import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
from scipy import signal #濾波等

xxx = np.arange(0, 1000)
yyy = np.sin(xxx*np.pi/180)

z1 = np.polyfit(xxx, yyy, 7) # 用7次多項(xiàng)式擬合
p1 = np.poly1d(z1) #多項(xiàng)式系數(shù)
print(p1) # 在屏幕上打印擬合多項(xiàng)式
yvals=p1(xxx) 

plt.plot(xxx, yyy, '*',label='original values')
plt.plot(xxx, yvals, 'r',label='polyfit values')
plt.xlabel('x axis')
plt.ylabel('y axis')
plt.legend(loc=4)
plt.title('polyfitting')
plt.show()

# 極值
num_peak_3 = signal.find_peaks(yvals, distance=10) #distance表極大值點(diǎn)的距離至少大于等于10個(gè)水平單位
print(num_peak_3[0])
print('the number of peaks is ' + str(len(num_peak_3[0])))
plt.plot(xxx, yyy, '*',label='original values')
plt.plot(xxx, yvals, 'r',label='polyfit values')
plt.xlabel('x axis')
plt.ylabel('y axis')
plt.legend(loc=4)
plt.title('polyfitting')
for ii in range(len(num_peak_3[0])):
 plt.plot(num_peak_3[0][ii], yvals[num_peak_3[0][ii]],'*',markersize=10)
plt.show()

yyyd = np.polyder(p1,1) # 1表示一階導(dǎo)
print(yyyd)

print(yvals[signal.argrelextrema(yvals, np.greater)]) #極大值的y軸, yvals為要求極值的序列
print(signal.argrelextrema(yvals, np.greater)) #極大值的x軸
peak_ind = signal.argrelextrema(yvals,np.greater)[0] #極大值點(diǎn)，改為np.less即可得到極小值點(diǎn)
plt.plot(xxx, yyy, '*',label='original values')
plt.plot(xxx, yvals, 'r',label='polyfit values')
plt.xlabel('x axis')
plt.ylabel('y axis')
plt.legend(loc=4)
plt.title('polyfitting')
plt.plot(signal.argrelextrema(yvals,np.greater)[0],yvals[signal.argrelextrema(yvals, np.greater)],'o', markersize=10) #極大值點(diǎn)
plt.plot(signal.argrelextrema(yvals,np.less)[0],yvals[signal.argrelextrema(yvals, np.less)],'+', markersize=10) #極小值點(diǎn)
plt.show()