Description Usage Arguments Details References Examples
Basis functions defining a Bernstein polynomial
1 2 3 4 |
var |
a |
order |
the order of the polynomial, one defines a linear function |
ui |
a character describing possible constraints |
extrapolate |
logical; if |
log_first |
logical; the Bernstein polynomial is defined on the
log-scale if |
Bernstein_basis
returns a function for the evaluation of
the basis functions with corresponding model.matrix
and predict
methods.
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
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")
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