卷积

激励函数：g(t)

单位激励下的响应函数：f(t)

绘制时间（t）与痛感（h）的函数关系图。

a = [1 2 3 4 5]       原数组
b = [8 7 6]           卷积核数组
使用b作为卷积核数组对a数组执行卷积运算的过程如下：

           44 65 86         有效卷积结果(valid):比原数组短
        23 44 65 86 59      同维卷积结果(same):卷积核中心元素
      8 23 44 65 86 59 30   完全卷积结果(full)
0  0  1  2  3  4  5  0  0
6  7  8
   6  7  8
      6  7  8
         6  7  8
            6  7  8
               6  7  8
                  6  7  8

c = numpy.convolve(a, b, 卷积类型)

5日移动均线序列可以直接使用卷积实现

a = [a, b, c, d, e, f, g, h, i, j] 
b = [1/5, 1/5, 1/5, 1/5, 1/5]

使用卷积函数numpy.convolve(a, b, 卷积类型)实现5日均线

sma52 = np.convolve( closing_prices, np.ones(5) / 5, 'valid')
mp.plot(dates[4:], sma52, c='limegreen', alpha=0.5,
        linewidth=6, label='SMA-5(2)')

# 卷积移动平均线
import numpy as np
import matplotlib.pyplot as mp
import datetime as dt
import matplotlib.dates as md


def dmy2ymd(dmy):
  """
  把日月年转年月日
  :param day:
  :return:
  """
  dmy = str(dmy, encoding='utf-8')
  t = dt.datetime.strptime(dmy, '%d-%m-%Y')
  s = t.date().strftime('%Y-%m-%d')
  return s


dates, opening_prices, 
highest_prices, lowest_prices, 
closing_prices = 
  np.loadtxt('aapl.csv',
             delimiter=',',
             usecols=(1, 3, 4, 5, 6),
             unpack=True,
             dtype='M8[D],f8,f8,f8,f8',
             converters={1: dmy2ymd})  # 日月年转年月日
# 绘制收盘价的折现图
mp.figure('APPL', facecolor='lightgray')
mp.title('APPL', fontsize=18)
mp.xlabel('Date', fontsize=14)
mp.ylabel('Price', fontsize=14)
mp.grid(linestyle=":")

# 设置刻度定位器
# 每周一一个主刻度,一天一个次刻度

ax = mp.gca()
ma_loc = md.WeekdayLocator(byweekday=md.MO)
ax.xaxis.set_major_locator(ma_loc)
ax.xaxis.set_major_formatter(md.DateFormatter('%Y-%m-%d'))
ax.xaxis.set_minor_locator(md.DayLocator())
# 修改dates的dtype为md.datetime.datetiem
dates = dates.astype(md.datetime.datetime)
mp.plot(dates, closing_prices,
        color='dodgerblue',
        linewidth=2,
        linestyle='--',
        alpha=0.8,
        label='APPL Closing Price')

#绘制5日移动平均线
ma5 = np.zeros(closing_prices.size-4)
for i in range(ma5.size):
  ma5[i] =np.mean(closing_prices[i:i+5])

mp.plot(dates[4:],ma5,color='orangered',label='MA5')

#基于卷积绘制5日均线
kernel = np.ones(5)/5
ma52 = np.convolve(
  closing_prices,kernel,'valid'
)
mp.plot(dates[4:],ma52,color='orangered',
        label='MA-52',linewidth=7,alpha=0.3)
#绘制10日移动平均线
ma10 = np.zeros(closing_prices.size-9)
for i in range(ma10.size):
  ma10[i] =np.mean(closing_prices[i:i+10])

mp.plot(dates[9:],ma10,color='green',label='MA10')
#基于卷积绘制10日移动平均线
kernel = np.ones(10)/10
ma102 = np.convolve(closing_prices,kernel,'valid')

mp.plot(dates[9:],ma102,color='green',
        label='MA-10',linewidth=7,alpha=0.3)


mp.legend()
mp.gcf().autofmt_xdate()
mp.show()

加权卷积

使用卷积函数numpy.convolve(a, b, 卷积类型)实现加权5日均线

weights = np.exp(np.linspace(-1, 0, 5))
weights /= weights.sum()
ema5 = np.convolve(closing_prices, weights[::-1], 'valid')
mp.plot(dates[4:], sma52, c='limegreen', alpha=0.5,
        linewidth=6, label='SMA-5')

# 卷积移动平均线
import numpy as np
import matplotlib.pyplot as mp
import datetime as dt
import matplotlib.dates as md


def dmy2ymd(dmy):
  """
  把日月年转年月日
  :param day:
  :return:
  """
  dmy = str(dmy, encoding='utf-8')
  t = dt.datetime.strptime(dmy, '%d-%m-%Y')
  s = t.date().strftime('%Y-%m-%d')
  return s


dates, opening_prices, 
highest_prices, lowest_prices, 
closing_prices = 
  np.loadtxt('aapl.csv',
             delimiter=',',
             usecols=(1, 3, 4, 5, 6),
             unpack=True,
             dtype='M8[D],f8,f8,f8,f8',
             converters={1: dmy2ymd})  # 日月年转年月日
# 绘制收盘价的折现图
mp.figure('APPL', facecolor='lightgray')
mp.title('APPL', fontsize=18)
mp.xlabel('Date', fontsize=14)
mp.ylabel('Price', fontsize=14)
mp.grid(linestyle=":")

# 设置刻度定位器
# 每周一一个主刻度,一天一个次刻度

ax = mp.gca()
ma_loc = md.WeekdayLocator(byweekday=md.MO)
ax.xaxis.set_major_locator(ma_loc)
ax.xaxis.set_major_formatter(md.DateFormatter('%Y-%m-%d'))
ax.xaxis.set_minor_locator(md.DayLocator())
# 修改dates的dtype为md.datetime.datetiem
dates = dates.astype(md.datetime.datetime)
mp.plot(dates, closing_prices,
        color='dodgerblue',
        linewidth=2,
        linestyle='--',
        alpha=0.8,
        label='APPL Closing Price')

#基础卷积实现5日加权平均线
#寻找一组卷积核
kernel = np.exp(np.linspace(-1,0,5))
#卷积核中所有元素之和=1
kernel/=kernel.sum()
print(kernel)
ema53 = np.convolve(closing_prices,kernel[::-1],'valid')
mp.plot(dates[4:],ema53,color='red',
        label='EMA-53')
mp.legend()
mp.gcf().autofmt_xdate()
mp.show()