python计算方程式根的方法

''' 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")