''' roots = polyRoots(a).
  Uses Laguerre's method to compute all the roots of
  a[0] + a[1]*x + a[2]*x^2 +...+ a[n]*x^n = 0.
  The roots are returned in the array 'roots',
'''  
from evalPoly import *
from numpy import zeros,complex
from cmath import sqrt
from random import random
def polyRoots(a,tol=1.0e-12):
  def laguerre(a,tol):
    x = random()
    # Starting value (random number)
    n = len(a) - 1
    for i in range(30):
      p,dp,ddp = evalPoly(a,x)
      if abs(p) < tol: return x
      g = dp/p
      h = g*g - ddp/p
      f = sqrt((n - 1)*(n*h - g*g))
      if abs(g + f) > abs(g - f): dx = n/(g + f)
      else: dx = n/(g - f)
      x = x - dx
      if abs(dx) < tol: return x
    print 'Too many iterations'
  def deflPoly(a,root): # Deflates a polynomial
    n = len(a)-1
    b = [(0.0 + 0.0j)]*n
    b[n-1] = a[n]
    for i in range(n-2,-1,-1):
      b[i] = a[i+1] + root*b[i+1]
    return b
  n = len(a) - 1
  roots = zeros((n),dtype=complex)
  for i in range(n):
    x = laguerre(a,tol)
    if abs(x.imag) < tol: x = x.real
    roots[i] = x
    a = deflPoly(a,x)
  return roots
  raw_input("\nPress return to exit")