# Legendre_basis: Legendre Basis Functions In basefun: Infrastructure for Computing with Basis Functions

## Description

Basis functions defining a Legendre polynomial

## Usage

 ```1 2``` ```Legendre_basis(var, order = 2, ui = c("none", "increasing", "decreasing", "cyclic", "positive", "negative"), ...) ```

## Arguments

 `var` a `numeric_var` object `order` the order of the polynomial, one defines a linear function `ui` a character describing possible constraints `...` additional arguments passed to `legendre.polynomials`

## Details

`Legendre_basis` returns a function for the evaluation of the basis functions with corresponding `model.matrix` and `predict` methods.

## References

Rida T. Farouki (2012), The Bernstein Polynomial Basis: A Centennial Retrospective, Computer Aided Geometric Design, 29(6), 379–419. http://dx.doi.org/10.1016/j.cagd.2012.03.001

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ``` ### set-up basis lb <- Legendre_basis(numeric_var("x", support = c(0, pi)), order = 3) ### generate data + coefficients x <- as.data.frame(mkgrid(lb, n = 100)) cf <- c(1, 2, 2.5, 1.75) ### evaluate basis (in two equivalent ways) lb(x[1:10,,drop = FALSE]) model.matrix(lb, data = x[1:10, ,drop = FALSE]) ### evaluate and plot Legendre polynomial defined by ### basis and coefficients plot(x\$x, predict(lb, newdata = x, coef = cf), type = "l") ```

basefun documentation built on Feb. 14, 2020, 9:06 a.m.