python计算方程式根的方法_Python

python计算方程式根的方法

2020-06-23 09:43songguo Python

这篇文章主要介绍了python计算方程式根的方法,涉及Python数学运算的相关技巧,需要的朋友可以参考下

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：

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									''' 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")