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numpy数组按某一维度相加_Python数据分析之NumPy（高级篇）

發布時間：2023/12/10 python 37 豆豆

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一些更高級的ndarray處理

where和一些其他的邏輯運算

np.where(cond,x,y)：滿足條件(cond)輸出x，不滿足輸出y

x_arr = np.array([1.1, 1.2, 1.3, 1.4, 1.5])y_arr = np.array([2.1, 2.2, 2.3, 2.4, 2.5])cond = np.array([True, False, True, True, False])print(np.where(cond, x_arr, y_arr))[ 1.1 ?2.2 ?1.3 ?1.4 ?2.5]arr = np.random.randn(4,4)print(arr)print(np.where(arr > 0, 2, -2))print(np.where(arr > 0, 2, arr))[[ -1.10484247e+00 ?-3.82422727e-01 ?-3.24361549e-01 ? 1.21286234e+00] [ ?1.54499855e-01 ?-4.77728163e-04 ? 1.44621074e+00 ?-2.64241611e-03] [ ?1.36394862e+00 ? 6.96638259e-02 ?-2.75237740e-01 ?-3.32892881e-01] [ -1.37165175e+00 ? 1.79997993e-01 ?-1.13509664e-01 ? 1.88373639e+00]][[-2 -2 -2 ?2] [ 2 -2 ?2 -2] [ 2 ?2 -2 -2] [-2 ?2 -2 ?2]][[ -1.10484247e+00 ?-3.82422727e-01 ?-3.24361549e-01 ? 2.00000000e+00] [ ?2.00000000e+00 ?-4.77728163e-04 ? 2.00000000e+00 ?-2.64241611e-03] [ ?2.00000000e+00 ? 2.00000000e+00 ?-2.75237740e-01 ?-3.32892881e-01] [ -1.37165175e+00 ? 2.00000000e+00 ?-1.13509664e-01 ? 2.00000000e+00]]

np.where可以嵌套使用

cond_1 = np.array([True, False, True, True, False])cond_2 = np.array([False, True, False, True, False])result = np.where(cond_1 & cond_2, 0, ? ? ? ? ?np.where(cond_1, 1, np.where(cond_2, 2, 3)))print(result)[1 2 1 0 3]arr = np.random.randn(10)print(arr)print((arr > 0).sum()) #數組中大于0的數相加[ 0.27350655 -1.51093462 ?0.26835915 -0.45991855 ?1.34450904 -1.86871203 ?0.04308971 ?1.69640444 -0.02191351 -0.43875275]5bools = np.array([False, False, True, False])print(bools.any()) # 有一個為True則返回Trueprint(bools.all()) # 有一個為False則返回FalseTrueFalse

reshape(數組變形)

numpy可以很容易地把一維數組轉成二維數組，三維數組。

import numpy as nparr = np.arange(8)print("(4,2):", arr.reshape((4,2)))print()print("(2,2,2):", arr.reshape((2,2,2)))(4,2): [[0 1] [2 3] [4 5] [6 7]](2,2,2): [[[0 1] ?[2 3]] [[4 5] ?[6 7]]]

-1( 維度自動推算)

如果我們在某一個維度上寫上-1，numpy會幫我們自動推導出正確的維度

arr = np.arange(15)print(arr.reshape((5,-1)))print(arr.reshape((5,-1)).shape)[[ 0 ?1 ?2] [ 3 ?4 ?5] [ 6 ?7 ?8] [ 9 10 11] [12 13 14]](5, 3)

ravel(拉平數組)

# 高維數組用ravel來拉平成為一維數組arr = np.arange(15)print(arr.ravel())[ 0 ?1 ?2 ?3 ?4 ?5 ?6 ?7 ?8 ?9 10 11 12 13 14]

concatenate(連接數組)

arr1 = np.array([[1, 2, 3], [4, 5, 6]])arr2 = np.array([[7, 8, 9], [10, 11, 12]])print(np.concatenate([arr1, arr2], axis = 0)) ?# 按行連接print(np.concatenate([arr1, arr2], axis = 1)) ?# 按列連接[[ 1 ?2 ?3] [ 4 ?5 ?6] [ 7 ?8 ?9] [10 11 12]][[ 1 ?2 ?3 ?7 ?8 ?9] [ 4 ?5 ?6 10 11 12]]

