这是在numpy邮件列表，stackoverflow和numpy文档中收集的练习集合。 该系列的目标是为新老用户提供快速参考，同时为教学人员提供一系列练习。
如果您发现错误或认为您有更好的方法来解决其中一些错误，请随时在https://github.com/rougier/numpy-100上打开一个issue
1. 以np为别名导入numpy包 (★☆☆)
import numpy as np
2. 打印numpy版本和配置 (★☆☆)
print(np.__version__)
np.show_config()
1.14.3
mkl_info:
libraries = ['mkl_rt', 'pthread']
library_dirs = ['/Users/iosdevlog/anaconda3/lib']
define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
include_dirs = ['/Users/iosdevlog/anaconda3/include']
blas_mkl_info:
libraries = ['mkl_rt', 'pthread']
library_dirs = ['/Users/iosdevlog/anaconda3/lib']
define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
include_dirs = ['/Users/iosdevlog/anaconda3/include']
blas_opt_info:
libraries = ['mkl_rt', 'pthread']
library_dirs = ['/Users/iosdevlog/anaconda3/lib']
define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
include_dirs = ['/Users/iosdevlog/anaconda3/include']
lapack_mkl_info:
libraries = ['mkl_rt', 'pthread']
library_dirs = ['/Users/iosdevlog/anaconda3/lib']
define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
include_dirs = ['/Users/iosdevlog/anaconda3/include']
lapack_opt_info:
libraries = ['mkl_rt', 'pthread']
library_dirs = ['/Users/iosdevlog/anaconda3/lib']
define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
include_dirs = ['/Users/iosdevlog/anaconda3/include']
3. 创建一个大小为10的空向量 (★☆☆)
Z = np.zeros(10)
print(Z)
[0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
4. 如何查找数组的内存大小 (★☆☆)
Z = np.zeros((10,10))
print("%d bytes" % (Z.size * Z.itemsize))
800 bytes
5. 如何从命令行获取numpy add函数的文档? (★☆☆)
%run `python -c "import numpy; numpy.info(numpy.add)"`
ERROR:root:File `'`python.py'` not found.
6. 创建大小为10的空向量，但第五个值为1 (★☆☆)
Z = np.zeros(10)
Z[4] = 1
print(Z)
[0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]
7. 创建一个值为10到49的向量 (★☆☆)
Z = np.arange(10,50)
print(Z)
[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]
8. 反转向量（第一个元素成为最后一个） (★☆☆)
Z = np.arange(50)
Z = Z[::-1]
print(Z)
[49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26
25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2
1 0]
9. 创建一个3x3矩阵，其值范围为0到8 (★☆☆)
Z = np.arange(9).reshape(3,3)
print(Z)
[[0 1 2]
[3 4 5]
[6 7 8]]
10.从 [1,2,0,0,4,0] 中查找非零元素的索引 (★☆☆)
nz = np.nonzero([1,2,0,0,4,0])
print(nz)
(array([0, 1, 4]),)
11. 创建3x3单位矩阵 (★☆☆)
Z = np.eye(3)
print(Z)
[[1. 0. 0.]
[0. 1. 0.]
[0. 0. 1.]]
12. 使用随机值创建3x3x3数组 (★☆☆)
Z = np.random.random((3,3,3))
print(Z)
[[[0. 0. 0.]
[0. 0. 0.]
[0.0 0. 0. ]]
[[0. 0. 0.]
[0. 0.00 0.]
[0. 0. 0.]]
[[0. 0. 0.]
[0. 0. 0.]
[0. 0. 0.]]]
13. 创建具有随机值的10x10数组，并查找最小值和最大值 (★☆☆)
Z = np.random.random((10,10))
Zmin, Zmax = Z.min(), Z.max()
print(Zmin, Zmax)
0.0055354 0.58699
14. 创建一个大小为30的随机向量并找到平均值 (★☆☆)
Z = np.random.random(30)
m = Z.mean()
print(m)
0.
15. 创建一个2d数组，边框为1，内部为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.]]
16. 如何在现有数组周围添加边框（填充0）？ (★☆☆)
Z = np.ones((5,5))
Z = np.pad(Z, pad_width=1, mode='constant', constant_values=0)
print(Z)
[[0. 0. 0. 0. 0. 0. 0.]
[0. 1. 1. 1. 1. 1. 0.]
[0. 1. 1. 1. 1. 1. 0.]
[0. 1. 1. 1. 1. 1. 0.]
[0. 1. 1. 1. 1. 1. 0.]
[0. 1. 1. 1. 1. 1. 0.]
[0. 0. 0. 0. 0. 0. 0.]]
17. 以下表达式的结果是什么？ (★☆☆)
print(0 * np.nan)
print(np.nan == np.nan)
print(np.inf > np.nan)
print(np.nan - np.nan)
print(0.3 == 3 * 0.1)
nan
False
False
nan
False
18. 在对角线下方创建一个值为1,2,3,4的5x5矩阵 (★☆☆)
Z = np.diag(1+np.arange(4),k=-1)
print(Z)
[[0 0 0 0 0]
[1 0 0 0 0]
[0 2 0 0 0]
[0 0 3 0 0]
[0 0 0 4 0]]
19. 创建一个8x8矩阵并用棋盘图案填充它 (★☆☆)
Z = np.zeros((8,8),dtype=int)
Z[1::2,::2] = 1
Z[::2,1::2] = 1
print(Z)
[[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）形状数组，第100个元素的索引（x，y，z）是什么？
print(np.unravel_index(100,(6,7,8)))
(1, 5, 4)
21. 使用tile函数创建棋盘格8x8矩阵 (★☆☆)
Z = np.tile( np.array([[0,1],[1,0]]), (4,4))
print(Z)
[[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]]
22. 归一化5x5随机矩阵 (★☆☆)
Z = np.random.random((5,5))
Zmax, Zmin = Z.max(), Z.min()
Z = (Z - Zmin)/(Zmax - Zmin)
print(Z)
[[0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0.]
[0. 0. 0. 0. 0.0]
[0. 0. 0. 0. 0.]
[1. 0.0 0. 0. 0.]]
