evaluate_spline: Evaluate a scalar spline at arbitrary locations.

In castor: Efficient Phylogenetics on Large Trees

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.

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.

This function is used to evaluate the spline's values at arbitrary points. To obtain the spline's polynomial coefficients, use spline_coefficients.

Value

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

Author(s)

Stilianos Louca

See Also

spline_coefficients

Examples

# 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')

castor documentation built on June 29, 2024, 9:08 a.m.