# Calculate Legendre Polynomials on a Dataset

### 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 |

### 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 |

`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.

### See Also

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)
``` |