利用Python进行数据分析（3）—— Numpy Basic（3）
2017-09-13 18:16
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Data processing using arrays
import numpy as np
from matplotlib.pyplot import imshow, title
import matplotlib.pyplot as plt
np.set_printoptions(precision=4, suppress=True)
# 起始点，终止点，步长
points = np.arange(-5, 5, 0.01) # 1000 equally spaced points
print(points)
# 接受两个一维数组，产生两个二维矩阵
xs, ys = np.meshgrid(points, points)
print('------------------')
# 行上从 -5.0 到 4.99
print(xs)
print('------------------')
# 列上从 -5.0 到 4.99
print(ys)
# xs和ys 两二维数组的元素，分别乘方，后两数组加和，再开方
z = np.sqrt(xs ** 2 + ys ** 2)
print(z)[-5. -4.99 -4.98 -4.97 -4.96 -4.95 -4.94 -4.93 -4.92 -4.91 -4.9 -4.89 -4.88 -4.87 -4.86 -4.85 -4.84 -4.83 -4.82 -4.81 -4.8 -4.79 -4.78 -4.77 -4.76 -4.75 -4.74 -4.73 -4.72 -4.71 -4.7 -4.69 -4.68 -4.67 -4.66 -4.65 -4.64 -4.63 -4.62 -4.61 -4.6 -4.59 -4.58 -4.57 -4.56 -4.55 -4.54 -4.53 -4.52 -4.51 -4.5 -4.49 -4.48 -4.47 -4.46 -4.45 -4.44 -4.43 -4.42 -4.41 -4.4 -4.39 -4.38 -4.37 -4.36 -4.35 -4.34 -4.33 -4.32 -4.31 -4.3 -4.29 -4.28 -4.27 -4.26 -4.25 -4.24 -4.23 -4.22 -4.21 -4.2 -4.19 -4.18 -4.17 -4.16 -4.15 -4.14 -4.13 -4.12 -4.11 -4.1 -4.09 -4.08 -4.07 -4.06 -4.05 -4.04 -4.03 -4.02 -4.01 -4. -3.99 -3.98 -3.97 -3.96 -3.95 -3.94 -3.93 -3.92 -3.91 -3.9 -3.89 -3.88 -3.87 -3.86 -3.85 -3.84 -3.83 -3.82 -3.81 -3.8 -3.79 -3.78 -3.77 -3.76 -3.75 -3.74 -3.73 -3.72 -3.71 -3.7 -3.69 -3.68 -3.67 -3.66 -3.65 -3.64 -3.63 -3.62 -3.61 -3.6 -3.59 -3.58 -3.57 -3.56 -3.55 -3.54 -3.53 -3.52 -3.51 -3.5 -3.49 -3.48 -3.47 -3.46 -3.45 -3.44 -3.43 -3.42 -3.41 -3.4 -3.39 -3.38 -3.37 -3.36 -3.35 -3.34 -3.33 -3.32 -3.31 -3.3 -3.29 -3.28 -3.27 -3.26 -3.25 -3.24 -3.23 -3.22 -3.21 -3.2 -3.19 -3.18 -3.17 -3.16 -3.15 -3.14 -3.13 -3.12 -3.11 -3.1 -3.09 -3.08 -3.07 -3.06 -3.05 -3.04 -3.03 -3.02 -3.01 -3. -2.99 -2.98 -2.97 -2.96 -2.95 -2.94 -2.93 -2.92 -2.91 -2.9 -2.89 -2.88 -2.87 -2.86 -2.85 -2.84 -2.83 -2.82 -2.81 -2.8 -2.79 -2.78 -2.77 -2.76 -2.75 -2.74 -2.73 -2.72 -2.71 -2.7 -2.69 -2.68 -2.67 -2.66 -2.65 -2.64 -2.63 -2.62 -2.61 -2.6 -2.59 -2.58 -2.57 -2.56 -2.55 -2.54 -2.53 -2.52 -2.51 -2.5 -2.49 -2.48 -2.47 -2.46 -2.45 -2.44 -2.43 -2.42 -2.41 -2.4 -2.39 -2.38 -2.37 -2.36 -2.35 -2.34 -2.33 -2.32 -2.31 -2.3 -2.29 -2.28 -2.27 -2.26 -2.25 -2.24 -2.23 -2.22 -2.21 -2.2 -2.19 -2.18 -2.17 -2.16 -2.15 -2.14 -2.13 -2.12 -2.11 -2.1 -2.09 -2.08 -2.07 -2.06 -2.05 -2.04 -2.03 -2.02 -2.01 -2. -1.99 -1.98 -1.97 -1.96 -1.95 -1.94 -1.93 -1.92 -1.91 -1.9 -1.89 -1.88 -1.87 -1.86 -1.85 -1.84 -1.83 -1.82 -1.81 -1.8 -1.79 -1.78 -1.77 -1.76 -1.75 -1.74 -1.73 -1.72 -1.71 -1.7 -1.69 -1.68 -1.67 -1.66 -1.65 -1.64 -1.63 -1.62 -1.61 -1.6 -1.59 -1.58 -1.57 -1.56 -1.55 -1.54 -1.53 -1.52 -1.51 -1.5 -1.49 -1.48 -1.47 -1.46 -1.45 -1.44 -1.43 -1.42 -1.41 -1.4 -1.39 -1.38 -1.37 -1.36 -1.35 -1.34 -1.33 -1.32 -1.31 -1.3 -1.29 -1.28 -1.27 -1.26 -1.25 -1.24 -1.23 -1.22 -1.21 -1.2 -1.19 -1.18 -1.17 -1.16 -1.15 -1.14 -1.13 -1.12 -1.11 -1.1 -1.09 -1.08 -1.07 -1.06 -1.05 -1.04 -1.03 -1.02 -1.01 -1. -0.99 -0.98 -0.97 -0.96 -0.95 -0.94 -0.93 -0.92 -0.91 -0.9 -0.89 -0.88 -0.87 -0.86 -0.85 -0.84 -0.83 -0.82 -0.81 -0.8 -0.79 -0.78 -0.77 -0.76 -0.75 -0.74 -0.73 -0.72 -0.71 -0.7 -0.69 -0.68 -0.67 -0.66 -0.65 -0.64 -0.63 -0.62 -0.61 -0.6 -0.59 -0.58 -0.57 -0.56 -0.55 -0.54 -0.53 -0.52 -0.51 -0.5 -0.49 -0.48 -0.47 -0.46 -0.45 -0.44 -0.43 -0.42 -0.41 -0.4 -0.39 -0.38 -0.37 -0.36 -0.35 -0.34 -0.33 -0.32 -0.31 -0.3 -0.29 -0.28 -0.27 -0.26 -0.25 -0.24 -0.23 -0.22 -0.21 -0.2 -0.19 -0.18 -0.17 -0.16 -0.15 -0.14 -0.13 -0.12 -0.11 -0.1 -0.09 -0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 -0. 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1. 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.2 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.3 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.4 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.5 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.6 1.61 1.62 1.63 1.64 1.65 1.66 1.67 1.68 1.69 1.7 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 1.8 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.9 1.91 1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2. 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.1 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.2 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.3 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39 2.4 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.5 2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59 2.6 2.61 2.62 2.63 2.64 2.65 2.66 2.67 2.68 2.69 2.7 2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.8 2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.9 2.91 2.92 2.93 2.94 2.95 2.96 2.97 2.98 2.99 3. 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.1 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.2 3.21 3.22 3.23 3.24 3.25 3.26 3.27 3.28 3.29 3.3 3.31 3.32 3.33 3.34 3.35 3.36 3.37 3.38 3.39 3.4 3.41 3.42 3.43 3.44 3.45 3.46 3.47 3.48 3.49 3.5 3.51 3.52 3.53 3.54 3.55 3.56 3.57 3.58 3.59 3.6 3.61 3.62 3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.7 3.71 3.72 3.73 3.74 3.75 3.76 3.77 3.78 3.79 3.8 3.81 3.82 3.83 3.84 3.85 3.86 3.87 3.88 3.89 3.9 3.91 3.92 3.93 3.94 3.95 3.96 3.97 3.98 3.99 4. 