(넘파이) 100_numpy_exercises

95 minute read

100 numpy exercises

This is a collection of exercises that have been collected in the numpy mailing list, on stack overflow and in the numpy documentation. The goal of this collection is to offer a quick reference for both old and new users but also to provide a set of exercises for those who teach.

If you find an error or think you’ve a better way to solve some of them, feel free to open an issue at https://github.com/rougier/numpy-100.

File automatically generated. See the documentation to update questions/answers/hints programmatically.

Run the initialize.py module, then for each question you can query the answer or an hint with hint(n) or answer(n) for n question number.

pip install mdutils

Requirement already satisfied: mdutils in c:\anaconda\envs\test3\lib\site-packages (1.3.0)Note: you may need to restart the kernel to use updated packages.

%run initialise.py

1. Import the numpy package under the name `np` (★☆☆)

import numpy as np

2. Print the numpy version and the configuration (★☆☆)

print(np.__version__)
np.show_config()

1.16.4
mkl_info:
    libraries = ['mkl_rt']
    library_dirs = ['C:/anaconda/envs/test3\\Library\\lib']
    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
    include_dirs = ['C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2019.0.117\\windows\\mkl', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2019.0.117\\windows\\mkl\\include', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2019.0.117\\windows\\mkl\\lib', 'C:/anaconda/envs/test3\\Library\\include']
blas_mkl_info:
    libraries = ['mkl_rt']
    library_dirs = ['C:/anaconda/envs/test3\\Library\\lib']
    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
    include_dirs = ['C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2019.0.117\\windows\\mkl', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2019.0.117\\windows\\mkl\\include', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2019.0.117\\windows\\mkl\\lib', 'C:/anaconda/envs/test3\\Library\\include']
blas_opt_info:
    libraries = ['mkl_rt']
    library_dirs = ['C:/anaconda/envs/test3\\Library\\lib']
    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
    include_dirs = ['C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2019.0.117\\windows\\mkl', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2019.0.117\\windows\\mkl\\include', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2019.0.117\\windows\\mkl\\lib', 'C:/anaconda/envs/test3\\Library\\include']
lapack_mkl_info:
    libraries = ['mkl_rt']
    library_dirs = ['C:/anaconda/envs/test3\\Library\\lib']
    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
    include_dirs = ['C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2019.0.117\\windows\\mkl', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2019.0.117\\windows\\mkl\\include', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2019.0.117\\windows\\mkl\\lib', 'C:/anaconda/envs/test3\\Library\\include']
lapack_opt_info:
    libraries = ['mkl_rt']
    library_dirs = ['C:/anaconda/envs/test3\\Library\\lib']
    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
    include_dirs = ['C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2019.0.117\\windows\\mkl', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2019.0.117\\windows\\mkl\\include', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2019.0.117\\windows\\mkl\\lib', 'C:/anaconda/envs/test3\\Library\\include']

3. Create a null vector of size 10 (★☆☆)

null = np.zeros(10)
print(null)

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

4. How to find the memory size of any array (★☆☆)

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

80 bytes

5. How to get the documentation of the numpy add function from the command line? (★☆☆)

%run python -c "import numpy; http://numpy.info(numpy.add)"

6. Create a null vector of size 10 but the fifth value which is 1 (★☆☆)

null = np.zeros(10)
null[4] = 1
print(null)

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

7. Create a vector with values ranging from 10 to 49 (★☆☆)

A = np.arange(10,50)
print(A)

[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. Reverse a vector (first element becomes last) (★☆☆)

revA = A[::-1]
print(revA)

[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. Create a 3x3 matrix with values ranging from 0 to 8 (★☆☆)

B = np.arange(9).reshape(3,3)
print(B)

[[0 1 2]
 [3 4 5]
 [6 7 8]]

10. Find indices of non-zero elements from [1,2,0,0,4,0] (★☆☆)

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

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

11. Create a 3x3 identity matrix (★☆☆)

D = np.eye(3,3)
print(D)

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

12. Create a 3x3x3 array with random values (★☆☆)

E = np.random.random((3,3,3))
print(E)

[[[0.88955393 0.98112763 0.46640694]
  [0.0579536  0.73861599 0.41378595]
  [0.32624121 0.82390778 0.57127886]]

 [[0.51582513 0.72181427 0.30160183]
  [0.47112808 0.21488492 0.42788323]
  [0.52347864 0.44673036 0.71306405]]

 [[0.83378212 0.39816917 0.1342307 ]
  [0.48785532 0.1660874  0.73683994]
  [0.28179303 0.84379035 0.78937268]]]

13. Create a 10x10 array with random values and find the minimum and maximum values (★☆☆)

F = np.random.random((10,10))
print("Minimum: ", F.min())
print("Maximum: ", F.max())

Minimum:  0.009520292609272674
Maximum:  0.9959038892108142

14. Create a random vector of size 30 and find the mean value (★☆☆)

G = np.random.random((30))
print("Mean Value: ", G.mean())

Mean Value:  0.5404396263808025

15. Create a 2d array with 1 on the border and 0 inside (★☆☆)

H = np.ones((3,3))
H[1:-1, 1:-1] = 0
print(H)

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

16. How to add a border (filled with 0’s) around an existing array? (★☆☆)

H = np.pad(H, pad_width=1, mode='constant', constant_values=0)
print(H)

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

17. What is the result of the following expression? (★☆☆)

0 * np.nan
np.nan == np.nan
np.inf > np.nan
np.nan - np.nan
np.nan in set([np.nan])
0.3 == 3 * 0.1

print(0 * np.nan)
print(np.nan == np.nan)
print(np.inf > np.nan)
print(np.nan - np.nan)
print(np.nan in set([np.nan]))
print(0.3 == 3 * 0.1)

nan
False
False
nan
True
False

18. Create a 5x5 matrix with values 1,2,3,4 just below the diagonal (★☆☆)

I = np.diag(1+np.arange(4), k=-1)
print(I)

[[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. Create a 8x8 matrix and fill it with a checkerboard pattern (★☆☆)

J = np.zeros((8,8),dtype=int)
J[1::2,::2] = 1
J[::2,1::2] = 1
print(J)

[[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. Consider a (6,7,8) shape array, what is the index (x,y,z) of the 100th element?

print(np.unravel_index(99,(6,7,8)))

(1, 5, 3)

21. Create a checkerboard 8x8 matrix using the tile function (★☆☆)

K = np.tile(np.array([[0,1],[1,0]]), (4,4))
print(K)

[[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. Normalize a 5x5 random matrix (★☆☆)

L = np.random.random((5,5))
normal = (L-np.mean(L)) / (np.std(L))
print(normal)

[[ 1.13778282 -0.70827067  0.06760223 -0.62703166  0.93941535]
 [ 1.56049203 -1.14490728 -0.96309582 -0.95953784  1.95886235]
 [ 0.20738374 -1.20366983  0.90856391  0.87263304  0.05733884]
 [-1.48357459  0.95218281 -1.39065995 -1.35269869  0.07898545]
 [ 0.60931897  1.32125095 -0.00665355 -0.60241605 -0.22929656]]

23. Create a custom dtype that describes a color as four unsigned bytes (RGBA) (★☆☆)

color = np.dtype([("R", np.ubyte, 1),
                  ("G", np.ubyte, 1),
                  ("B", np.ubyte, 1),
                  ("A", np.ubyte, 1)])
print(color)

[('R', 'u1'), ('G', 'u1'), ('B', 'u1'), ('A', 'u1')]

24. Multiply a 5x3 matrix by a 3x2 matrix (real matrix product) (★☆☆)

M = np.dot(np.ones((5,3)), np.ones((3,2)))
print(M)

[[3. 3.]
 [3. 3.]
 [3. 3.]
 [3. 3.]
 [3. 3.]]

