https://github.com/cran/pracma
Tip revision: a9b4d5f19cb88cd9d0d31fdde0d654737327d085 authored by HwB on 15 April 2012, 00:00:00 UTC
version 1.0.5
version 1.0.5
Tip revision: a9b4d5f
bisect.R
##
## b i s e c t . R
##
bisect <- function(f, a, b, maxiter=100, tol=.Machine$double.eps^0.5)
# Bisection search for zero of a univariate function in a bounded interval
{
if (f(a)*f(b) > 0) stop("f(a) and f(b) must have different signs.")
x1 <- min(a, b); x2 <- max(a,b)
xm <- (x1+x2)/2.0
n <- 0
while (abs(x1-x2)/2.0 > tol) {
n <- n+1
if (abs(f(xm)) <= tol) break
if (f(x1)*f(xm) < 0) {
x2 <- xm
} else {
x1 <- xm
}
xm <- (x1+x2)/2.0 # xm <- x1 - f(x1) * (x2-x1) / (f(x2)-f(x1))
if (n >= maxiter) break
}
return(list(root=xm, f.root=f(xm), iter=n, estim.prec=abs(x1-x2)/2.0))
}
regulaFalsi <- function(f, a, b, maxiter=100, tol=.Machine$double.eps^0.5)
#Regula Falsi search for zero of a univariate function in a bounded interval
{
x1 <- a; x2 <- b
f1 <- f(x1); f2 <- f(x2)
if (f1*f2 > 0) stop("f(a) and f(b) must have different signs.")
m <- 0.5 # Illinois rule
niter <- 0
while (abs(x2-x1) >= tol && niter <= maxiter) {
niter <- niter + 1
x3 <- (x1*f2-x2*f1)/(f2-f1); f3 <- f(x3)
if(f3*f2 < 0) {
x1 <- x2; f1 <- f2
x2 <- x3; f2 <- f3
} else {
# m <- f2/(f2+f3) # Pegasus rule
# m <- if (1-f3/f2 > 0) 1-f3/f2 else 0.5 # Andersen/Bjoerk
f1 <- m * f1
x2 <- x3; f2 <- f3
}
}
if (niter > maxiter && abs(x2-x1) >= tol)
cat("regulaFalsi stopped without converging.\n")
return(list(root = x3, f.root = f3, niter = niter, estim.prec = x1-x2))
}
ridder <- function(f, a, b, maxiter = 100, tol = .Machine$double.eps^0.5) {
# (!is.numeric(a) && !is.complex(a) && !is(a,"mpfr") ||
# !is.numeric(b) && !is.complex(b) && !is(b,"mpfr"))
# stop("Arguments 'a' and 'b' must be numeric, complex, or mpfr.")
x1 <- a; x2 <- b
f1 <- f(x1); f2 <- f(x2)
if (f1*f2 >= 0) stop("f(a) and f(b) must have different signs.")
niter <- 2
while(abs(x1 - x2) > tol && niter < maxiter) {
xm <- (x1 + x2)/2; fm <- f(xm)
if (fm == 0)
return(list(root = xm, f.root = 0, niter = niter, estim.prec = 0))
x3 <- xm + (xm - x1) * sign(f1 - f2) * fm / sqrt(fm^2 - f1 * f2)
f3 <- f(x3); niter <- niter + 2
if (f3 == 0)
return(list(root = x3, f.root = 0, niter = niter, estim.prec = 0))
if (fm * f3 < 0) {
x1 <- xm; f1 <- fm
x2 <- x3; f2 <- f3
} else if (f1 * f3 < 0) {
x2 <- x3; f2 <- f3
} else if (f2 * f3 < 0) {
x1 <- x3; f1 <- f3
} else {
stop("Inform the maintainer: you should never get here.")
}
}
if (abs(f1) < abs(f2)) {
x0 <- x1; f0 <- f1
} else {
x0 <- x2; f0 <- f2
}
ep <- abs(x1 - x2)
return(list(root = x0, f.root = f0, niter = niter, estim.prec = ep))
}