# polyLeg: Calculate Legendre Polynomials on a Dataset In plspolychaos: Sensitivity Indexes from Polynomial Chaos Expansions and PLS

## Description

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].

## Usage

 `1` ```polyLeg(lhs, Y, degree, forward=NULL) ```

## Arguments

 `lhs` 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. `Y` vector of length equal to the number of rows in `lhs`. Model outputs. `degree` integer greater than 1 and less than 11. Degree of the polynomial. `forward` 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.

## 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`). The `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 are kept.

## Value

An objet of class `PCEpoly`.

## References

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.

• Function `analyticsPolyLeg` builds Legendre polynomials from a simulated dataset.

• Function `calcPLSPCE` calculates PLS-PCE sensivity indexes from the returned object.

## Examples

 ``` 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) ```

plspolychaos documentation built on May 29, 2017, 10:44 a.m.