25. Given a 1D array, negate all elements which are between 3 and 8, in place. (★☆☆)

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

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

26. What is the output of the following script? (★☆☆)

# Author: Jake VanderPlas

print(sum(range(5),-1))
from numpy import *
print(sum(range(5),-1))

print(sum(range(5),-1))
from numpy import *
print(sum(range(5),-1))

9
10

27. Consider an integer vector Z, which of these expressions are legal? (★☆☆)

Z**Z
2 << Z >> 2
Z <- Z
1j*Z
Z/1/1
Z<Z>Z

Z=np.ones((3,3))
print(Z**Z) #legal

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

print(2 << Z >> 2)

---------------------------------------------------------------------------

TypeError                                 Traceback (most recent call last)

<ipython-input-42-7913fb4e850f> in <module>
----> 1 print(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''

print(Z <- Z) #legal

[[False False False]
 [False False False]
 [False False False]]

print(1j*Z) #legal

[[0.+1.j 0.+1.j 0.+1.j]
 [0.+1.j 0.+1.j 0.+1.j]
 [0.+1.j 0.+1.j 0.+1.j]]

print(Z/1/1) #legal

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

print(Z<Z>Z)

---------------------------------------------------------------------------

ValueError                                Traceback (most recent call last)

<ipython-input-46-20f36d1d6fd9> in <module>
----> 1 print(Z<Z>Z)

ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

28. What are the result of the following expressions?

np.array(0) / np.array(0)
np.array(0) // np.array(0)
np.array([np.nan]).astype(int).astype(float)

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
[-2.14748365e+09]


C:\anaconda\envs\test3\lib\site-packages\ipykernel_launcher.py:1: RuntimeWarning: invalid value encountered in true_divide
  """Entry point for launching an IPython kernel.
C:\anaconda\envs\test3\lib\site-packages\ipykernel_launcher.py:2: RuntimeWarning: divide by zero encountered in floor_divide

29. How to round away from zero a float array ? (★☆☆)

O = np.random.uniform(-10,+10,10)

print(np.copysign(np.ceil(np.abs(O)), O))

[ -6.  -6.   3.   9.   4. -10.  -6.  -1.  -1.  -6.]

30. How to find common values between two arrays? (★☆☆)

P1 = np.random.randint(0,10,10)
P2 = np.random.randint(0,10,10)
print(np.intersect1d(P1,P2))

[0 2 4 7]

31. How to ignore all numpy warnings (not recommended)? (★☆☆)

defaults = np.seterr(all="ignore")
Q = np.ones(1) / 0

_ = np.seterr(**defaults)

with np.errstate(all="ignore"):
    np.arange(3) / 0

32. Is the following expressions true? (★☆☆)

np.sqrt(-1) == np.emath.sqrt(-1)

np.sqrt(-1) == np.emath.sqrt(-1) #False

C:\anaconda\envs\test3\lib\site-packages\ipykernel_launcher.py:1: RuntimeWarning: invalid value encountered in sqrt
  """Entry point for launching an IPython kernel.

False

33. How to get the dates of yesterday, today and tomorrow? (★☆☆)

yesterday = np.datetime64('today') - np.timedelta64(1)
today = np.datetime64('today')
tomorrow = np.datetime64('today') + np.timedelta64(1)

print(yesterday)
print(today)
print(tomorrow)

2021-03-17
2021-03-18
2021-03-19

34. How to get all the dates corresponding to the month of July 2016? (★★☆)

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

['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. How to compute ((A+B)*(-A/2)) in place (without copy)? (★★☆)

A = np.ones(3)*1
B = np.ones(3)*2
C = np.ones(3)*3

np.add(A,B,out=B)
np.negative(A,out=A)
np.divide(A,2,out=A)
print(np.multiply(A,B))

[-1.5 -1.5 -1.5]

36. Extract the integer part of a random array of positive numbers using 4 different methods (★★☆)

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

print(S.astype(int))
print(S - S%1)
print(S//1)
print(np.trunc(S))

[6 3 0 5 3 1 9 2 5 7]
[6. 3. 0. 5. 3. 1. 9. 2. 5. 7.]
[6. 3. 0. 5. 3. 1. 9. 2. 5. 7.]
[6. 3. 0. 5. 3. 1. 9. 2. 5. 7.]

37. Create a 5x5 matrix with row values ranging from 0 to 4 (★★☆)

T = np.zeros((5,5))
T += np.arange(5)
print(T)

[[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. Consider a generator function that generates 10 integers and use it to build an array (★☆☆)

def generator():
    for n in range(15):
        yield n
U = np.fromiter(generator(), dtype=float, count=-1)
print("New array:")
print(U)

New array:
[ 0.  1.  2.  3.  4.  5.  6.  7.  8.  9. 10. 11. 12. 13. 14.]

39. Create a vector of size 10 with values ranging from 0 to 1, both excluded (★★☆)

V = np.linspace(0,1,11, endpoint=False)[1:]
print(V)

[0.09090909 0.18181818 0.27272727 0.36363636 0.45454545 0.54545455
 0.63636364 0.72727273 0.81818182 0.90909091]

40. Create a random vector of size 10 and sort it (★★☆)

W = np.random.random(10)
W.sort()
print(W)

[0.5584296  0.61552445 0.61715017 0.63253334 0.64167466 0.88979863
 0.95315703 0.99116861 0.99556807 0.9996095 ]

41. How to sum a small array faster than np.sum? (★★☆)

import timeit

x = range(10)

def pure_sum():
    return sum(x)

def numpy_sum():
    return np.sum(x)

n = 10

t1 = timeit.timeit(pure_sum, number = n)
print('Pure Python Sum:', t1)
t2 = timeit.timeit(numpy_sum, number = n)
print('Numpy Sum:', t2)

Pure Python Sum: 0.0002090000002681336
Numpy Sum: 0.00012800000013157842

42. Consider two random array A and B, check if they are equal (★★☆)

A = np.random.randint(0,2,5)
B = np.random.randint(0,2,5)

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

False

43. Make an array immutable (read-only) (★★☆)

Y = np.zeros(10)
Y.flags.writeable = False
Y[0] = 1 #False b/c it's read-only

---------------------------------------------------------------------------

ValueError                                Traceback (most recent call last)

<ipython-input-95-3f51ce5e8326> in <module>
      1 Y = np.zeros(10)
      2 Y.flags.writeable = False
----> 3 Y[0] = 1 #False b/c it's read-only


ValueError: assignment destination is read-only

44. Consider a random 10x2 matrix representing cartesian coordinates, convert them to polar coordinates (★★☆)

Z = np.random.random((10,2))
X,Y = Z[:,0], Z[:,1] #cartesian coordinates

#polar coordinates
r = np.sqrt(X**2+Y**2)
t = np.arctan2(Y,X)
print(r)
print(t)

[0.52876165 0.76571798 0.3440532  0.78717041 0.75241364 0.46443636
 0.15386324 0.50034923 0.78066439 0.71660423]
[0.61278737 0.28355119 1.31721709 1.23009356 0.30895321 0.86647182
 0.17920324 0.53640291 1.1402757  0.34880996]

45. Create random vector of size 10 and replace the maximum value by 0 (★★☆)

AA = np.random.random(10)
AA[AA.argmax()] = 0 #maximum value=0
print(AA)

[0.60039572 0.31895738 0.         0.63321949 0.3610798  0.6650984
 0.07804473 0.63399538 0.31730633 0.17490917]

46. Create a structured array with `x` and `y` coordinates covering the [0,1]x[0,1] area (★★☆)

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

[[(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. Given two arrays, X and Y, construct the Cauchy matrix C (Cij =1/(xi - yj))

