Searching Multiple Roots Numerically.

This Python code only works with function that crossing x-axis.

The idea is we started from x=0 and walking to the positive direction and evaluating f(x) as we walk.

If there's change of the sign of f(x) from + to -, or vice versa, there must be a root in that area.

We began to surround it to find the-x that correspond to f(x)=0. That x value is the root.

After the root is found, we began to walk along x-axis again until found any sign change of f(x), or until x limit set on code.


Here's the code, I use Pythonista on my iPad and, because I use cosine function, I got several root value.

import numpy as np

def f(x):
 return np.cos(x)

def findRoot(xa,xb):
 if f(xa)==0:
  print 'the root is a ', xa
 if f(xb)==0:
  print 'the root is b ', xb
 xc = (xa+xb)/2.
 while f(xc)>abs(1./64.):
  if f(xc)*f(xa)>0:
   xa = xc
  else:
   xb = xc
  xc = (xa+xb)/2.
  
 print 'the root is', xc

limit = 10
dx = 1./8.
xa = 0.
xb = 0.

while xb<limit:
 xb += dx
 if (f(xa)*f(xb)<0):
  print xa, f(xa), f(xb)
  findRoot(xa,xb)
 xa = xb
 
 

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