4.01 4.02 4.03 4.04 4.05 4.06 4.07 4.08 4.09 4.1 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.2 4.21 4.22 4.23 4.24 4.25 4.26 4.27 4.28 4.29 4.3 4.31 4.32 4.33 4.34 4.35 4.36 4.37 4.38 4.39 4.4 4.41 4.42 4.43 4.44 4.45 4.46 4.47 4.48 4.49 4.5 4.51 4.52 4.53 4.54 4.55 4.56 4.57 4.58 4.59 4.6 4.61 4.62 4.63 4.64 4.65 4.66 4.67 4.68 4.69 4.7 4.71 4.72 4.73 4.74 4.75 4.76 4.77 4.78 4.79 4.8 4.81 4.82 4.83 4.84 4.85 4.86 4.87 4.88 4.89 4.9 4.91 4.92 4.93 4.94 4.95 4.96 4.97 4.98 4.99] ------------------ [[-5. -4.99 -4.98 ..., 4.97 4.98 4.99] [-5. -4.99 -4.98 ..., 4.97 4.98 4.99] [-5. -4.99 -4.98 ..., 4.97 4.98 4.99] ..., [-5. -4.99 -4.98 ..., 4.97 4.98 4.99] [-5. -4.99 -4.98 ..., 4.97 4.98 4.99] [-5. -4.99 -4.98 ..., 4.97 4.98 4.99]] ------------------ [[-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]] [[ 7.0711 7.064 7.0569 ..., 7.0499 7.0569 7.064 ] [ 7.064 7.0569 7.0499 ..., 7.0428 7.0499 7.0569] [ 7.0569 7.0499 7.0428 ..., 7.0357 7.0428 7.0499] ..., [ 7.0499 7.0428 7.0357 ..., 7.0286 7.0357 7.0428] [ 7.0569 7.0499 7.0428 ..., 7.0357 7.0428 7.0499] [ 7.064 7.0569 7.0499 ..., 7.0428 7.0499 7.0569]] Process finished with exit code 0
Expressing conditional logic as array operations
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]) print(xarr[~cond]) # 二者等价 # np.where 是三元表达式 x if condition else y 的矢量化版本 # result = [(x if c else y) for x, y, c in zip(xarr, yarr, cond)] result = np.where(cond, xarr, yarr) print(result) arr = np.random.randn(4, 4) # 大于 0 的替换为 2， 否则替换为 -2 arr_1 = np.where(arr > 0, 2, -2) print(arr_1) # 大于 0 的替换为 2， 否则 保留原值 arr_2 = np.where(arr > 0, 2, arr) # set only positive values to 2 print(arr_2)
[ 1.2 1.5] [ 1.1 2.2 1.3 1.4 2.5] [[ 2 2 2 -2] [-2 2 -2 2] [ 2 -2 -2 -2] [ 2 -2 -2 -2]] [[ 2. 2. 2. -0.572 ] [-0.0768 2. -1.0821 2. ] [ 2. -0.9678 -0.1732 -1.0441] [ 2. -0.4337 -0.7777 -0.8902]] Process finished with exit code 0
Mathematical and statistical methods
arr = np.random.randn(5, 4) # normally-distributed data print(arr.mean()) print(np.mean(arr)) print(arr.sum()) # mean 和 sum 可以接受一个 axis 参数（用于计算该轴向上的统计值），最终结果是一个少一维的数组 print(arr.mean(axis=1)) print(arr.sum(0)) arr = np.array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) print(arr) print(arr.cumsum(0)) print(arr.cumsum(1)) print(arr.cumprod(1))
-0.10294284368 -0.10294284368 -2.0588568736 [-0.7362 0.3252 -0.5837 0.5134 -0.0333] [-2.5793 1.8575 1.2828 -2.6199] [[0 1 2] [3 4 5] [6 7 8]] [[ 0 1 2] [ 3 5 7] [ 9 12 15]] [[ 0 1 3] [ 3 7 12] [ 6 13 21]] [[ 0 0 0] [ 3 12 60] [ 6 42 336]] Process finished with exit code 0
Methods for boolean arrays
arr = np.random.randn(100) print((arr > 0).sum()) # Number of positive values print(arr[arr>0]) bools = np.array([False, False, True, False]) # any 用于检测数组中是否存在一个或多个True 存在 # all 检查数组中是否所有值都是 True bools.any() bools.all() # -----------------------------------------
