python数学方程计算_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")