熟悉 NumPy 常用函數(shù)
# 來源：NumPy Biginner's Guide 2e ch3
讀寫文件
import numpy as np
# eye 用于創(chuàng)建單位矩陣
i2 = np.eye(2)
print i2
'''
[[ 1. 0.]
[ 0. 1.]]
'''
# 將數(shù)組以純文本保存到 eye.txt 中
np.savetxt("eye.txt", i2)
'''
eye.txt:
1.000000000000000000e+00 0.000000000000000000e+00
0.000000000000000000e+00 1.000000000000000000e+00
'''
# 還可以讀進(jìn)來
print np.loadtxt('eye.txt')
[[ 1. 0.]
[ 0. 1.]]
讀取 CSV
'''
data.csv:
AAPL,28-01-2011, ,344.17,344.4,333.53,336.1,21144800
分別為：
名稱，日期糕非，空朽肥，開盤，最高衡招，最低，收盤州刽，成交量
'''
# delimiter 是分隔符，設(shè)置為 ','
# usecols 設(shè)置需要取的列辨绊，這里只選擇了收盤和成交量
# unpack 設(shè)置為 True房待，返回的數(shù)組是以列為主
# 可以分別將收盤和成交量賦給 c 和 v
c, v = np.loadtxt('data.csv', delimiter=',', usecols=(6,7), unpack=True)
均值
import numpy as np
c, v = np.loadtxt('data.csv', delimiter=',', usecols=(6,7), unpack=True)
# 計算成交量加權(quán)均價
# average 用于計算均值
# weights 參數(shù)指定權(quán)重
vwap = np.average(c, weights=v)
print "VWAP =", vwap
# VWAP = 350.589549353
# mean 函數(shù)也能用于計算均值
print "mean =", np.mean(c)
# mean = 351.037666667
# 計算時間時間加權(quán)均價
t = np.arange(len(c))
print "twap =", np.average(c, weights=t)
# twap = 352.428321839
最大最小值
import numpy as np
# 這次讀入了最高價和最低價
h, l = np.loadtxt('data.csv', delimiter=',', usecols=(4,5), unpack=True)
# 計算歷史最高價和最低價
print "highest =", np.max(h)
# highest = 364.9
print "lowest =", np.min(l)
# lowest = 333.53
# ptp 函數(shù)用于計算極差
print "Spread high price", np.ptp(h)
# Spread high price 24.86
print "Spread low price", np.ptp(l)
# Spread low price 26.97
簡單統(tǒng)計
import numpy as np
# 讀入收盤價
c = np.loadtxt('data.csv', delimiter=',', usecols=(6,), unpack=True)
# 計算中位數(shù)
print "median =", np.median(c)
# median = 352.055
# 手動計算中位數(shù)
# 首先排個序
sorted_close = np.msort(c)
print "sorted =", sorted_close
# 然后取中間元素
N = len(c)
print "middle =", sorted[(N - 1)/2]
# middle = 351.99
# 由于我們的數(shù)組長度是偶數(shù)
# 中位數(shù)應(yīng)該是中間兩個數(shù)的均值
# print "average middle =", (sorted[N /2] + sorted[(N - 1) / 2]) / 2
# average middle = 352.055
# 方差
print "variance =", np.var(c)
# variance = 50.1265178889
# 手動計算方差
print "variance from definition =", np.mean((c - c.mean())**2)
# variance from definition = 50.1265178889
股票收益
import numpy as np
# 簡單收益
# 當(dāng)天收盤價減去前一天收盤價桑孩，再除以前一天收盤價
# returns = np.diff( arr ) / arr[ : -1]
# 我們計算一下標(biāo)準(zhǔn)差（方差的平方根）
print "Standard deviation =", np.std(returns)
# Standard deviation = 0.0129221344368
# 對數(shù)收益
# 當(dāng)天收盤價的對數(shù)前前一天收盤價的對數(shù)
logreturns = np.diff( np.log(c) )
# 計算收益為正的下標(biāo)
# where 將布爾索引變成位置索引
posretindices = np.where(returns > 0)
print "Indices with positive returns", posretindices
# Indices with positive returns (array([ 0, 1, 4, 5, 6, 7, 9, 10, 11, 12, 16, 17, 18, 19, 21, 22, 23, 25, 28]),)
# 年化波動
annual_volatility = np.std(logreturns)/np.mean(logreturns)
annual_volatility = annual_volatility / np.sqrt(1./252.)
print annual_volatility
# 月化波動
print "Monthly volatility", annual_volatility * np.sqrt(1./12.)