51 [ 1.0179 0.4661 0.035 0.3081 0.5339 1.9648 0.4265 1.942 1.2556 0.1283 2.0778 0.2201 0.732 0.8652 1.0453 0.1707 0.3444 0.1044 0.8468 0.071 0.2321 0.3639 0.1994 1.3033 0.8468 0.7713 2.0785 0.9529 1.6031 0.157 0.5425 0.0212 0.659 0.6765 0.3032 1.8217 4.0663 0.107 0.4904 0.9526 0.8232 0.9066 1.0254 0.2625 1.4222 0.6134 0.7314 1.1774 0.0021 0.3598 2.4056] Process finished with exit code 0
Sorting
arr = np.random.randn(8) print(arr) arr.sort() print(arr) arr = np.random.randn(2,5) print(arr) # 升序排列，按行排列 arr.sort() print(arr) arr.sort(1) print(arr) arr.sort(0) print(arr) large_arr = np.random.randn(1000) large_arr.sort() # 5%分位数 print(large_arr[int(0.05 * len(large_arr))]) # 5% quantile
[ 1.2906 0.7066 -3.3 0.126 -1.3173 -0.2734 -0.7938 -0.9861] [-3.3 -1.3173 -0.9861 -0.7938 -0.2734 0.126 0.7066 1.2906] [[ 0.6627 -0.3837 0.8278 -0.4906 0.8111] [ 0.4463 -0.3823 -1.0958 0.4684 -0.4863]] [[-0.4906 -0.3837 0.6627 0.8111 0.8278] [-1.0958 -0.4863 -0.3823 0.4463 0.4684]] [[-0.4906 -0.3837 0.6627 0.8111 0.8278] [-1.0958 -0.4863 -0.3823 0.4463 0.4684]] [[-1.0958 -0.4863 -0.3823 0.4463 0.4684] [-0.4906 -0.3837 0.6627 0.8111 0.8278]] -1.63847027424 Process finished with exit code 0
Unique and other set logic
# np.unique()用于找出数组中的唯一值，并返回已排序的结果 names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe']) print(np.unique(names)) ints = np.array([3, 3, 3, 2, 2, 1, 1, 4, 4]) print(np.unique(ints)) # np.in1d() 用于测试一个数组中的值在另一个数组中的成员资格，返回一个布尔型数组 values = np.array([6, 0, 0, 3, 2, 5, 6]) print(np.in1d(values, [2, 3, 6])) print(np.in1d([2, 3, 6], values))
['Bob' 'Joe' 'Will'] [1 2 3 4] [ True False False True True False True] [ True True True] Process finished with exit code 0
Linear algebra
np.random.seed(12345) from numpy.linalg import inv, qr X = np.random.randn(5, 5) print(X) # 转置 print(X.T) mat = X.T.dot(X) print(mat) # 矩阵的逆 print(inv(mat)) mat.dot(inv(mat)) q, r = qr(mat) print(r)
[[-0.2047 0.4789 -0.5194 -0.5557 1.9658] [ 1.3934 0.0929 0.2817 0.769 1.2464] [ 1.0072 -1.2962 0.275 0.2289 1.3529] [ 0.8864 -2.0016 -0.3718 1.669 -0.4386] [-0.5397 0.477 3.2489 -1.0212 -0.5771]] [[-0.2047 1.3934 1.0072 0.8864 -0.5397] [ 0.4789 0.0929 -1.2962 -2.0016 0.477 ] [-0.5194 0.2817 0.275 -0.3718 3.2489] [-0.5557 0.769 0.2289 1.669 -1.0212] [ 1.9658 1.2464 1.3529 -0.4386 -0.5771]] [[ 4.075 -3.3059 -1.3073 3.4466 2.6197] [ -3.3059 6.1523 1.7149 -4.3193 -0.0938] [ -1.3073 1.7149 11.1187 -3.3702 -2.0097] [ 3.4466 -4.3193 -3.3702 4.7812 0.0331] [ 2.6197 -0.0938 -2.0097 0.0331 7.7736]] [[ 3.0361 -0.1808 -0.6878 -2.8285 -1.1911] [-0.1808 0.5035 0.1215 0.6702 0.0956] [-0.6878 0.1215 0.2904 0.8081 0.3049] [-2.8285 0.6702 0.8081 3.4152 1.1557] [-1.1911 0.0956 0.3049 1.1557 0.6051]] [[ -6.9271 7.389 6.1227 -7.1163 -4.9215] [ 0. -3.9735 -0.8671 2.9747 -5.7402] [ 0. 0. -10.2681 1.8909 1.6079] [ 0. 0. 0. -1.2996 3.3577] [ 0. 0. 0. 0. 0.5571]] Process finished with exit code 0
