6 # polynomial degree
set.seed(42)# fix the seed for reproductible results
pce <- analyticsPolyLeg(nlhs, degree, 'ishigami') # build Legendre polynomial
ret <- PCESI(pce) # compute the PCE sensitivity indexes
print(ret)
# Illustrate the result by a plot:
# plot the computer model output against the metamodel output
y.hat <- ret@y.hat   # metamodel output
y.obs <- pce[, "Y"] # computer model output
## Not run: 
X11() 
plot(y.hat, y.obs,
      xlab="metamodel output", ylab="computer model output",
      main="Ishigami test", sub="Scatter plot and regression line")
# Add the regression line
reg <- lm(y.hat ~ y.obs) # linear regression
lines(reg$fitted.values, y.obs)

## End(Not run)

# Second example:
# the dataset is a user dataset
load(system.file("extdata", "FLORSYS1extract.Rda",
   package="polychaosbasics"))
degree <- 4 # polynomial degree
lhs <- FLORSYS1extract[, -ncol(FLORSYS1extract)] # inputs
Y <- FLORSYS1extract[,ncol(FLORSYS1extract)] #  output 
pce <- polyLeg(lhs, Y, degree) # build Legendre polynomial
ret <- PCESI(pce) # compute the PCE sensitivity indexes
print(ret, all=TRUE)