Bernstein_basis: Bernstein Basis Functions In basefun: Infrastructure for Computing with Basis Functions

Description

Basis functions defining a Bernstein polynomial

Usage

 ```1 2 3``` ```Bernstein_basis(var, order = 2, ui = c("none", "increasing", "decreasing", "cyclic", "zerointegral", "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

Details

`Bernstein_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 16 17 18 19 20 21 22 23 24``` ``` ### set-up basis bb <- Bernstein_basis(numeric_var("x", support = c(0, pi)), order = 3, ui = "increasing") ### generate data + coefficients x <- as.data.frame(mkgrid(bb, n = 100)) cf <- c(1, 2, 2.5, 2.6) ### evaluate basis (in two equivalent ways) bb(x[1:10,,drop = FALSE]) model.matrix(bb, data = x[1:10, ,drop = FALSE]) ### check constraints cnstr <- attr(bb(x[1:10,,drop = FALSE]), "constraint") all(cnstr\$ui %*% cf > cnstr\$ci) ### evaluate and plot Bernstein polynomial defined by ### basis and coefficients plot(x\$x, predict(bb, newdata = x, coef = cf), type = "l") ### evaluate and plot first derivative of ### Bernstein polynomial defined by basis and coefficients plot(x\$x, predict(bb, newdata = x, coef = cf, deriv = c(x = 1)), type = "l") ```

basefun documentation built on May 31, 2017, 2:27 a.m.