NumPy 数值计算

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一．实验目的与实验要求

1、要求学生掌握Numpy的数组创建及随机数生成；
2、要求学生掌握Numpy中用于统计分析的基本运算函数；
3、要求学生掌握Numpy矩阵创建方法；
4、要求学生掌握Numpy数组索引的方法。

二．实验内容

任务1创建数组并进行运算

1.需求说明
Numpy数组在数值运算方面的效率优于Python提供的list，所以灵活掌握Numpy中数组的创建以及基础的运算是有必要的。
2.实现思路及步骤
(1)创建一个数值范围为0~1，间隔为0.01的数组。
(2)创建100个服从正态分布的随机数。
(3)对创建的两个数组进行四则运算。
(4)对创建的随机数组进行简单的统计分析。

任务2创建一个国际象棋的棋盘
1.需求说明
创建国际象棋棋盘,填充8×8矩阵。国际象棋棋盘是个正方形,由横纵向各8格、颜色一深一浅交错排列的64个小方格组成,深色格为黑格,浅色格为白格,棋子就在这些格子中移动,如下图所示。

2.实现思路及步骤
(1) 创建一个8×8矩阵。
(2) 把1,3,5,7行的0,2,4,6列的元素设置为1;0,2,4,6行的1,3,5,7列的元素设置为1,规律是行号和列号之和是奇数的位置设置为1。

三．实验结果

（1）任务1创建数组并进行运算：

test3-1.py文件的代码如下：

import numpy as np#导入NumPy库
#代码test3-1
#创建一个数值范围为01，间隔为0.01的数组
arr1=np.arange(0,1,0.01)
print("使用arange函数创建的数组为：\n",arr1)
#创建由100个服从正态分布的随机数构成的数组
#arr2=np.random.randn（10，10）
arr2=np.random.randn(100)
print('生成的随机数组为：\n',arr2)
#对创建的两个数组进行四则运算
arr3=arr1+arr2
print('arr1 + arr2：\n',arr3)
arr4=arr1-arr2
print('arrl-arr2：\n',arr4)
arr5=arr1*arr2
print('arrl*arr2：\n',arr5)
arr6=arr1/arr2
print('arrl/arr2：\n',arr6)
arr7=arr1**arr2
print('arrl**arr2：\n',arr6)
#对创建的数组进行简单的统计分析
arr2.sort()#对数据进行排序
print('排序后的随机数数组为：',arr2)
#去除重复值
print('去重后的正态分布随机数数组为：',np.unique(arr2))
print('正态分布随机数数组的总和为：',np.sum(arr2))#计算数组总和
#计算所有元素的累计和
print('正态分随机数数组的累计和为：',np.cumsum(arr2))
print('正态分布随机数数组的均值为：',np.mean(arr2))#计算数组均值
#计算数组标准差
print('正态分布随机数数组的标准差为:',np.std(arr2))
print('正态分布随机数数组的方差为：',np.var(arr2))#计算数组方差
print('正态分布随机数数组的最小值为:',np.min(arr2))#计算最小值
print('正态分布随机数数组的最大值为：',np.max(arr2))#计算最大值