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

[[-2.         -0.66666667 -0.4        -0.28571429 -0.22222222 -0.18181818
  -0.15384615 -0.13333333]
 [ 2.         -2.         -0.66666667 -0.4        -0.28571429 -0.22222222
  -0.18181818 -0.15384615]
 [ 0.66666667  2.         -2.         -0.66666667 -0.4        -0.28571429
  -0.22222222 -0.18181818]
 [ 0.4         0.66666667  2.         -2.         -0.66666667 -0.4
  -0.28571429 -0.22222222]
 [ 0.28571429  0.4         0.66666667  2.         -2.         -0.66666667
  -0.4        -0.28571429]
 [ 0.22222222  0.28571429  0.4         0.66666667  2.         -2.
  -0.66666667 -0.4       ]
 [ 0.18181818  0.22222222  0.28571429  0.4         0.66666667  2.
  -2.         -0.66666667]
 [ 0.15384615  0.18181818  0.22222222  0.28571429  0.4         0.66666667
   2.         -2.        ]]
3638.1636371179666

48. Print the minimum and maximum representable value for each numpy scalar type (★★☆)

for dtype in [np.int8, np.int32, np.int64]:
    print(np.iinfo(dtype).min)
    print(np.iinfo(dtype).max)

-128
127
-2147483648
2147483647
-9223372036854775808
9223372036854775807

49. How to print all the values of an array? (★★☆)

np.set_printoptions(threshold=float("inf"))
CC = np.zeros((10,10))
print(CC)

[[0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 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. How to find the closest value (to a given scalar) in a vector? (★★☆)

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

51. Create a structured array representing a position (x,y) and a color (r,g,b) (★★☆)

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

[((1., 1.), (1., 1., 1.)) ((1., 1.), (1., 1., 1.))
 ((1., 1.), (1., 1., 1.)) ((1., 1.), (1., 1., 1.))
 ((1., 1.), (1., 1., 1.)) ((1., 1.), (1., 1., 1.))
 ((1., 1.), (1., 1., 1.)) ((1., 1.), (1., 1., 1.))
 ((1., 1.), (1., 1., 1.)) ((1., 1.), (1., 1., 1.))]

52. Consider a random vector with shape (100,2) representing coordinates, find point by point distances (★★☆)

FF = np.random.random((100,2))
X,Y = np.atleast_2d(FF[:,0], FF[:,1])
dist = np.sqrt( (X-X.T)**2 + (Y-Y.T)**2)
print(dist)