23. 创建一个自定义dtype，将颜色描述为四个无符号字节（RGBA） (★☆☆)
color = np.dtype([("r", np.ubyte, 1),
("g", np.ubyte, 1),
("b", np.ubyte, 1),
("a", np.ubyte, 1)])
24. 将5x3矩阵乘以3x2矩阵（实矩阵乘积） (★☆☆)
Z = np.dot(np.ones((5,3)), np.ones((3,2)))
print(Z)
# Alternative solution, in Python 3.5 and above
Z = np.ones((5,3)) @ np.ones((3,2))
[[3. 3.]
[3. 3.]
[3. 3.]
[3. 3.]
[3. 3.]]
25. 给定一维数组，否定所有在3到8之间的元素。(★☆☆)
# Author: Evgeni Burovski
Z = np.arange(11)
Z[(3 < Z) & (Z <= 8)] *= -1
print(Z)
[ 0 1 2 3 -4 -5 -6 -7 -8 9 10]
26. 以下脚本的输出是什么？ (★☆☆)
# Author: Jake VanderPlas
print(sum(range(5),-1))
from numpy import *
print(sum(range(5),-1))
9
10
27. 考虑整数向量Z，这些表达式中哪些是合法的？ (★☆☆)
Z = np.zeros(10)
ZZ
# 2 << Z >> 2 TypeError: ufunc 'left_shift' not supported for the input types, and the inputs could not be safely coerced to any supported types according to the casting rule ''safe''
Z Z ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()
array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
28. 以下表达式的结果是什么？
print(np.array(0) / np.array(0))
print(np.array(0) // np.array(0))
print(np.array([np.nan]).astype(int).astype(float))
nan
0
[-9.e+18]
/Users/iosdevlog/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:1: RuntimeWarning: invalid value encountered in true_divide
"""Entry point for launching an IPython kernel.
/Users/iosdevlog/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:2: RuntimeWarning: divide by zero encountered in floor_divide
29. 如何从零浮点数舍入？ (★☆☆)
# Author: Charles R Harris
Z = np.random.uniform(-10,+10,10)
print (np.copysign(np.ceil(np.abs(Z)), Z))
[10. -8. 2. 7. 10. -1. -6. -3. -5. 5.]
30. 如何在两个数组之间找到常用值？ (★☆☆)
Z1 = np.random.randint(0,10,10)
Z2 = np.random.randint(0,10,10)
print(np.intersect1d(Z1,Z2))
[2 4 6 7 8]
31. 如何忽略所有numpy警告（不推荐）？ (★☆☆)
# Suicide mode on
defaults = np.seterr(all="ignore")
Z = np.ones(1) / 0
# Back to sanity
_ = np.seterr(defaults)
# An equivalent way, with a context manager:
with np.errstate(divide='ignore'):
Z = np.ones(1) / 0
32. 以下表达式是 true 吗？(★☆☆)
np.sqrt(-1) == np.emath.sqrt(-1)
/Users/iosdevlog/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:1: RuntimeWarning: invalid value encountered in sqrt
"""Entry point for launching an IPython kernel.
False
33. 如何获取昨天，今天和明天的日期？ (★☆☆)
yesterday = np.datetime64('today', 'D') - np.timedelta64(1, 'D')
today = np.datetime64('today', 'D')
tomorrow = np.datetime64('today', 'D') + np.timedelta64(1, 'D')
34. 如何获得与2016年7月相对应的所有日期？ (★★☆)
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']
35. 如何计算((A+B)*(-A/2)) （不copy）？(★★☆)
A = np.ones(3)*1
B = np.ones(3)*2
C = np.ones(3)*3
np.add(A,B,out=B)
np.divide(A,2,out=A)
np.negative(A,out=A)
np.multiply(A,B,out=A)
array([-1.5, -1.5, -1.5])
36. 使用5种不同的方法提取随机数组的整数部分 (★★☆)
Z = np.random.uniform(0,10,10)
print (Z - Z%1)
print (np.floor(Z))
print (np.ceil(Z)-1)
print (Z.astype(int))
print (np.trunc(Z))
[2. 0. 0. 3. 9. 8. 8. 4. 8. 6.]
[2. 0. 0. 3. 9. 8. 8. 4. 8. 6.]
[2. 0. 0. 3. 9. 8. 8. 4. 8. 6.]
[2 0 0 3 9 8 8 4 8 6]
[2. 0. 0. 3. 9. 8. 8. 4. 8. 6.]
37. 创建一个5x5矩阵，行值范围为0到4 (★★☆)
Z = np.zeros((5,5))
Z += np.arange(5)
print(Z)
[[0. 1. 2. 3. 4.]
[0. 1. 2. 3. 4.]
[0. 1. 2. 3. 4.]
[0. 1. 2. 3. 4.]
[0. 1. 2. 3. 4.]]
38. 考虑生成10个整数并使用它来构建数组的生成器函数(★☆☆)
def generate():
for x in range(10):
yield x
Z = np.fromiter(generate(),dtype=float,count=-1)
print(Z)
[0. 1. 2. 3. 4. 5. 6. 7. 8. 9.]
39. 创建一个大小为10的向量，其值范围为0到1，两者都被排除(★★☆)
Z = np.linspace(0,1,11,endpoint=False)[1:]
print(Z)
[0.0 0. 0. 0. 0. 0.
0. 0. 0. 0.]
40. 创建一个大小为10的随机向量并对其进行排序(★★☆)
Z = np.random.random(10)
Z.sort()
print(Z)
[0. 0. 0. 0. 0. 0.
0. 0. 0. 0.]
41. 如何比np.sum更快地求和一个小数组？ (★★☆)
# Author: Evgeni Burovski
Z = np.arange(10)
np.add.reduce(Z)
45
42. 考虑两个随机数组A和B，检查它们是否相等(★★☆)
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)
print(equal)
# Checking both the shape and the element values, no tolerance (values have to be exactly equal)
equal = np.array_equal(A,B)
print(equal)
False
False
43. 使数组不可变（只读） (★★☆)
Z = np.zeros(10)
Z.flags.writeable = False
# Z[0] = 1 ValueError: assignment destination is read-only
44. 考虑一个代表笛卡尔坐标的随机10x2矩阵，将它们转换为极坐标 (★★☆)
Z = np.random.random((10,2))
X,Y = Z[:,0], Z[:,1]
R = np.sqrt(X2+Y2)
T = np.arctan2(Y,X)
print(R)
print(T)
[0. 0. 0. 0. 0. 0.
