numpy练习

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#numpy

本文介绍了使用numpy进行版本检查、配置显示、数组操作、类型转换、信息获取、索引与重塑、非零值查找、矩阵运算、数据填充、形状操作、坐标变换、数组构造、数组比较、日期处理、随机数生成、数组统计、结构化数组、直角坐标转换、极坐标转换、数组优化及搜索最值等内容。

import numpy as np

print(np.__version__)
np.show_config()

1.19.1
blas_mkl_info:
    libraries = ['mkl_rt']
    library_dirs = ['E:/ProgramData/Anaconda3/envs/tf2.3\\Library\\lib']
    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
    include_dirs = ['E:/ProgramData/Anaconda3/envs/tf2.3\\Library\\include']
blas_opt_info:
    libraries = ['mkl_rt']
    library_dirs = ['E:/ProgramData/Anaconda3/envs/tf2.3\\Library\\lib']
    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
    include_dirs = ['E:/ProgramData/Anaconda3/envs/tf2.3\\Library\\include']
lapack_mkl_info:
    libraries = ['mkl_rt']
    library_dirs = ['E:/ProgramData/Anaconda3/envs/tf2.3\\Library\\lib']
    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
    include_dirs = ['E:/ProgramData/Anaconda3/envs/tf2.3\\Library\\include']
lapack_opt_info:
    libraries = ['mkl_rt']
    library_dirs = ['E:/ProgramData/Anaconda3/envs/tf2.3\\Library\\lib']
    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
    include_dirs = ['E:/ProgramData/Anaconda3/envs/tf2.3\\Library\\include']

Z = np.ones(10)
print(Z)

[1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]

Z = np.zeros((10,10))
Z

array([[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., 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.],
       [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., 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.]])

print("%d bytes" % (Z.size * Z.itemsize))

800 bytes

print("{}".format(Z.size * Z.itemsize))

Z.itemsize

np.info

<function numpy.info(object=None, maxwidth=76, output=<ipykernel.iostream.OutStream object at 0x0000021C2EE26AC8>, toplevel='numpy')>

Z = np.zeros(10)
Z[5] = 1
Z

array([0., 0., 0., 0., 0., 1., 0., 0., 0., 0.])

Z = np.arange(10,50)
Z

array([10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26,
       27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43,
       44, 45, 46, 47, 48, 49])

Z = np.arange(9)

np.reshape(Z,(3,3))

array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])

nz = np.nonzero([1,2,0,0,4,0])
print(nz)

(array([0, 1, 4], dtype=int64),)

Z = np.eye(3)
Z

array([[1., 0., 0.],
       [0., 1., 0.],
       [0., 0., 1.]])

np.random.random((3,3,3)).shape

(3, 3, 3)

Z = np.random.random((10,10))

np.max(Z),np.min(Z)

(0.9995614828372513, 0.008748034129026694)

Z = np.random.random(30)
Z.mean()

0.4525193349949122

创建一个二维数组，其中边界值为1，其余值为0

Z = np.ones((10,10))
Z[1:-1,1:-1] = 0
print(Z)

[[1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]
 [1. 0. 0. 0. 0. 0. 0. 0. 0. 1.]
 [1. 0. 0. 0. 0. 0. 0. 0. 0. 1.]
 [1. 0. 0. 0. 0. 0. 0. 0. 0. 1.]
 [1. 0. 0. 0. 0. 0. 0. 0. 0. 1.]
 [1. 0. 0. 0. 0. 0. 0. 0. 0. 1.]
 [1. 0. 0. 0. 0. 0. 0. 0. 0. 1.]
 [1. 0. 0. 0. 0. 0. 0. 0. 0. 1.]
 [1. 0. 0. 0. 0. 0. 0. 0. 0. 1.]
 [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]]

Z = np.ones((5,5))

np.pad(Z,pad_width = 2,mode='constant', constant_values=2)

array([[2., 2., 2., 2., 2., 2., 2., 2., 2.],
       [2., 2., 2., 2., 2., 2., 2., 2., 2.],
       [2., 2., 1., 1., 1., 1., 1., 2., 2.],
       [2., 2., 1., 1., 1., 1., 1., 2., 2.],
       [2., 2., 1., 1., 1., 1., 1., 2., 2.],
       [2., 2., 1., 1., 1., 1., 1., 2., 2.],
       [2., 2., 1., 1., 1., 1., 1., 2., 2.],
       [2., 2., 2., 2., 2., 2., 2., 2., 2.],
       [2., 2., 2., 2., 2., 2., 2., 2., 2.]])