連接的另一種表述垂直stack與水平stack

print(np.vstack((arr1, arr2))) # 垂直堆疊print(np.hstack((arr1, arr2))) # 水平堆疊[[ 1 ?2 ?3] [ 4 ?5 ?6] [ 7 ?8 ?9] [10 11 12]][[ 1 ?2 ?3 ?7 ?8 ?9] [ 4 ?5 ?6 10 11 12]]

split(拆分數組)

arr = np.random.rand(5,5)print(arr)[[ 0.08218151 ?0.25291976 ?0.990262 ? ?0.74980044 ?0.92433676] [ 0.57215647 ?0.88759783 ?0.67939949 ?0.18618301 ?0.64810013] [ 0.21424794 ?0.5812622 ? 0.33170632 ?0.40780156 ?0.00946797] [ 0.46223634 ?0.53574553 ?0.25289433 ?0.33226224 ?0.26110024] [ 0.81823359 ?0.98863697 ?0.13713923 ?0.3520669 ? 0.38301044]]first, second, third = np.split(arr, [1,3], axis = 0) # 按行拆分print(first)print()print(second)print()print(third)[[ 0.08218151 ?0.25291976 ?0.990262 ? ?0.74980044 ?0.92433676]][[ 0.57215647 ?0.88759783 ?0.67939949 ?0.18618301 ?0.64810013] [ 0.21424794 ?0.5812622 ? 0.33170632 ?0.40780156 ?0.00946797]][[ 0.46223634 ?0.53574553 ?0.25289433 ?0.33226224 ?0.26110024] [ 0.81823359 ?0.98863697 ?0.13713923 ?0.3520669 ? 0.38301044]]first, second, third = np.split(arr, [1, 3], axis = 1) # 按列拆分print(first)print()print(second)print()print(third)[[ 0.08218151] [ 0.57215647] [ 0.21424794] [ 0.46223634] [ 0.81823359]][[ 0.25291976 ?0.990262 ?] [ 0.88759783 ?0.67939949] [ 0.5812622 ? 0.33170632] [ 0.53574553 ?0.25289433] [ 0.98863697 ?0.13713923]][[ 0.74980044 ?0.92433676] [ 0.18618301 ?0.64810013] [ 0.40780156 ?0.00946797] [ 0.33226224 ?0.26110024] [ 0.3520669 ? 0.38301044]]

堆疊輔助

arr = np.arange(6)arr1 = arr.reshape((3, 2))arr2 = np.random.randn(3, 2)#r_用于按行堆疊print(np.r_[arr1, arr2])print()#c_用于按列堆疊print(np.c_[np.r_[arr1, arr2], arr])print()#切片直接轉為數組print(np.c_[1:6, -10:-5])print()[[ 0. ? ? ? ? ?1. ? ? ? ?] [ 2. ? ? ? ? ?3. ? ? ? ?] [ 4. ? ? ? ? ?5. ? ? ? ?] [ 0.04811148 -1.93674347] [ 1.19646481 ?0.17346639] [-1.4388562 ?-1.41584843]][[ 0. ? ? ? ? ?1. ? ? ? ? ?0. ? ? ? ?] [ 2. ? ? ? ? ?3. ? ? ? ? ?1. ? ? ? ?] [ 4. ? ? ? ? ?5. ? ? ? ? ?2. ? ? ? ?] [ 0.04811148 -1.93674347 ?3. ? ? ? ?] [ 1.19646481 ?0.17346639 ?4. ? ? ? ?] [-1.4388562 ?-1.41584843 ?5. ? ? ? ?]][[ ?1 -10] [ ?2 ?-9] [ ?3 ?-8] [ ?4 ?-7] [ ?5 ?-6]]

repeat(數組重復)

repeat(a,repeats, axis=None)