1. 0. 0. 0.]
[1. 0. 0. 0. 1. 1.
0. 0. 1.0 0. ]
45. 创建大小为10的随机向量，并将最大值替换为0 (★★☆)
Z = np.random.random(10)
Z[Z.argmax()] = 0
print(Z)
[0. 0. 0.0044212 0. 0. 0.
0.00 0. 0. 0.]
46. 创建一个带有x和y坐标的结构化数组，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. )]]
47. 给定两个数组X和Y，构造Cauchy矩阵C (Cij =1/(xi - yj))
# Author: Evgeni Burovski
X = np.arange(8)
Y = X + 0.5
C = 1.0 / np.subtract.outer(X, Y)
print(np.linalg.det(C))
3638.66
48. 打印每个numpy标量类型的最小和最大可表示值 (★★☆)
for dtype in [np.int8, np.int32, np.int64]:
print(np.iinfo(dtype).min)
print(np.iinfo(dtype).max)
for dtype in [np.float32, np.float64]:
print(np.finfo(dtype).min)
print(np.finfo(dtype).max)
print(np.finfo(dtype).eps)
-128
127
-
-
-3.e+38
3.e+38
1.e-07
-1.23157e+308
1.23157e+308
2.0313e-16
49. 如何打印数组的所有值？ (★★☆)
np.set_printoptions(threshold=np.nan)
Z = np.zeros((16,16))
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. 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. 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. 0. 0. 0. 0. 0. 0.]]
50. 如何在向量中找到最接近的值（给定标量）？ (★★☆)
Z = np.arange(100)
v = np.random.uniform(0,100)
index = (np.abs(Z-v)).argmin()
print(Z[index])
21
51. 创建表示位置（x，y）和颜色（r，g，b）的结构化数组 (★★☆)
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.))]
52. 考虑一个随机向量，其形状（100,2）代表坐标，逐点找到 (★★☆)
Z = np.random.random((10,2))
X,Y = np.atleast_2d(Z[:,0], Z[:,1])
D = np.sqrt( (X-X.T)2 + (Y-Y.T)2)
print(D)
# Much faster with scipy
import scipy
# Thanks Gavin Heverly-Coulson (#issue 1)
import scipy.spatial
Z = np.random.random((10,2))
D = scipy.spatial.distance.cdist(Z,Z)
print(D)
[[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. 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. 1.0 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. 1.0
0. 0. 0. 0.]
[0. 0. 0. 0. 0.0 0.
0. 0. 0. 0. ]]
53. 如何将float（32位）数组转换为整数（32位）？
Z = np.arange(10, dtype=np.float32)
Z = Z.astype(np.int32, copy=False)
print(Z)
[0 1 2 3 4 5 6 7 8 9]
54. 如何阅读以下文件？ (★★☆)
from io import StringIO
# Fake file
s = StringIO("""1, 2, 3, 4, 5\n
6, , , 7, 8\n
, , 9,10,11\n""")
Z = np.genfromtxt(s, delimiter=",", dtype=np.int)
print(Z)
[[ 1 2 3 4 5]
[ 6 -1 -1 7 8]
[-1 -1 9 10 11]]
55. numpy数组的枚举相当于什么？ (★★☆)
Z = np.arange(9).reshape(3,3)
for index, value in np.ndenumerate(Z):
print(index, value)
for index in np.ndindex(Z.shape):
print(index, Z[index])
(0, 0) 0
(0, 1) 1
(0, 2) 2
(1, 0) 3
(1, 1) 4
(1, 2) 5
(2, 0) 6
(2, 1) 7
(2, 2) 8
(0, 0) 0
(0, 1) 1
(0, 2) 2
(1, 0) 3
(1, 1) 4
(1, 2) 5
(2, 0) 6
(2, 1) 7
(2, 2) 8
56. 生成通用的2D高斯类数组 (★★☆)
X, Y = np.meshgrid(np.linspace(-1,1,10), np.linspace(-1,1,10))
D = np.sqrt(X*X+Y*Y)
sigma, mu = 1.0, 0.0
G = np.exp(-( (D-mu)2 / ( 2.0 * sigma2 ) ) )
print(G)
[[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.]]
57. 如何将p元素随机放置在2D数组中？ (★★☆)
# Author: Divakar
n = 10
p = 3
Z = np.zeros((n,n))
np.put(Z, np.random.choice(range(n*n), p, replace=False),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. 1. 0. 0. 0.]
[0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 0. 1. 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.]]
58. 减去矩阵每行的平均值 (★★☆)
# Author: Warren Weckesser
X = np.random.rand(5, 10)
# Recent versions of numpy
Y = X - X.mean(axis=1, keepdims=True)
# Older versions of numpy
Y = X - X.mean(axis=1).reshape(-1, 1)
print(Y)
[[-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.]]
59. 如何按第n列对数组进行排序？ (★★☆)
# Author: Steve Tjoa
Z = np.random.randint(0,10,(3,3))
print(Z)
print(Z[Z[:,1].argsort()])
[[7 9 1]
[4 9 9]
[1 7 6]]
[[1 7 6]
[7 9 1]
[4 9 9]]
60. 如何判断给定的2D数组是否具有空列？(★★☆)
# Author: Warren Weckesser
Z = np.random.randint(0,3,(3,10))
print((~Z.any(axis=0)).any())
False
61. 从数组中的给定值中查找最接近的值 (★★☆)
Z = np.random.uniform(0,1,10)
z = 0.5
m = Z.flat[np.abs(Z - z).argmin()]
print(m)
0.37276
62. 考虑两个形状为（1,3）和（3,1）的数组，如何使用迭代器计算它们的总和？ (★★☆)
A = np.arange(3).reshape(3,1)
B = np.arange(3).reshape(1,3)
it = np.nditer([A,B,None])
for x,y,z in it: z[...] = x + y
print(it.operands[2])
[[0 1 2]
[1 2 3]
[2 3 4]]
63. 创建一个具有name属性的数组类 (★★☆)
class NamedArray(np.ndarray):
def __new__(cls, array, name="no name"):
obj = np.asarray(array).view(cls)
obj.name = name
return obj
def __array_finalize__(self, obj):
if obj is None: return
self.info = getattr(obj, 'name', "no name")
Z = NamedArray(np.arange(10), "range_10")
print (Z.name)
range_10
64. 考虑一个给定的向量，如何为每个由第二个向量索引的元素添加1（小心重复索引）？ (★★★)
# Author: Brett Olsen
Z = np.ones(10)
I = np.random.randint(0,len(Z),20)
Z += np.bincount(I, minlength=len(Z))
print(Z)
# Another solution
# Author: Bartosz Telenczuk
np.add.at(Z, I, 1)
print(Z)
[4. 1. 2. 5. 3. 2. 4. 3. 4. 2.]
