interpol: Polynomial and rational interpolation

In cwhmisc: Miscellaneous Functions for Math, Plotting, Printing, Statistics, Strings, and Tools

Description

Determine the argument of the minimum by polynomial or rational interpolation of given points x, y.

Usage

setupInterp(x, y, doPoly = TRUE)
evalInterp(xi, ss)
minInterp(x, y, add = FALSE, doPoly = TRUE)
quadmin(x, y)
lerp(p1, p2, t)

Arguments

x	vector of x-coordinates
y	vector of y-coordinates
xi	argument x of interpolation
p1,p2	point coordinates for linear interpolation
t	0 <= t <= 1, linear interpolation distance
ss	setup given by setupInterp
add	if TRUE, one more point is used than for FALSE (default)
doPoly	if TRUE, polynomial interpolation is used, if FALSE, rational interpolation is used, with three points and four points respectively (latter for add=FALSE)

Value

setupInterp	Generate structure ss for evaluation in evalInterp
minInterp, quadmin	x-value of the minimum. NA if too few points are given or no minimumm exists in x.
lerp	linerly interpolated point, t=0 -> p1, t=1 -> p2

Author(s)

Christian W. Hoffmann <[e-mail]>

References

Stoer, J., 1989. Numerische Mathematik 1ed. 5. Springer, Berlin. Applied and Computational Complex Analysis, Vol.2. Wiley,

Examples

  opar <- par(mfrow=c(2,2))
  x <- c(1,2,4,6); y <- 1/x
  pint <- function( x, y, add, dopoly, ylab="" ) {
    print(paste(" minimum at = ", minInterp(x,y,add=add,doPoly=dopoly) ) )
    xP <- setupInterp(x,y,TRUE)
    xT <- setupInterp(x,y,FALSE)
    x0 <- seq(0,7,0.1); yP <- evalInterp(x0,xP)
    yT <- evalInterp(x0,xT)
    plot(x,y,xlim=c(-0.5,7.5),ylim=c(min(y)-2,max(y)+2),cex=2,ylab=ylab)
    lines(x0,yP,col=2,cex=0.5)
    lines(x0,yT,col=4,cex=0.5,pch="+")
    legend(x="bottom",c("polynomial", "rational"), col = c(2,4),
     text.col= "black", lty = 1, merge = TRUE, bg='white')
  }
  pint(x,y,add=FALSE,dopoly=TRUE,"1/x") # 6 ?? = minimum
  pint(x, (x-3)^2,add=FALSE,dopoly=TRUE,"(x-3)^2") # 3
  pint(x,x+1.0/x,add=FALSE,dopoly=FALSE,"x+1.0/x dopoly=F") # 1 -1
  pint(x,x+1.0/x,add=TRUE,dopoly=TRUE,"x+1.0/x dopoly=T") # 8.3471982 0.3194685
  par(opar)
  

cwhmisc documentation built on May 1, 2019, 7:55 p.m.