castor (version 1.6.1)

evaluate_spline: Evaluate a scalar spline at arbitrary locations.

Description

Given a natural spline function \(Y:\R\to\R\), defined as a series of Y values on a discrete X grid, evaluate its values (or derivative) at arbitrary X points. Supported splines degrees are 0 (Y is piecewise constant), 1 (piecewise linear), 2 (piecewise quadratic) and 3 (piecewise cubic).

Usage

evaluate_spline(Xgrid, 
                Ygrid,
                splines_degree,
                Xtarget,
                extrapolate = "const",
                derivative  = 0)

Arguments

Xgrid

Numeric vector, listing x-values in ascending order.

Ygrid

Numeric vector of the same length as Xgrid, listing the values of Y on Xgrid.

splines_degree

Integer, either 0, 1, 2 or 3, specifying the polynomial degree of the spline curve Y between grid points. For example, 0 means Y is piecewise constant, 1 means Y is piecewise linear and so on.

Xtarget

Numeric vector, listing arbitrary X values on which to evaluate Y.

extrapolate

Character, specifying how to extrapolate Y beyond Xgrid if needed. Available options are "const" (i.e. use the value of Y on the nearest Xgrid point) or "splines" (i.e. use the polynomial coefficients from the nearest grid point).

derivative

Integer, specifying which derivative to return. To return the spline's value, set derivative=0. Currently only the options 0,1,2 are supported.

Value

A numeric vector of the same length as Xtarget, listing the values (or derivatives, if derivative>0) of Y on Xtarget.

Details

Spline functions are returned by some of castor's fitting routines, so evaluate_spline is meant to aid with the evaluation and plotting of such functions. A spline function of degree \(D\geq1\) has continuous derivatives up to degree \(D-1\). The function evaluate_spline is much more efficient if Xtarget is monotonically increasing or decreasing.

Examples

# NOT RUN {
# specify Y on a coarse X grid
Xgrid = seq(from=0,to=10,length.out=10)
Ygrid = sin(Xgrid)

# define a fine grid of target X values
Xtarget = seq(from=0,to=10,length.out=1000)

# evaluate Y on Xtarget, either as piecewise linear or piecewise cubic function
Ytarget_lin = evaluate_spline(Xgrid,Ygrid,splines_degree=1,Xtarget=Xtarget)
Ytarget_cub = evaluate_spline(Xgrid,Ygrid,splines_degree=3,Xtarget=Xtarget)

# plot both the piecewise linear and piecewise cubic curves
plot(x=Xtarget, y=Ytarget_cub, type='l', col='red', xlab='X', ylab='Y')
lines(x=Xtarget, y=Ytarget_lin, type='l', col='blue', xlab='X', ylab='Y')
# }