bezmisc.py 文件源码

def rootWrapper(a,b,c,d):
    if a:
        # Monics formula see http://en.wikipedia.org/wiki/Cubic_function#Monic_formula_of_roots
        a,b,c = (b/a, c/a, d/a)
        m = 2.0*a**3 - 9.0*a*b + 27.0*c
        k = a**2 - 3.0*b
        n = m**2 - 4.0*k**3
        w1 = -.5 + .5*cmath.sqrt(-3.0)
        w2 = -.5 - .5*cmath.sqrt(-3.0)
        if n < 0:
            m1 = pow(complex((m+cmath.sqrt(n))/2),1./3)
            n1 = pow(complex((m-cmath.sqrt(n))/2),1./3)
        else:
            if m+math.sqrt(n) < 0:
                m1 = -pow(-(m+math.sqrt(n))/2,1./3)
            else:
                m1 = pow((m+math.sqrt(n))/2,1./3)
            if m-math.sqrt(n) < 0:
                n1 = -pow(-(m-math.sqrt(n))/2,1./3)
            else:
                n1 = pow((m-math.sqrt(n))/2,1./3)
        x1 = -1./3 * (a + m1 + n1)
        x2 = -1./3 * (a + w1*m1 + w2*n1)
        x3 = -1./3 * (a + w2*m1 + w1*n1)
        return (x1,x2,x3)
    elif b:
        det=c**2.0-4.0*b*d
        if det:
            return (-c+cmath.sqrt(det))/(2.0*b),(-c-cmath.sqrt(det))/(2.0*b)
        else:
            return -c/(2.0*b),
    elif c:
        return 1.0*(-d/c),
    return ()