python计算方程式根的方法

本文实例讲述了python/' target='_blank'>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,complexfrom cmath import sqrtfrom random import randomdef 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")

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