get_spline: Get the Control Polygon and the Spline Function

Description

Generate data.frames for interpolating and plotting a spline function, given a cpr_cp or cpr_cn object.

Usage

get_spline(x, margin = 1, at, n = 100, se = FALSE, derivative = 0)

Value

a data.frame

n rows and two columns x and y, the values for the spline. A third column with the standard error is returned if requested.

Arguments

x: a cpr_cp or cpr_cn object.
margin: an integer identifying the marginal of the control net to slice along. Only used when working with x as a cpr_cn object.
at: a point value for marginals not defined in the margin. Only used when x is a cpr_cn object. Expected input is a list of length length(attr(x, "bspline_list")). Entries for elements marginal are ignored. If omitted, the midpoint between the boundary knots for each marginal is used.
n: the length of sequence to use for interpolating the spline function.
se: if TRUE return the estimated standard error for the spline or the derivative.
derivative: A value of 0 (default) returns the spline, 1 the first derivative, 2 the second derivative.

Details

A control polygon, cpr\_cp object, has a spline function f(x). get_spline returns a list of two data.frames. The cp element is a data.frame with the (x, y) coordinates of control points and the spline element is a data.frame with n rows for interpolating f(x).

For a control net, cpr\_cn object, the return is the same as for a cpr\_cp object, but conceptually different. Where cpr\_cp objects have a univariate spline function, cpr\_cn objects have multivariate spline surfaces. get_spline returns a "slice" of the higher-dimensional object. For example, consider a three-dimensional control net defined on the unit cube with marginals x1, x2, and x3. The implied spline surface is the function f(x1, x2, x3). get_spline(x, margin = 2, at = list(0.2, NA, 0.5)) would return the control polygon and spline surface for f(0.2, x, 0.5).

See get_surface for taking a two-dimensional slice of a three-plus dimensional control net, or, for generating a useful data set for plotting the surface of a two-dimensional control net.

Examples

Run this code

data(spdg, package = "cpr")

## Extract the control polygon and spline for plotting.  We'll use base R
## graphics for this example.
a_cp <- cp(pdg ~ bsplines(day, df = 10, bknots = c(-1, 1)), data = spdg)

spline <- get_spline(a_cp)
plot(spline$x, spline$y, type = "l")

# compare to the plot.cpr_cp method
plot(a_cp, show_spline = TRUE)

# derivatives
f0 <- function(x) {
  #(x + 2) * (x - 1) * (x - 3)
  x^3 - 2 * x^2 - 5 * x + 6
}
f1 <- function(x) {
  3 * x^2 - 4 * x - 5
}
f2 <- function(x) {
  6 * x - 4
}

x <- sort(runif(n = 100, min = -3, max = 5))
bknots = c(-3, 5)
bmat <- bsplines(x, bknots = bknots)
theta <- coef(lm(f0(x) ~ bsplines(x, bknots = bknots) + 0) )

cp0 <- cp(bmat, theta)
spline0 <- get_spline(cp0, derivative = 0)
spline1 <- get_spline(cp0, derivative = 1)
spline2 <- get_spline(cp0, derivative = 2)

old_par <- par()

par(mfrow = c(1, 3))
plot(x, f0(x), type = "l", main = "spline")
points(spline0$x, spline0$y, pch = 2, col = 'blue')

plot(x, f1(x), type = "l", main = "first derivative")
points(spline1$x, spline1$y, pch = 2, col = 'blue')

plot(x, f2(x), type = "l", main = "second derivative")
points(spline2$x, spline2$y, pch = 2, col = 'blue')

par(old_par)