按元素重復

arr = np.arange(3)print(arr.repeat(3))print(arr.repeat([2,3,4]))print()[0 0 0 1 1 1 2 2 2][0 0 1 1 1 2 2 2 2]

指定axis來重復

arr = np.arange(4)print(arr)[[ 0.468845 ? ?0.43227877] [ 0.13822954 ?0.14501615]]print(arr.repeat(2, axis=0))print(arr.repeat(2, axis=1))[[ 0.468845 ? ?0.43227877] [ 0.468845 ? ?0.43227877] [ 0.13822954 ?0.14501615] [ 0.13822954 ?0.14501615]][[ 0.468845 ? ?0.468845 ? ?0.43227877 ?0.43227877] [ 0.13822954 ?0.13822954 ?0.14501615 ?0.14501615]]

tile(按規則重復數組)

tile通過重復給定的次數來構造數組。tile(A, reps)：初始數組是A，重復規則是reps。reps表示數組A需要重復的次數、結果的行數。

arr = np.arange(4).reshape((2, 2))print(np.tile(arr, 2))print(np.tile(arr, (2,3)))[[0 1 0 1] [2 3 2 3]][[0 1 0 1 0 1] [2 3 2 3 2 3] [0 1 0 1 0 1] [2 3 2 3 2 3]]

numpy的文件輸入輸出

讀取csv文件作為數組

import numpy as nparr = np.loadtxt('array_ex.txt', delimiter=',')print(arr)[[ 0.580052 ?0.18673 ? 1.040717 ?1.134411] [ 0.194163 -0.636917 -0.938659 ?0.124094] [-0.12641 ? 0.268607 -0.695724 ?0.047428] [-1.484413 ?0.004176 -0.744203 ?0.005487] [ 2.302869 ?0.200131 ?1.670238 -1.88109 ] [-0.19323 ? 1.047233 ?0.482803 ?0.960334]]

數組文件讀寫

arr = np.arange(10)np.save('some_array', arr)print(np.load('some_array.npy'))[0 1 2 3 4 5 6 7 8 9]

多個數組可以一起壓縮存儲

arr2 = np.arange(15).reshape(3,5)np.savez('array_archive.npz', a=arr, b=arr2)arch = np.load('array_archive.npz')print(arch['a'])print(arch['b'])[0 1 2 3 4 5 6 7 8 9][[ 0 ?1 ?2 ?3 ?4] [ 5 ?6 ?7 ?8 ?9] [10 11 12 13 14]]

用numpy寫一個softmax

步驟：

數據預處理
計算exponential
每行求和
每一行除以計算的和

import numpy as np# 產生(10，10)隨機數m = np.random.rand(10, 10) * 10 + 1000print(m)[[ 1002.4195769 ? 1000.59428635 ?1004.19947044 ?1009.17641327 ? 1004.89329928 ?1001.02496808 ?1007.79619575 ?1005.61568017 ? 1009.28511386 ?1000.11608716] [ 1002.9870141 ? 1005.59523328 ?1001.99337934 ?1008.79319814 ? 1004.78921679 ?1003.91814186 ?1009.38777432 ?1005.20436416 ? 1009.27099589 ?1008.69823987] [ 1006.68713949 ?1009.02893339 ?1008.2656608 ? 1002.27620211 ?1009.2256124 ? 1004.14144532 ?1007.09728075 ?1006.21626467 ?1004.60860132 ? 1004.51547132] [ 1005.57757481 ?1001.6026775 ? 1004.79229078 ?1004.28025577 ? 1008.68219699 ?1005.6379599 ? 1008.07958879 ?1006.35060616 ? 1009.03418483 ?1003.50279599] [ 1003.22924339 ?1006.62272977 ?1008.5591972 ? 1009.72498967 ? 1004.49414198 ?1004.21450523 ?1008.32652935 ?1000.90418303 ? 1009.24606203 ?1001.27113066] [ 1006.84865072 ?1005.24619541 ?1000.04356362 ?1003.38870582 ? 1008.59759772 ?1008.80052236 ?1007.92905671 ?1006.16987466 ?1002.3761379 ? 1001.55941284] [ 1006.80724007 ?1004.46597582 ?1003.25453387 ?1008.55713243 ? 1009.19618236 ?1002.06897172 ?1004.69874948 ?1006.51535711 ? 1005.23735087 ?1006.85265988] [ 1002.22993628 ?1000.59475018 ?1007.52711923 ?1000.36311206 ? 1008.22254861 ?1003.94553055 ?1004.23517969 ?1005.26438502 ? 1006.39421888 ?1005.22133756] [ 1006.92863693 ?1003.23688304 ?1007.11513614 ?1003.28880837 ? 1009.11093137 ?1006.35136574 ?1002.04684923 ?1001.13114541 ? 1008.50487627 ?1008.67481458] [ 1002.65347387 ?1001.90472796 ?1004.02149562 ?1009.63548587 ? 1009.16220671 ?1006.39781332 ?1008.1526219 ? 1003.57220839 ? 1008.60930803 ?1004.41645034]]

直接對m進行e指數運算會產生上溢

print(np.exp(m))[[ inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf] [ inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf] [ inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf] [ inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf] [ inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf] [ inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf] [ inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf] [ inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf] [ inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf] [ inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf ?inf]]G:Anaconda3libsite-packagesipykernel_launcher.py:1: RuntimeWarning: overflow encountered in exp ?"""Entry point for launching an IPython kernel.

尋找每一行的最大值

#按列取最大值(即取每一行的最大值)m_row_max = m.max(axis=1).reshape(10,1)print(m_row_max, m_row_max.shape)[[ 1009.28511386] [ 1009.38777432] [ 1009.2256124 ] [ 1009.03418483] [ 1009.72498967] [ 1008.80052236] [ 1009.19618236] [ 1008.22254861] [ 1009.11093137] [ 1009.63548587]] (10, 1)

通過廣播的方式將每行數據減去對應行的最大值

# 采用廣播的方式進行減法操作m = m - m_row_maxprint(m)[[-6.86553696 -8.69082751 -5.08564343 -0.1087006 ?-4.39181458 -8.26014579 ?-1.48891811 -3.66943369 ?0. ? ? ? ? -9.16902671] [-6.40076022 -3.79254104 -7.39439498 -0.59457618 -4.59855753 -5.46963247 ? 0. ? ? ? ? -4.18341016 -0.11677843 -0.68953445] [-2.5384729 ?-0.19667901 -0.95995159 -6.94941029 ?0. ? ? ? ? -5.08416708 ?-2.12833165 -3.00934773 -4.61701107 -4.71014107] [-3.45661002 -7.43150733 -4.24189405 -4.75392907 -0.35198784 -3.39622493 ?-0.95459604 -2.68357867 ?0. ? ? ? ? -5.53138884] [-6.49574628 -3.1022599 ?-1.16579247 ?0. ? ? ? ? -5.23084769 -5.51048445 ?-1.39846033 -8.82080664 -0.47892764 -8.45385902] [-1.95187164 -3.55432696 -8.75695874 -5.41181655 -0.20292464 ?0. ?-0.87146565 -2.63064771 -6.42438446 -7.24110952] [-2.3889423 ?-4.73020655 -5.94164849 -0.63904993 ?0. ? ? ? ? -7.12721064 ?-4.49743288 -2.68082526 -3.95883149 -2.34352249] [-5.99261232 -7.62779843 -0.69542937 -7.85943655 ?0. ? ? ? ? -4.27701805 ?-3.98736891 -2.95816359 -1.82832972 -3.00121104] [-2.18229443 -5.87404833 -1.99579523 -5.82212299 ?0. ? ? ? ? -2.75956563 ?-7.06408214 -7.97978595 -0.6060551 ?-0.43611679] [-6.982012 ? -7.73075791 -5.61399025 ?0. ? ? ? ? -0.47327916 -3.23767255 ?-1.48286397 -6.06327748 -1.02617783 -5.21903553]]