0 * np.nan

nan

np.nan == np.nan

False

np.inf

inf

np.inf > np.nan

False

np.nan - np.nan

nan

0.3 == 3 * 0.1

False

3 * 0.1

0.30000000000000004

创建一个 5x5的矩阵，并设置值1,2,3,4落在其对角线下方位置 (★☆☆)

np.arange(4)

array([0, 1, 2, 3])

Z = np.diag(1+np.arange(4))
Z

array([[1, 0, 0, 0],
       [0, 2, 0, 0],
       [0, 0, 3, 0],
       [0, 0, 0, 4]])

Z = np.diag(1+np.arange(4),k=1) # K在主对角线上面，还是下面
Z

array([[0, 1, 0, 0, 0],
       [0, 0, 2, 0, 0],
       [0, 0, 0, 3, 0],
       [0, 0, 0, 0, 4],
       [0, 0, 0, 0, 0]])

创建一个8x8 的矩阵，并且设置成棋盘样式 (★☆☆）

Z = np.zeros((8,8),dtype=int)
Z

array([[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, 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, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0]])

Z[1::2,::2] = 1
Z

array([[0, 0, 0, 0, 0, 0, 0, 0],
       [1, 0, 1, 0, 1, 0, 1, 0],
       [0, 0, 0, 0, 0, 0, 0, 0],
       [1, 0, 1, 0, 1, 0, 1, 0],
       [0, 0, 0, 0, 0, 0, 0, 0],
       [1, 0, 1, 0, 1, 0, 1, 0],
       [0, 0, 0, 0, 0, 0, 0, 0],
       [1, 0, 1, 0, 1, 0, 1, 0]])

Z[::2,1::2] = 1

array([[0, 1, 0, 1, 0, 1, 0, 1],
       [1, 0, 1, 0, 1, 0, 1, 0],
       [0, 1, 0, 1, 0, 1, 0, 1],
       [1, 0, 1, 0, 1, 0, 1, 0],
       [0, 1, 0, 1, 0, 1, 0, 1],
       [1, 0, 1, 0, 1, 0, 1, 0],
       [0, 1, 0, 1, 0, 1, 0, 1],
       [1, 0, 1, 0, 1, 0, 1, 0]])

20. 考虑一个 (6,7,8) 形状的数组，其第100个元素的索引(x,y,z)是什么?

Q = np.random.random((6,7,8))

unravel_index(indices, shape, order=‘C’)
indices 就是索引值，可以是一个数，也可以是一个列表。
例如 indices = 1 ，indices = [3,12] 。
shape 代表的是数组的形状
函数的作用就是得到 indices 中每一项对应到形状为shape的数组中的坐标。

print(np.unravel_index(100,(6,7,8)))

(1, 5, 4)

np.unravel_index([22, 41, 37], (7,6))
(np.array([3, 6, 6]), np.array([4, 5, 1]))
np.unravel_index([31, 41, 13], (7,6), order='F')
(np.array([3, 6, 6]), np.array([4, 5, 1]))

(array([3, 6, 6]), array([4, 5, 1]))

a = [2,3,4,5,6,7,8,1,12,23,34,55]
b = np.array(a).reshape((3,4))
print(b)

[[ 2  3  4  5]
 [ 6  7  8  1]
 [12 23 34 55]]

np.unravel_index(7,(3,4),order="C")

(1, 3)

21用tile函数去创建一个 8x8的棋盘样式矩阵(★☆☆)

Z = np.tile( np.array([[0,1],[1,0]]), (3,3))
print(Z)

[[0 1 0 1 0 1]
 [1 0 1 0 1 0]
 [0 1 0 1 0 1]
 [1 0 1 0 1 0]
 [0 1 0 1 0 1]
 [1 0 1 0 1 0]]

a = [1, 2, 3]
b = np.tile(a, 2)
b

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

b = np.tile(a, 3)
b

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

Z = np.random.random((4,5))
Z

array([[0.40190652, 0.30602045, 0.78660736, 0.79006286, 0.46857736],
       [0.73928607, 0.25034014, 0.78878815, 0.9053959 , 0.44941201],
       [0.53044218, 0.13904618, 0.95918547, 0.98779074, 0.27377363],
       [0.84429444, 0.24627403, 0.09384873, 0.18253855, 0.63075715]])

Z.max(-1)

array([0.79006286, 0.9053959 , 0.98779074, 0.84429444])

color = np.dtype([("r", np.ubyte, 1),
                  ("g", np.ubyte, 1),
                  ("b", np.ubyte, 1),
                  ("a", np.ubyte, 1)])
color

E:\ProgramData\Anaconda3\envs\tf2.3\lib\site-packages\ipykernel_launcher.py:4: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.
  after removing the cwd from sys.path.