Random Walks
nsteps = 1000 # 生成 1000 个 或为 0 ，或者为 1 的随机数 draws = np.random.randint(0, 2, size=nsteps) # print(draws) # 将 draws 中的 0 转换为 -1，将 1 转换为 0 steps = np.where(draws > 0, 1, -1) print(steps) walk = steps.cumsum() print(walk) print(walk.min()) print(walk.max()) # argmax() 返回该布尔型数组第一个最大值得索引（True就是最大值） print((np.abs(walk) >= 10).argmax())
[ 1 1 -1 -1 1 1 -1 1 -1 -1 -1 -1 -1 -1 -1 1 1 1 -1 1 1 1 1 1 -1 1 1 1 -1 -1 1 -1 1 1 -1 -1 -1 -1 -1 -1 1 -1 1 -1 1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 -1 1 1 1 1 1 1 -1 1 1 1 1 1 1 1 -1 1 1 1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 1 -1 1 1 1 1 1 1 1 -1 1 -1 -1 1 1 1 -1 -1 -1 -1 1 1 -1 1 1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 -1 1 1 1 -1 -1 1 -1 -1 -1 1 -1 -1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 -1 1 1 1 -1 1 1 -1 1 1 -1 1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 -1 -1 -1 -1 1 1 -1 1 -1 1 -1 -1 -1 -1 1 1 -1 1 1 1 1 -1 1 1 -1 1 -1 -1 -1 -1 1 -1 -1 1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 -1 1 1 1 1 -1 1 -1 1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 1 -1 1 -1 1 -1 -1 -1 -1 1 -1 1 -1 1 1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 1 1 1 1 -1 1 -1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 1 -1 -1 1 1 1 -1 1 1 -1 1 -1 -1 -1 1 1 -1 -1 1 -1 -1 1 -1 1 -1 -1 -1 1 1 1 -1 -1 -1 -1 1 1 1 -1 -1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1 -1 1 1 1 -1 1 -1 -1 1 -1 1 -1 -1 1 -1 -1 1 -1 1 1 -1 -1 1 1 1 1 1 -1 -1 -1 -1 1 -1 1 1 1 1 -1 1 1 1 1 -1 -1 1 1 -1 1 1 -1 1 -1 1 1 1 -1 -1 -1 1 1 -1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 -1 1 1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 -1 1 1 -1 1 -1 -1 -1 1 -1 1 -1 -1 -1 -1 1 -1 -1 1 1 1 1 1 -1 1 -1 -1 1 -1 -1 1 -1 1 1 1 -1 1 1 1 1 1 -1 1 1 -1 1 1 -1 1 -1 1 1 -1 -1 1 -1 1 -1 1 1 -1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 1 -1 -1 -1 1 -1 -1 1 -1 -1 -1 1 -1 -1 1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 -1 -1 1 -1 -1 -1 1 1 1 1 1 -1 1 1 1 1 -1 1 -1 1 1 1 -1 -1 1 1 1 -1 -1 1 -1 1 1 -1 1 -1 1 1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 -1 -1 1 1 1 -1 -1 -1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 -1 1 -1 1 1 1 -1 1 1 -1 -1 -1 -1 1 -1 1 1 -1 -1 1 -1 -1 1 1 -1 1 1 1 1 1 -1 1 -1 1 -1 1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 1 -1 1 -1 1 -1 1 1 1 1 1 -1 -1 -1 1 1 -1 1 1 -1 1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 -1 1 -1 1 1 -1 -1 -1 -1 -1 1 1 -1 1 1 1 -1 1 1 -1 1 -1 1 1 -1 1 -1 -1 1 1 -1 1 1 1 1 1 1 -1 1 1 1 1 -1 1 1 -1 1 1 -1 -1 -1 -1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 1 -1 -1 -1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 1 1 1 1 -1 1 1 1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 -1 1 1 1 -1 1 -1 -1 1 1 1 1 1 1 1 -1 1 1 -1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 1 1 1 -1 -1 -1 -1 1 1 1 -1 -1 -1 1 1 1 1 -1 -1 1 -1 -1 1 -1 1 -1 1 1 -1 -1 -1 1 -1 -1 1 1 -1 1 1 1 -1 1 1 -1 -1 1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 1 1 -1 -1 1 -1 1 1 1 1 -1 1 1 1 -1 1 1 -1 -1 1 -1] [ 1 2 1 0 1 2 1 2 1 0 -1 -2 -3 -4 -5 -4 -3 -2 -3 -2 -1 0 1 2 1 2 3 4 3 2 3 2 3 4 3 2 1 0 -1 -2 -1 -2 -1 -2 -1 0 -1 -2 -1 -2 -1 -2 -1 -2 -1 0 -1 -2 -1 0 1 2 3 4 3 4 5 6 7 8 9 10 9 10 11 12 13 14 13 12 13 14 13 12 11 10 11 12 13 14 13 12 13 12 13 14 15 16 17 18 19 18 19 18 17 18 19 20 19 18 17 16 17 18 17 18 19 20 19 18 19 18 19 20 19 20 19 18 17 18 19 20 19 18 19 18 17 16 17 16 15 16 17 18 19 18 19 18 19 20 19 18 19 18 19 20 21 20 21 22 21 22 23 22 23 22 23 24 23 24 23 22 23 24 23 22 21 20 19 18 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-12 -13 -12 -11 -12 -11 -10 -11 -12 -13 -14 -15 -16 -15 -14 -15 -16 -15 -16 -15 -16 -17 -18 -17 -18 -19 -20 -21 -22 -21 -20 -21 -20 -21 -22 -21 -20 -21 -20 -19 -18 -17 -18 -17 -16 -15 -14 -15 -14 -15 -14 -13 -14 -13 -14 -13 -14 -13 -14 -15 -16 -15 -14 -13 -14 -13 -14 -15 -14 -13 -12 -11 -10 -9 -8 -9 -8 -7 -8 -7 -8 -7 -8 -7 -6 -7 -8 -7 -6 -7 -8 -9 -10 -9 -8 -7 -6 -7 -8 -9 -8 -7 -6 -7 -8 -9 -10 -9 -8 -7 -8 -9 -10 -9 -8 -7 -6 -7 -8 -7 -8 -9 -8 -9 -8 -9 -8 -7 -8 -9 -10 -9 -10 -11 -10 -9 -10 -9 -8 -7 -8 -7 -6 -7 -8 -7 -8 -9 -10 -9 -8 -9 -10 -9 -8 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -7 -6 -5 -6 -5 -6 -5 -4 -3 -4 -5 -4 -5 -4 -3 -2 -1 -2 -1 0 1 0 1 2 1 0 1 0] -26 24 71 Process finished with exit code 0
Simulating many random walks at once
nwalks = 5000 nsteps = 1000 draws = np.random.randint(0, 2, size=(nwalks, nsteps)) # 0 or 1 steps = np.where(draws > 0, 1, -1) # 行累加 walks = steps.cumsum(1) print(walks) walks.max() walks.min() # 以行为轴 hits30 = (np.abs(walks) >= 30).any(1) print(hits30) print(hits30.sum()) # Number that hit 30 or -30 # 每行中，最大数的索引 crossing_times = (np.abs(walks[hits30]) >= 30).argmax(1) print(crossing_times) print(crossing_times.mean())
[[ -1 -2 -3 ..., 42 41 42] [ -1 0 1 ..., 6 7 8] [ 1 0 1 ..., 38 37 36] ..., [ 1 0 -1 ..., -6 -5 -6] [ -1 -2 -3 ..., -18 -19 -18] [ 1 2 3 ..., 0 1 2]] [ True True True ..., False True True] 3374 [913 397 697 ..., 241 715 313] 499.988737404 Process finished with exit code 0
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