test3-1.py文件运行结果如下图：

C:\Users\Administrator\PycharmProjects\untitled2\venv\Scripts\python.exe "C:/Users/Administrator/PycharmProjects/untitled2/实验3 NumPy 数值计算.py"
使用arange函数创建的数组为：
 [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]
生成的随机数组为：
 [-1.2783294   0.24002811  1.49770725 -0.60390594  0.73603185 -1.83914297
  0.27969558  1.32044787 -0.3349159   0.90103135 -0.13823456  1.07399786
  0.83546135 -0.02366977  0.26120438  0.55912516  2.12782286 -1.12316108
 -0.55913823  1.03825603 -0.86057583  0.98010486 -0.8811894   0.97040155
 -1.31560281 -0.44995378  1.50118303 -0.23533371  0.8372029   0.36848146
  1.30949118  0.27959808  0.30869752 -0.10799034  0.56045826  1.84752278
 -0.54461232 -0.25940063 -1.42393404  1.69664679 -0.20710902  2.33072437
  0.39531101 -1.45085246  0.17232173 -1.10358701 -0.3704594  -1.24774508
 -1.05758405 -1.41474231 -0.48062729 -1.72557077  0.16399003 -1.27777708
  0.32078791 -0.06617431  0.13511144 -0.50585365 -0.55199406 -0.78310458
 -0.48914752  0.51763085  0.13869361 -1.02052812  0.1042048  -0.1820081
 -0.20527944 -0.03472024 -0.04238655  1.09200848  0.706178    2.16058522
  0.35661529  1.03401514 -0.46666045 -0.27756572 -0.36598629 -1.23465018
  0.86108988 -0.73406985 -0.20553496  0.22097487 -1.58529585 -0.81920717
 -0.37615116  2.03300722 -1.42733399 -1.05254279  0.52317522  1.48607789
 -0.50381381 -0.29548552 -0.7379603  -0.50981591  1.34279925 -0.39325828
  0.12407724  0.79036736 -0.21348131  0.04722244]
arr1 + arr2：
 [-1.2783294   0.25002811  1.51770725 -0.57390594  0.77603185 -1.78914297
  0.33969558  1.39044787 -0.2549159   0.99103135 -0.03823456  1.18399786
  0.95546135  0.10633023  0.40120438  0.70912516  2.28782286 -0.95316108
 -0.37913823  1.22825603 -0.66057583  1.19010486 -0.6611894   1.20040155
 -1.07560281 -0.19995378  1.76118303  0.03466629  1.1172029   0.65848146
  1.60949118  0.58959808  0.62869752  0.22200966  0.90045826  2.19752278
 -0.18461232  0.11059937 -1.04393404  2.08664679  0.19289098  2.74072437
  0.81531101 -1.02085246  0.61232173 -0.65358701  0.0895406  -0.77774508
 -0.57758405 -0.92474231  0.01937271 -1.21557077  0.68399003 -0.74777708
  0.86078791  0.48382569  0.69511144  0.06414635  0.02800594 -0.19310458
  0.11085248  1.12763085  0.75869361 -0.39052812  0.7442048   0.4679919
  0.45472056  0.63527976  0.63761345  1.78200848  1.406178    2.87058522
  1.07661529  1.76401514  0.27333955  0.47243428  0.39401371 -0.46465018
  1.64108988  0.05593015  0.59446504  1.03097487 -0.76529585  0.01079283
  0.46384884  2.88300722 -0.56733399 -0.18254279  1.40317522  2.37607789
  0.39618619  0.61451448  0.1820397   0.42018409  2.28279925  0.55674172
  1.08407724  1.76036736  0.76651869  1.03722244]
arrl-arr2：
 [ 1.2783294  -0.23002811 -1.47770725  0.63390594 -0.69603185  1.88914297
 -0.21969558 -1.25044787  0.4149159  -0.81103135  0.23823456 -0.96399786
 -0.71546135  0.15366977 -0.12120438 -0.40912516 -1.96782286  1.29316108
  0.73913823 -0.84825603  1.06057583 -0.77010486  1.1011894  -0.74040155
  1.55560281  0.69995378 -1.24118303  0.50533371 -0.5572029  -0.07848146
 -1.00949118  0.03040192  0.01130248  0.43799034 -0.22045826 -1.49752278
  0.90461232  0.62940063  1.80393404 -1.30664679  0.60710902 -1.92072437
  0.02468899  1.88085246  0.26767827  1.55358701  0.8304594   1.71774508
  1.53758405  1.90474231  0.98062729  2.23557077  0.35600997  1.80777708
  0.21921209  0.61617431  0.42488856  1.07585365  1.13199406  1.37310458
  1.08914752  0.09236915  0.48130639  1.65052812  0.5357952   0.8320081
  0.86527944  0.70472024  0.72238655 -0.40200848 -0.006178   -1.45058522
  0.36338471 -0.30401514  1.20666045  1.02756572  1.12598629  2.00465018
 -0.08108988  1.52406985  1.00553496  0.58902513  2.40529585  1.64920717
  1.21615116 -1.18300722  2.28733399  1.92254279  0.35682478 -0.59607789
  1.40381381  1.20548552  1.6579603   1.43981591 -0.40279925  1.34325828
  0.83592276  0.17963264  1.19348131  0.94277756]
arrl*arr2：
 [-0.          0.00240028  0.02995414 -0.01811718  0.02944127 -0.09195715
  0.01678173  0.09243135 -0.02679327  0.08109282 -0.01382346  0.11813976
  0.10025536 -0.00307707  0.03656861  0.08386877  0.34045166 -0.19093738
 -0.10064488  0.19726865 -0.17211517  0.20582202 -0.19386167  0.22319236
 -0.31574468 -0.11248844  0.39030759 -0.0635401   0.23441681  0.10685962
  0.39284735  0.08667541  0.09878321 -0.03563681  0.19055581  0.64663297
 -0.19606044 -0.09597823 -0.54109493  0.66169225 -0.08284361  0.95559699
  0.16603062 -0.62386656  0.07582156 -0.49661416 -0.17041133 -0.58644019
 -0.50764034 -0.69322373 -0.24031364 -0.88004109  0.08527481 -0.67722185
  0.17322547 -0.03639587  0.0756624  -0.28833658 -0.32015656 -0.4620317
 -0.29348851  0.31575482  0.08599004 -0.64293272  0.06669107 -0.11830526
 -0.13548443 -0.02326256 -0.02882285  0.75348585  0.4943246   1.5340155
  0.25676301  0.75483105 -0.34532873 -0.20817429 -0.27814958 -0.95068064
  0.67165011 -0.57991518 -0.16442796  0.17898965 -1.2999426  -0.67994195
 -0.31596698  1.72805614 -1.22750723 -0.91571222  0.46039419  1.32260932
 -0.45343243 -0.26889183 -0.67892348 -0.4741288   1.2622313  -0.37359537
  0.11911415  0.76665634 -0.20921169  0.04675021]
arrl/arr2：
 [-0.00000000e+00  4.16617868e-02  1.33537445e-02 -4.96766100e-02
  5.43454742e-02 -2.71865759e-02  2.14518940e-01  5.30123161e-02
 -2.38865937e-01  9.98855368e-02 -7.23408074e-01  1.02421061e-01
  1.43633216e-01 -5.49223832e+00  5.35978754e-01  2.68276249e-01
  7.51942294e-02 -1.51358521e-01 -3.21923972e-01  1.82999177e-01
 -2.32402530e-01  2.14262789e-01 -2.49662560e-01  2.37015284e-01
 -1.82425879e-01 -5.55612625e-01  1.73196736e-01 -1.14730693e+00
  3.34447003e-01  7.87013815e-01  2.29096618e-01  1.10873436e+00
  1.03661344e+00 -3.05582898e+00  6.06646421e-01  1.89442860e-01
 -6.61020663e-01 -1.42636506e+00 -2.66866294e-01  2.29865169e-01
 -1.93134997e+00  1.75910976e-01  1.06245461e+00 -2.96377482e-01
  2.55336339e+00 -4.07761232e-01 -1.24170151e+00 -3.76679507e-01
 -4.53864638e-01 -3.46352828e-01 -1.04030714e+00 -2.95554380e-01
  3.17092454e+00 -4.14782834e-01  1.68335523e+00 -8.31138275e+00
  4.14472684e+00 -1.12680813e+00 -1.05073594e+00 -7.53411501e-01
 -1.22662381e+00  1.17844600e+00  4.47028527e+00 -6.17327428e-01
  6.14175159e+00 -3.57126968e+00 -3.21512952e+00 -1.92971010e+01
 -1.60428249e+01  6.31863227e-01  9.91251504e-01  3.28614671e-01
  2.01898242e+00  7.05985793e-01 -1.58573542e+00 -2.70206281e+00
 -2.07658052e+00 -6.23658436e-01  9.05828784e-01 -1.07619186e+00
 -3.89228195e+00  3.66557512e+00 -5.17253608e-01 -1.01317473e+00
 -2.23314477e+00  4.18099844e-01 -6.02521909e-01 -8.26569723e-01
