python计算方程式根的方法

本文实例讲述了python计算方程式根的方法。分享给大家供大家参考。具体实现方法如下：

    ''' 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")

希望本文所述对大家的Python程序设计有所帮助。