處理日期
import numpy as np
from datetime import datetime
# 將日期映射為星期
# Monday 0
# Tuesday 1
# Wednesday 2
# Thursday 3
# Friday 4
# Saturday 5
# Sunday 6
def datestr2num(s):
return datetime.strptime(s, "%d-%m-%Y").date().weekday()
# 讀取星期和收盤價流椒，converters 將日期映射成星期
dates, close = np.loadtxt('data.csv', delimiter=',', usecols=(1,6), converters={1: datestr2num}, unpack=True)
print "Dates =", dates
# Dates = [ 4. 0. 1. 2. 3. 4. 0. 1. 2. 3. 4. 0. 1. 2. 3. 4. 1. 2. 4. 0. 1. 2. 3. 4. 0. 1. 2. 3. 4.]
# 計算一周中每一天的均值
averages = np.zeros(5)
for i in range(5):
indices = np.where(dates == i)
prices = np.take(close, indices)
avg = np.mean(prices)
print "Day", i, "prices", prices, "Average", avg
averages[i] = avg
'''
Day 0 prices [[ 339.32 351.88 359.18 353.21 355.36]] Average 351.79
Day 1 prices [[ 345.03 355.2 359.9 338.61 349.31 355.76]] Average 350.635
Day 2 prices [[ 344.32 358.16 363.13 342.62 352.12 352.47]] Average 352.136666667
Day 3 prices [[ 343.44 354.54 358.3 342.88 359.56 346.67]] Average 350.898333333
Day 4 prices [[ 336.1 346.5 356.85 350.56 348.16 360. 351.99]] Average 350.022857143
'''
# 計算星期幾最高，星期幾最低
top = np.max(averages)
print "Highest average", top
# Highest average 352.136666667
print "Top day of the week", np.argmax(averages)
# Top day of the week 2
bottom = np.min(averages)
print "Lowest average", bottom
# Lowest average 350.022857143
print "Bottom day of the week", np.argmin(averages
# Bottom day of the week 4
真實波動幅度均值（ATR）
# 真實波動幅度（TR）定義為以下三個度量的最大值
# 1. 當(dāng)天最高價減當(dāng)天最低價
# 2. 當(dāng)天最高價減前一天的收盤價的絕對值
# 3. 前一天收盤價減當(dāng)天最低價的絕對值
import numpy as np
import sys
# 讀入最高價惯裕、最低價绣硝、收盤價
h, l, c = np.loadtxt('data.csv', delimiter=',', usecols=(4, 5, 6), unpack=True)
# 讀入數(shù)據(jù)數(shù)量
N = int(sys.argv[1])
# 獲取最近 N 天的最高價和最低價
h = h[-N:]
l = l[-N:]
print "len(h)", len(h), "len(l)", len(l)
print "Close", c
# 由于需要前一天的收盤價鹉胖，所以往天移動一天
previousclose = c[-N -1: -1]
print "len(previousclose)", len(previousclose)
print "Previous close", previousclose
# maximum 逐元素獲得最大值
truerange = np.maximum(h - l, h - previousclose, previousclose - l)
print "True range", truerange
# 計算 ATR
atr = np.zeros(N)
# 第一個 ATR 通過均值來計算
atr[0] = np.mean(truerange)
# 計算之后每一個 ATR
# atr[i] = ((N - 1) * atr[i - 1] + tr[i]) / N
for i in range(1, N):
atr[i] = (N - 1) * atr[i - 1] + truerange[i]
atr[i] /= N
print "ATR", atr
簡單滑動均值
