Skr-Eric的数据分析课堂（四）--Numpy的常用函数（上）
Numpy的常用函数
1.读取矩阵文件
xxx,xxx,xxx,xxx
xxx,xxx,xxx,xxx
xxx,xxx,xxx,xxx
由若干行若干列的数据项组成，每行数据的项数必须相等，每列数据项的类型必须相同，而且数据项之间有明确的分隔符。
np.loadtxt(
文件路径,
delimiter=分隔符字符串,
usecols=选择列集,
unpack=是否按列展开(缺省False),
dtype=目标类型(缺省float),
converters=转换器字典)->
一个二维(unpack=False)或多个一维数组(unpack=True)
# -*- coding: utf-8 -*-
from __future__ import unicode_literals
import datetime as dt
import numpy as np
import matplotlib.pyplot as mp
import matplotlib.dates as md
# 将日-月-年格式的日期变为年-月-日格式的转换器函数
def dmy2ymd(dmy):
# 将UTF-8编码的字节串转换为UCS-4编码字符串
dmy = str(dmy, encoding='utf-8')
'''
d, m, y = dmy.split('-')
ymd = y + "-" + m + "-" + d
'''
# 将日-月-年格式的日期字符串解析为datetime
# 类型的对象，再取其date类型的日期子对象
date = dt.datetime.strptime(
dmy, '%d-%m-%Y').date()
# 将date类型的日期对象格式
# 化为年-月-日形式的字符串
ymd = date.strftime('%Y-%m-%d')
return ymd
# 从aapl.csv文件中读取苹果公司一段时间内的
# 股票价格：开盘价，最高价，最低价和收盘价
dates, opening_prices, highest_prices, \
lowest_prices, closing_prices = np.loadtxt(
'../../data/aapl.csv', delimiter=",",
usecols=(1, 3, 4, 5, 6), unpack=True,
dtype='M8[D], f8, f8, f8, f8',
converters={1: dmy2ymd})
mp.figure('Candlestick', facecolor='lightgray')
mp.title('Candlestick', fontsize=20)
mp.xlabel('Date', fontsize=14)
mp.ylabel('Price', fontsize=14)
ax = mp.gca()
# 主刻度表示每个星期的星期一
ax.xaxis.set_major_locator(
md.WeekdayLocator(byweekday=md.MO))
# 次刻度表示每一天
ax.xaxis.set_minor_locator(md.DayLocator())
# 设置主刻度的标签格式：日 月(英文缩写) 年
ax.xaxis.set_major_formatter(
md.DateFormatter('%d %b %Y'))
mp.tick_params(labelsize=10)
mp.grid(axis='y', linestyle=':')
# Numpy.datetime64[D]->
# Matplotlib.dates.datetime.datetime
dates = dates.astype(md.datetime.datetime)
rise = closing_prices - opening_prices >= 0.01
fall = opening_prices - closing_prices >= 0.01
fc = np.zeros(dates.size, dtype='3f4')
ec = np.zeros(dates.size, dtype='3f4')
fc[rise], fc[fall] = (1, 1, 1), (0, 0.5, 0)
ec[rise], ec[fall] = (1, 0, 0), (0, 0.5, 0)
mp.bar(dates, highest_prices - lowest_prices,
0, lowest_prices, color=fc, edgecolor=ec)
mp.bar(dates, closing_prices - opening_prices,
0.8, opening_prices, color=fc, edgecolor=ec)
mp.gcf().autofmt_xdate()
mp.show()mask掩码数组
2.算术平均值
样本：S = [s1, s2, ..., sn]
算术平均值：m = (s1+s2+...+sn)/n
s1 = s + d1
s2 = s + d2
...
sn = s + dn
m = s + (d1+d2+...+dn)/n
n->oo: (d1+d2+...+dn)/n->0
算术平均值就是当样本数足够的条件下对真值得无偏估计。
np.mean(样本数组)->算术平均值
样本数组.mean()->算术平均值
# -*- coding: utf-8 -*-
from __future__ import unicode_literals
import numpy as np
closing_prices = np.loadtxt(
'../../data/aapl.csv', delimiter=',',
usecols=(6), unpack=True)
mean = 0
for closing_price in closing_prices:
mean += closing_price
mean /= closing_prices.size
print(mean)
mean = np.mean(closing_prices)
print(mean)
mean = closing_prices.mean()
print(mean)
3.加权平均值
样本：S = [s1, s2, ..., sn]
权重：W = [w1, w2, ..., wn]
加权平均值：
a = (s1w1+s2w2+...+snwn)/(w1+w2+...+wn)
算术平均值就是权重相等的加权平均值
np.average(样本数组, weights=权重数组)
->加权平均值
# -*- coding: utf-8 -*-
from __future__ import unicode_literals
import numpy as np
closing_prices, volumes = np.loadtxt(
'../../data/aapl.csv', delimiter=',',
usecols=(6, 7), unpack=True)
vwap, wsum = 0, 0
for closing_price, volume in zip(
closing_prices, volumes):
vwap += closing_price * volume
wsum += volume
vwap /= wsum
print(vwap)
vwap = np.average(closing_prices, weights=volumes)
print(vwap)时间：早------------------>晚
价格：10 ... 52 48 51 50
权重：低------------------>高
？
# -*- coding: utf-8 -*-
from __future__ import unicode_literals
import datetime as dt
import numpy as np
def dmy2days(dmy):
dmy = str(dmy, encoding='utf-8')
date = dt.datetime.strptime(
dmy, '%d-%m-%Y').date()
days = (date - dt.date.min).days
return days
days, closing_prices = np.loadtxt(
'../../data/aapl.csv', delimiter=',',
usecols=(1, 6), unpack=True,
converters={1: dmy2days})
twap, wsum = 0, 0
for closing_price, day in zip(
closing_prices, days):
twap += closing_price * day
wsum += day
twap /= wsum
print(twap)
twap = np.average(closing_prices, weights=days)
print(twap)时间->数值
4.最值
np.max() \ 在一个数组中求最
np.min() / 大值或最小值元素
np.argmax() \ 在一个数组中求最
np.argmin() / 大值或最小值下标
np.maximum() \ 把两个数组中对应位置的最大值
np.minimum() / 或最小值收集到一个新的数组中
np.ptp() - 一个数组的极差——最大元素与最小元素之差
# -*- coding: utf-8 -*-
from __future__ import unicode_literals
import numpy as np
# 产生9个位于[10, 100)区间的服从均匀分布的随机数
a = np.random.randint(10, 100, 9).reshape(3, 3)
print(a)
b, c = np.max(a), np.min(a)
print(b, c)
d, e = np.argmax(a), np.argmin(a)
print(d, e)
names = np.array(['zhangfei', 'zhaoyun', 'guanyu'])
scores = np.array([70, 90, 80])
print(names[np.argmax(scores)])
f = np.random.randint(10, 100, 9).reshape(3, 3)
print(f)
g, h = np.maximum(a, f), np.minimum(a, f)
print(g, h, sep='\n')
i = np.ptp(a)
print(i)价格波动范围
# -*- coding: utf-8 -*-
from __future__ import unicode_literals
import numpy as np
highest_prices, lowest_prices = np.loadtxt(
'../../data/aapl.csv', delimiter=',',
usecols=(4, 5), unpack=True)
max_highest_price, min_lowest_price = \
highest_prices[0], lowest_prices[0]
for highest_price, lowest_price in zip(
highest_prices[1:], lowest_prices[1:]):
if max_highest_price < highest_price:
max_highest_price = highest_price
if min_lowest_price > lowest_price:
min_lowest_price = lowest_price
print(max_highest_price - min_lowest_price)
print(np.max(highest_prices) - np.min(lowest_prices))价格波动幅度
# -*- coding: utf-8 -*-
from __future__ import unicode_literals
import numpy as np
highest_prices, lowest_prices = np.loadtxt(
'../../data/aapl.csv', delimiter=',',
usecols=(4, 5), unpack=True)
max_highest_price, min_highest_price, \
max_lowest_price, min_lowest_price = \
highest_prices[0], highest_prices[0], \
lowest_prices[0], lowest_prices[0]
for highest_price, lowest_price in zip(
highest_prices[1:], lowest_prices[1:]):
if max_highest_price < highest_price:
max_highest_price = highest_price
if min_highest_price > highest_price:
min_highest_price = highest_price
if max_lowest_price < lowest_price:
max_lowest_price = lowest_price
if min_lowest_price > lowest_price:
min_lowest_price = lowest_price
print(max_highest_price - min_highest_price,
max_lowest_price - min_lowest_price)
print(np.ptp(highest_prices), np.ptp(lowest_prices))
5.中位数
5000 3000 4000 6000 1 10000000000
1 3000 4000 5000 6000 10000000000
\____/
|
4500
(a[(6-1)/2] + a[6/2]) / 2
1 3000 4000 5000 10000000000
|
4000
(a[(5-1)/2] + a[5/2]) / 2
通用公式：(a[(L-1)/2] + a[L/2]) / 2
np.median(数组)->中位数
# -*- coding: utf-8 -*-
from __future__ import unicode_literals
import numpy as np
closing_prices = np.loadtxt(
'../../data/aapl.csv', delimiter=',',
usecols=(6), unpack=True)
sorted_prices = np.msort(closing_prices)
l = len(sorted_prices)
median = (sorted_prices[int((l - 1) / 2)] +
sorted_prices[int(l / 2)]) / 2
print(median)
median = np.median(closing_prices)
print(median)
6.标准差
样本：S = [s1, s2, ..., sn]
均值：m = (s1+s2+...+sn)/n -> 真值
离差：D = [d1, d2, ..., dn], di = si - m
离差方：Q = [q1, q2, ..., qn], qi = di^2
(总体)方差：v = (q1+q2+...+qn)/n
(总体)标准差：std = sqrt(v) -> 方均根误差，表示所有样本相对于真值的偏离程度。将其作为表征一组随机量分散性的指标
(样本)方差：v' = (q1+q2+...+qn)/(n-1)
(样本)标准差：std' = sqrt(v')
np.std(样本数组, ddof=非自由度(缺省0))->标准差
# -*- coding: utf-8 -*-
from __future__ import unicode_literals
import numpy as np
closing_prices = np.loadtxt(
'../../data/aapl.csv', delimiter=',',
usecols=(6), unpack=True)
# 均值
mean = closing_prices.mean()
# 离差
devs = closing_prices - mean
# 总体方差
pvar = (devs ** 2).sum() / devs.size
# 总体标准差
pstd = np.sqrt(pvar)
# 样本方差
svar = (devs ** 2).sum() / (devs.size - 1)
# 样本标准差
sstd = np.sqrt(svar)
print(pstd, sstd)
pstd = np.std(closing_prices)
sstd = np.std(closing_prices, ddof=1)
print(pstd, sstd)
7.星期数据
Mon Tue Wed Thu Fri
xxx xxx xxx xxx xxx
xxx xxx xxx xxx xxx
...
np.where(条件) -> 数组中满足该条件的元素的下标数组
np.take(数组, 下标数组) -> 数组中与下标数组相对应的元素所构成的子数组
数组[掩码数组] -> 数组中与掩码数组为True的元素相对应的元素所构成的子数组
计算星期均值
# -*- coding: utf-8 -*-
from __future__ import unicode_literals
import datetime as dt
import numpy as np
def dmy2wday(dmy):
dmy = str(dmy, encoding='utf-8')
date = dt.datetime.strptime(
dmy, '%d-%m-%Y').date()
wday = date.weekday() # 用0-6表示周一到周日
return wday
wdays, closing_prices = np.loadtxt(
'../../data/aapl.csv', delimiter=',',
usecols=(1, 6), unpack=True,
converters={1: dmy2wday})
ave_closing_prices = np.zeros(5)
for wday in range(len(ave_closing_prices)):
'''
ave_closing_prices[wday] = np.take(
closing_prices,
np.where(wdays == wday)).mean()
ave_closing_prices[wday] = closing_prices[
np.where(wdays == wday)].mean()
'''
ave_closing_prices[wday] = closing_prices[
wdays == wday].mean()
for wday, ave_closing_price in zip(
['MON', 'TUE', 'WED', 'THU', 'FRI'],
ave_closing_prices):
print(wday, np.round(ave_closing_price, 2))np.apply_along_axis(处理函数, 轴向, 数组)
将n维数组按照给定的轴向分解为若干个n-1维子数组作为参数调用处理函数，并将其返回值重新组合成数组的形式返回
# -*- coding: utf-8 -*-
from __future__ import unicode_literals
import numpy as np
def foo(a):
return a.sum()
a = np.arange(1, 10).reshape(3, 3)
print(a)
b = np.apply_along_axis(foo, 0, a)
print(b)
c = np.apply_along_axis(foo, 1, a)
print(c)统计每周的开高低收价格
# -*- coding: utf-8 -*-
from __future__ import unicode_literals
import datetime as dt
import numpy as np
def dmy2wday(dmy):
dmy = str(dmy, encoding='utf-8')
date = dt.datetime.strptime(
dmy, '%d-%m-%Y').date()
wday = date.weekday() # 用0-6表示周一到周日
return wday
wdays, opening_prices, highest_prices, \
lowest_prices, closing_prices = np.loadtxt(
'../../data/aapl.csv', delimiter=',',
usecols=(1, 3, 4, 5, 6), unpack=True,