[[0.         0.91854126 0.44995083 0.43690496 0.53557062 0.8089086
26371791 0.50149768 0.48143974 0.27536152 0.94079421 0.55587673
12572354 0.14916603 0.87482577 0.83404339 0.62458091 0.99277894
46138186 0.69389721 0.62048006 0.73102603 0.99089598 0.01899664
47857725 0.87209275 0.73736255 0.47852969 0.95982844 0.949522
84013565 0.237863   0.71316254 0.96184572 0.44410298 0.7686839
52506073 0.44510861 0.18455109 0.48331246 0.76920867 0.603923
42434667 0.07473332 0.39638668 0.79487484 0.79685475 0.17861037
62781959 0.5063502  0.94798491 0.71747491 0.22745595 0.87924405
19043443 0.63890733 0.3401459  0.08542128 0.9677003  0.65457805
79748203 0.5597721  0.25851529 0.04025251 0.6582398  0.05696231
44790438 0.63455942 0.62989905 0.80393708 0.67132107 0.06409746
4842931  1.12365258 0.22957671 0.62721207 0.51719004 0.6354869
25107651 0.23196116 0.86181871 0.86127632 0.17192532 0.5449139
77426494 0.81591414 0.90621223 0.82990998 0.477394   0.66801588
55354684 0.39666186 0.86614298 0.3583906  0.75628932 0.3377061
7312605  0.15469025 0.63639499 0.26363147]
 [0.91854126 0.         0.49761057 0.61344787 0.40586638 0.4470463
77595231 0.49434227 0.61094385 0.78088818 0.045303   0.38302368
80096858 0.86071772 0.22743494 0.15811871 0.63979271 0.26264512
59679352 0.68103247 0.44721724 0.41137395 0.2953584  0.92501129
48781223 0.54673092 0.20581628 0.450617   0.08638827 0.38261408
25853903 0.91529677 0.3359363  0.39772805 0.47807209 0.58904707
60746625 0.54514064 0.87714066 0.49696294 0.60010903 0.95097425
49717856 0.85259491 0.54301268 0.21234155 0.59285161 1.03237914
5171555  0.44755718 0.43790083 0.20155891 0.79962459 0.58494091
72814396 0.77223738 0.76803769 0.83656358 0.51052279 0.51959816
6146094  0.38964763 0.90647141 0.87924314 0.28953701 0.86158581
49770576 0.32598877 0.56203358 0.47517078 0.87772227 0.92694751
67907566 0.36957236 0.88845673 0.34060025 0.86790601 0.28574433
9060904  0.79479134 0.5886902  0.21098747 0.80047281 0.58081063
36126574 0.16856414 0.47264938 0.39476834 0.5638906  0.28119458
65152829 0.94033057 0.55947894 0.56150033 0.45097929 0.6433421
21839209 0.92166002 0.83338997 0.81856525]
 [0.44995083 0.49761057 0.         0.37404341 0.09212924 0.57785371
27887906 0.08128147 0.18409816 0.28477814 0.5288305  0.11480725
35322751 0.36694397 0.42493701 0.45929267 0.31848575 0.54283283
15322932 0.39677363 0.19625467 0.30128184 0.54160687 0.46092925
03926597 0.47723746 0.29888181 0.19013876 0.55678745 0.50908766
39038178 0.41801158 0.42213066 0.52292513 0.15724405 0.40582157
44688041 0.30151292 0.38023331 0.05762816 0.4114524  0.53693283
15359769 0.37716461 0.2192365  0.44098011 0.43108742 0.59848623
46499645 0.25073422 0.51674692 0.30111825 0.41807919 0.49680382
26909    0.42101847 0.28201423 0.37885986 0.55052223 0.4906254
44138322 0.11251901 0.53502574 0.40974883 0.30974958 0.39545352
00418152 0.18662087 0.27137831 0.392299   0.51373461 0.47622228
47542242 0.67438119 0.39100808 0.31457703 0.43498425 0.21676674
53126615 0.41544292 0.48360885 0.41181974 0.38602803 0.4413568
33381892 0.44328275 0.48594171 0.39603612 0.36116974 0.22458183
27448864 0.46207572 0.47651733 0.16026474 0.5353303  0.31125265
36148397 0.42649819 0.46364995 0.45811005]
 [0.43690496 0.61344787 0.37404341 0.         0.38988525 0.37680129
48999896 0.45455274 0.54317062 0.50468573 0.61837898 0.39391816
31761011 0.48027593 0.675819   0.48194524 0.69029394 0.78712488
51030046 0.76944844 0.55514484 0.6425417  0.80101141 0.43220243
41149342 0.8336559  0.50351609 0.21363728 0.62271964 0.81147047
65948822 0.58375015 0.31692455 0.82790702 0.22530251 0.77625842
09436473 0.08110414 0.51968947 0.43142552 0.78269242 0.85284313
22255745 0.40701172 0.15499082 0.42989629 0.80018427 0.47351591
19195796 0.1790571  0.83688498 0.44470999 0.22993579 0.85831457
3039221  0.77992972 0.54731583 0.35742607 0.88637    0.21803834
81222443 0.41360938 0.30998874 0.41057873 0.32437741 0.39100403
3698669  0.46360469 0.64522489 0.74281778 0.86079058 0.40932839
10139094 0.92363647 0.55931808 0.27299294 0.74715859 0.39516581
31166786 0.22439658 0.84725855 0.65512315 0.26751875 0.10901453
65371307 0.4647818  0.8224161  0.72174516 0.05223683 0.46798795
638824   0.70596549 0.83563765 0.22567956 0.32438379 0.10739572
39558595 0.53375612 0.81230313 0.22703049]
 [0.53557062 0.40586638 0.09212924 0.38988525 0.         0.52777539
37012135 0.10977787 0.2385079  0.37535569 0.43789598 0.02286291
43171134 0.45864304 0.34154815 0.37636461 0.34101686 0.46026929
21384623 0.41327489 0.1686265  0.25350775 0.46223967 0.54541618
08597583 0.44379177 0.20696411 0.1798931  0.46690215 0.44240596
31041831 0.50944229 0.3649897  0.45747803 0.1656144  0.39374902
44769119 0.31033396 0.47236244 0.10101226 0.40138743 0.59904582
17306933 0.46416967 0.244404   0.36408609 0.41565267 0.67626038
44144349 0.23333564 0.45806777 0.21158352 0.47826481 0.46906513
34958601 0.45994133 0.36740985 0.46074457 0.50094447 0.46430868
42980914 0.02667794 0.59555673 0.49532817 0.24299151 0.47996638
09264489 0.0995527  0.27752064 0.35304171 0.55985753 0.55723019
48931666 0.59444454 0.48259157 0.26103304 0.50157117 0.12926617
59261294 0.47489719 0.45870768 0.32666856 0.45505947 0.43635938
2721627  0.36130429 0.4363075  0.33880497 0.36504273 0.13355287
31415346 0.54526657 0.44600295 0.2104007  0.49031076 0.35040009
28342008 0.51847476 0.51006429 0.51354958]
 [0.8089086  0.4470463  0.57785371 0.37680129 0.52777539 0.
80226601 0.63456659 0.75912775 0.8143996  0.42372033 0.51435161
68535906 0.8275221  0.6258713  0.29146964 0.86724275 0.70003973
72999697 0.93585026 0.67699532 0.71369498 0.72824496 0.80590464
59945662 0.8992812  0.4816565  0.39898847 0.40306317 0.79035278
63492776 0.92094943 0.16569681 0.80729749 0.44089382 0.89132488
3049306  0.36713963 0.86177993 0.6195799  0.90094701 1.11461564
45591721 0.76969237 0.43797754 0.24472343 0.90684578 0.84732729
18651846 0.34261505 0.83653358 0.40623448 0.60627025 0.93379425
65125229 0.98763313 0.837667   0.72614555 0.90398658 0.16425031
92535602 0.53592946 0.67295491 0.77914398 0.29232223 0.75921408
57478493 0.53295372 0.79872974 0.80945661 1.08642951 0.78548685
37344022 0.81619183 0.89414258 0.26684721 1.01174221 0.43221359
6761446  0.60074583 0.93010682 0.60364434 0.64296272 0.27796248
69185612 0.28587433 0.8505349  0.75153756 0.33199    0.50443143
84130932 1.01490736 0.90755135 0.50822694 0.05264568 0.47121407
29417966 0.88645659 1.03641207 0.597711  ]
 [0.26371791 0.77595231 0.27887906 0.48999896 0.37012135 0.80226601
        0.2939338  0.2313389  0.0155864  0.80769281 0.39297918
24892692 0.12277834 0.67847435 0.73298311 0.36333376 0.79094248
21960451 0.43060053 0.39598344 0.5023076  0.7822995  0.28157869
2897349  0.62046692 0.57438286 0.40799041 0.83550193 0.72308529
63847834 0.13937414 0.66558419 0.73333956 0.36536233 0.51153065
58329754 0.45242805 0.11369055 0.2842989  0.51106196 0.37868171
34834282 0.19716304 0.36846791 0.70864664 0.53956634 0.44199439
6495547  0.46035167 0.71262535 0.57988984 0.38305704 0.623897