# 每一天的簡單滑動均值
# 就是當(dāng)天與前 (N - 1) 天的均值
# 其中 N 是窗口大小
import numpy as np
import sys
from matplotlib.pyplot import plot
from matplotlib.pyplot import show
N = int(sys.argv[1])
# 使用 ones 函數(shù)創(chuàng)建大小為 N 的數(shù)組
# 并除以 N 來創(chuàng)建權(quán)重
weights = np.ones(N) / N
print "Weights", weights
# 假設(shè) N 為 5：
# Weights [ 0.2 0.2 0.2 0.2 0.2]
# 讀入收盤價
c = np.loadtxt('data.csv', delimiter=',', usecols=(6,), unpack=True)
# 調(diào)用 convolve 函數(shù)來計算滑動平均
sma = np.convolve(weights, c)[N-1:-N+1]
# 繪制函數(shù)圖像
# 要注意橫軸從 (N - 1) 開始
t = np.arange(N - 1, len(c))
plot(t, c[N-1:], lw=1.0)
plot(t, sma, lw=2.0)
show()
注：
np.convolve計算離散卷積甫菠，定義為：
離散卷積其實就是系數(shù)數(shù)組的多項式乘法。例如計算[1, 2, 0, 3]和[1, -2, 5]的卷積：
結(jié)果為[1, 1, 13, -6, 15]拂苹。
指數(shù)滑動均值
import numpy as np
import sys
from matplotlib.pyplot import plot
from matplotlib.pyplot import show
x = np.arange(5)
# exp 計算 e 的 x 次方
print "Exp", np.exp(x)
# Exp [ 1. 2.71828183 7.3890561 20.08553692 54.59815003]
# linspace 使用起始值痰洒、終止值和數(shù)量，返回等間隔的數(shù)組
print "Linspace", np.linspace(-1, 0, 5)
# Linspace [-1. -0.75 -0.5 -0.25 0. ]
N = int(sys.argv[1])
# 計算權(quán)重
weights = np.exp(np.linspace(-1., 0., N))
weights /= weights.sum()
print "Weights", weights
# 假設(shè) N 為 5：
# Weights [ 0.11405072 0.14644403 0.18803785 0.24144538 0.31002201]
# 讀入收盤價
c = np.loadtxt('data.csv', delimiter=',', usecols=(6,), unpack=True)
# 使用 convolve 計算指數(shù)滑動均值
ema = np.convolve(weights, c)[N-1:-N+1]
# 繪制函數(shù)圖像
t = np.arange(N - 1, len(c))
plot(t, c[N-1:], lw=1.0)
plot(t, ema, lw=2.0)
show()
布林帶
import numpy as np
import sys
from matplotlib.pyplot import plot
from matplotlib.pyplot import show
# 讀取窗口大小
N = int(sys.argv[1])
# 這是簡單滑動平均的權(quán)重
weights = np.ones(N) / N
print "Weights", weights
# 讀取收盤價
c = np.loadtxt('data.csv', delimiter=',', usecols=(6,), unpack=True)
# 計算簡單滑動平均
sma = np.convolve(weights, c)[N-1:-N+1]
# 手動計算滑動標(biāo)準(zhǔn)差
deviation = []
C = len(c)
for i in range(N - 1, C):
# 對于每一天
# 滑動標(biāo)準(zhǔn)差是當(dāng)天與前 (N - 1) 天的標(biāo)準(zhǔn)差
# 和滑動均值類似，原書這里有誤
dev = c[i - (N - 1): i + 1]
averages = np.zeros(N)
# 這里的 fill 將數(shù)組元素全部變?yōu)橹付ㄖ? # 相當(dāng)于 averages.flat = sma[i - (N - 1)]
# 但是比它快
averages.fill(sma[i - (N - 1)])
# 也可以直接寫 dev -= sma[i - (N - 1)]
dev = dev - averages
dev = dev ** 2
dev = np.sqrt(np.mean(dev))
deviation.append(dev)
deviation = 2 * np.array(deviation)
print len(deviation), len(sma)
