python計算方程式根的方法

 　　這篇文章主要介紹了python計算方程式根的方法,涉及Python數學運算的相關技巧,需要的朋友可以參考下

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 ''' 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")

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