[7. 1. 3. 9. 5. 3. 7. 5. 7. 3.]
65. 如何基于索引列表（I）将向量（X）的元素累积到数组（F）？ (★★★)
# Author: Alan G Isaac
X = [1,2,3,4,5,6]
I = [1,3,9,3,4,1]
F = np.bincount(I,X)
print(F)
[0. 7. 0. 6. 5. 0. 0. 0. 0. 3.]
66. 考虑（dtype = ubyte）的（w，h，3）图像，计算唯一颜色的数量 (★★★)
# Author: Nadav Horesh
w,h = 16,16
I = np.random.randint(0,2,(h,w,3)).astype(np.ubyte)
#Note that we should compute 256*256 first.
#Otherwise numpy will only promote F.dtype to 'uint16' and overfolw will occur
F = I[...,0]*(256*256) + I[...,1]*256 +I[...,2]
n = len(np.unique(F))
print(n)
8
67. 考虑四维数组，如何一次得到最后两个轴的总和？ (★★★)
A = np.random.randint(0,10,(3,4,3,4))
# solution by passing a tuple of axes (introduced in numpy 1.7.0)
sum = A.sum(axis=(-2,-1))
print(sum)
# solution by flattening the last two dimensions into one
# (useful for functions that don't accept tuples for axis argument)
sum = A.reshape(A.shape[:-2] + (-1,)).sum(axis=-1)
print(sum)
[[72 80 48 56]
[51 63 65 54]
[46 67 54 43]]
[[72 80 48 56]
[51 63 65 54]
[46 67 54 43]]
68. 考虑一维向量D，如何使用描述子集索引的相同大小的向量S来计算D的子集的均值？ (★★★)
# Author: Jaime Fernández del Río
D = np.random.uniform(0,1,100)
S = np.random.randint(0,10,100)
D_sums = np.bincount(S, weights=D)
D_counts = np.bincount(S)
D_means = D_sums / D_counts
print(D_means)
# Pandas solution as a reference due to more intuitive code
import pandas as pd
print(pd.Series(D).groupby(S).mean())
[0. 0. 0. 0. 0. 0.
0. 0. 0. 0.]
0 0.
1 0.
2 0.
3 0.
4 0.
5 0.
6 0.
7 0.
8 0.
9 0.
dtype: float64
69. 如何获得点积的对角线？ (★★★)
# Author: Mathieu Blondel
A = np.random.uniform(0,1,(5,5))
B = np.random.uniform(0,1,(5,5))
# Slow version
np.diag(np.dot(A, B))
# Fast version
np.sum(A * B.T, axis=1)
# Faster version
np.einsum("ij,ji->i", A, B)
array([1., 1., 1.0, 1., 1.])
70. 考虑向量 [1,2,3,4,5]，如何构建一个新的向量，在每个值之间插入3个连续的零？ (★★★)
# Author: Warren Weckesser
Z = np.array([1,2,3,4,5])
nz = 3
Z0 = np.zeros(len(Z) + (len(Z)-1)*(nz))
Z0[::nz+1] = Z
print(Z0)
[1. 0. 0. 0. 2. 0. 0. 0. 3. 0. 0. 0. 4. 0. 0. 0. 5.]
71. 考虑一个维度数组（5,5,3），如何将它乘以一个维数为（5,5）的数组？(★★★)
A = np.ones((5,5,3))
B = 2*np.ones((5,5))
print(A * B[:,:,None])
[[[2. 2. 2.]
[2. 2. 2.]
[2. 2. 2.]
[2. 2. 2.]
[2. 2. 2.]]
[[2. 2. 2.]
[2. 2. 2.]
[2. 2. 2.]
[2. 2. 2.]
[2. 2. 2.]]
[[2. 2. 2.]
[2. 2. 2.]
[2. 2. 2.]
[2. 2. 2.]
[2. 2. 2.]]
[[2. 2. 2.]
[2. 2. 2.]
[2. 2. 2.]
[2. 2. 2.]
[2. 2. 2.]]
[[2. 2. 2.]
[2. 2. 2.]
[2. 2. 2.]
[2. 2. 2.]
[2. 2. 2.]]]
72. 如何交换数组的两行？ (★★★)
# Author: Eelco Hoogendoorn
A = np.arange(25).reshape(5,5)
A[[0,1]] = A[[1,0]]
print(A)
[[ 5 6 7 8 9]
[ 0 1 2 3 4]
[10 11 12 13 14]
[15 16 17 18 19]
[20 21 22 23 24]]
73. 考虑一组描述10个三角形（具有共享顶点）的10个三元组，找到组成所有三角形的唯一线段的集合 (★★★)
# Author: Nicolas P. Rougier
faces = np.random.randint(0,100,(10,3))
F = np.roll(faces.repeat(2,axis=1),-1,axis=1)
F = F.reshape(len(F)*3,2)
F = np.sort(F,axis=1)
G = F.view( dtype=[('p0',F.dtype),('p1',F.dtype)] )
G = np.unique(G)
print(G)
[( 0, 70) ( 0, 91) ( 3, 29) ( 3, 53) ( 3, 90) ( 3, 98) (24, 55) (24, 64)
(27, 63) (27, 85) (29, 35) (29, 40) (29, 90) (35, 40) (35, 52) (35, 74)
(38, 42) (38, 81) (42, 81) (52, 74) (53, 56) (53, 62) (53, 67) (53, 92)
(53, 98) (55, 64) (56, 67) (62, 92) (63, 85) (70, 91)]
74. 给定一个bincount的数组C，如何生成一个数组A，使得 np.bincount(A) == C? (★★★)
# Author: Jaime Fernández del Río
C = np.bincount([1,1,2,3,4,4,6])
A = np.repeat(np.arange(len(C)), C)
print(A)
[1 1 2 3 4 4 6]
75. 如何使用数组上的滑动窗口计算平均值？ (★★★)
# Author: Jaime Fernández del Río
def moving_average(a, n=3) :
ret = np.cumsum(a, dtype=float)
ret[n:] = ret[n:] - ret[:-n]
return ret[n - 1:] / n
Z = np.arange(20)
print(moving_average(Z, n=3))
[ 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.]
