import numpy as np
from sklearn.linear_model import LinearRegression

x = np.array([143, 145, 147, 149, 150, 153, 154, 155, 156, 157, 158, 159, 160, 162, 164]).reshape(-1,1)
y = np.array([88, 85, 88, 91, 92, 93, 95, 96, 98, 97, 96, 98, 99, 100, 102])

model = LinearRegression().fit(x, y)
print('截距：', model.intercept_)
print('斜率：', model.coef_)

import matplotlib.pyplot as plt
import numpy as np

x = np.arange(1/30,15/30,1/30)
y = np.array([11.86, 15.67, 20.60, 26.69, 33.71, 41.93, 51.13, 61.49, 72.9, 85.44, 99.08, 113.77, 129.54, 146.48])
print("一元二次多項式方程為：\n",np.poly1d(np.polyfit(x,y,2)))

plt.figure()
plt.rcParams["font.sans-serif"] = ['SimHei']
plt.title('回歸擬合一元二次方程', fontproperties="SimHei", fontsize=20)
plt.xlabel('t',fontsize=14)
plt.ylabel('s',fontsize=14)
plt.tick_params(labelsize=10)
plt.grid(linestyle=':')
plt.scatter(x, y, c = '#7f7f7f', label='(s,t)', marker='^')
fit_y=np.polyval(np.polyfit(x,y,deg = 2),x)
plt.plot(x,fit_y,label='目標曲線')
plt.legend()
plt.show()

from sklearn.metrics import r2_score

getmodel=np.poly1d(np.polyfit(x,y,2))
R_square=r2_score(y,getmodel(x))
# 0表示不相關，1表示相關。
print('R_square: {:.2f}'.format(R_square))

import numpy as np
from sklearn import linear_model

x = np.array([[1000,5,1000000,25],
             [600,7,3600,49],
             [1200,6,1440000,36],
             [500,6,2500,36],
             [300,8,90000,64],
             [400,7,160000,49],
             [1300,5,1690000,25],
             [1100,4,1210000,16],
             [1300,3,1690000,9],
             [300,9,90000,81]])
y = np.array([100,75,80,70,50,65,90,100,110,60])
regr = linear_model.LinearRegression()#關鍵程式碼

regr.fit(x,y) #進行擬合

print("擬合評價R^2: ",regr.score(x,y))#相關關係
print("關係係數",regr.coef_) # y = k1*x1+k2*x2係數

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

# 忽略除以0的報錯
np.seterr(divide='ignore', invalid='ignore')

# 擬合數據集
x_arr = np.arange(2, 17, 1)
y_arr = np.array([6.48, 8.2, 9.58, 9.5, 9.7, 10, 9.93, 9.99, 10.49, 10.59, 10.60, 10.8, 10.6, 10.9, 10.76])

def exp_func(x, a, b):
    return a * np.exp(b / x)

# #################################擬合優度R^2的計算######################################
def __sst(y_no_fitting):
    """
    計算SST(total sum of squares) 總平方和
    :param y_no_predicted: List[int] or array[int] 待擬合的y
    :return: 總平方和SST
    """
    y_mean = sum(y_no_fitting) / len(y_no_fitting)
    s_list =[(y - y_mean)**2 for y in y_no_fitting]
    sst = sum(s_list)
    return sst


def __ssr(y_fitting, y_no_fitting):
    """
    計算SSR(regression sum of squares) 回歸平方和
    :param y_fitting: List[int] or array[int]  擬合好的y值
    :param y_no_fitting: List[int] or array[int] 待擬合y值
    :return: 回歸平方和SSR
    """
    y_mean = sum(y_no_fitting) / len(y_no_fitting)
    s_list =[(y - y_mean)**2 for y in y_fitting]
    ssr = sum(s_list)
    return ssr


def __sse(y_fitting, y_no_fitting):
    """
    計算SSE(error sum of squares) 殘差平方和
    :param y_fitting: List[int] or array[int] 擬合好的y值
    :param y_no_fitting: List[int] or array[int] 待擬合y值
    :return: 殘差平方和SSE
    """
    s_list = [(y_fitting[i] - y_no_fitting[i])**2 for i in range(len(y_fitting))]
    sse = sum(s_list)
    return sse


def goodness_of_fit(y_fitting, y_no_fitting):
    """
    計算擬合優度R^2
    :param y_fitting: List[int] or array[int] 擬合好的y值
    :param y_no_fitting: List[int] or array[int] 待擬合y值
    :return: 擬合優度R^2
    """
    SSR = __ssr(y_fitting, y_no_fitting)
    SST = __sst(y_no_fitting)
    rr = SSR /SST
    return rr

popt , pcov = curve_fit(exp_func, x_arr, y_arr)
a_exp = popt[0]
b_exp = popt[1]
print("係數為a = %.5f,b = %.5f"%(a_exp,b_exp))

pre_y = exp_func(x_arr, a_exp, b_exp)
print("e^x曲線預測值為: ", pre_y)

rr_exp = goodness_of_fit(pre_y, y_arr)
# R^2檢驗
print("e^x曲線擬合優度為%.5f" % rr_exp)

figure5 = plt.figure(figsize=(8,6))
plt.plot(x_arr, pre_y, color="#4682B4", label='e^x曲線擬合曲線')
plt.scatter(x_arr, y_arr, color='#FFB6C1', marker="*", label='原始數據')
plt.xlabel('x')
plt.ylabel('y')
plt.legend(loc=4)    # 指定legend的位置右下角
plt.title('curve_fit 指數函數擬合')
plt.rcParams['font.sans-serif'] = ['SimHei']  # 用來正常顯示中文標籤
plt.rcParams['axes.unicode_minus'] = False  # 用來正常顯示負號
plt.show()