19989407 0.37764708 0.07884542 0.24130719 0.72300562 0.67782835
5383997  0.38706648 0.4718638  0.2332264  0.57100961 0.23204288
27915677 0.45660258 0.37775932 0.56100157 0.4218016  0.31866812
57560403 0.91271321 0.1128695  0.56103222 0.27811908 0.49522511
4653009  0.38421949 0.60579598 0.669485   0.32135188 0.59143529
55356622 0.71621273 0.66460005 0.60021283 0.50712697 0.49862278
29219324 0.21693421 0.61303962 0.29441806 0.75321087 0.38598574
63192071 0.16647556 0.38186664 0.43171472]
 [0.50149768 0.49434227 0.08128147 0.45455274 0.10977787 0.63456659
2939338  0.         0.12888269 0.2956269  0.53035929 0.1284992
41640094 0.39950906 0.38529478 0.48208558 0.24246228 0.49963218
10610221 0.31921223 0.12242732 0.23211059 0.4937025  0.51438068
04307859 0.39920011 0.28878843 0.26249393 0.56249492 0.44818956
34637684 0.43126959 0.47330476 0.46082507 0.23413654 0.3246231
52510091 0.38063178 0.4045195  0.02392833 0.33018566 0.48936727
23280209 0.42702254 0.300049   0.47276836 0.35005267 0.65976176
53559365 0.32184332 0.44979523 0.31142662 0.49322479 0.41728617
33182124 0.35396314 0.27451608 0.43747383 0.47807277 0.56016585
36013479 0.11219636 0.60927222 0.46195333 0.35257155 0.44979551
08544171 0.16851405 0.19070049 0.31699494 0.4518784  0.53469574
55593969 0.62579619 0.40595724 0.3678546  0.39270058 0.23442047
60514108 0.49092336 0.40360647 0.37569232 0.45669953 0.51813127
27276932 0.46774671 0.4141159  0.33003295 0.43967183 0.21315133
20700863 0.44645178 0.39771618 0.2409851  0.59524359 0.39218648
3920559  0.45483482 0.40189297 0.53487455]
 [0.48143974 0.61094385 0.18409816 0.54317062 0.2385079  0.75912775
2313389  0.12888269 0.         0.22642396 0.64933387 0.25733349
42568876 0.35253278 0.47169859 0.60952846 0.15654135 0.5769125
03287354 0.23534612 0.17951366 0.27698061 0.56399728 0.49744344
15974526 0.39130959 0.40571128 0.37390863 0.68337751 0.49576697
42896417 0.35290303 0.59984838 0.50507789 0.33888552 0.28818349
62313804 0.47711723 0.34405553 0.14008898 0.28954455 0.36053793
3320837  0.40818285 0.38984728 0.60151308 0.31631461 0.65424058
64860498 0.43459307 0.4822332  0.43683264 0.53120129 0.39783816
34715964 0.23864178 0.18204075 0.43540539 0.49178127 0.67447581
31867805 0.24023107 0.64053467 0.44535201 0.48075676 0.43816212
18769063 0.28727316 0.14852972 0.32969002 0.32964238 0.52724015
64319788 0.69130753 0.3315893  0.49334328 0.26433853 0.36246251
63524763 0.53017063 0.38054907 0.46682394 0.48237364 0.62026956
33233384 0.59557091 0.43329887 0.37262856 0.53754638 0.33251435
09597626 0.33364546 0.38488513 0.31792561 0.71797999 0.46324187
52081331 0.39721659 0.27955256 0.57753106]
 [0.27536152 0.78088818 0.28477814 0.50468573 0.37535569 0.8143996
0155864  0.2956269  0.22642396 0.         0.81322074 0.39821523
26404081 0.13162038 0.6790981  0.74078186 0.3541917  0.79072852
21678976 0.42010322 0.39448259 0.49968493 0.78138589 0.29344808
29367412 0.6136792  0.57844216 0.41909021 0.84155777 0.72017011
63867424 0.13573674 0.67639282 0.73013181 0.37645242 0.50357013
59783828 0.46616986 0.11767922 0.2871688  0.50281096 0.36310768
35974608 0.21023258 0.38165378 0.71737298 0.53152566 0.45388198
6630018  0.47217465 0.70849816 0.58588464 0.39852172 0.61625703
21545763 0.36461021 0.06528042 0.25562752 0.71738627 0.6912502
52981891 0.39148649 0.48673725 0.24589886 0.58021946 0.24542754
28526822 0.45999366 0.37142624 0.55598062 0.40707406 0.33136533
59073944 0.91131792 0.1104171  0.57138268 0.26269617 0.5014824
48013985 0.39970959 0.59800834 0.67058938 0.33669054 0.6056948
55183692 0.7241444  0.65958997 0.59713934 0.52123377 0.50252577
28316905 0.2030872  0.60594052 0.30702282 0.7655831  0.40096649
64017516 0.17087918 0.3675792  0.4471642 ]
 [0.94079421 0.045303   0.5288305  0.61837898 0.43789598 0.42372033
80769281 0.53035929 0.64933387 0.81322074 0.         0.41504798
82129607 0.88875854 0.27215762 0.14473295 0.68277623 0.30011373
63400563 0.72522554 0.48861887 0.45591392 0.33404168 0.94649877
52141441 0.59181698 0.24364967 0.46752408 0.04114254 0.42522795
30380044 0.94682925 0.32694554 0.44001502 0.49772858 0.63415874
6054414  0.55363966 0.90674632 0.53166402 0.64521569 0.9924819
51721886 0.87643948 0.55859418 0.20093016 0.6381058  1.04880499
50903581 0.45876024 0.48109909 0.22865825 0.81268358 0.63004284
75078981 0.81533348 0.80283841 0.8578239  0.55381176 0.50903491
65985307 0.4233185  0.9169059  0.90190952 0.29809427 0.88385468
52865706 0.36282411 0.6049432  0.52046971 0.9209178  0.94645591
67844031 0.39861958 0.91976523 0.34596795 0.9080485  0.31377193
91688447 0.80771106 0.63390309 0.25608617 0.8169593  0.5779551
40633459 0.15887879 0.51708606 0.44002214 0.56770567 0.31764019
69276432 0.97680084 0.60462893 0.58258994 0.43244054 0.65545121
22377122 0.95012438 0.87621172 0.8291875 ]
 [0.55587673 0.38302368 0.11480725 0.39391816 0.02286291 0.51435161
39297918 0.1284992  0.25733349 0.39821523 0.41504798 0.
45032646 0.48093911 0.32343347 0.35505241 0.35298953 0.44220568
23381802 0.4233819  0.17221258 0.2487531  0.4453597  0.56540148
10804453 0.44131324 0.18474008 0.18134052 0.4441586  0.42995482
29380032 0.53229496 0.35041434 0.44537237 0.17234176 0.39727222
44758388 0.31351333 0.49500977 0.12194692 0.40535183 0.61766145
18201968 0.48492553 0.25257038 0.34428505 0.41815334 0.69432231
43521463 0.23124185 0.44811295 0.18898039 0.49235256 0.46799357
36890152 0.47449917 0.38987554 0.48014972 0.4935653  0.4572378
43318641 0.02251493 0.6093897  0.51566025 0.22665246 0.50002773
11518742 0.08175847 0.28670987 0.34960777 0.57550998 0.5762736
49219558 0.57714289 0.50543318 0.24834873 0.52114067 0.10743072
60665343 0.48882287 0.45845475 0.3078611  0.47133523 0.43487548
26257084 0.34024096 0.42922146 0.33002391 0.36636562 0.11228668
32975083 0.56736771 0.44431574 0.22464603 0.47831235 0.36031922
26357057 0.54092519 0.52591628 0.52637616]
 [0.12572354 0.80096858 0.35322751 0.31761011 0.43171134 0.68535906
24892692 0.41640094 0.42568876 0.26404081 0.82129607 0.45032646
        0.18145532 0.77325942 0.7108184  0.57924011 0.89196987
39975404 0.65464023 0.53864559 0.64847423 0.89307205 0.12716655
38664213 0.80608443 0.62691558 0.35587016 0.83881197 0.86163595
74128421 0.28962146 0.58744278 0.87508817 0.3235675  0.71200464
40882115 0.32007605 0.2245017  0.39543652 0.71420265 0.62412847
30411959 0.09164131 0.27139635 0.6705014  0.7398951  0.24530508
50636052 0.38116928 0.86605774 0.60114651 0.13972336 0.81800188
08465298 0.61918259 0.32645959 0.04086889 0.89315461 0.53361409
74372844 0.45728669 0.22370722 0.09380836 0.53485113 0.07391901
35049303 0.53122383 0.56976615 0.73031898 0.67031126 0.1268232
3763339  1.02562521 0.27044995 0.50233723 0.52619964 0.52129455
21738794 0.14213049 0.80183013 0.75814704 0.07520221 0.42654133
68594147 0.69265092 0.82976149 0.74591289 0.35505055 0.56094485
51061527 0.43658515 0.80204226 0.23953851 0.63282256 0.21468336
60855003 0.22409914 0.62913233 0.18692566]
 [0.14916603 0.86071772 0.36694397 0.48027593 0.45864304 0.8275221
