Bernstein_basis: Bernstein Basis Functions

In basefun: Infrastructure for Computing with Basis Functions

Description

Basis functions defining a Bernstein polynomial

Usage

Bernstein_basis(var, order = 2, ui = c("none", "increasing", "decreasing", 
                                       "cyclic", "zerointegral", "positive",
                                       "negative"),
                extrapolate = FALSE, log_first = FALSE)

Arguments

var	a numeric_var object
order	the order of the polynomial, one defines a linear function
ui	a character describing possible constraints
extrapolate	logical; if TRUE, the polynomial is extrapolated linearily outside support(var). In particular, the second derivative of the polynomial at support(var) is constrained to zero.
log_first	logical; the Bernstein polynomial is defined on the log-scale if TRUE. It makes sense to define the support as c(1, q)$, ie putting the first basis function of the Bernstein polynomial on log(1).

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

  ### 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 Feb. 2, 2021, 3 p.m.