dtype([('r', 'u1'), ('g', 'u1'), ('b', 'u1'), ('a', 'u1')])

Z1 = np.random.random((5,3))
Z2 = np.random.random((3,2))
Z1,Z2

(array([[0.20547996, 0.3273501 , 0.15984982],
        [0.09920915, 0.60710609, 0.09866898],
        [0.90849081, 0.94514143, 0.25371245],
        [0.61277969, 0.63544792, 0.08197526],
        [0.12803159, 0.01340407, 0.69079278]]),
 array([[0.86560206, 0.18972041],
        [0.85147056, 0.63382571],
        [0.78857142, 0.21271258]]))

Z1@Z2

array([[0.58264585, 0.28046872],
       [0.68061615, 0.42460959],
       [1.79122201, 0.82538202],
       [1.13613191, 0.53645722],
       [0.66697702, 0.17972637]])

给定一个一维数组，对其在3到8之间的所有元素取反 (★☆☆)

Z = np.arange(11)
Z[(3 < Z) & (Z <= 8)] *= -1
print(Z)

[ 0  1  2  3 -4 -5 -6 -7 -8  9 10]

Z = np.arange(5)
Z ** Z  # legal

array([  1,   1,   4,  27, 256], dtype=int32)

print(np.array(0) // np.array(0))

0


E:\ProgramData\Anaconda3\envs\tf2.3\lib\site-packages\ipykernel_launcher.py:1: RuntimeWarning: divide by zero encountered in floor_divide
  """Entry point for launching an IPython kernel.

Z1 = np.random.randint(0,10,10)
Z2 = np.random.randint(0,10,10)
print(np.intersect1d(Z1,Z2))

[1 2 5 9]

Z1,Z2

(array([3, 1, 2, 5, 7, 2, 5, 1, 2, 9]), array([8, 6, 2, 0, 5, 0, 2, 9, 8, 1]))

yesterday = np.datetime64('today', 'D') - np.timedelta64(1, 'D')
today     = np.datetime64('today', 'D')
tomorrow  = np.datetime64('today', 'D') + np.timedelta64(1, 'D')
print ("Yesterday is " + str(yesterday))
print ("Today is " + str(today))
print ("Tomorrow is "+ str(tomorrow))

Yesterday is 2020-10-05
Today is 2020-10-06
Tomorrow is 2020-10-07

np.datetime64(‘today’, ‘D’)

Z = np.arange('2016-07', '2016-08', dtype='datetime64[D]')
print(Z)

['2016-07-01' '2016-07-02' '2016-07-03' '2016-07-04' '2016-07-05'
 '2016-07-06' '2016-07-07' '2016-07-08' '2016-07-09' '2016-07-10'
 '2016-07-11' '2016-07-12' '2016-07-13' '2016-07-14' '2016-07-15'
 '2016-07-16' '2016-07-17' '2016-07-18' '2016-07-19' '2016-07-20'
 '2016-07-21' '2016-07-22' '2016-07-23' '2016-07-24' '2016-07-25'
 '2016-07-26' '2016-07-27' '2016-07-28' '2016-07-29' '2016-07-30'
 '2016-07-31']

## 提取随机数的整数部分

Z = np.random.uniform(0,10,10)
Z

array([0.16810903, 9.59121764, 7.71395414, 7.21803664, 7.69366273,
       6.9222278 , 4.06226357, 6.49995964, 9.59689444, 9.34069033])

print (np.floor(Z))

[0. 9. 7. 7. 7. 6. 4. 6. 9. 9.]

print (np.ceil(Z)-1)

[0. 9. 7. 7. 7. 6. 4. 6. 9. 9.]

np.ceil(Z)

array([ 1., 10.,  8.,  8.,  8.,  7.,  5.,  7., 10., 10.])

Z = np.linspace(0,10,10,endpoint=False)[1:]
print (Z)

[1. 2. 3. 4. 5. 6. 7. 8. 9.]