求預處理后的e指數

#求預處理后的e指數m_exp = np.exp(m)print(m_exp, m_exp.shape)[[ ?1.04312218e-03 ? 1.68120847e-04 ? 6.18490628e-03 ? 8.96998943e-01 ? ?1.23782475e-02 ? 2.58621284e-04 ? 2.25616615e-01 ? 2.54909015e-02 ? ?1.00000000e+00 ? 1.04217895e-04] [ ?1.66029460e-03 ? 2.25382585e-02 ? 6.14688467e-04 ? 5.51796380e-01 ? ?1.00663457e-02 ? 4.21278021e-03 ? 1.00000000e+00 ? 1.52464260e-02 ? ?8.89782323e-01 ? 5.01809632e-01] [ ?7.89869284e-02 ? 8.21454272e-01 ? 3.82911421e-01 ? 9.59200640e-04 ? ?1.00000000e+00 ? 6.19404411e-03 ? 1.19035722e-01 ? 4.93238409e-02 ? ?9.88228942e-03 ? 9.00350735e-03] [ ?3.15364890e-02 ? 5.92294057e-04 ? 1.43803289e-02 ? 8.61776882e-03 ? ?7.03288672e-01 ? 3.34994945e-02 ? 3.84967625e-01 ? 6.83182276e-02 ? ?1.00000000e+00 ? 3.96048477e-03] [ ?1.50984802e-03 ? 4.49475108e-02 ? 3.11675571e-01 ? 1.00000000e+00 ? ?5.34898908e-03 ? 4.04414773e-03 ? 2.46976935e-01 ? 1.47629228e-04 ? ?6.19447308e-01 ? 2.13076561e-04] [ ?1.42008035e-01 ? 2.86006179e-02 ? 1.57362462e-04 ? 4.46352464e-03 ? ?8.16339758e-01 ? 1.00000000e+00 ? 4.18337963e-01 ? 7.20317916e-02 ? ?1.62153108e-03 ? 7.16516327e-04] [ ?9.17266523e-02 ? 8.82464816e-03 ? 2.62769434e-03 ? 5.27793627e-01 ? ?1.00000000e+00 ? 8.02955997e-04 ? 1.11375513e-02 ? 6.85065952e-02 ? ?1.90854027e-02 ? 9.59889224e-02] [ ?2.49713221e-03 ? 4.86731255e-04 ? 4.98860204e-01 ? 3.86091355e-04 ? ?1.00000000e+00 ? 1.38840018e-02 ? 1.85484526e-02 ? 5.19141655e-02 ? ?1.60681727e-01 ? 4.97268106e-02] [ ?1.12782462e-01 ? 2.81146852e-03 ? 1.35905535e-01 ? 2.96131163e-03 ? ?1.00000000e+00 ? 6.33192663e-02 ? 8.55279590e-04 ? 3.42312686e-04 ? ?5.45498570e-01 ? 6.46542214e-01] [ ?9.28433319e-04 ? 4.39111184e-04 ? 3.64648989e-03 ? 1.00000000e+00 ? ?6.22956140e-01 ? 3.92551533e-02 ? 2.26986674e-01 ? 2.32676246e-03 ? ?3.58374111e-01 ? 5.41254683e-03]] (10, 10)

將求指數后的數據按列加和(每行求和)，然后將一維數據(10,)reshape成(10,1)

m_exp_row_sum = m_exp.sum(axis = 1).reshape(10,1)print(m_exp_row_sum, m_exp_row_sum.shape)[[ 2.1682437 ] [ 2.99772713] [ 2.47775123] [ 2.24916138] [ 2.23431102] [ 2.4842771 ] [ 1.82649405] [ 1.79698532] [ 2.51101842] [ 2.26032542]] (10, 1)

