Question

我有几个数据点：

X = np.array([0.01,0.05,0.2,1,10,100,400,2000])
Y = np.array([623,3245.5,710564,332456,540124.5,1851657,5679457,10096844])

我希望将这些数据点适合sigmoid函数：

S=D+(A-D)/(1+(X/C)**B)

A,B,C,D需要通过给出初始值p(A0,B0,C0,D0)来确定四个参数。

此外，每个点应该为残差添加权重因子，从而使平方和达到全局最小值：

weight = ([100,90,80,70,60,50,40,30])

我是算法和编码方面的新手，有人可以就如何拟合这些数据提出一些想法吗？百万谢谢！

这是我的Levenberg-Maquardt代码：

from numpy import *

def function(p):

    r = array([10*(p[1]-p[0]**2),(1-p[0])])
    fp = dot(transpose(r),r) #= 100*(p[1]-p[0]**2)**2 + (1-p[0])**2
    J = (array([[-20*p[0],10],[-1,0]]))
    grad = dot(transpose(J),transpose(r))
    return fp,r,grad,J

def lm(p0,tol=10**(-5),maxits=100):

    nvars=shape(p0)[0]
    nu=0.01
    p = p0
    fp,r,grad,J = function(p)
    e = sum(dot(transpose(r),r))
    nits = 0
    while nits<maxits and linalg.norm(grad)>tol:
        nits += 1
        fp,r,grad,J = function(p)
        H=dot(transpose(J),J) + nu*eye(nvars)

    pnew = zeros(shape(p))
    nits2 = 0
    while (p!=pnew).all() and nits2<maxits:
        nits2 += 1
        dp,resid,rank,s = linalg.lstsq(H,grad)
        pnew = p-dp
        fpnew,rnew,gradnew,Jnew = function(pnew)
        enew = sum(dot(transpose(rnew),rnew))
        rho = linalg.norm(dot(transpose(r),r)-dot(transpose(rnew),rnew))
        rho /= linalg.norm(dot(transpose(grad),pnew-p))

        if rho>0:
            update = 1
            p = pnew
            e = enew
        if rho>0.25:
            nu=nu/10
        else: 
            nu=nu*10
            update = 0
        print fp, p, e, linalg.norm(grad), nu

p0 = array([-1.92,2])

lm(p0)

将多个数据点拟合到逻辑函数

0 个答案: