Python数据分析_第04课：NumPy基础_笔记

古城微笑少年丶 2021-11-02 11:20 415阅读 0赞

### 文章目录 ###

*  numpy
 *   *  np.maximum 元素级最大值
     *  np.modf 按元素返回数组的小数部分和整数部分
     *  np.meshgrid 从坐标向量返回坐标矩阵
     *  np.where
 *  数学与统计方法
 *   *  randn 标准正态分布数据
     *  用于布尔型数组的方法
     *  排序
     *  5%分位数
     *  np.unique 唯一化 以及其他的集合逻辑
 *  线性代数
 *   *  随机数生成
 *  范例：随机漫步
 *  利用NumPy进行历史股价分析
 *   *  统计分析
     *  股票收益率
     *  日期分析
     *  周汇总
     *  真实波动幅度均值
     *  简单移动平均线
     *  指数移动平均线
     *  布林带
     *  线性模型
     *  趋势线

GitHub: [https://github.com/RealEmperor/Python-for-Data-Analysis][https_github.com_RealEmperor_Python-for-Data-Analysis]

# numpy #

import numpy as np
    from numpy.random import randn
    
    #通用函数
    arr = np.arange(10)
    np.sqrt(arr)

array([ 0.        ,  1.        ,  1.41421356,  1.73205081,  2.        ,
            2.23606798,  2.44948974,  2.64575131,  2.82842712,  3.        ])

np.exp(arr)

array([  1.00000000e+00,   2.71828183e+00,   7.38905610e+00,
             2.00855369e+01,   5.45981500e+01,   1.48413159e+02,
             4.03428793e+02,   1.09663316e+03,   2.98095799e+03,
             8.10308393e+03])

## np.maximum 元素级最大值 ##

x = randn(8)
    y = randn(8)
    print(x)
    print(y)
    # 元素级最大值
    np.maximum(x, y)

[-1.03760196 -1.0035245  -0.19109603  2.27398057 -0.51605815 -1.25481649
     -1.95118717 -0.09423245]
    [-1.26195712 -0.70857631 -0.18729477  2.58847014  2.46277713 -1.04523397
      1.13501218  1.3499591 ]
    
    
    
    
    
    array([-1.03760196, -0.70857631, -0.18729477,  2.58847014,  2.46277713,
           -1.04523397,  1.13501218,  1.3499591 ])

## np.modf 按元素返回数组的小数部分和整数部分 ##

arr = randn(7) * 5
    print(arr)
    # 按元素返回数组的小数部分和整数部分
    np.modf(arr)

[ 8.01175821  3.46248512 -4.11785287  1.34226648  0.40194097  5.81213218
     -0.40446832]
    
    
    
    
    
    (array([ 0.01175821,  0.46248512, -0.11785287,  0.34226648,  0.40194097,
             0.81213218, -0.40446832]), array([ 8.,  3., -4.,  1.,  0.,  5., -0.]))

## np.meshgrid 从坐标向量返回坐标矩阵 ##

###利用数组进行数据处理
    # 向量化
    points = np.arange(-5, 5, 0.01)  # 1000 equally spaced points
    # 从坐标向量返回坐标矩阵
    xs, ys = np.meshgrid(points, points)
    print(ys)

[[-5.   -5.   -5.   ..., -5.   -5.   -5.  ]
     [-4.99 -4.99 -4.99 ..., -4.99 -4.99 -4.99]
     [-4.98 -4.98 -4.98 ..., -4.98 -4.98 -4.98]
     ..., 
     [ 4.97  4.97  4.97 ...,  4.97  4.97  4.97]
     [ 4.98  4.98  4.98 ...,  4.98  4.98  4.98]
     [ 4.99  4.99  4.99 ...,  4.99  4.99  4.99]]

import matplotlib.pyplot as plt
    
    z = np.sqrt(xs ** 2 + ys ** 2)
    print(z)
    plt.imshow(z, cmap=plt.cm.gray)
    plt.colorbar()
    plt.title("Image plot of $\sqrt{x^2 + y^2}$ for a grid of values")
    
    plt.draw()

[[ 7.07106781  7.06400028  7.05693985 ...,  7.04988652  7.05693985
       7.06400028]
     [ 7.06400028  7.05692568  7.04985815 ...,  7.04279774  7.04985815
       7.05692568]
     [ 7.05693985  7.04985815  7.04278354 ...,  7.03571603  7.04278354
       7.04985815]
     ..., 
     [ 7.04988652  7.04279774  7.03571603 ...,  7.0286414   7.03571603
       7.04279774]
     [ 7.05693985  7.04985815  7.04278354 ...,  7.03571603  7.04278354
       7.04985815]
     [ 7.06400028  7.05692568  7.04985815 ...,  7.04279774  7.04985815
       7.05692568]]

## np.where ##

# 将条件逻辑表达为数组运算
    xarr = np.array([1.1, 1.2, 1.3, 1.4, 1.5])
    yarr = np.array([2.1, 2.2, 2.3, 2.4, 2.5])
    cond = np.array([True, False, True, True, False])
    
    result = [(x if c else y)
              for x, y, c in zip(xarr, yarr, cond)]
    print(result)

[1.1000000000000001, 2.2000000000000002, 1.3, 1.3999999999999999, 2.5]

result = np.where(cond, xarr, yarr)
    print(result)

[ 1.1  2.2  1.3  1.4  2.5]

arr = randn(4, 4)
    print(arr)
    print(np.where(arr > 0, 2, -2))
    print(np.where(arr > 0, 2, arr))  # set only positive values to 2

[[-0.09677059 -0.78473401 -0.00841639  1.39892368]
     [-1.14999224  0.33586593 -0.1844864   0.47664971]
     [-0.67508722  0.56130304 -0.8018509   0.07338623]
     [ 0.10375292  1.44174994  0.42788598 -0.66850794]]
    [[-2 -2 -2  2]
     [-2  2 -2  2]
     [-2  2 -2  2]
     [ 2  2  2 -2]]
    [[-0.09677059 -0.78473401 -0.00841639  2.        ]
     [-1.14999224  2.         -0.1844864   2.        ]
     [-0.67508722  2.         -0.8018509   2.        ]
     [ 2.          2.          2.         -0.66850794]]

"""
    # 多条件一般表示方法
    # Not to be executed
    result = []
    for i in range(n):
        if cond1[i] and cond2[i]:
            result.append(0)
        elif cond1[i]:
            result.append(1)
        elif cond2[i]:
            result.append(2)
        else:
            result.append(3)
    
    # 多条件where表示方法
    # Not to be executed
    np.where(cond1 & cond2, 0,
             np.where(cond1, 1,
                      np.where(cond2, 2, 3)))
    
    # Not to be executed
    result = 1 * cond1 + 2 * cond2 + 3 * -(cond1 | cond2)
    """

'\n# 多条件一般表示方法\n# Not to be executed\nresult = []\nfor i in range(n):\n    if cond1[i] and cond2[i]:\n        result.append(0)\n    elif cond1[i]:\n        result.append(1)\n    elif cond2[i]:\n        result.append(2)\n    else:\n        result.append(3)\n\n# 多条件where表示方法\n# Not to be executed\nnp.where(cond1 & cond2, 0,\n         np.where(cond1, 1,\n                  np.where(cond2, 2, 3)))\n\n# Not to be executed\nresult = 1 * cond1 + 2 * cond2 + 3 * -(cond1 | cond2)\n'

# 数学与统计方法 #

## randn 标准正态分布数据 ##

# 数学与统计方法
    
    arr = np.random.randn(5, 4)  # 标准正态分布数据
    print(arr.mean())
    print(np.mean(arr))
    print(arr.sum())
    
    print(arr.mean(axis=1))
    print(arr.sum(0))
    
    arr = np.array([[0, 1, 2], [3, 4, 5], [6, 7, 8]])
    print(arr.cumsum(0))
    print(arr.cumprod(1))

0.299738473867
    0.299738473867
    5.99476947734
    [ 0.33172725 -0.49981575  0.35973217  0.39621625  0.91083245]
    [ 4.58629248  2.22968175 -1.88744743  1.06624268]
    [[ 0  1  2]
     [ 3  5  7]
     [ 9 12 15]]
    [[  0   0   0]
     [  3  12  60]
     [  6  42 336]]

## 用于布尔型数组的方法 ##

# 用于布尔型数组的方法
    arr = randn(100)
    (arr > 0).sum()  # 正值的数量
    
    bools = np.array([False, False, True, False])
    print(bools.any())
    print(bools.all())

True
    False

## 排序 ##

# 排序
    arr = randn(8)
    print(arr)
    arr.sort()
    print(arr)
    
    arr = randn(5, 3)
    print(arr)
    arr.sort(1)
    print(arr)

[-0.17018254  1.29292169  1.87999871 -0.25529225  1.1058983  -0.27456269
     -1.17911236  0.30155365]
    [-1.17911236 -0.27456269 -0.25529225 -0.17018254  0.30155365  1.1058983
      1.29292169  1.87999871]
    [[-0.31552106  0.95227657  0.08006334]
     [ 0.86493167  0.66028869  0.56929258]
     [-1.30046025 -1.03020373 -0.80371581]
     [-0.74412785  0.2413104  -0.81418268]
     [-1.16001837 -0.70517682 -0.5816708 ]]
    [[-0.31552106  0.08006334  0.95227657]
     [ 0.56929258  0.66028869  0.86493167]
     [-1.30046025 -1.03020373 -0.80371581]
     [-0.81418268 -0.74412785  0.2413104 ]
     [-1.16001837 -0.70517682 -0.5816708 ]]

## 5%分位数 ##

large_arr = randn(1000)
    large_arr.sort()
    large_arr[int(0.05 * len(large_arr))]  # 5%分位数

-1.7061490455426676

## np.unique 唯一化 以及其他的集合逻辑 ##

# 唯一化以及其他的集合逻辑
    names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'])
    np.unique(names)

array(['Bob', 'Joe', 'Will'], 
          dtype='<U4')

ints = np.array([3, 3, 3, 2, 2, 1, 1, 4, 4])
    np.unique(ints)

array([1, 2, 3, 4])

sorted(set(names))

['Bob', 'Joe', 'Will']

values = np.array([6, 0, 0, 3, 2, 5, 6])
    np.in1d(values, [2, 3, 6])

array([ True, False, False,  True,  True, False,  True], dtype=bool)

