root: One Dimensional Root (Zero) Finding

In IRSN/DiceView: Methods for Visualization of Computer Experiments Design and Surrogate

One Dimensional Root (Zero) Finding

Description

Search one root with given precision (on y). Iterate over uniroot as long as necessary.

Usage

root(
  f,
  lower,
  upper,
  maxerror_f = 1e-07,
  f_lower = f(lower, ...),
  f_upper = f(upper, ...),
  tol = .Machine$double.eps^0.25,
  convexity = FALSE,
  rec = 0,
  max.rec = NA,
  ...
)

Arguments

f	the function for which the root is sought.
lower	the lower end point of the interval to be searched.
upper	the upper end point of the interval to be searched.
maxerror_f	the maximum error on f evaluation (iterates over uniroot to converge).
f_lower	the same as f(lower).
f_upper	the same as f(upper).
tol	the desired accuracy (convergence tolerance on f arg).
convexity	the learned convexity factor of the function, used to reduce the boundaries for uniroot.
rec	counter of recursive level.
max.rec	maximal number of recursive level before failure (stop).
...	additional named or unnamed arguments to be passed to f.

Author(s)

Yann Richet, IRSN

Examples

f=function(x) {cat("f");1-exp(x)}; f(root(f,lower=-1,upper=2))
f=function(x) {cat("f");exp(x)-1}; f(root(f,lower=-1,upper=2))

.f = function(x) 1-exp(1*x)
f=function(x) {cat("f");y=.f(x);points(x,y,pch=20,col=rgb(0,0,0,.2));y}
plot(.f,xlim=c(-1,2)); f(root(f,lower=-1,upper=2))

.f = function(x) exp(10*x)-1
f=function(x) {cat("f");y=.f(x);points(x,y,pch=20);y}
plot(.f,xlim=c(-1,2)); f(root(f,lower=-1,upper=2))

.f = function(x) exp(100*x)-1
f=function(x) {cat("f");y=.f(x);points(x,y,pch=20);y}
plot(.f,xlim=c(-1,2)); f(root(f,lower=-1,upper=2))

f=function(x) {cat("f");exp(100*x)-1}; f(root(f,lower=-1,upper=2))

## Not run: 

  # Quite hard functions to find roots

  ## Increasing function
  ## convex
  n.f=0
  .f = function(x) exp(10*x)-1
  f=function(x) {n.f<<-n.f+1;y=.f(x);points(x,y,pch=20);y}
  plot(.f,xlim=c(-.1,.2)); f(root(f,lower=-1,upper=2))
  print(n.f)
  ## non-convex
  n.f=0
  .f = function(x) 1-exp(-10*x)
  f=function(x) {n.f<<-n.f+1;y=.f(x);points(x,y,pch=20);y}
  plot(.f,xlim=c(-.1,.2)); f(root(f,lower=-1,upper=2))
  print(n.f)

  # ## Decreasing function
  # ## non-convex
  n.f=0
  .f = function(x) 1-exp(10*x)
  f=function(x) {n.f<<-n.f+1;y=.f(x);points(x,y,pch=20,col=rgb(0,0,0,.2));y}
  plot(.f,xlim=c(-.1,.2)); f(root(f,lower=-1,upper=2))
  print(n.f)
  # ## convex
  n.f=0
  .f = function(x) exp(-10*x)-1
  f=function(x) {n.f<<-n.f+1;y=.f(x);points(x,y,pch=20,col=rgb(0,0,0,.2));y}
  plot(.f,xlim=c(-.1,.2)); f(root(f,lower=-1,upper=2))
  print(n.f)

## End(Not run)

IRSN/DiceView documentation built on Jan. 31, 2024, 10:09 a.m.