12277834 0.39950906 0.35253278 0.13162038 0.88875854 0.48093911
18145532 0.         0.78404395 0.79955181 0.48572017 0.8991172
33797108 0.55146061 0.5099277  0.61846505 0.89284391 0.16800613
38669096 0.74283117 0.66560539 0.45312168 0.91310525 0.83936382
74579497 0.1082154  0.70729393 0.85028161 0.41240769 0.63430865
57433051 0.46255352 0.04313044 0.38579352 0.63382239 0.45855613
39310733 0.0988504  0.39090869 0.76837485 0.66234434 0.32693345
65916323 0.49597897 0.83150814 0.66029546 0.32047728 0.74663332
17801156 0.49110195 0.19428337 0.15626097 0.84421728 0.68732286
66108431 0.4793025  0.38715957 0.12747136 0.6288411  0.13402772
36609819 0.55249653 0.49993084 0.68154936 0.52227509 0.21008798
55101418 1.02448545 0.08988949 0.60905355 0.36883332 0.57532796
38000937 0.32320385 0.72855876 0.77325599 0.2558278  0.58814123
66727565 0.78197815 0.78502293 0.71711224 0.5089853  0.59151754
41464022 0.25886374 0.73558443 0.32928645 0.77613134 0.37294346
69631174 0.06211541 0.4872665  0.3663757 ]
 [0.87482577 0.22743494 0.42493701 0.675819   0.34154815 0.6258713
67847435 0.38529478 0.47169859 0.6790981  0.27215762 0.32343347
77325942 0.78404395 0.         0.34390021 0.45470851 0.11877445
4684787  0.48035533 0.29224866 0.21547524 0.12564    0.88549597
39879129 0.32034684 0.17301967 0.4711262  0.31320373 0.16500574
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39676001 0.80767505 0.46207623 0.18527541 0.57129328 0.77506063
62083123 0.60951352 0.26477248 0.79171591 0.20577749 0.75658302
0857874  0.06045769 0.54674734 0.41740464 0.7635727  0.86046978
20758584 0.44200283 0.14924905 0.37795446 0.77954218 0.5231448
15158083 0.14044447 0.80295351 0.4002032  0.27841145 0.83390377
33102945 0.77594179 0.55901144 0.39559544 0.85495227 0.17926235
79267175 0.3871774  0.36200703 0.44878765 0.27578037 0.42895215
35706159 0.43124667 0.6298154  0.71589589 0.86097957 0.45382447
12840437 0.88027776 0.58413845 0.22332213 0.75462195 0.35623746
36357068 0.27287692 0.82374155 0.61387333 0.31112737 0.08539851
62185189 0.41328676 0.7916046  0.68991309 0.         0.43166434
63212935 0.72404535 0.81051383 0.22607539 0.27934776 0.14038893
34563682 0.56487884 0.81179287 0.2783443 ]
 [0.66801588 0.28119458 0.22458183 0.46798795 0.13355287 0.50443143
49862278 0.21315133 0.33251435 0.50252577 0.31764019 0.11228668
56094485 0.59151754 0.21710121 0.28767107 0.38782542 0.33508619
31637723 0.44560531 0.18715685 0.20985241 0.34183891 0.67734567
20891249 0.40040013 0.07605009 0.25761503 0.35093057 0.34361163
19352837 0.63784796 0.33996062 0.36016658 0.26339338 0.38758868
50504963 0.38719524 0.60378546 0.216413   0.39746582 0.68313766
27757628 0.59720671 0.34330119 0.29370957 0.40245499 0.80387752
46656661 0.29123576 0.37218209 0.11235913 0.59435487 0.4329111
48039247 0.51862462 0.48705742 0.59163541 0.4280795  0.4838035
42117716 0.11234615 0.71023869 0.62781732 0.21572719 0.61203938
22553187 0.04527152 0.31193535 0.3084283  0.6236832  0.68730401
56006834 0.47160642 0.61148632 0.25803294 0.59403196 0.07986112
70802458 0.59046408 0.42766895 0.19956143 0.57810653 0.48714605
19755428 0.27652835 0.36691025 0.2640276  0.43166434 0.
38439381 0.65935659 0.40710265 0.32952952 0.47798901 0.45307815
21851248 0.65085334 0.57613163 0.6250933 ]
 [0.55354684 0.65152829 0.27448864 0.638824   0.31415346 0.84130932
29219324 0.20700863 0.09597626 0.28316905 0.69276432 0.32975083
51061527 0.41464022 0.48417093 0.67031332 0.07115823 0.57763146
12872019 0.14408731 0.20431738 0.2720548  0.55917633 0.57065764
24496631 0.33683661 0.45162951 0.46442615 0.72939425 0.47543021
44011496 0.39180934 0.67913654 0.48182286 0.43126059 0.22209061
71784096 0.57177985 0.39778457 0.22400402 0.22046503 0.29983714
42564076 0.4828076  0.48508789 0.66858893 0.24966033 0.73006049
73920007 0.52483946 0.45120112 0.49478791 0.62245714 0.33538874
43550374 0.1471858  0.22463321 0.51620819 0.44704894 0.76451065
24683144 0.30976428 0.72938199 0.51994665 0.5563882  0.51510035
27834587 0.34084737 0.10868235 0.29449824 0.24578251 0.60407593
73901902 0.67917761 0.37529953 0.57448118 0.21998661 0.42855307
72382068 0.62170532 0.31669769 0.4837612  0.57116357 0.71420549
33188916 0.65780649 0.39515892 0.35572171 0.63212935 0.38439381
        0.33141922 0.32748341 0.41378913 0.80225207 0.5591017
58860333 0.45032035 0.19617868 0.6694607 ]
 [0.39666186 0.94033057 0.46207572 0.70596549 0.54526657 1.01490736
21693421 0.44645178 0.33364546 0.2030872  0.97680084 0.56736771
43658515 0.25886374 0.80348963 0.92062469 0.38757692 0.90430087
34389626 0.42268126 0.51168909 0.59893148 0.88802592 0.41537579
45934609 0.65693991 0.7345244  0.6171707  1.0087684  0.80684583
7601511  0.15888923 0.87238706 0.81316902 0.57473296 0.53758218
79963328 0.66924885 0.21671521 0.44654626 0.53268632 0.21496726
55907074 0.35767617 0.58452464 0.90289476 0.56227645 0.56247907
8660196  0.6722925  0.78150019 0.75572293 0.57628178 0.64750122
40836851 0.32428568 0.18073657 0.41486227 0.77153231 0.89425043
55272512 0.55558797 0.64565968 0.38377278 0.76926667 0.39244291
46365876 0.61437486 0.43988913 0.62504546 0.30960598 0.46064626
78887462 1.01012729 0.16955777 0.76584284 0.15776778 0.67452819
63845294 0.57853598 0.62814581 0.79966779 0.51177327 0.80824711
65761465 0.90493435 0.72373212 0.68664067 0.72404535 0.65935659
33141922 0.         0.64534957 0.50923756 0.96678591 0.60079571
8235589  0.24316022 0.29184923 0.62332703]
 [0.86614298 0.55947894 0.47651733 0.83563765 0.44600295 0.90755135
61303962 0.39771618 0.38488513 0.60594052 0.60462893 0.44431574
80204226 0.73558443 0.3335893  0.65331196 0.2608528  0.36433612
40543437 0.22836278 0.28222899 0.19935759 0.33214118 0.88190946
4373215  0.01564533 0.42794926 0.62526254 0.64577073 0.21908659
30130544 0.71929105 0.74526098 0.2149996  0.61053603 0.10782471
89181605 0.75633568 0.72268125 0.42141084 0.11290575 0.53591854
61540611 0.79251702 0.68650516 0.67850891 0.08383279 1.03732978
86972255 0.67493076 0.16833413 0.50181245 0.89011286 0.02642513
71938055 0.34077649 0.55090956 0.81626641 0.13040775 0.88863857
09810826 0.42333649 1.00527118 0.82958067 0.62266053 0.82152531
48047606 0.38916262 0.23635978 0.09867455 0.42257348 0.91023814
93531805 0.41495094 0.70244342 0.66439558 0.5036083  0.48538302
00083988 0.8879968  0.03138686 0.34855406 0.85019917 0.87836027
21638425 0.64871977 0.10636126 0.16558989 0.81051383 0.40710265
32748341 0.64534957 0.         0.63638361 0.88409214 0.78637086
61445709 0.77567677 0.39831141 0.9324312 ]
 [0.3583906  0.56150033 0.16026474 0.22567956 0.2104007  0.50822694
29441806 0.2409851  0.31792561 0.30702282 0.58258994 0.22464603
23953851 0.32928645 0.54592889 0.47791699 0.46764755 0.66438342
2850936  0.54722955 0.35492268 0.4557611  0.66925515 0.36391863
19952143 0.63671885 0.39088259 0.1245005  0.60148625 0.65272846
51809559 0.41487114 0.37858253 0.66768749 0.08625975 0.56546667
3098319  0.16659331 0.35888662 0.21707021 0.57078395 0.63482825
06638494 0.29670272 0.07762324 0.44234208 0.59103163 0.47677061