# 线性代数 #

#线性代数
    x = np.array([[1., 2., 3.], [4., 5., 6.]])
    y = np.array([[6., 23.], [-1, 7], [8, 9]])
    print(x)
    print(y)
    print(x.dot(y))  # 等价于np.dot(x, y)
    
    print(np.dot(x, np.ones(3)))
    
    np.random.seed(12345)
    
    from numpy.linalg import inv, qr
    
    X = randn(5, 5)
    mat = X.T.dot(X)
    # 计算矩阵的逆矩阵
    inv(mat)
    mat.dot(inv(mat))
    # 计算矩阵的QR因子分解
    q, r = qr(mat)
    print(r)

[[ 1.  2.  3.]
     [ 4.  5.  6.]]
    [[  6.  23.]
     [ -1.   7.]
     [  8.   9.]]
    [[  28.   64.]
     [  67.  181.]]
    [  6.  15.]
    [[ -6.92714002   7.38899524   6.12272905  -7.11625341  -4.92150833]
     [  0.          -3.97347612  -0.86707993   2.97472904  -5.74024113]
     [  0.           0.         -10.26810228   1.89090298   1.60790112]
     [  0.           0.           0.          -1.29964934   3.35772244]
     [  0.           0.           0.           0.           0.55705805]]

## 随机数生成 ##

#随机数生成
    samples = np.random.normal(size=(4, 4))
    print(samples)

[[  1.24121276e-01   3.02613562e-01   5.23772068e-01   9.40277775e-04]
     [  1.34380979e+00  -7.13543985e-01  -8.31153539e-01  -2.37023165e+00]
     [ -1.86076079e+00  -8.60757398e-01   5.60145293e-01  -1.26593449e+00]
     [  1.19827125e-01  -1.06351245e+00   3.32882716e-01  -2.35941881e+00]]

# 范例：随机漫步 #

# 范例：随机漫步
    import random
    
    position = 0
    walk = [position]
    steps = 1000
    for i in range(steps):
        step = 1 if random.randint(0, 1) else -1
        position += step
        walk.append(position)
        
    print(walk)

[0, 1, 0, -1, 0, -1, 0, -1, -2, -1, 0, -1, 0, 1, 2, 1, 0, -1, -2, -1, -2, -3, -4, -5, -4, -3, -2, -3, -4, -5, -6, -5, -4, -3, -4, -3, -4, -5, -4, -5, -6, -7, -6, -5, -4, -5, -6, -7, -6, -7, -6, -7, -6, -5, -4, -3, -4, -3, -4, -3, -2, -3, -4, -3, -2, -3, -4, -5, -6, -7, -8, -9, -8, -9, -8, -9, -8, -7, -6, -5, -6, -5, -6, -7, -8, -9, -8, -7, -8, -9, -10, -11, -12, -13, -12, -11, -12, -11, -12, -11, -12, -11, -12, -11, -10, -11, -12, -11, -12, -13, -12, -11, -12, -11, -10, -11, -12, -13, -12, -11, -10, -9, -10, -9, -10, -11, -10, -11, -10, -9, -8, -9, -10, -11, -12, -13, -12, -13, -14, -15, -14, -13, -12, -13, -12, -11, -10, -9, -8, -9, -8, -9, -8, -9, -8, -9, -8, -9, -10, -9, -8, -7, -8, -9, -10, -11, -12, -11, -12, -11, -12, -13, -12, -13, -12, -11, -12, -11, -10, -9, -8, -7, -6, -7, -6, -7, -6, -5, -6, -5, -4, -5, -6, -7, -8, -7, -8, -7, -6, -7, -6, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 1, 0, -1, 0, 1, 0, 1, 0, 1, 2, 1, 0, -1, -2, -3, -2, -3, -2, -3, -4, -3, -2, -1, -2, -3, -4, -3, -2, -3, -4, -3, -4, -5, -6, -7, -8, -9, -10, -9, -8, -7, -8, -7, -8, -7, -6, -7, -6, -7, -6, -7, -6, -5, -6, -5, -6, -5, -4, -5, -6, -5, -6, -7, -6, -7, -8, -7, -6, -7, -6, -5, -4, -3, -4, -5, -4, -5, -6, -5, -6, -5, -4, -3, -4, -3, -4, -5, -6, -5, -6, -5, -6, -5, -4, -3, -2, -1, -2, -1, -2, -1, -2, -3, -4, -3, -4, -3, -4, -3, -2, -1, -2, -1, 0, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 3, 2, 1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, -2, -1, 0, 1, 2, 3, 4, 5, 4, 5, 4, 3, 2, 3, 4, 5, 6, 5, 6, 7, 6, 5, 6, 5, 4, 5, 4, 5, 6, 7, 6, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 6, 7, 6, 7, 6, 7, 8, 9, 10, 9, 10, 9, 10, 9, 10, 9, 8, 9, 8, 7, 8, 9, 10, 11, 12, 13, 12, 11, 10, 11, 12, 13, 14, 15, 14, 15, 16, 15, 16, 15, 14, 13, 14, 13, 14, 13, 12, 11, 10, 9, 10, 11, 10, 11, 12, 11, 12, 11, 10, 9, 10, 9, 8, 9, 10, 9, 8, 7, 8, 7, 6, 5, 6, 7, 6, 7, 8, 9, 10, 11, 12, 13, 12, 13, 14, 13, 12, 13, 12, 13, 12, 11, 12, 11, 10, 11, 12, 13, 12, 11, 10, 9, 10, 11, 12, 13, 12, 13, 12, 13, 12, 13, 14, 15, 14, 13, 12, 13, 14, 15, 14, 15, 14, 15, 14, 15, 16, 17, 16, 17, 18, 17, 16, 17, 18, 19, 18, 19, 20, 21, 22, 21, 22, 21, 20, 19, 18, 17, 16, 15, 16, 15, 16, 17, 18, 19, 20, 19, 18, 19, 20, 19, 18, 19, 18, 19, 18, 17, 18, 19, 18, 17, 16, 15, 14, 13, 12, 13, 14, 15, 14, 13, 14, 13, 12, 13, 12, 13, 12, 11, 10, 11, 12, 13, 14, 15, 14, 13, 14, 13, 12, 13, 14, 15, 14, 13, 14, 15, 16, 17, 18, 19, 18, 19, 20, 19, 20, 19, 18, 19, 20, 21, 20, 21, 20, 19, 18, 19, 20, 19, 18, 17, 18, 19, 18, 17, 16, 15, 14, 15, 14, 13, 12, 11, 12, 11, 10, 11, 12, 11, 10, 9, 8, 9, 10, 9, 10, 9, 10, 11, 10, 11, 12, 13, 12, 13, 12, 13, 12, 13, 14, 13, 12, 13, 12, 13, 14, 13, 12, 13, 12, 13, 12, 13, 12, 13, 12, 11, 10, 11, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 5, 4, 5, 6, 7, 6, 7, 6, 5, 6, 7, 8, 9, 8, 9, 10, 9, 8, 9, 10, 11, 10, 11, 12, 13, 12, 11, 12, 13, 14, 15, 14, 15, 16, 17, 16, 15, 14, 15, 16, 15, 14, 13, 14, 15, 16, 15, 16, 17, 18, 17, 16, 15, 16, 17, 18, 17, 18, 19, 20, 19, 20, 19, 20, 19, 18, 19, 18, 17, 16, 15, 14, 13, 14, 15, 16, 15, 16, 17, 18, 19, 20, 21, 20, 19, 18, 17, 16, 15, 16, 17, 16, 15, 16, 15, 14, 13, 12, 11, 10, 11, 12, 11, 12, 11, 12, 11, 10, 9, 10, 9, 8, 7, 8, 7, 8, 7, 8, 7, 6, 7, 6, 5, 6, 5, 4, 3, 2, 1, 2, 1, 0, 1, 0, 1, 0, 1, 2, 3, 4, 3, 4, 5, 6, 5, 4, 5, 4, 3, 4, 3, 2, 3, 2, 3, 4, 3, 2, 3, 2, 3, 4, 3, 2, 1, 2, 1, 0, 1, 2, 3, 2, 3, 2, 1, 2, 3, 4, 3, 4, 3, 2, 3, 2, 3, 4, 5, 4, 3, 4, 3, 4, 5, 4, 5, 6, 5, 4, 5, 6, 7, 8, 9, 8, 9, 8, 7, 6, 7, 8, 7, 6, 7, 8, 9, 10, 9, 10, 11, 12, 13, 14, 13, 12, 11, 12, 11, 12, 13, 12, 11, 10, 11, 12, 11, 10, 11, 10, 9, 8, 7, 6, 5, 6, 5, 6, 7, 6, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 0, -1, 0, 1, 2, 1, 0, -1, -2, -3, -4, -5, -4, -3, -4, -3, -4, -3, -4, -5, -4, -5, -4]

np.random.seed(12345)
    
    nsteps = 1000
    draws = np.random.randint(0, 2, size=nsteps)
    steps = np.where(draws > 0, 1, -1)
    walk = steps.cumsum()
    print(walk)
    print(walk.min())
    print(walk.max())
    
    print((np.abs(walk) >= 10).argmax())

