#
#
# Nim's Runtime Library
# (c) Copyright 2013 Robert Persson
#
# See the file "copying.txt", included in this
# distribution, for details about the copyright.
#
## **Warning:** This module will be moved out of the stdlib and into a
## Nimble package, don't use it.
type OneVarFunction* = proc (x: float): float
{.deprecated: [TOneVarFunction: OneVarFunction].}
proc brent*(xmin,xmax:float, function:OneVarFunction, tol:float,maxiter=1000):
tuple[rootx, rooty: float, success: bool]=
## Searches `function` for a root between `xmin` and `xmax`
## using brents method. If the function value at `xmin`and `xmax` has the
## same sign, `rootx`/`rooty` is set too the extrema value closest to x-axis
## and succes is set to false.
## Otherwise there exists at least one root and success is set to true.
## This root is searched for at most `maxiter` iterations.
## If `tol` tolerance is reached within `maxiter` iterations
## the root refinement stops and success=true.
# see http://en.wikipedia.org/wiki/Brent%27s_method
var
a=xmin
b=xmax
c=a
d=1.0e308
fa=function(a)
fb=function(b)
fc=fa
s=0.0
fs=0.0
mflag:bool
i=0
tmp2:float
if fa*fb>=0:
if abs(fa)<abs(fb):
return (a,fa,false)
else:
return (b,fb,false)
if abs(fa)<abs(fb):
swap(fa,fb)
swap(a,b)
while fb!=0.0 and abs(a-b)>tol:
if fa!=fc and fb!=fc: # inverse quadratic interpolation
s = a * fb * fc / (fa - fb) / (fa - fc) + b * fa * fc / (fb - fa) / (fb - fc) + c * fa * fb / (fc - fa) / (fc - fb)
else: #secant rule
s = b - fb * (b - a) / (fb - fa)
tmp2 = (3.0 * a + b) / 4.0
if not((s > tmp2 and s < b) or (s < tmp2 and s > b)) or
(mflag and abs(s - b) >= (abs(b - c) / 2.0)) or
(not mflag and abs(s - b) >= abs(c - d) / 2.0):
s=(a+b)/2.0
mflag=true
else:
if (mflag and (abs(b - c) < tol)) or (not mflag and (abs(c - d) < tol)):
s=(a+b)/2.0
mflag=true
else:
mflag=false
fs = function(s)
d = c
c = b
fc = fb
if fa * fs<0.0:
b=s
fb=fs
else:
a=s
fa=fs
if abs(fa)<abs(fb):
swap(a,b)
swap(fa,fb)
inc i
if i>maxiter:
break
return (b,fb,true)