python中使用牛顿迭代法，python牛顿代法,''' root = n

python中使用牛顿迭代法，python牛顿代法,''' root = n

''' root = newtonRaphson(f,df,a,b,tol=1.0e-9).    Finds a root of f(x) = 0 by combining the Newton-Raphson    method with bisection. The root must be bracketed in (a,b).    Calls user-supplied functions f(x) and its derivative df(x).   '''    def newtonRaphson(f,df,a,b,tol=1.0e-9):    import error    fa = f(a)    if fa == 0.0: return a    fb = f(b)    if fb == 0.0: return b    if fa*fb > 0.0: error.err('Root is not bracketed')    x = 0.5*(a + b)                        for i in range(30):        fx = f(x)        if abs(fx) < tol: return x      # Tighten the brackets on the root         if fa*fx < 0.0:            b = x          else:                              a = x      # Try a Newton-Raphson step            dfx = df(x)      # If division by zero, push x out of bounds        try: dx = -fx/dfx        except ZeroDivisionError: dx = b - a        x = x + dx      # If the result is outside the brackets, use bisection          if (b - x)*(x - a) < 0.0:              dx = 0.5*(b - a)                                  x = a + dx      # Check for convergence             if abs(dx) < tol*max(abs(b),1.0): return x    print 'Too many iterations in Newton-Raphson'