データの並び x, y を3本の線分で近似

# ３本の線分で x, y を近似

from scipy import optimize
%matplotlib inline
import matplotlib.pyplot as plt
import warnings
warnings.filterwarnings('ignore')   # Suppress Matplotlib warnings
import numpy as np

x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ,11, 12, 13, 14, 15], dtype=float)
y = np.array([22, 16, 10, 4, 4, 4, 4, 4, 4, 4, 24, 44, 64, 84, 104])

# ３本の線分で x, y を近似
# i は最初の端点（添字。添え字は０から始まる数字）
residuals = np.ones((x.shape[0]-2, x.shape[0]-1)) * 1e+16
for i in np.arange(1, x.shape[0] - 2):
    seg1_x = x[0:i + 1]
    seg1_y = y[0:i + 1]
    # y = ax + b で近似
    coef1, residuals1, rank1, singular_values1, th1 = np.polyfit(seg1_x, seg1_y, 1, full=True)
    a1 = coef1[0]
    b1 = coef1[1]
    # j は2番目の端点（添字。添え字は０から始まる数字）
    for j in np.arange(i + 1, x.shape[0] - 1):
#        print(i, j)
        seg2_x = x[i:j + 1]
        seg2_y = y[i:j + 1]
        seg3_x = x[j:x.shape[0]]
        seg3_y = y[j:x.shape[0]]

        coef2, residuals2, rank2, singular_values2, th2 = np.polyfit(seg2_x, seg2_y, 1, full=True)
        a2 = coef2[0]
        b2 = coef2[1]
        coef3, residuals3, rank3, singular_values3, th3 = np.polyfit(seg3_x, seg3_y, 1, full=True)
        a3 = coef3[0]
        b3 = coef3[1]
# 確認表示
#        plt.plot(seg1_x, np.poly1d(np.polyfit(seg1_x, seg1_y, 1))(seg1_x))
#        plt.plot(seg2_x, np.poly1d(np.polyfit(seg2_x, seg2_y, 1))(seg2_x)) 
#        plt.plot(seg3_x, np.poly1d(np.polyfit(seg3_x, seg3_y, 1))(seg3_x))   
        residuals[i, j] = sum(residuals1) + sum(residuals2) + sum(residuals3)
        
# 確認表示
# from mpl_toolkits.mplot3d import Axes3D       
# fig = plt.figure()
# ax = Axes3D(fig)
# ii = np.arange(0,residuals.shape[0])
# jj = np.arange(0,residuals.shape[1])
# XX, YY = np.meshgrid(jj, ii)
# ax.plot_wireframe(XX, YY, residuals) 

i, j = np.unravel_index(np.argmin(residuals), residuals.shape)
plt.plot(x, y, "o")
plt.plot(x[0:i + 1], np.poly1d(np.polyfit(x[0:i + 1], y[0:i + 1], 1))(x[0:i + 1]))
plt.plot(x[i:j + 1], np.poly1d(np.polyfit(x[i:j + 1], y[i:j + 1], 1))(x[i:j + 1]))
plt.plot(x[j:x.shape[0]], np.poly1d(np.polyfit(x[j:x.shape[0]], y[j:x.shape[0]], 1))(x[j:x.shape[0]]))
plt.show()       

# heatmap 表示
import seaborn as sns
sns.heatmap(residuals - ( residuals == 1e+16 ) * 1e+16)