每行的數據除以對應行e指數求和

m_softmax = m_exp / m_exp_row_sumprint(m_softmax)[[ ?4.81090841e-04 ? 7.75378004e-05 ? 2.85249591e-03 ? 4.13698398e-01 ? ?5.70888203e-03 ? 1.19276853e-04 ? 1.04055008e-01 ? 1.17564744e-02 ? ?4.61202771e-01 ? 4.80655820e-05] [ ?5.53851145e-04 ? 7.51844898e-03 ? 2.05051507e-04 ? 1.84071584e-01 ? ?3.35799265e-03 ? 1.40532478e-03 ? 3.33586066e-01 ? 5.08599528e-03 ? ?2.96818985e-01 ? 1.67396701e-01] [ ?3.18784741e-02 ? 3.31532183e-01 ? 1.54539898e-01 ? 3.87125483e-04 ? ?4.03591769e-01 ? 2.49986522e-03 ? 4.80418376e-02 ? 1.99066962e-02 ? ?3.98841067e-03 ? 3.63374146e-03] [ ?1.40214434e-02 ? 2.63339955e-04 ? 6.39364033e-03 ? 3.83154756e-03 ? ?3.12689288e-01 ? 1.48942156e-02 ? 1.71160517e-01 ? 3.03749780e-02 ? ?4.44610159e-01 ? 1.76087176e-03] [ ?6.75755530e-04 ? 2.01169445e-02 ? 1.39495159e-01 ? 4.47565264e-01 ? ?2.39402171e-03 ? 1.81002005e-03 ? 1.10538297e-01 ? 6.60737144e-05 ? ?2.77243098e-01 ? 9.53656673e-05] [ ?5.71627193e-02 ? 1.15126521e-02 ? 6.33433613e-05 ? 1.79670965e-03 ? ?3.28602537e-01 ? 4.02531586e-01 ? 1.68394243e-01 ? 2.89950713e-02 ? ?6.52717479e-04 ? 2.88420453e-04] [ ?5.02200663e-02 ? 4.83146833e-03 ? 1.43865475e-03 ? 2.88965424e-01 ? ?5.47496993e-01 ? 4.39615994e-04 ? 6.09777585e-03 ? 3.75071549e-02 ? ?1.04492006e-02 ? 5.25536464e-02] [ ?1.38962304e-03 ? 2.70859896e-04 ? 2.77609505e-01 ? 2.14855041e-04 ? ?5.56487574e-01 ? 7.72627449e-03 ? 1.03219834e-02 ? 2.88895880e-02 ? ?8.94173844e-02 ? 2.76723522e-02] [ ?4.49150276e-02 ? 1.11965269e-03 ? 5.41236712e-02 ? 1.17932692e-03 ? ?3.98244789e-01 ? 2.52165679e-02 ? 3.40610640e-04 ? 1.36324243e-04 ? ?2.17241963e-01 ? 2.57482067e-01] [ ?4.10752058e-04 ? 1.94269011e-04 ? 1.61325881e-03 ? 4.42414172e-01 ? ?2.75604625e-01 ? 1.73670361e-02 ? 1.00422121e-01 ? 1.02939269e-03 ? ?1.58549786e-01 ? 2.39458743e-03]]

驗證一下，對輸出值進行按列求和，每行結果應該均為1

print(m_softmax.sum(axis=1))[ 1. ?1. ?1. ?1. ?1. ?1. ?1. ?1. ?1. ?1.]

參考

[numpy指南]http://docs.scipy.org/doc/numpy/reference/

[numpy ndarray詳解]https://danzhuibing.github.io/py_numpy_ndarray.html

[NumPy-快速處理數據]http://old.sebug.net/paper/books/scipydoc/numpy_intro.html

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