Z = np.arange(10)
np.add.reduce(Z)

sum(Z)

X = np.arange(8).reshape((2,2,2))
X

array([[[0, 1],
        [2, 3]],

       [[4, 5],
        [6, 7]]])

sum(X)

array([[ 4,  6],
       [ 8, 10]])

np.add.reduce(X)

array([[ 4,  6],
       [ 8, 10]])

A = np.random.randint(0,2,5)
B = np.random.randint(0,2,5)
# Assuming identical shape of the arrays and a tolerance for the comparison of values
equal = np.allclose(A,B) # 比较两个array是不是每一元素都相等
print(equal)

False

equal = np.array_equal(A,B)
print(equal)

False

直角坐标转化为极坐标

Z = np.random.random((10,2))
X,Y = Z[:,0], Z[:,1]
R = np.sqrt(X**2+Y**2)
T = np.arctan2(Y,X)
print (R)
print (T)

[0.72628514 0.72675508 0.72716821 0.7558053  1.01990372 0.72662107
 0.9731911  1.30019838 0.73533109 0.69792346]
[0.4138511  1.26658697 0.63877982 0.20687776 0.35887851 1.34449106
 0.05132117 0.80118363 0.78778002 0.30213957]

两者输入不同, arctan仅仅输入正切值,arctan2要输入对边和直角边的具体数值,用来确定象限
两者的值域不同,arctan的值域是[ − π 2 , π 2 ] [-\frac{\pi}{2}, \frac{\pi}{2}][−
2
π

,
2
π

], arctan2的值域是[ − π , π ] [-\pi, \pi][−π,π]

创建一个长度为10的向量，并将向量中最大值替换为1 (★★☆)

Z = np.random.random(10)

print (Z)

[0.56945164 0.71671363 0.87783409 0.64726814 0.61884474 0.11584415
 0.20293375 0.64979239 0.11855371 0.70896716]

Z.argmax()

Z[Z.argmax()] = 0
print (Z)

[0.56945164 0.71671363 0.         0.64726814 0.61884474 0.11584415
 0.20293375 0.64979239 0.11855371 0.70896716]

创建一个结构化数组，并实现 x 和 y 坐标覆盖 [0,1]x[0,1] 区域 (★★☆)

Z = np.zeros((5,5), [('x',float),('y',float)])
Z['x'], Z['y'] = np.meshgrid(np.linspace(0,1,5),
                             np.linspace(0,1,5))
print(Z)

[[(0.  , 0.  ) (0.25, 0.  ) (0.5 , 0.  ) (0.75, 0.  ) (1.  , 0.  )]
 [(0.  , 0.25) (0.25, 0.25) (0.5 , 0.25) (0.75, 0.25) (1.  , 0.25)]
 [(0.  , 0.5 ) (0.25, 0.5 ) (0.5 , 0.5 ) (0.75, 0.5 ) (1.  , 0.5 )]
 [(0.  , 0.75) (0.25, 0.75) (0.5 , 0.75) (0.75, 0.75) (1.  , 0.75)]
 [(0.  , 1.  ) (0.25, 1.  ) (0.5 , 1.  ) (0.75, 1.  ) (1.  , 1.  )]]

np.linspace(0,1,5) # 返回几个数

array([0.  , 0.25, 0.5 , 0.75, 1.  ])

np.linspace(0,1,5,retstep=True)

(array([0.  , 0.25, 0.5 , 0.75, 1.  ]), 0.25)

np.linspace(0,1,5,endpoint=False)

array([0. , 0.2, 0.4, 0.6, 0.8])

np.arange(0,10,1)

array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

X = np.arange(8)
Y = X + 0.5
C = 1.0 / np.subtract.outer(X, Y)
print(np.linalg.det(C))

3638.1636371179666

X,Y

(array([0, 1, 2, 3, 4, 5, 6, 7]),
 array([0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5]))

np.subtract.outer(X, X) ##B中的每个元素减去A中每个元素的值

array([[ 0, -1, -2, -3, -4, -5, -6, -7],
       [ 1,  0, -1, -2, -3, -4, -5, -6],
       [ 2,  1,  0, -1, -2, -3, -4, -5],
       [ 3,  2,  1,  0, -1, -2, -3, -4],
       [ 4,  3,  2,  1,  0, -1, -2, -3],
       [ 5,  4,  3,  2,  1,  0, -1, -2],
       [ 6,  5,  4,  3,  2,  1,  0, -1],
       [ 7,  6,  5,  4,  3,  2,  1,  0]])

50. 给定标量时，如何找到数组中最接近标量的值？(★★☆)

Z = np.arange(100)
v = np.random.uniform(0,100)
index = (np.abs(Z-v)).argmin()
print (Z[index])

Z,v

(array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
        17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
        34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50,
        51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67,
        68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84,
        85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]),
 6.059749238050916)

Z = np.zeros(10, [ ('position', [ ('x', float, 1),
                                  ('y', float, 1)]),
                   ('color',    [ ('r', float, 1),
                                  ('g', float, 1),
                                  ('b', float, 1)])])
print (Z)

[((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.)) ((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.))]


E:\ProgramData\Anaconda3\envs\tf2.3\lib\site-packages\ipykernel_launcher.py:5: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.
  """