76. 考虑一维数组Z，构建一个二维数组，其第一行为(Z[0],Z[1],Z[2])，每个后续行移1 行 (最后一行应该是Z[-3],Z[-2],Z[-1]) (★★★)
# Author: Joe Kington / Erik Rigtorp
from numpy.lib import stride_tricks
def rolling(a, window):
shape = (a.size - window + 1, window)
strides = (a.itemsize, a.itemsize)
return stride_tricks.as_strided(a, shape=shape, strides=strides)
Z = rolling(np.arange(10), 3)
print(Z)
[[0 1 2]
[1 2 3]
[2 3 4]
[3 4 5]
[4 5 6]
[5 6 7]
[6 7 8]
[7 8 9]]
77. 如何否定布尔值，或改变浮点数的符号？ (★★★)
# Author: Nathaniel J. Smith
Z = np.random.randint(0,2,100)
np.logical_not(Z, out=Z)
Z = np.random.uniform(-1.0,1.0,100)
np.negative(Z, out=Z)
array([ 5.e-01, 8.e-01, -4.e-01, 2.e-01,
6.e-01, -1.e-01, -4.e-04, 9.e-01,
-7.e-01, 3.e-01, 5.e-02, 5.0e-01,
-1.e-01, 2.e-01, 4.e-01, 9.e-01,
9.e-01, 8.e-01, -8.e-01, -8.e-01,
-1.e-01, 9.e-01, 6.e-01, -2.0e-01,
-1.e-01, -5.e-01, -9.e-01, -6.e-01,
6.e-01, -7.0e-01, 7.e-01, -3.e-01,
-1.0e-01, -4.e-01, 3.e-01, 1.0e-02,
1.0e-01, -6.e-01, 7.e-01, 7.0e-01,
6.e-01, 2.e-01, -4.e-01, 2.e-01,
7.e-01, -5.e-01, -2.e-01, 7.e-02,
-3.e-01, 2.e-01, 2.e-01, -2.e-01,
5.e-01, -5.e-01, -2.0e-01, 9.e-01,
8.00e-01, -3.e-01, -1.e-01, -2.e-01,
-3.e-01, 5.e-01, -6.e-01, -1.e-01,
-7.e-01, 5.e-01, 6.e-01, -4.e-02,
-5.e-01, -3.e-01, 2.e-02, -1.e-01,
2.e-02, -9.e-01, -3.e-01, -2.e-01,
-9.e-01, 2.e-01, 9.e-01, 5.e-01,
1.e-01, -3.e-01, 7.e-01, -5.e-02,
1.e-01, -9.e-02, 1.e-02, 3.e-01,
-2.e-01, 3.e-01, -4.e-01, 3.0e-01,
4.e-01, 3.e-01, 3.e-01, -1.e-01,
-8.e-01, -5.e-01, 7.e-01, 7.e-01])
78. 考虑2组点P0，P1描述线（2d）和点p，如何计算从p到每条线的距离i (P0[i],P1[i])? (★★★)
def distance(P0, P1, p):
T = P1 - P0
L = (T2).sum(axis=1)
U = -((P0[:,0]-p[...,0])*T[:,0] + (P0[:,1]-p[...,1])*T[:,1]) / L
U = U.reshape(len(U),1)
D = P0 + U*T - p
return np.sqrt((D2).sum(axis=1))
P0 = np.random.uniform(-10,10,(10,2))
P1 = np.random.uniform(-10,10,(10,2))
p = np.random.uniform(-10,10,( 1,2))
print(distance(P0, P1, p))
[ 6. 4. 6. 0.0 11. 10.
6. 2. 13. 12. ]
79. 考虑2组点P0，P1描述线（2d）和一组点P，如何计算从每个点j (P[j])到每条线的距离i (P0[i],P1[i])? (★★★)
# Author: Italmassov Kuanysh
# based on distance function from previous question
P0 = np.random.uniform(-10, 10, (10,2))
P1 = np.random.uniform(-10,10,(10,2))
p = np.random.uniform(-10, 10, (10,2))
print(np.array([distance(P0,P1,p_i) for p_i in p]))
[[ 0. 5. 3. 2.00 14. 5.
14. 9. 1. 8. ]
[ 9. 1. 4. 4. 5. 1.
5. 3. 7. 10.]
[ 0. 7. 0. 3. 15. 3.
14. 7. 1. 6.]
[14. 3. 0. 5. 1. 6.
0. 4. 13. 5.]
[ 7. 2. 10. 6. 7. 7.
8. 9. 3.0 15. ]
[ 4. 1. 5. 1. 11.0 4.
10. 8.0 1. 10.]
[18. 10.0 7. 12. 2. 1.
3. 0. 15. 13.]
[ 0. 11. 8.0 8. 16. 5.
14.00 0.0 1. 2.]
[ 1. 4. 3. 1. 13. 5.0
13. 8. 0. 9.]
[11. 2. 3.0 5. 4. 1.
3. 1.0 9. 8.]]