[-1  0  1  2  1  2  1  0  1  0  1  2  1  2  3  2  3  4  5  4  3  2  3  4  5
      4  5  4  3  4  5  6  7  8  7  8  9 10 11 12 13 12 11 12 13 12 11 12 13 14
     15 14 15 16 17 18 17 18 19 18 19 18 17 18 19 20 19 18 19 18 19 18 17 16 17
     18 17 16 15 14 13 12 13 12 11 10 11 10  9 10 11 12 13 14 15 14 13 12 13 12
     11 12 11 12 11 12 11 10  9 10 11 10  9 10  9 10  9  8  9 10  9 10 11 10  9
     10  9  8  9 10 11 12 11 10  9 10  9 10  9  8  9 10  9 10  9 10  9 10 11 12
     11 12 11 10  9 10 11 10  9  8  7  6  5  6  7  8  7  6  7  6  7  6  7  6  5
      6  7  6  7  8  7  8  9  8  7  8  7  6  7  8  9 10  9 10 11 10 11 12 13 12
     11 10  9  8  9 10 11 10  9 10  9 10  9 10  9  8  7  6  7  6  5  6  7  8  7
      6  5  6  7  6  7  8  7  8  7  6  5  4  3  4  3  2  3  4  5  6  7  6  5  4
      5  4  3  2  3  4  5  6  5  6  5  6  7  6  7  8  7  6  7  6  7  8  9  8  9
      8  9  8  7  6  5  4  3  2  1  0  1  0 -1 -2 -1 -2 -3 -2 -1  0  1  2  3  4
      5  6  7  6  5  6  5  4  3  2  1  2  3  4  3  4  5  4  5  4  5  4  3  2  1
      2  3  4  5  6  5  4  5  6  5  6  7  6  5  6  5  4  5  4  3  4  5  6  5  4
      5  6  7  6  7  8  7  6  5  4  5  6  7  6  5  6  7  6  7  8  9 10 11 10 11
     10 11 10  9 10 11 12 11 10 11 10 11 10 11 12 13 14 13 12 11 12 11 10  9  8
      9  8  7  8  7  6  7  8  9  8  9  8  9 10 11 12 13 14 15 14 13 12 13 14 15
     14 15 16 17 16 15 16 15 16 17 18 19 18 19 18 17 16 15 14 13 12 13 12 13 14
     13 14 13 14 15 14 13 12 11 10 11 10 11 12 11 12 11 10 11 12 11 12 13 12 13
     14 13 14 13 14 15 14 15 14 13 12 11 10  9  8  7  8  7  6  5  4  5  4  3  4
      3  2  3  4  5  6  5  4  3  2  1  2  1  2  3  4  3  4  3  4  5  4  3  4  3
      4  5  4  5  4  3  2  3  2  1  2  3  2  1  2  1  2  1  0  1  2  1  2  1  2
      3  2  1  2  3  4  5  4  3  2  3  2  1  2  1  2  3  2  1  2  3  4  3  2  3
      4  5  6  7  6  5  4  3  2  1  2  3  2  1  2  3  4  5  6  7  6  7  8  7  8
      7  8  9  8  9  8  7  6  5  6  5  4  3  4  3  4  5  6  5  6  7  8  9  8  9
      8  9 10  9 10 11 12 13 14 13 12 11 12 11 12 13 12 13 14 13 14 13 12 13 12
     13 14 15 14 13 12 11 10  9 10  9  8  7  6  7  8  7  8  9  8  9 10  9 10 11
     10 11 10 11 10 11 10  9 10 11 12 13 12 13 12 13 14 15 14 13 12 13 12 11 10
     11 10  9  8  7  6  7  6  5  4  5  4  5  6  5  4  5  4  5  4  3  4  3  4  3
      4  5  6  7  8  9  8  7  8  9 10 11 10  9  8  7  6  7  8  7  8  7  8  7  6
      5  6  5  6  7  8  7  8  9 10  9  8  9  8  9 10  9 10  9  8  9  8  7  8  9
      8  9  8  9  8  9  8  9 10 11 10 11 12 11 12 13 14 15 14 13 14 15 16 15 14
     15 16 17 16 15 14 13 14 13 14 13 14 13 14 13 14 15 16 17 16 17 18 17 16 17
     18 17 18 17 18 19 20 19 18 19 20 19 18 17 18 17 18 19 20 19 18 17 16 15 16
     17 18 19 20 21 22 21 20 21 22 21 22 21 22 21 20 21 22 23 22 23 22 23 22 21
     22 23 24 23 24 23 24 25 24 25 26 27 28 29 28 29 28 27 26 25 26 27 26 27 28
     27 26 27 26 27 28 27 28 29 30 31 30 31 30 29 30 29 28 29 28 29 30 29 28 27
     26 25 24 23 22 23 22 23 22 21 20 19 18 17 18 17 18 19 18 19 18 17 16 17 16
     17 18 17 18 17 16 15 14 13 14 15 16 17 16 17 18 17 16 15 14 13 14 13 14 13
     14 15 14 13 14 13 14 15 16 15 16 15 16 15 14 15 14 13 14 13 12 13 12 13 14]
    -3
    31
    37

# 一次模拟多个随机漫步
    nwalks = 5000
    nsteps = 1000
    draws = np.random.randint(0, 2, size=(nwalks, nsteps))  # 0 or 1
    steps = np.where(draws > 0, 1, -1)
    walks = steps.cumsum(1)
    print(walks)
    
    print(walks.max())
    print(walks.min())
    
    hits30 = (np.abs(walks) >= 30).any(1)
    print(hits30)
    print(hits30.sum())  # 到达30或-30的数量
    
    crossing_times = (np.abs(walks[hits30]) >= 30).argmax(1)
    print(crossing_times.mean())

[[  1   0   1 ...,   8   7   8]
     [  1   0  -1 ...,  34  33  32]
     [  1   0  -1 ...,   4   5   4]
     ..., 
     [  1   2   1 ...,  24  25  26]
     [  1   2   3 ...,  14  13  14]
     [ -1  -2  -3 ..., -24 -23 -22]]
    138
    -133
    [False  True False ..., False  True False]
    3410
    498.88973607

steps = np.random.normal(loc=0, scale=0.25, size=(nwalks, nsteps))
    print(steps)

[[-0.02565707  0.36310961  0.41720151 ...,  0.15726638 -0.16256773
       0.05423703]
     [-0.10456259  0.07877516  0.19110411 ...,  0.07678875 -0.18545695
       0.0333151 ]
     [-0.16728617  0.12034941 -0.30427248 ..., -0.30982359 -0.17291787
       0.02772071]
     ..., 
     [ 0.27987403  0.05477886 -0.02167382 ...,  0.02795479  0.25268149
       0.06510672]
     [ 0.31853634 -0.15109745 -0.1121375  ...,  0.14705719  0.18206871
      -0.02473096]
     [-0.13101904 -0.24008233 -0.03925202 ..., -0.18320903 -0.20967376
       0.20705573]]

