This function calculates Legendre polynomials, optionally reducted to the most significant monomials, on a user dataset.
Legendre polynomials are computed after calibration within the bounds [-1, +1].
matrix with as many columns as inputs. Dataset of inputs. Generally, a space filling design is used for forming this dataset. Typically, this is a simple LHS (see McKay, 1979) or a modified LHS.
vector of length equal to the number of rows in
integer greater than 1 and less than 11. Degree of the polynomial.
NULL or an integer equal to the required number of monomials. A null value (the default), or a value less than the number of inputs or greater than the total number of monomials, means that all the monomials are kept. See details.
When the value of the argument
forward is non NULL,
it should be an integer equal to the required
number of the monomials (let say
q monomials are selected,
among all the monomials of the full polynomial, by all the
linear simple regressions of the output versus all the monomials.
Those associated with the
q largest R^2 values
An objet of class
McKay, M.D. and Beckman, R.J. and Conover, W.J. 1979. “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code”.In Technometrics, 21 (2). 239-245p.
Legendre polynomials from a simulated dataset.
calcPLSPCE calculates PLS-PCE sensivity indexes
from the returned
1 2 3 4 5 6 7 8 9 10 11
### Load the dataset load(system.file("extdata", "ishigami200.Rda", package="plspolychaos")) X <- ishi200[, -ncol(ishi200)] # inputs Y <- ishi200[, ncol(ishi200)] # output degree <- 6 # polynomial degree ### Creation of the full polynomials pce <- polyLeg(X, Y, degree) print(pce) ### Selection of the 50 most significant monomials pcef <- polyLeg(X, Y, degree, forward=50) print(pcef)