80. 考虑一个任意数组，编写一个函数，提取具有固定形状的子部分并以给定元素为中心（必要时使用“fill”值填充） (★★★)
# Author: Nicolas Rougier
Z = np.random.randint(0,10,(10,10))
shape = (5,5)
fill = 0
position = (1,1)
R = np.ones(shape, dtype=Z.dtype)*fill
P = np.array(list(position)).astype(int)
Rs = np.array(list(R.shape)).astype(int)
Zs = np.array(list(Z.shape)).astype(int)
R_start = np.zeros((len(shape),)).astype(int)
R_stop = np.array(list(shape)).astype(int)
Z_start = (P-Rs//2)
Z_stop = (P+Rs//2)+Rs%2
R_start = (R_start - np.minimum(Z_start,0)).tolist()
Z_start = (np.maximum(Z_start,0)).tolist()
R_stop = np.maximum(R_start, (R_stop - np.maximum(Z_stop-Zs,0))).tolist()
Z_stop = (np.minimum(Z_stop,Zs)).tolist()
r = [slice(start,stop) for start,stop in zip(R_start,R_stop)]
z = [slice(start,stop) for start,stop in zip(Z_start,Z_stop)]
R[r] = Z[z]
print(Z)
print(R)
[[8 3 9 2 0 9 1 1 1 4]
[9 3 2 2 1 3 8 7 1 9]
[1 5 6 6 3 5 0 9 5 5]
[3 6 4 9 7 8 6 1 6 5]
[7 9 3 9 9 1 8 9 6 9]
[9 0 3 0 7 4 9 7 2 9]
[8 1 9 9 8 9 2 9 9 0]
[2 5 4 4 7 1 0 0 1 1]
[9 9 0 4 8 2 3 4 1 1]
[3 5 6 4 5 2 7 5 1 0]]
[[0 0 0 0 0]
[0 8 3 9 2]
[0 9 3 2 2]
[0 1 5 6 6]
[0 3 6 4 9]]
81. 考虑一个数组 Z = [1,2,3,4,5,6,7,8,9,10,11,12,13,14], 如何生成一个数组 R = [[1,2,3,4], [2,3,4,5], [3,4,5,6], ..., [11,12,13,14]]?
# Author: Stefan van der Walt
Z = np.arange(1,15,dtype=np.uint32)
R = stride_tricks.as_strided(Z,(11,4),(4,4))
print(R)
[[ 1 2 3 4]
[ 2 3 4 5]
[ 3 4 5 6]
[ 4 5 6 7]
[ 5 6 7 8]
[ 6 7 8 9]
[ 7 8 9 10]
[ 8 9 10 11]
[ 9 10 11 12]
[10 11 12 13]
[11 12 13 14]]
82. 计算矩阵排名(★★★)
# Author: Stefan van der Walt
Z = np.random.uniform(0,1,(10,10))
U, S, V = np.linalg.svd(Z) # Singular Value Decomposition
rank = np.sum(S > 1e-10)
print(rank)
10
83. 如何在数组中找到最常见的值？
Z = np.random.randint(0,10,50)
print(np.bincount(Z).argmax())
8
84. 从随机10x10矩阵中提取所有连续的3x3块(★★★)
# Author: Chris Barker
Z = np.random.randint(0,5,(10,10))
n = 3
i = 1 + (Z.shape[0]-3)
j = 1 + (Z.shape[1]-3)
C = stride_tricks.as_strided(Z, shape=(i, j, n, n), strides=Z.strides + Z.strides)
print(C)
[[[[2 2 2]
[0 4 0]
[3 4 3]]
[[2 2 0]
[4 0 2]
[4 3 4]]
[[2 0 4]
[0 2 2]
[3 4 0]]
[[0 4 1]
[2 2 4]
[4 0 1]]
[[4 1 2]
[2 4 0]
[0 1 2]]
[[1 2 3]
[4 0 1]
[1 2 1]]
[[2 3 3]
[0 1 4]
[2 1 1]]
[[3 3 2]
[1 4 1]
[1 1 4]]]
[[[0 4 0]
[3 4 3]
[3 4 0]]
[[4 0 2]
[4 3 4]
[4 0 0]]
[[0 2 2]
[3 4 0]
[0 0 3]]
[[2 2 4]
[4 0 1]
[0 3 0]]
[[2 4 0]
[0 1 2]
[3 0 3]]
[[4 0 1]
[1 2 1]
[0 3 4]]
[[0 1 4]
[2 1 1]
[3 4 3]]
[[1 4 1]
[1 1 4]
[4 3 0]]]
[[[3 4 3]
[3 4 0]
[2 4 1]]
[[4 3 4]
[4 0 0]
[4 1 2]]
[[3 4 0]
[0 0 3]
[1 2 0]]
[[4 0 1]
[0 3 0]
[2 0 2]]
[[0 1 2]
[3 0 3]
[0 2 0]]
[[1 2 1]
[0 3 4]
[2 0 4]]
[[2 1 1]
[3 4 3]
[0 4 3]]
[[1 1 4]
[4 3 0]
[4 3 2]]]
[[[3 4 0]
[2 4 1]
[4 0 2]]
[[4 0 0]
[4 1 2]
[0 2 0]]
[[0 0 3]
[1 2 0]
[2 0 2]]
[[0 3 0]
[2 0 2]
[0 2 4]]
[[3 0 3]
[0 2 0]
[2 4 4]]
[[0 3 4]
[2 0 4]
[4 4 0]]
[[3 4 3]
[0 4 3]
[4 0 0]]
[[4 3 0]
[4 3 2]
[0 0 4]]]
[[[2 4 1]
[4 0 2]
[2 2 3]]
[[4 1 2]
[0 2 0]
[2 3 4]]
[[1 2 0]
[2 0 2]
[3 4 0]]
[[2 0 2]
[0 2 4]
[4 0 2]]
[[0 2 0]
[2 4 4]
[0 2 2]]
[[2 0 4]
[4 4 0]
[2 2 4]]
[[0 4 3]
[4 0 0]
[2 4 4]]
[[4 3 2]
[0 0 4]
[4 4 0]]]
[[[4 0 2]
[2 2 3]
[4 4 2]]
[[0 2 0]
[2 3 4]
[4 2 2]]
[[2 0 2]
[3 4 0]
[2 2 1]]
[[0 2 4]
[4 0 2]
[2 1 1]]
[[2 4 4]
[0 2 2]
[1 1 3]]
[[4 4 0]
[2 2 4]
[1 3 4]]
[[4 0 0]
[2 4 4]
[3 4 3]]
[[0 0 4]
[4 4 0]
[4 3 1]]]
[[[2 2 3]
[4 4 2]
[0 4 2]]
[[2 3 4]
[4 2 2]
[4 2 1]]
[[3 4 0]
[2 2 1]
[2 1 0]]
[[4 0 2]
[2 1 1]
[1 0 2]]
[[0 2 2]
[1 1 3]
[0 2 4]]
[[2 2 4]
[1 3 4]
[2 4 1]]
[[2 4 4]
[3 4 3]
[4 1 0]]
[[4 4 0]
[4 3 1]
[1 0 1]]]
[[[4 4 2]
[0 4 2]
[0 2 2]]
[[4 2 2]
[4 2 1]
[2 2 3]]
[[2 2 1]
[2 1 0]
[2 3 3]]
[[2 1 1]
[1 0 2]
[3 3 0]]
[[1 1 3]
[0 2 4]
[3 0 0]]
[[1 3 4]
[2 4 1]
[0 0 2]]
[[3 4 3]
[4 1 0]
[0 2 1]]
[[4 3 1]
[1 0 1]
[2 1 3]]]]
85. 创建一个二维数组子类，使 Z[i,j] == Z[j,i]
# Author: Eric O. Lebigot
# Note: only works for 2d array and value setting using indices
class Symetric(np.ndarray):
def __setitem__(self, index, value):
i,j = index
super(Symetric, self).__setitem__((i,j), value)
super(Symetric, self).__setitem__((j,i), value)
def symetric(Z):
return np.asarray(Z + Z.T - np.diag(Z.diagonal())).view(Symetric)
S = symetric(np.random.randint(0,10,(5,5)))
S[2,3] = 42
print(S)
[[ 3 10 4 5 5]
[10 1 8 13 9]
[ 4 8 6 42 16]
[ 5 13 42 5 3]
[ 5 9 16 3 9]]
86. 考虑一组具有形状（n，n）的p矩阵和一组具有形状（n，1）的p向量。 如何一次计算p矩阵乘积的总和？ （结果有形状（n，1）） (★★★)
# Author: Stefan van der Walt
p, n = 10, 20
M = np.ones((p,n,n))
V = np.ones((p,n,1))
S = np.tensordot(M, V, axes=[[0, 2], [0, 1]])
print(S)
# It works, because:
# M is (p,n,n)
# V is (p,n,1)
# Thus, summing over the paired axes 0 and 0 (of M and V independently),
# and 2 and 1, to remain with a (n,1) vector.
[[200.]
[200.]
[200.]
[200.]
[200.]
[200.]
[200.]
[200.]