35826642 0.16830064 0.66667543 0.36167089 0.26790274 0.65693632
16943093 0.55425051 0.33707068 0.27527853 0.70552907 0.38627324
60082228 0.23707785 0.38515834 0.31991449 0.30340621 0.30152262
1562143  0.30613262 0.4285884  0.55027911 0.63612879 0.36591377
32528229 0.80037348 0.38763069 0.27997102 0.52902209 0.28285222
38225029 0.26450142 0.64385447 0.52901414 0.24866697 0.31123993
4810559  0.459923   0.64072416 0.54647341 0.22607539 0.32952952
41378913 0.50923756 0.63638361 0.         0.45885312 0.15125733
37455594 0.39088536 0.58731241 0.30365943]
 [0.75628932 0.45097929 0.5353303  0.32438379 0.49031076 0.05264568
75321087 0.59524359 0.71797999 0.7655831  0.43244054 0.47831235
63282256 0.77613134 0.61494985 0.29295337 0.83108015 0.6962277
68819583 0.90141369 0.6445075  0.68784048 0.72265669 0.7532605
55876029 0.87653788 0.46246194 0.35282293 0.41630596 0.77801879
62044617 0.87038916 0.13917104 0.79511708 0.39415332 0.8623991
25453034 0.31501637 0.81077719 0.57922359 0.8717354  1.07115692
40843349 0.71739609 0.3874302  0.24098298 0.87907892 0.7955926
13507727 0.29502618 0.8218711  0.3861923  0.55401884 0.91013936
59951016 0.94909391 0.79048127 0.67359602 0.88761913 0.11462627
89698367 0.50031661 0.62235235 0.72661665 0.26268388 0.70669213
53210794 0.503298   0.76442225 0.7855552  1.04653175 0.73289639
32464343 0.81719191 0.84370258 0.23004761 0.96762352 0.40276602
6253934  0.54848995 0.90549039 0.59246099 0.59034587 0.22700046
66984433 0.28430761 0.83215761 0.73161304 0.27934776 0.47798901
80225207 0.96678591 0.88409214 0.45885312 0.         0.41860501
27705377 0.83480546 0.99643264 0.54617841]
 [0.3377061  0.6433421  0.31125265 0.10739572 0.35040009 0.47121407
38598574 0.39218648 0.46324187 0.40096649 0.65545121 0.36031922
21468336 0.37294346 0.66907426 0.52945829 0.61608194 0.78526924
43080349 0.69578005 0.50430735 0.60188861 0.79447246 0.33512747
35044573 0.7862369  0.50259665 0.20001635 0.66608219 0.7897047
64636826 0.47641206 0.38480157 0.8053471  0.19014002 0.71671945
20167463 0.11137376 0.41229532 0.36828417 0.72203708 0.75464329
1783512  0.3019763  0.10977816 0.48261023 0.74223758 0.39993836
2918483  0.19671852 0.80818357 0.45618209 0.15762144 0.80733025
19661791 0.6950986  0.44695787 0.25528811 0.85085024 0.31929867
75207875 0.37648324 0.2640367  0.30845201 0.35776773 0.28859626
30716193 0.43844901 0.57955713 0.69852082 0.77026308 0.31796139
19059324 0.9224964  0.45210456 0.31470567 0.64949262 0.39073651
26321119 0.15251613 0.79454046 0.65011112 0.17564627 0.21542234
62235694 0.51145423 0.78609462 0.68920196 0.14038893 0.45307815
5591017  0.60079571 0.78637086 0.15125733 0.41860501 0.
43286867 0.42693672 0.72285173 0.17631094]
 [0.7312605  0.21839209 0.36148397 0.39558595 0.28342008 0.29417966
63192071 0.3920559  0.52081331 0.64017516 0.22377122 0.26357057
60855003 0.69631174 0.33932784 0.10350767 0.60125331 0.42897038
49719192 0.66272553 0.40239084 0.4236192  0.4522247  0.7352824
36805559 0.60578565 0.18749702 0.2527938  0.23339029 0.5012923
34339774 0.76752391 0.14016836 0.51842639 0.28830201 0.60493481
39072285 0.32988286 0.71992077 0.38436712 0.61502319 0.88080247
30817672 0.67125542 0.34010933 0.08071462 0.61841821 0.82916876
30940548 0.23630431 0.54483384 0.11266746 0.59041927 0.6407899
54389499 0.72933965 0.64333041 0.64671023 0.61097935 0.31700467
63780374 0.2809389  0.69332871 0.69359423 0.07522424 0.67475827
35992716 0.25444155 0.52734527 0.51687029 0.83289973 0.73149526
46133956 0.557827   0.73988    0.12261196 0.78470505 0.16005044
69340401 0.58535964 0.63784092 0.31674873 0.59804389 0.36486616
39828755 0.08571823 0.55657936 0.45736079 0.34563682 0.21851248
58860333 0.8235589  0.61445709 0.37455594 0.27705377 0.43286867
        0.75842025 0.78407444 0.60569959]
 [0.15469025 0.92166002 0.42649819 0.53375612 0.51847476 0.88645659
16647556 0.45483482 0.39721659 0.17087918 0.95012438 0.54092519
22409914 0.06211541 0.84008014 0.86164844 0.52060749 0.9541508
38605001 0.58156232 0.56153274 0.66857707 0.94671897 0.17305558
44453112 0.78376907 0.72537556 0.51492231 0.9747739  0.88943539
80109158 0.0845597  0.76844601 0.89977569 0.47435856 0.67209325
62720637 0.52038141 0.05320942 0.44240411 0.67076689 0.45393367
45500619 0.13318668 0.45104456 0.83045675 0.69984723 0.32065232
7158071  0.55701364 0.87900979 0.7215613  0.35833137 0.78518676
23535081 0.51131371 0.22573886 0.19149386 0.88821041 0.74383026
69697592 0.53852026 0.41013099 0.14878944 0.69092245 0.16220469
42583288 0.61110854 0.54202803 0.72684362 0.5303995  0.21876309
59960238 1.07773749 0.08319599 0.67078474 0.37368536 0.6365239
40275465 0.36172222 0.76670243 0.82994032 0.29479631 0.64233149
71917188 0.84408252 0.83045508 0.7666275  0.56487884 0.65085334
45032035 0.24316022 0.77567677 0.39088536 0.83480546 0.42693672
75842025 0.         0.49994617 0.40149838]
 [0.63639499 0.83338997 0.46364995 0.81230313 0.51006429 1.03641207
38186664 0.40189297 0.27955256 0.3675792  0.87621172 0.52591628
62913233 0.4872665  0.64549463 0.86348308 0.19370575 0.72216118
31090469 0.1742287  0.39067401 0.43076544 0.69743956 0.65516757
43772216 0.41254026 0.63960158 0.65328982 0.91429524 0.59673927
60202898 0.42096268 0.87492768 0.59825124 0.61743208 0.29870994
89665159 0.75142736 0.45550587 0.4172093  0.29019273 0.13765956
60943669 0.57657261 0.66269453 0.86375924 0.31622773 0.81392656
92773897 0.71399243 0.55750376 0.68776178 0.75768575 0.39269809
56801026 0.06300833 0.30320624 0.62315609 0.52868039 0.95380105
30020347 0.50592399 0.85279032 0.61100784 0.75253561 0.6122422
46723016 0.53380692 0.27136008 0.41273729 0.05012638 0.69595238
90985215 0.80251008 0.4167505  0.76974716 0.13422123 0.62409083
84637588 0.75807591 0.37406253 0.64944452 0.69899491 0.8958302
48910458 0.85155653 0.49474991 0.49184783 0.81179287 0.57613163
19617868 0.29184923 0.39831141 0.58731241 0.99643264 0.72285173
78407444 0.49994617 0.         0.8063205 ]
 [0.26363147 0.81856525 0.45811005 0.22703049 0.51354958 0.597711
43171472 0.53487455 0.57753106 0.4471642  0.8291875  0.52637616
18692566 0.3663757  0.8419928  0.69928679 0.73406799 0.95907303
54764091 0.81246175 0.65430949 0.75820336 0.96692929 0.25170773
49669414 0.93407433 0.67763955 0.37585776 0.83794954 0.95590592
81733537 0.47372469 0.54233336 0.97102711 0.36197283 0.85276111
2943121  0.27652282 0.40948045 0.51135707 0.8566253  0.80946693
34758801 0.26998662 0.28386869 0.64988066 0.87969621 0.2498867
41122265 0.37104568 0.97030285 0.63248264 0.04875176 0.951392
23850906 0.79049703 0.50697281 0.21110628 1.00796855 0.43428362
88674126 0.5401793  0.08791826 0.25415436 0.5310941  0.23932697
45437916 0.6067963  0.71115434 0.85037418 0.84957045 0.21485718
23672924 1.09613292 0.45610482 0.48507899 0.7098309  0.56582724
08770459 0.04830062 0.93697705 0.82359399 0.11178802 0.32001169
78471529 0.68153988 0.94323085 0.85000583 0.2783443  0.6250933
6694607  0.62332703 0.9324312  0.30365943 0.54617841 0.17631094
60569959 0.40149838 0.8063205  0.        ]]