# 上布林帶是簡單滑動均值加上兩倍滑動標(biāo)準(zhǔn)差
# 下布林帶是簡單滑動均值減去兩倍滑動標(biāo)準(zhǔn)差
upperBB = sma + deviation
lowerBB = sma - deviation
c_slice = c[N-1:]
between_bands = np.where((c_slice < upperBB) & (c_slice > lowerBB))
print lowerBB[between_bands]
print c[between_bands]
print upperBB[between_bands]
between_bands = len(np.ravel(between_bands))
print "Ratio between bands", float(between_bands)/len(c_slice)
# 繪制收盤價嗅绰、簡單滑動均值
# 上布林帶和下布林帶的圖像
# 要注意橫軸從 N - 1 開始
t = np.arange(N - 1, C)
plot(t, c_slice, lw=1.0)
plot(t, sma, lw=2.0)
plot(t, upperBB, lw=3.0)
plot(t, lowerBB, lw=4.0)
show()
使用線性模型預(yù)測收盤價
import numpy as np
import sys
N = int(sys.argv[1])
# 讀入收盤價
c = np.loadtxt('data.csv', delimiter=',', usecols=(6,), unpack=True)
# 取后 N 天的收盤價，并倒序
b = c[-N:]
bbx = b[::-1]
print "bbx", bbx
# bbx [ 351.99 346.67 352.47 355.76 355.36]
# 構(gòu)建 NxN 的二維數(shù)組
A = np.zeros((N, N), float)
print "Zeros N by N", A
'''
A = np.zeros((N, N), float)
print "Zeros N by N", A
Zeros N by N [[ 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0.]]
'''
# A[i] 是倒數(shù)第 i 天的前 N 天的收盤價
for i in range(N):
A[i, ] = c[-N - 1 - i: - 1 - i]
print "A", A
'''
A [[ 360. 355.36 355.76 352.47 346.67]
[ 359.56 360. 355.36 355.76 352.47]
[ 352.12 359.56 360. 355.36 355.76]
[ 349.31 352.12 359.56 360. 355.36]
[ 353.21 349.31 352.12 359.56 360. ]]
'''
# 根據(jù)每一天前 N 天收盤價來預(yù)測當(dāng)天收盤價
# np.linalg.lstsq 是最小二乘法的多元線性回歸
# A 是輸入屬性的數(shù)據(jù)集翠语，行是記錄财边，列是屬性
# b 是輸出屬性的數(shù)組
# x 是系數(shù)數(shù)組，x = (A^T A)^(-1) A^T b
(x, residuals, rank, s) = np.linalg.lstsq(A, b)
print x, residuals, rank, s
# [ 0.78111069 -1.44411737 1.63563225 -0.89905126 0.92009049] [] 5 [ 1.77736601e+03 1.49622969e+01 8.75528492e+00 5.15099261e+00 1.75199608e+00]
# 通過后 N 天收盤價來預(yù)測下一天的收盤價
print np.dot(b, x)
# 357.939161015
剪切和壓縮數(shù)組
import numpy as np
a = np.arange(5)
print "a =", a
# a = [0 1 2 3 4]
# clip 用于剪切數(shù)組
# 小于最小值的元素會替換成最小值
# 大于最大值的元素會替換成最大值
print "Clipped", a.clip(1, 2)
# Clipped [1 1 2 2 2]
a = np.arange(4)
print a
# [0 1 2 3]
# compress 用于過濾元素
# 等價于 a[a > 2]
print "Compressed", a.compress(a > 2)
# Compressed [3]
計算階乘
import numpy as np
b = np.arange(1, 9)
print "b =", b
# b = [1 2 3 4 5 6 7 8]
# prod 用于求出各元素乘積
print "Factorial", b.prod()
# Factorial 40320
# cumprod 求出累積連乘
# P[i] = a[0] * ... * a[i]
print "Factorials", b.cumprod()
# Factorials [ 1 2 6 24 120 720 5040 40320]