[200.]
[200.]
[200.]
[200.]
[200.]
[200.]
[200.]
[200.]
[200.]
[200.]
[200.]
[200.]]
87. 考虑一个16x16阵列，如何获得块总和（块大小为4x4）？ (★★★)
# Author: Robert Kern
Z = np.ones((16,16))
k = 4
S = np.add.reduceat(np.add.reduceat(Z, np.arange(0, Z.shape[0], k), axis=0),
np.arange(0, Z.shape[1], k), axis=1)
print(S)
[[16. 16. 16. 16.]
[16. 16. 16. 16.]
[16. 16. 16. 16.]
[16. 16. 16. 16.]]
88. 如何使用numpy数组实现游戏生命？ (★★★)
# Author: Nicolas Rougier
def iterate(Z):
# Count neighbours
N = (Z[0:-2,0:-2] + Z[0:-2,1:-1] + Z[0:-2,2:] +
Z[1:-1,0:-2] + Z[1:-1,2:] +
Z[2: ,0:-2] + Z[2: ,1:-1] + Z[2: ,2:])
# Apply rules
birth = (N==3) & (Z[1:-1,1:-1]==0)
survive = ((N==2) | (N==3)) & (Z[1:-1,1:-1]==1)
Z[...] = 0
Z[1:-1,1:-1][birth | survive] = 1
return Z
Z = np.random.randint(0,2,(50,50))
for i in range(100): Z = iterate(Z)
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]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 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 1 1 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 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 1 1 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 1 0 1 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 1 0 0 0 1 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 1 1 0 0 0 1 0 1 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 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 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 1 0 0 1 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 1 1 0 0 0
0 0 0 0 0 0 0 1 1 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 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 1 1 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 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 0 1 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 1 1 1 1 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 1 1 1 1 1 0 0 0 0 0 0 0 0 1 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 1 1 0 0 0 1 1 0 0 0 0 0 0 1 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 1 1 0 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0 0 0 0 0]
[0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 0 1 1 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 1 0 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 1 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 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 1 0]
[0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 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 1 1 0 0]
[0 0 0 0 1 1 1 0 0 1 0 0 0 1 1 1 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 1 0 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1
0 0 0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1
0 0 0 0 0 0 0 0 0 1 1 0 0 0]
[0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 1 0 1 0 0 1 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 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 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 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 1 0 0 1 1 0 0 0 0]
[0 0 0 0 0 0 0 1 1 1 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 1 1 1 0 0 1 1 1 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 1 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 1 1 0 0 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 1 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 1 0 0 1 1 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 1 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 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 1 0 0 1 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 1 0 1 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 1 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]]
89. 如何获取数组的n个最大值 (★★★)
Z = np.arange(10000)
np.random.shuffle(Z)
n = 5
# Slow
print (Z[np.argsort(Z)[-n:]])
# Fast
print (Z[np.argpartition(-Z,n)[:n]])
[9995 9996 9997 9998 9999]
[9997 9999 9998 9996 9995]
90. 给定任意数量的向量，构建笛卡尔积（每个项的每个组合） (★★★)
# Author: Stefan Van der Walt
def cartesian(arrays):
arrays = [np.asarray(a) for a in arrays]
shape = (len(x) for x in arrays)
ix = np.indices(shape, dtype=int)
ix = ix.reshape(len(arrays), -1).T
for n, arr in enumerate(arrays):
ix[:, n] = arrays[n][ix[:, n]]
return ix
print (cartesian(([1, 2, 3], [4, 5], [6, 7])))
[[1 4 6]
[1 4 7]
[1 5 6]
[1 5 7]
[2 4 6]
[2 4 7]
[2 5 6]
[2 5 7]
[3 4 6]
[3 4 7]
[3 5 6]
[3 5 7]]
91. 如何从常规数组创建记录数组？ (★★★)
Z = np.array([("Hello", 2.5, 3),
("World", 3.6, 2)])
R = np.core.records.fromarrays(Z.T,
names='col1, col2, col3',
formats = 'S8, f8, i8')
print(R)
[(b'Hello', 2.5, 3) (b'World', 3.6, 2)]
92. 考虑一个大的向量Z，使用3种不同的方法将Z计算为3的幂 (★★★)
