Python 分段重网格

嗨，我想知道如何用分段线性函数拟合这些值。我已经读了这个问题，但我不能继续了（）。在本例中，将演示如何为2段情况实现分段函数。但我需要在一个三段的情况下进行，如图所示

我已经编写了以下代码：

from scipy import optimize
import matplotlib.pyplot as plt
import numpy as np


x1 = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ,11, 12, 13, 14, 15,16,17,18,19,20,21], dtype=float)
y1 = np.array([5, 7, 9, 11, 13, 15, 28.92, 42.81, 56.7, 70.59, 84.47, 98.36, 112.25, 126.14, 140.03,145,147,149,151,153,155])



x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ,11, 12, 13, 14, 15], dtype=float)
y = np.array([5, 7, 9, 11, 13, 15, 28.92, 42.81, 56.7, 70.59, 84.47, 98.36, 112.25, 126.14, 140.03])

def piecewise(x,x0,x1,y0,y1,k0,k1,k2):
    return np.piecewise(x , [x <= x0, (x>= x1)] , [lambda x:k0*x + y0-k0*x0, lambda x:k1*(x-(x1+x0))-y1, lambda x:k2*x + y1-k2*x1])

p , e = optimize.curve_fit(piecewise_linear, x1, y1)
xd = np.linspace(0, 15, 100)
plt.figure()
plt.plot(x1, y1, "o")
plt.plot(xd, piecewise_linear(xd, *p))

及

---

分段线性函数的拟合是一个可能存在局部最优解的非线性优化问题。您看到的结果可能是一个局部最优解，您的优化算法陷入了这个局部最优解

解决此问题的一种方法是使用不同的初始值重复优化算法，并采用最佳拟合。我用平均绝对误差（MAE）来比较不同的拟合

perr = np.sum(np.abs(y1-piecewise(x1, *p)))

我还改变了你的分段函数，因为它让我有点困惑。但它仍然像以前一样是一个分段函数

进一步想想，您忘了将x和xd数组的值扩展到21。（这就是绿线提前结束的原因）

从scipy导入优化
将matplotlib.pyplot作为plt导入
将numpy作为np导入
def分段（x、x0、x1、y0、y1、k0、k1、k2）：
返回np.分段（x，[x我不确定你是否应该发布一个新问题，而不是编辑旧问题？你知道在原始功能中添加了哪种噪音吗？我根据你对问题的编辑编辑了我的答案。这是否回答了你的问题？不是真的，你发现的问题不是最合适的。但是，请以任何方式寻求帮助！
y=[ 2.36846863,  2.73722628,  2.77177583,  2.63930636,  2.80864749,
        2.57066667,  2.65277287,  2.57162347,  2.76295667,  2.79835391,
        2.60431154,  2.17326401,  2.67740698,  2.47138153,  2.49882574,
        2.60987338,  2.69935565,  2.60755362,  2.77702029,  2.62996942,
        2.45959517,  2.52750434,  2.73833005,  2.52009   ,  2.80933226,
        1.63807085,  2.49230099,  2.55441614,  3.19256506,  2.52609288,
        1.02931596,  2.40266963,  2.3306463 ,  2.69094276,  2.60779985,
        2.48351648,  2.45131766,  2.40526763,  2.03952569,  1.86217009,
        1.79971848,  1.91772218,  1.85895421,  2.32725731,  2.28189713,
        2.11835833,  2.09636517,  2.2230303 ,  1.85863317,  1.77550406,
        1.68862391,  1.79187765,  1.70887476,  1.81911193,  1.74802483,
        1.65776432,  1.58012849,  1.67781494,  1.62451541,  1.60555884,
        1.56172214,  1.60083809,  1.65256994,  2.74794704,  2.27089627,
        1.80364982,  1.51412482,  1.77738757,  1.56979564,  2.46538633,
        2.37679625,  2.40389294,  2.04165763,  1.82086407,  1.90609219,
        1.87480978,  1.8877854 ,  1.76080074,  1.68369028,  1.57419297,
        1.66470126,  1.74522552,  1.72459756,  1.65510503,  1.72131148,
        1.6254417 ,  1.57091907,  1.68755268,  1.70307911,  1.59445121,
        1.74393783,  1.72913779,  1.66883237,  1.59859545,  1.62335831,
        1.73378184,  1.62621588,  1.79532164,  1.78289992,  1.79475101,
        1.7826266 ,  1.68778918,  1.64484127,  1.62332696,  1.75372393,
        1.99038021,  1.87268137,  1.86124502,  1.82435911,  1.62927102,
        1.66443723,  1.86743516,  1.62745098,  2.20200312,  2.09641026,
        2.26649111,  2.63271605,  2.18050721,  2.57138433,  2.51833359,
        2.74684184,  2.57209998,  2.63762019,  2.30027877,  2.28471286,
        2.40323668,  2.37103313,  2.16414489,  1.01027109,  2.64181007,
        2.45467765,  2.05773672,  1.73624917,  2.05233688,  2.70820669,
        2.65594222,  2.67445635,  2.37212985,  2.48221803,  2.77655216,
        2.62839879,  2.26481307,  2.58005799,  2.1188172 ,  2.14017268,
        2.16459571,  1.95083406,  1.46224418]