converters={1: dmy2wday})
wdays = wdays[:16]
opening_prices = opening_prices[:16]
highest_prices = highest_prices[:16]
lowest_prices = lowest_prices[:16]
closing_prices = closing_prices[:16]
first_monday = np.where(wdays == 0)[0][0]
last_friday = np.where(wdays == 4)[0][-1]
indices = np.arange(first_monday, last_friday + 1)
indices = np.array(np.split(indices, 3))
def week_summary(indices):
opening_price = opening_prices[indices[0]]
highest_price = np.take(
highest_prices, indices).max()
lowest_price = np.take(
lowest_prices, indices).min()
closing_price = closing_prices[indices[-1]]
return opening_price, highest_price, \
lowest_price, closing_price
summaries = np.apply_along_axis(
week_summary, 1, indices)
np.savetxt('../../data/summary.csv',
summaries, delimiter=',', fmt='%g')
8.一维卷积
a = [1 2 3 4 5]
b = [6 7 8]
c = a @ b = [6 19 40 61 82 67 40] - 完全卷积(full)
[19 40 61 82 67] - 同维卷积(same)
[40 61 82] - 有效卷积(valid)
6 19 40 61 82 67 40
0 0 1 2 3 4 5 0 0
8 7 6
8 7 6
8 7 6
8 7 6
8 7 6
8 7 6
8 7 6
c = np.convolve(a, b, ['full']/'same'/'valid')
^ ^ ^
| |____ |
被卷积数组 | 卷积类型
卷积核数组
# -*- coding: utf-8 -*-
from __future__ import unicode_literals
import numpy as np
a = np.array([1, 2, 3, 4, 5])
b = np.array([6, 7, 8])
print(np.convolve(a, b))
print(np.convolve(a, b, 'same'))
print(np.convolve(a, b, 'valid'))
9.移动平均线
a b c d e f g h i j k l m n
^^^ ^^
[1/5 1/5 1/5 1/5 1/5]
A B C D E -> S=A+B+C+D+E
(aA + bB + cC + dD +eE)/S
aA/S + bB/S +cC/S + dD/S + eE/S
[A/S B/S C/S D/S E/S]
# -*- coding: utf-8 -*-
from __future__ import unicode_literals
import datetime as dt
import numpy as np
import matplotlib.pyplot as mp
import matplotlib.dates as md
# 将日-月-年格式的日期变为年-月-日格式的转换器函数
def dmy2ymd(dmy):
# 将UTF-8编码的字节串转换为UCS-4编码字符串
dmy = str(dmy, encoding='utf-8')
'''
d, m, y = dmy.split('-')
ymd = y + "-" + m + "-" + d
'''
# 将日-月-年格式的日期字符串解析为datetime
# 类型的对象，再取其date类型的日期子对象
date = dt.datetime.strptime(
dmy, '%d-%m-%Y').date()
# 将date类型的日期对象格式
# 化为年-月-日形式的字符串
ymd = date.strftime('%Y-%m-%d')
return ymd
# 从aapl.csv文件中读取苹果公司一段时间内的
# 股票价格：开盘价，最高价，最低价和收盘价
dates, closing_prices = np.loadtxt(
'../../data/aapl.csv', delimiter=",",
usecols=(1, 6), unpack=True,
dtype='M8[D], f8', converters={1: dmy2ymd})
sma51 = np.zeros(closing_prices.size - 4)
for i in range(sma51.size):
sma51[i] = closing_prices[i:i + 5].mean()
sma52 = np.convolve(closing_prices,
np.ones(5) / 5, 'valid')
sma10 = np.convolve(closing_prices,
np.ones(10) / 10, 'valid')
weights = np.exp(np.linspace(-1, 0, 5))
weights /= weights.sum()
ema5 = np.convolve(closing_prices,
weights[::-1], 'valid')
mp.figure('Moving Average', facecolor='lightgray')
mp.title('Moving Average', fontsize=20)
mp.xlabel('Date', fontsize=14)
mp.ylabel('Price', fontsize=14)
ax = mp.gca()
# 主刻度表示每个星期的星期一
ax.xaxis.set_major_locator(
md.WeekdayLocator(byweekday=md.MO))
# 次刻度表示每一天
ax.xaxis.set_minor_locator(md.DayLocator())
# 设置主刻度的标签格式：日 月(英文缩写) 年
ax.xaxis.set_major_formatter(
md.DateFormatter('%d %b %Y'))
mp.tick_params(labelsize=10)
mp.grid(linestyle=':')
# Numpy.datetime64[D]->
# Matplotlib.dates.datetime.datetime
dates = dates.astype(md.datetime.datetime)
mp.plot(dates, closing_prices, c='lightgray',
label='Closing Price')
mp.plot(dates[4:], sma51, c='orangered',
label='SMA-51')
mp.plot(dates[4:], sma52, c='orangered', alpha=0.3,
linewidth=6, label='SMA-52')
mp.plot(dates[9:], sma10, c='dodgerblue',
label='SMA-10')
mp.plot(dates[4:], ema5, c='limegreen',
label='EMA-5')
mp.legend()
mp.gcf().autofmt_xdate()
mp.show()
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