comphy (version 1.0.5)

polydivdif: Approximating polynomial for divided differences

Description

Calculation of a polynomial of order n via divided differences. All n tabulated points provided (with n greater or equal than 2) are used by default for the calculation, but the option is available to use only np points, where np must be greater or equal than 2. In case only part of the n available tabulated points is used (np < n), the first two points are fixed to be equal to the smallest and largest tabulated grid x points; the remaining np-2 points are selected randomly among the n-2 remaining ones.

Usage

polydivdif(x0, x, f, np = length(x))

Value

A named list of length 3 and names x, f and f0.

x

Tabulated grid points used for the interpolation.

f

Tabulated function points used for the interpolation. They correspond to x.

f0

Interpolated values. They correspond to the input vector x0.

Arguments

x0

A vector of real numbers. These are the grid points chosen for the interpolation.

x

A vector of real numbers. Grid points corresponding to the tabulated (known) values of the function.

f

A vector of real numbers. Tabulated (known) values of the function, corresponding to the grid x.

np

An integer. The number of known points used for the interpolation. np > 2 because the smallest and largest value of x have to be always among the known points. Aside from the points at the extremes of the interpolation interval, the other points are chosen randomly.

Examples

# Tabulated grid points for function sin(x)
x <- seq(0,3*pi/2,length=20)
f <- sin(x)

# Grid of interpolated points
x0 <- seq(0,3*pi/2,length=200)

# Interpolation using all 20 tabulated points
ltmp <- polydivdif(x0,x,f)
plot(ltmp$x,ltmp$f,pch=16)
points(x0,ltmp$f0,type="l")

# Interpolation using only five points (dangerous!)
ltmp <- polydivdif(x0,x,f,np=5)
points(ltmp$x,ltmp$f,col=2,cex=1.5)
points(x0,ltmp$f0,type="l",col=2)