# Author: Ryan G.
x = np.random.rand(int(5e7))
%timeit np.power(x,3)
%timeit x*x*x
%timeit np.einsum('i,i,i->i',x,x,x)
1.26 s ± 38.6 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
171 ms ± 31.1 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
288 ms ± 27.2 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
93. 考虑形状 (8,3) 和 (2,2) 的两个阵列A和B. 如何查找包含B的每一行元素的A行，而不管B中元素的顺序如何？ (★★★)
# Author: Gabe Schwartz
A = np.random.randint(0,5,(8,3))
B = np.random.randint(0,5,(2,2))
C = (A[..., np.newaxis, np.newaxis] == B)
rows = np.where(C.any((3,1)).all(1))[0]
print(rows)
[0 5 6]
94. 考虑10x3矩阵，提取具有不等值的行 (e.g. [2,2,3]) (★★★)
# Author: Robert Kern
Z = np.random.randint(0,5,(10,3))
print(Z)
# solution for arrays of all dtypes (including string arrays and record arrays)
E = np.all(Z[:,1:] == Z[:,:-1], axis=1)
U = Z[~E]
print(U)
# soluiton for numerical arrays only, will work for any number of columns in Z
U = Z[Z.max(axis=1) != Z.min(axis=1),:]
print(U)
[[1 0 1]
[1 3 3]
[2 0 3]
[0 0 4]
[4 1 1]
[2 3 4]
[0 0 1]
[1 0 3]
[2 1 1]
[3 1 2]]
[[1 0 1]
[1 3 3]
[2 0 3]
[0 0 4]
[4 1 1]
[2 3 4]
[0 0 1]
[1 0 3]
[2 1 1]
[3 1 2]]
[[1 0 1]
[1 3 3]
[2 0 3]
[0 0 4]
[4 1 1]
[2 3 4]
[0 0 1]
[1 0 3]
[2 1 1]
[3 1 2]]
95. 将int的向量转换为矩阵二进制表示 (★★★)
# Author: Warren Weckesser
I = np.array([0, 1, 2, 3, 15, 16, 32, 64, 128])
B = ((I.reshape(-1,1) & (2np.arange(8))) != 0).astype(int)
print(B[:,::-1])
# Author: Daniel T. McDonald
I = np.array([0, 1, 2, 3, 15, 16, 32, 64, 128], dtype=np.uint8)
print(np.unpackbits(I[:, np.newaxis], axis=1))
[[0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 1 1]
[0 0 0 0 1 1 1 1]
[0 0 0 1 0 0 0 0]
[0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0]
[1 0 0 0 0 0 0 0]]
[[0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 1 1]
[0 0 0 0 1 1 1 1]
[0 0 0 1 0 0 0 0]
[0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0]
[1 0 0 0 0 0 0 0]]
96. 给定一个二维数组，如何提取唯一的行？(★★★)
# Author: Jaime Fernández del Río
Z = np.random.randint(0,2,(6,3))
T = np.ascontiguousarray(Z).view(np.dtype((np.void, Z.dtype.itemsize * Z.shape[1])))
_, idx = np.unique(T, return_index=True)
uZ = Z[idx]
print(uZ)
[[0 0 1]
[0 1 1]
[1 0 0]
[1 1 1]]
97. 考虑2个向量A & B，写出einsum等效的inner，outer，sum和mul函数(★★★)
# Author: Alex Riley
# Make sure to read: http://ajcr.net/Basic-guide-to-einsum/
A = np.random.uniform(0,1,10)
B = np.random.uniform(0,1,10)
np.einsum('i->', A) # np.sum(A)
np.einsum('i,i->i', A, B) # A * B
np.einsum('i,i', A, B) # np.inner(A, B)
np.einsum('i,j->ij', A, B) # np.outer(A, B)
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, 0.047382 , 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],
[0.0040046 , 0.00, 0.0, 0.00, 0.0,
0.0066891 , 0.00, 0.0, 0.0 , 0.0 ],
[0., 0., 0., 0.0, 0.,
0., 0., 0., 0., 0.]])
98. 考虑两个矢量(X,Y)描述的路径，如何使用等距样本对其进行采样 (★★★)?
# Author: Bas Swinckels
phi = np.arange(0, 10*np.pi, 0.1)
a = 1
x = a*phi*np.cos(phi)
y = a*phi*np.sin(phi)
dr = (np.diff(x)2 + np.diff(y)2).5 # segment lengths
r = np.zeros_like(x)
r[1:] = np.cumsum(dr) # integrate path
r_int = np.linspace(0, r.max(), 200) # regular spaced path
x_int = np.interp(r_int, r, x) # integrate path
y_int = np.interp(r_int, r, y)
99. 给定整数n和2D数组X，从X中选择可以解释为具有n度的多项分布的绘制的行，即，仅包含整数并且总和为n的行。 (★★★)
# Author: Evgeni Burovski
X = np.asarray([[1.0, 0.0, 3.0, 8.0],
[2.0, 0.0, 1.0, 1.0],
[1.5, 2.5, 1.0, 0.0]])
n = 4
M = np.logical_and.reduce(np.mod(X, 1) == 0, axis=-1)
M &= (X.sum(axis=-1) == n)
print(X[M])
[[2. 0. 1. 1.]]
100. 计算一维阵列X的平均值的自举95％置信区间（即，重新采样具有替换N次的阵列的元素，计算每个样本的平均值，然后计算均值上的百分位数）。(★★★)
# Author: Jessica B. Hamrick
X = np.random.randn(100) # random 1D array
N = 1000 # number of bootstrap samples
idx = np.random.randint(0, X.size, (N, X.size))
means = X[idx].mean(axis=1)
confint = np.percentile(means, [2.5, 97.5])
print(confint)
[-0. 0.]
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