perr = np.sum(np.abs(y1-piecewise(x1, *p)))

from scipy import optimize
import matplotlib.pyplot as plt
import numpy as np


def piecewise(x,x0,x1,y0,y1,k0,k1,k2):
    return np.piecewise(x , [x <= x0, np.logical_and(x0<x, x<= x1),x>x1] , [lambda x:k0*x + y0, lambda x:k1*(x-x0)+y1+k0*x0,
                                                                            lambda x:k2*(x-x1) + y0+y1+k0*x0+k1*(x1-x0)])

x1 = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ,11, 12, 13, 14, 15,16,17,18,19,20,21], dtype=float)
y1 = np.array([5, 7, 9, 11, 13, 15, 28.92, 42.81, 56.7, 70.59, 84.47, 98.36, 112.25, 126.14, 140.03,145,147,149,151,153,155])
x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ,11, 12, 13, 14, 15,16,17,18,19,20,21], dtype=float)
y = np.array([5, 7, 9, 11, 13, 15, 28.92, 42.81, 56.7, 70.59, 84.47, 98.36, 112.25, 126.14, 140.03,145,147,149,151,153,155])


perr_min = np.inf
p_best = None
for n in range(100):
    k = np.random.rand(7)*20
    p , e = optimize.curve_fit(piecewise, x1, y1,p0=k)
    perr = np.sum(np.abs(y1-piecewise(x1, *p)))
    if(perr < perr_min):
        perr_min = perr
        p_best = p

xd = np.linspace(0, 21, 100)
plt.figure()
plt.plot(x1, y1, "o")
y_out = piecewise(xd, *p_best)
plt.plot(xd, y_out)
plt.show()

from scipy import optimize
import matplotlib.pyplot as plt
import numpy as np
def piecewise(x,x0,x1,y0,y1,k0,k1,k2):
    return np.piecewise(x , [x <= x0, np.logical_and(x0<x, x<= x1),x>x1] , [lambda x:k0*x + y0, lambda x:k1*(x-x0)+y1+k0*x0,
                                                                            lambda x:k2*(x-x1) + y0+y1+k0*x0+k1*(x1-x0)])

x = np.array(x)
y = np.array(y)

x1 = x
y1 = y



perr_min = np.inf
p_best = None
for n in range(100):
    idx = np.random.choice(np.arange(len(x)), 10, replace=False)
    x_sample = x[idx]
    y_sample = y[idx]
    k = np.random.rand(7)*20
    try:
        p , e = optimize.curve_fit(piecewise, x_sample,y_sample ,p0=k)
        each_error = np.abs(y-piecewise(x, *p))
        x_inliner = x[each_error < 1]
        y_inlier = y[each_error < 1]
        if(x_inliner.shape[0] < 0.8 * x.shape[0]):
            continue

        p_inlier , e_inlier = optimize.curve_fit(piecewise, x_inliner,y_inlier ,p0=p)
        perr = np.sum(np.abs(y-piecewise(x, *p_inlier)))


        if(perr < perr_min):
            perr_min = perr
            p_best = p_inlier
    except RuntimeError:
        pass

xd = np.linspace(0, 21, 100)
plt.figure()
plt.plot(x, y, "o")
y_out = piecewise(xd, *p_best)
plt.plot(xd, y_out)
print p_best
plt.show()