https://github.com/cran/pracma
Tip revision: 6b5162225f1e90f742ac53c32bf06c8053cff577 authored by HwB on 26 July 2011, 00:00:00 UTC
version 0.7.5
version 0.7.5
Tip revision: 6b51622
newton.R
##
## n e w t o n . R Newton Root finding
##
newtonRaphson <- function(fun, x0, dfun = NULL, ...,
maxiter = 100, tol = .Machine$double.eps^0.5) {
# Newton method for finding function zeros
if (is.null(dfun)) {
dfun <- function(x, ...) { h <- tol^(2/3)
(fun(x+h, ...) - fun(x-h, ...)) / (2*h)
}
}
x <- x0
fx <- fun(x, ...)
dfx <- dfun(x, ...)
niter <- 0
diff <- tol + 1
while (diff >= tol && niter <= maxiter) {
niter <- niter + 1
diff <- - fx/dfx
x <- x + diff
diff <- abs(diff)
fx <- fun(x, ...)
dfx <- dfun(x, ...)
}
if (niter > maxiter) {
warning("Maximum number of iterations 'maxiter' was reached.")
}
return(list(root=x, f.root=fx, niter=niter, estim.prec=diff))
}
newtonHorner <- function(p, x0,
maxiter = 50, tol = .Machine$double.eps^0.5) {
n <- length(p) - 1
niter <- 0
x <- x0
diff <- 1 + tol
while (niter <= maxiter && diff >= tol) {
H <- horner(p, x)
if (abs(H$dy) <= tol) {
warning("Newton's method encountered a slope almost zero.")
return(list(root = NULL, f.root = NULL, deflate = NULL,
iters = niter, estim.prec = Inf))
}
xnew <- x - H$y / H$dy
diff <- abs(x - xnew)
niter <- niter + 1
x <- xnew
}
if (niter > maxiter) {
warning("Maximum number of iterations exceeded.")
}
defl <- hornerdefl(p, x)
return(list(root = x, f.root = defl$y, deflate = defl$q,
iters = niter, estim.prec = diff))
}
secant <- function(fun, a, b, ...,
maxiter = 100, tol = .Machine$double.eps^0.5)
# Secant search for zero of a univariate function
{
fun <- match.fun(fun)
f <- function(x) fun(x, ...)
x1 <- a; x2 <- b
f1 <- f(x1); if (abs(f1) <= tol) return(x1)
f2 <- f(x2); if (abs(f2) <= tol) return(x1)
n <- 0
while (n <= maxiter && abs(x2 - x1) > tol) {
n <- n+1
slope <- (f2 - f1)/(x2 - x1)
if (slope == 0) return(root=NA, f.root=NA, iter=n, estim.prec=NA)
x3 <- x2 - f2/slope
f3 <- f(x3); if (abs(f3) <= tol) break
x1 <- x2; f1 <- f2
x2 <- x3; f2 <- f3
}
if (n > maxiter) {
warning("Maximum number of iterations 'maxiter' was reached.")
}
return(list(root=x3, f.root=f3, iter=n, estim.prec=2*abs(x3-x2)))
}