  1.68203685e+00  5.98891894e-01 -1.78637422e+00 -3.07967709e+00
 -1.24667953e+00 -1.82418786e+00  7.00030177e-01 -2.41571519e+00
  7.73711581e+00  1.22727741e+00 -4.59056571e+00  2.09646111e+01]
arrl**arr2：
C:/Users/Administrator/PycharmProjects/untitled2/实验3 NumPy 数值计算.py:19: RuntimeWarning: divide by zero encountered in power
  arr7=arr1**arr2
 [-0.00000000e+00  4.16617868e-02  1.33537445e-02 -4.96766100e-02
  5.43454742e-02 -2.71865759e-02  2.14518940e-01  5.30123161e-02
 -2.38865937e-01  9.98855368e-02 -7.23408074e-01  1.02421061e-01
  1.43633216e-01 -5.49223832e+00  5.35978754e-01  2.68276249e-01
  7.51942294e-02 -1.51358521e-01 -3.21923972e-01  1.82999177e-01
 -2.32402530e-01  2.14262789e-01 -2.49662560e-01  2.37015284e-01
 -1.82425879e-01 -5.55612625e-01  1.73196736e-01 -1.14730693e+00
  3.34447003e-01  7.87013815e-01  2.29096618e-01  1.10873436e+00
  1.03661344e+00 -3.05582898e+00  6.06646421e-01  1.89442860e-01
 -6.61020663e-01 -1.42636506e+00 -2.66866294e-01  2.29865169e-01
 -1.93134997e+00  1.75910976e-01  1.06245461e+00 -2.96377482e-01
  2.55336339e+00 -4.07761232e-01 -1.24170151e+00 -3.76679507e-01
 -4.53864638e-01 -3.46352828e-01 -1.04030714e+00 -2.95554380e-01
  3.17092454e+00 -4.14782834e-01  1.68335523e+00 -8.31138275e+00
  4.14472684e+00 -1.12680813e+00 -1.05073594e+00 -7.53411501e-01
 -1.22662381e+00  1.17844600e+00  4.47028527e+00 -6.17327428e-01
  6.14175159e+00 -3.57126968e+00 -3.21512952e+00 -1.92971010e+01
 -1.60428249e+01  6.31863227e-01  9.91251504e-01  3.28614671e-01
  2.01898242e+00  7.05985793e-01 -1.58573542e+00 -2.70206281e+00
 -2.07658052e+00 -6.23658436e-01  9.05828784e-01 -1.07619186e+00
 -3.89228195e+00  3.66557512e+00 -5.17253608e-01 -1.01317473e+00
 -2.23314477e+00  4.18099844e-01 -6.02521909e-01 -8.26569723e-01
  1.68203685e+00  5.98891894e-01 -1.78637422e+00 -3.07967709e+00
 -1.24667953e+00 -1.82418786e+00  7.00030177e-01 -2.41571519e+00
  7.73711581e+00  1.22727741e+00 -4.59056571e+00  2.09646111e+01]
排序后的随机数数组为： [-1.83914297 -1.72557077 -1.58529585 -1.45085246 -1.42733399 -1.42393404
 -1.41474231 -1.31560281 -1.2783294  -1.27777708 -1.24774508 -1.23465018
 -1.12316108 -1.10358701 -1.05758405 -1.05254279 -1.02052812 -0.8811894
 -0.86057583 -0.81920717 -0.78310458 -0.7379603  -0.73406985 -0.60390594
 -0.55913823 -0.55199406 -0.54461232 -0.50981591 -0.50585365 -0.50381381
 -0.48914752 -0.48062729 -0.46666045 -0.44995378 -0.39325828 -0.37615116
 -0.3704594  -0.36598629 -0.3349159  -0.29548552 -0.27756572 -0.25940063
 -0.23533371 -0.21348131 -0.20710902 -0.20553496 -0.20527944 -0.1820081
 -0.13823456 -0.10799034 -0.06617431 -0.04238655 -0.03472024 -0.02366977
  0.04722244  0.1042048   0.12407724  0.13511144  0.13869361  0.16399003
  0.17232173  0.22097487  0.24002811  0.26120438  0.27959808  0.27969558
  0.30869752  0.32078791  0.35661529  0.36848146  0.39531101  0.51763085
  0.52317522  0.55912516  0.56045826  0.706178    0.73603185  0.79036736
  0.83546135  0.8372029   0.86108988  0.90103135  0.97040155  0.98010486
  1.03401514  1.03825603  1.07399786  1.09200848  1.30949118  1.32044787
  1.34279925  1.48607789  1.49770725  1.50118303  1.69664679  1.84752278
  2.03300722  2.12782286  2.16058522  2.33072437]
去重后的正态分布随机数数组为： [-1.83914297 -1.72557077 -1.58529585 -1.45085246 -1.42733399 -1.42393404
 -1.41474231 -1.31560281 -1.2783294  -1.27777708 -1.24774508 -1.23465018
 -1.12316108 -1.10358701 -1.05758405 -1.05254279 -1.02052812 -0.8811894
 -0.86057583 -0.81920717 -0.78310458 -0.7379603  -0.73406985 -0.60390594
 -0.55913823 -0.55199406 -0.54461232 -0.50981591 -0.50585365 -0.50381381
 -0.48914752 -0.48062729 -0.46666045 -0.44995378 -0.39325828 -0.37615116
 -0.3704594  -0.36598629 -0.3349159  -0.29548552 -0.27756572 -0.25940063
 -0.23533371 -0.21348131 -0.20710902 -0.20553496 -0.20527944 -0.1820081
 -0.13823456 -0.10799034 -0.06617431 -0.04238655 -0.03472024 -0.02366977
  0.04722244  0.1042048   0.12407724  0.13511144  0.13869361  0.16399003
  0.17232173  0.22097487  0.24002811  0.26120438  0.27959808  0.27969558
  0.30869752  0.32078791  0.35661529  0.36848146  0.39531101  0.51763085
  0.52317522  0.55912516  0.56045826  0.706178    0.73603185  0.79036736
  0.83546135  0.8372029   0.86108988  0.90103135  0.97040155  0.98010486
  1.03401514  1.03825603  1.07399786  1.09200848  1.30949118  1.32044787
  1.34279925  1.48607789  1.49770725  1.50118303  1.69664679  1.84752278
  2.03300722  2.12782286  2.16058522  2.33072437]
正态分布随机数数组的总和为： 1.1924119720296829
正态分随机数数组的累计和为： [ -1.83914297  -3.56471374  -5.1500096   -6.60086206  -8.02819605
  -9.45213009 -10.8668724  -12.18247521 -13.46080461 -14.7385817
 -15.98632678 -17.22097696 -18.34413803 -19.44772505 -20.50530909
 -21.55785188 -22.57838    -23.45956939 -24.32014523 -25.13935239
 -25.92245698 -26.66041728 -27.39448713 -27.99839307 -28.5575313
 -29.10952536 -29.65413769 -30.1639536  -30.66980725 -31.17362106
 -31.66276858 -32.14339587 -32.61005632 -33.06001009 -33.45326837
 -33.82941954 -34.19987894 -34.56586523 -34.90078113 -35.19626665
 -35.47383237 -35.733233   -35.96856672 -36.18204803 -36.38915705
 -36.59469201 -36.79997145 -36.98197955 -37.12021411 -37.22820445
 -37.29437876 -37.33676531 -37.37148555 -37.39515531 -37.34793288
 -37.24372808 -37.11965083 -36.9845394  -36.84584579 -36.68185576
 -36.50953403 -36.28855916 -36.04853104 -35.78732666 -35.50772858
 -35.22803299 -34.91933547 -34.59854757 -34.24193228 -33.87345082
 -33.47813981 -32.96050896 -32.43733374 -31.87820858 -31.31775032
 -30.61157232 -29.87554047 -29.08517312 -28.24971177 -27.41250887
 -26.55141899 -25.65038764 -24.67998609 -23.69988123 -22.66586609
 -21.62761006 -20.5536122  -19.46160372 -18.15211255 -16.83166468
 -15.48886542 -14.00278754 -12.50508029 -11.00389726  -9.30725047
  -7.45972769  -5.42672047  -3.29889762  -1.1383124    1.19241197]
正态分布随机数数组的均值为： 0.011924119720296828
正态分布随机数数组的标准差为: 0.944262338901446
正态分布随机数数组的方差为： 0.8916313646676293
正态分布随机数数组的最小值为: -1.8391429692420478
正态分布随机数数组的最大值为： 2.330724371843149

Process finished with exit code 0

（2）任务2创建一个国际象棋的棋盘：

test3-2.py文件的代码如下：

import numpy as np#导入NumPy库
#代码test3-2#创建一个8*8矩阵
matr1=np.int8(np.zeros((8,8)))
print('创建的矩阵为：\n',matr1)
#把1，3，5，7行的0，2，4，6列的元素设置为1；0，2，4，6行的1，3，5，7列的元素设置为1，规律是行号和列号之和是奇数的位置设置为1
for i in range(8):
    for j in range(8):
        if(i+j)%2!=0:
            matr1[i,j]=1
print('国际棋盘对应的矩阵为：\n',matr1)
#输出国际象棋模盘
for i in range(0,8):
    for j in range(0,8):
        if matr1[i,j]==0:
            print("口",end='  ')#将print默认的换行变为加两个空格
        else:
            print("■", end='  ')#将print默认的换行变为加两个空格
    print('\n')#此行结束，换行