cwhmisc (version 6.0)

interpol: Polynomial and rational interpolation

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)

Arguments

x

vector of x-coordinates

y

vector of y-coordinates

xi

argument x of interpolation

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.

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)