# 利用NumPy进行历史股价分析 #

#利用NumPy进行历史股价分析
    import sys
    
    # 读入文件
    fname = 'data\AAPL.csv'
    # c:价格，v:成交量
    c, v = np.loadtxt(fname, delimiter=',', usecols=(6, 7), unpack=True)
    
    # 计算成交量加权平均价格
    vwap = np.average(c, weights=v)
    print("vwap =", vwap)
    
    # 算术平均值函数
    print("mean =", np.mean(c))
    
    # 时间加权平均价格
    t = np.arange(len(c))
    print("twap =", np.average(c, weights=t))
    
    # 寻找最大值和最小值
    h, l = np.loadtxt(fname, delimiter=',', usecols=(4, 5), unpack=True)
    print("highest =", np.max(h))
    print("lowest =", np.min(l))
    print((np.max(h) + np.min(l)) / 2)
    
    print("Spread high price", np.ptp(h))
    print("Spread low price", np.ptp(l))

VWAP = 350.589549353
    mean = 351.037666667
    twap = 352.428321839
    highest = 364.9
    lowest = 333.53
    349.215
    Spread high price 24.86
    Spread low price 26.97

## 统计分析 ##

# 统计分析
    
    c = np.loadtxt(fname, delimiter=',', usecols=(6,), unpack=True)
    print("median =", np.median(c))
    msorted = np.msort(c)
    print("sorted =", msorted)
    
    N = len(c)
    print("middle =", msorted[int((N - 1) / 2)])
    print("average middle =", (msorted[int(N / 2)] + msorted[int((N - 1) / 2)]) / 2)
    
    print("variance =", np.var(c))
    print("variance from definition =", np.mean((c - c.mean()) ** 2))

median = 352.055
    sorted = [ 336.1   338.61  339.32  342.62  342.88  343.44  344.32  345.03  346.5
      346.67  348.16  349.31  350.56  351.88  351.99  352.12  352.47  353.21
      354.54  355.2   355.36  355.76  356.85  358.16  358.3   359.18  359.56
      359.9   360.    363.13]
    middle = 351.99
    average middle = 352.055
    variance = 50.1265178889
    variance from definition = 50.1265178889

## 股票收益率 ##

# 股票收益率
    c = np.loadtxt(fname, delimiter=',', usecols=(6,), unpack=True)
    
    returns = np.diff(c) / c[: -1]
    print("Standard deviation =", np.std(returns))
    
    logreturns = np.diff(np.log(c))
    
    posretindices = np.where(returns > 0)
    print("Indices with positive returns", posretindices)
    
    daily_volatility = np.std(logreturns) / np.mean(logreturns)
    annual_volatility = daily_volatility * np.sqrt(252.)
    print('Annual volatility', annual_volatility)
    print('Monthly volatility', annual_volatility / np.sqrt(12))

Standard deviation = 0.0129221344368
    Indices with positive returns (array([ 0,  1,  4,  5,  6,  7,  9, 10, 11, 12, 16, 17, 18, 19, 21, 22, 23,
           25, 28], dtype=int64),)
    Annual volatility 129.274789911
    Monthly volatility 37.3184173773

## 日期分析 ##

# 日期分析
    from datetime import datetime
    
    
    # Monday 0
    # Tuesday 1
    # Wednesday 2
    # Thursday 3
    # Friday 4
    # Saturday 5
    # Sunday 6
    def datestr2num(s):
        s = str(s, 'utf-8')
        return datetime.strptime(s, "%d-%m-%Y").date().weekday()
    
    
    dates, close = np.loadtxt(fname, delimiter=',', usecols=(1, 6),
                              converters={
        1: datestr2num},
                              unpack=True)
    print("Dates =", dates)
    
    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
    
    top = np.max(averages)
    print("Highest average", top)
    print("Top day of the week", np.argmax(averages))
    
    bottom = np.min(averages)
    print("Lowest average", bottom)
    print("Bottom day of the week", np.argmin(averages))

Dates = [ 4.  0.  1.  2.  3.  4.  0.  1.  2.  3.  4.  0.  1.  2.  3.  4.  1.  2.
      3.  4.  0.  1.  2.  3.  4.  0.  1.  2.  3.  4.]
    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
    Highest average 352.136666667
    Top day of the week 2
    Lowest average 350.022857143
    Bottom day of the week 4

## 周汇总 ##

# 周汇总
    def datestr2num(s):
        s = str(s, 'utf-8')
        return datetime.strptime(s, "%d-%m-%Y").date().weekday()
    
    
    dates, open, high, low, close = np.loadtxt(fname, delimiter=',',
                                               usecols=(1, 3, 4, 5, 6), converters={
        1: datestr2num}, unpack=True)
    close = close[:16]
    dates = dates[:16]
    
    # get first Monday
    first_monday = np.ravel(np.where(dates == 0))[0]
    print("The first Monday index is", first_monday)
    
    # get last Friday
    last_friday = np.ravel(np.where(dates == 4))[-1]
    print("The last Friday index is", last_friday)
    
    weeks_indices = np.arange(first_monday, last_friday + 1)
    print("Weeks indices initial", weeks_indices)
    
    weeks_indices = np.split(weeks_indices, 3)
    print("Weeks indices after split", weeks_indices)
    
    
    def summarize(a, o, h, l, c):
        monday_open = o[a[0]]
        week_high = np.max(np.take(h, a))
        week_low = np.min(np.take(l, a))
        friday_close = c[a[-1]]
    
        return ("APPL", monday_open, week_high, week_low, friday_close)
    
    
    weeksummary = np.apply_along_axis(summarize, 1, weeks_indices, open, high, low, close)
    print("Week summary", weeksummary)
    
    np.savetxt("data/weeksummary.csv", weeksummary, delimiter=",", fmt="%s")

The first Monday index is 1
    The last Friday index is 15
    Weeks indices initial [ 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15]
    Weeks indices after split [array([1, 2, 3, 4, 5], dtype=int64), array([ 6,  7,  8,  9, 10], dtype=int64), array([11, 12, 13, 14, 15], dtype=int64)]
    Week summary [['APPL' '335.8' '346.7' '334.3' '346.5']
     ['APPL' '347.8' '360.0' '347.6' '356.8']
     ['APPL' '356.7' '364.9' '349.5' '350.5']]

## 真实波动幅度均值 ##

# 真实波动幅度均值
    
    h, l, c = np.loadtxt(fname, delimiter=',', usecols=(4, 5, 6), unpack=True)
    
    N = 20
    h = h[-N:]
    l = l[-N:]
    
    print("len(h)", len(h), "len(l)", len(l))
    print("Close", c)
    previousclose = c[-N - 1: -1]
    
    print("len(previousclose)", len(previousclose))
    print("Previous close", previousclose)
    truerange = np.maximum(h - l, h - previousclose, previousclose - l)
    
    print("True range", truerange)
    
    atr = np.zeros(N)
    
    atr[0] = np.mean(truerange)
    
    for i in range(1, N):
        atr[i] = (N - 1) * atr[i - 1] + truerange[i]
        atr[i] /= N
    
    print("ATR", atr)

len(h) 20 len(l) 20
    Close [ 336.1   339.32  345.03  344.32  343.44  346.5   351.88  355.2   358.16
      354.54  356.85  359.18  359.9   363.13  358.3   350.56  338.61  342.62
      342.88  348.16  353.21  349.31  352.12  359.56  360.    355.36  355.76
      352.47  346.67  351.99]
    len(previousclose) 20
    Previous close [ 354.54  356.85  359.18  359.9   363.13  358.3   350.56  338.61  342.62
      342.88  348.16  353.21  349.31  352.12  359.56  360.    355.36  355.76
      352.47  346.67]
    True range [  4.26   2.77   2.42   5.     3.75   9.98   7.68   6.03   6.78   5.55
       6.89   8.04   5.95   7.67   2.54  10.36   5.15   4.16   4.87   7.32]
    ATR [ 5.8585      5.704075    5.53987125  5.51287769  5.4247338   5.65249711
      5.75387226  5.76767864  5.81829471  5.80487998  5.85913598  5.96817918
      5.96727022  6.05240671  5.87678637  6.10094705  6.0533997   5.95872972
      5.90429323  5.97507857]

## 简单移动平均线 ##

# 简单移动平均线
    from matplotlib.pyplot import plot
    from matplotlib.pyplot import show
    
    N = 5
    
    weights = np.ones(N) / N
    print("Weights", weights)
    
    c = np.loadtxt(fname, delimiter=',', usecols=(6,), unpack=True)
    sma = np.convolve(weights, c)[N - 1:-N + 1]
    t = np.arange(N - 1, len(c))
    plot(t, c[N - 1:], lw=1.0)
    plot(t, sma, lw=2.0)
    show()

Weights [ 0.2  0.2  0.2  0.2  0.2]

![简单移动平均线][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70]

## 指数移动平均线 ##

# 指数移动平均线
    x = np.arange(5)
    print("Exp", np.exp(x))
    print("Linspace", np.linspace(-1, 0, 5))
    
    N = 5
    
    weights = np.exp(np.linspace(-1., 0., N))
    weights /= weights.sum()
    print("Weights", weights)
    
    c = np.loadtxt(fname, delimiter=',', usecols=(6,), unpack=True)
    ema = np.convolve(weights, c)[N - 1:-N + 1]
    t = np.arange(N - 1, len(c))
    plot(t, c[N - 1:], lw=1.0)
    plot(t, ema, lw=2.0)
    show()

Exp [  1.           2.71828183   7.3890561   20.08553692  54.59815003]
    Linspace [-1.   -0.75 -0.5  -0.25  0.  ]
    Weights [ 0.11405072  0.14644403  0.18803785  0.24144538  0.31002201]

![指数移动平均线][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 1]

## 布林带 ##

# 布林带
    N = 5
    
    weights = np.ones(N) / N
    print("Weights", weights)
    
    c = np.loadtxt(fname, delimiter=',', usecols=(6,), unpack=True)
    sma = np.convolve(weights, c)[N - 1:-N + 1]
    deviation = []
    C = len(c)
    
    for i in range(N - 1, C):
        if i + N < C:
            dev = c[i: i + N]
        else:
            dev = c[-N:]
    
        averages = np.zeros(N)
        averages.fill(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))
    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))
    
    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()

Weights [ 0.2  0.2  0.2  0.2  0.2]
    26 26
    [ 329.23044409  335.70890572  318.53386282  321.90858271  327.74175968
      331.5628136   337.94259734  343.84172744  339.99900409  336.58687297
      333.15550418  328.64879207  323.61483771  327.25667796  334.30323599
      335.79295948  326.55905786  324.27329493  325.47601386  332.85867025
      341.63882551  348.75558399  348.48014357  348.01342992  343.56371701
      341.85163786]
    [ 336.1   339.32  345.03  344.32  343.44  346.5   351.88  355.2   358.16
      354.54  356.85  359.18  359.9   363.13  358.3   350.56  338.61  342.62
      342.88  348.16  353.21  349.31  352.12  359.56  360.    355.36]
    [ 354.05355591  351.73509428  373.93413718  374.62741729  374.33024032
      374.9491864   372.70940266  369.73027256  375.45299591  380.85312703
      385.78849582  387.77920793  384.58516229  374.03132204  358.88476401
      353.33904052  363.63294214  370.19870507  372.79598614  372.08532975
      368.04117449  361.78441601  364.63985643  365.24657008  364.54028299
      363.04836214]
    Ratio between bands 1.0

![布林带][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 2]

## 线性模型 ##

# 线性模型
    # N = int(sys.argv[1])
    N = 5
    
    c = np.loadtxt(fname, delimiter=',', usecols=(6,), unpack=True)
    
    b = c[-N:]
    b = b[::-1]
    print("b", b)
    
    A = np.zeros((N, N), float)
    print("Zeros N by N", A)
    
    for i in range(N):
        A[i,] = c[-N - 1 - i: - 1 - i]
    
    print("A", A)
    
    (x, residuals, rank, s) = np.linalg.lstsq(A, b)
    
    print(x, residuals, rank, s)
    
    print(np.dot(b, x))

b [ 351.99  346.67  352.47  355.76  355.36]
    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 [[ 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.  ]]
    [ 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]
    357.939161015

## 趋势线 ##

# 趋势线
    def fit_line(t, y):
        A = np.vstack([t, np.ones_like(t)]).T
    
        return np.linalg.lstsq(A, y)[0]
    
    
    h, l, c = np.loadtxt(fname, delimiter=',', usecols=(4, 5, 6), unpack=True)
    
    pivots = (h + l + c) / 3
    print("Pivots", pivots)
    
    t = np.arange(len(c))
    sa, sb = fit_line(t, pivots - (h - l))
    ra, rb = fit_line(t, pivots + (h - l))
    
    support = sa * t + sb
    resistance = ra * t + rb
    condition = (c > support) & (c < resistance)
    print("Condition", condition)
    between_bands = np.where(condition)
    print(support[between_bands])
    print(c[between_bands])
    print(resistance[between_bands])
    between_bands = len(np.ravel(between_bands))
    print("Number points between bands", between_bands)
    print("Ratio between bands", float(between_bands) / len(c))
    
    print("Tomorrows support", sa * (t[-1] + 1) + sb)
    print("Tomorrows resistance", ra * (t[-1] + 1) + rb)
    
    a1 = c[c > support]
    a2 = c[c < resistance]
    print("Number of points between bands 2nd approach", len(np.intersect1d(a1, a2)))
    
    plot(t, c)
    plot(t, support)
    plot(t, resistance)
    show()

Pivots [ 338.01        337.88666667  343.88666667  344.37333333  342.07666667
      345.57        350.92333333  354.29        357.34333333  354.18
      356.06333333  358.45666667  359.14        362.84333333  358.36333333
      353.19333333  340.57666667  341.95666667  342.13333333  347.13
      353.12666667  350.90333333  351.62333333  358.42333333  359.34666667
      356.11333333  355.13666667  352.61        347.11333333  349.77      ]
    Condition [False False  True  True  True  True  True False False  True False False
     False False False  True False False False  True  True  True  True False
     False  True  True  True False  True]
    [ 341.92421382  342.19081893  342.45742405  342.72402917  342.99063429
      343.79044964  345.39008034  346.4565008   346.72310592  346.98971104
      347.25631615  348.0561315   348.32273662  348.58934174  349.12255197]
    [ 345.03  344.32  343.44  346.5   351.88  354.54  350.56  348.16  353.21
      349.31  352.12  355.36  355.76  352.47  351.99]
    [ 352.61688271  352.90732765  353.19777259  353.48821753  353.77866246
      354.64999728  356.39266691  357.55444667  357.84489161  358.13533655
      358.42578149  359.2971163   359.58756124  359.87800618  360.45889606]
    Number points between bands 15
    Ratio between bands 0.5
    Tomorrows support 349.389157088
    Tomorrows resistance 360.749340996
    Number of points between bands 2nd approach 15

![趋势线][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 3]

参考资料：炼数成金Python数据分析课程

[https_github.com_RealEmperor_Python-for-Data-Analysis]: https://github.com/RealEmperor/Python-for-Data-Analysis
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70]: /images/20211101/8cba990c663442faa112a4673db3270d.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 1]: /images/20211101/4b06a96fa1b44360af4bf87cbf6b8dfb.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 2]: /images/20211101/184b8eb174d6450697ac3a3932bb702c.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjAxODI1OA_size_16_color_FFFFFF_t_70 3]: /images/20211101/be1fc11782a94822942825ff2540241b.png