53. How to convert a float (32 bits) array into an integer (32 bits) in place?

G = (np.random.rand(10)*100).astype(np.float32)
GG = G.view(np.int32)
GG[:] = G
print(GG)

[48 20  1 10 21 46 12 35 51 75]

54. How to read the following file? (★★☆)

1, 2, 3, 4, 5
6,  ,  , 7, 8
 ,  , 9,10,11

from io import StringIO

s = StringIO('''1, 2, 3, 4, 5

                6,  ,  , 7, 8

                 ,  , 9,10,11
''')
HH = np.genfromtxt(s, delimiter=",", dtype=np.int)
print(HH)

[[ 1  2  3  4  5]
 [ 6 -1 -1  7  8]
 [-1 -1  9 10 11]]

55. What is the equivalent of enumerate for numpy arrays? (★★☆)

II = np.arange(9).reshape(3,3)

for index, value in np.ndenumerate(II):
    print(index, value)

(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. Generate a generic 2D Gaussian-like array (★★☆)

X, Y = np.meshgrid(np.linspace(-1,1,10), np.linspace(-1,1,10))
D = np.sqrt(X**2+Y**2)
sigma, mu = (1.0, 0.0)
Gaussian = np.exp(-( (D-mu)**2 / ( 2.0 * sigma**2 ) ) )
print(Gaussian)

[[0.36787944 0.44822088 0.51979489 0.57375342 0.60279818 0.60279818
  0.57375342 0.51979489 0.44822088 0.36787944]
 [0.44822088 0.54610814 0.63331324 0.69905581 0.73444367 0.73444367
  0.69905581 0.63331324 0.54610814 0.44822088]
 [0.51979489 0.63331324 0.73444367 0.81068432 0.85172308 0.85172308
  0.81068432 0.73444367 0.63331324 0.51979489]
 [0.57375342 0.69905581 0.81068432 0.89483932 0.9401382  0.9401382
  0.89483932 0.81068432 0.69905581 0.57375342]
 [0.60279818 0.73444367 0.85172308 0.9401382  0.98773022 0.98773022
  0.9401382  0.85172308 0.73444367 0.60279818]
 [0.60279818 0.73444367 0.85172308 0.9401382  0.98773022 0.98773022
  0.9401382  0.85172308 0.73444367 0.60279818]
 [0.57375342 0.69905581 0.81068432 0.89483932 0.9401382  0.9401382
  0.89483932 0.81068432 0.69905581 0.57375342]
 [0.51979489 0.63331324 0.73444367 0.81068432 0.85172308 0.85172308
  0.81068432 0.73444367 0.63331324 0.51979489]
 [0.44822088 0.54610814 0.63331324 0.69905581 0.73444367 0.73444367
  0.69905581 0.63331324 0.54610814 0.44822088]
 [0.36787944 0.44822088 0.51979489 0.57375342 0.60279818 0.60279818
  0.57375342 0.51979489 0.44822088 0.36787944]]

57. How to randomly place p elements in a 2D array? (★★☆)

n = 5
p = 3
out = np.zeros((n,n),dtype=bool)
np.put(out,np.random.choice(range(n*n), p, replace=False),1)
print(out)

[[False False False False False]
 [ True False False False False]
 [False False False False False]
 [ True False False False False]
 [False False False False  True]]

58. Subtract the mean of each row of a matrix (★★☆)

X = np.random.rand(5, 10)
Y = X - X.mean(axis=1).reshape(-1, 1)
print(Y)

[[ 0.22912809  0.29042889  0.23488493  0.46221904 -0.13732101 -0.13707458
  -0.04228463 -0.45018358 -0.01939715 -0.4304    ]
 [-0.03698973 -0.11223178 -0.29723432  0.48031381 -0.30312297  0.07384592
   0.0349981   0.02515311 -0.07757645  0.2128443 ]
 [-0.04524787  0.30987995 -0.12940049  0.02014424  0.13105117 -0.35837574
  -0.17263158  0.4108267  -0.18361852  0.01737213]
 [-0.30744895  0.32515614  0.12169629  0.3134796  -0.19528196 -0.09636294
  -0.24450892 -0.34056596  0.45926822 -0.03543152]
 [-0.21719634  0.19320923  0.28517109  0.28977779 -0.04063178 -0.12799435
  -0.11810656  0.01952228  0.30193847 -0.58568983]]

59. How to sort an array by the nth column? (★★☆)

JJ = np.random.randint(0,10,(3,3))
print(JJ[JJ[:,1].argsort()]) #1th column sort

[[0 0 5]
 [5 4 3]
 [5 9 0]]

60. How to tell if a given 2D array has null columns? (★★☆)

KK = np.random.randint(0,3,(3,10))

print((~KK.any(axis=0)).any()) #KK has null column

True

61. Find the nearest value from a given value in an array (★★☆)

Z = np.random.uniform(0,1,10)
z = 0.5

LL = Z.flat[np.abs(Z - z).argmin()]
print(LL)

0.5052663766905205

62. Considering two arrays with shape (1,3) and (3,1), how to compute their sum using an iterator? (★★☆)

A = np.arange(3).reshape(3,1)
B = np.arange(3).reshape(1,3)

MM = np.nditer([A,B,None])
for x,y,z in MM: 
    z[...] = x + y
print(MM.operands[2])

[[0 1 2]
 [1 2 3]
 [2 3 4]]

63. Create an array class that has a name attribute (★★☆)

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. Consider a given vector, how to add 1 to each element indexed by a second vector (be careful with repeated indices)? (★★★)

Z = np.ones(10)
I = np.random.randint(0,len(Z),20)
Z += np.bincount(I, minlength=len(Z))
print(Z)

[4. 6. 3. 3. 3. 3. 3. 2. 1. 2.]

65. How to accumulate elements of a vector (X) to an array (F) based on an index list (I)? (★★★)

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. Considering a (w,h,3) image of (dtype=ubyte), compute the number of unique colors (★★☆)

w = 256
h = 256
I = np.random.randint(0, 4, (w, h, 3)).astype(np.ubyte)
colors = np.unique(I.reshape(-1, 3), axis=0)
num = len(colors)
print(num)

67. Considering a four dimensions array, how to get sum over the last two axis at once? (★★★)

A = np.random.randint(0,10,(3,4,3,4))

sum = A.sum(axis=(-2,-1))
print(sum)

[[62 54 44 74]
 [41 70 66 63]
 [57 54 63 69]]

68. Considering a one-dimensional vector D, how to compute means of subsets of D using a vector S of same size describing subset indices? (★★★)

D = np.random.uniform(0,1,100)
S = np.random.randint(0,10,100)

D_sum = np.bincount(S, weights=D)
D_count = np.bincount(S)
D_mean = D_sum / D_count
print(D_mean)

[0.52887457 0.62078144 0.52496113 0.52517822 0.50669445 0.53260253
 0.46096442 0.50142084 0.40550489 0.62887479]

69. How to get the diagonal of a dot product? (★★★)

A = np.random.uniform(0,1,(5,5))
B = np.random.uniform(0,1,(5,5))

np.diag(np.dot(A, B))

array([1.42702726, 1.30717856, 1.21652205, 1.9493525 , 0.82901742])

70. Consider the vector [1, 2, 3, 4, 5], how to build a new vector with 3 consecutive zeros interleaved between each value? (★★★)

MM = np.array([1,2,3,4,5])
newMM = 3
MM0 = np.zeros(len(MM) + (len(MM)-1)*(newMM))
MM0[::newMM+1] = MM
print(MM0)

[1. 0. 0. 0. 2. 0. 0. 0. 3. 0. 0. 0. 4. 0. 0. 0. 5.]

71. Consider an array of dimension (5,5,3), how to mulitply it by an array with dimensions (5,5)? (★★★)

M = np.ones((5,5,3))
N = 2*np.ones((5,5))
print(M*N[:,:,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. How to swap two rows of an array? (★★★)

NN = np.arange(25).reshape(5,5)
NN[[0,1]] = NN[[1,0]] #swap
print(NN)

[[ 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. Consider a set of 10 triplets describing 10 triangles (with shared vertices), find the set of unique line segments composing all the triangles (★★★)

faces = np.random.randint(0,100,(10,3))
OO = np.roll(faces.repeat(2,axis=1),-1,axis=1)
OO = OO.reshape(len(OO)*3,2)
OO = np.sort(OO,axis=1)

PP = OO.view( dtype=[('p0',OO.dtype),('p1',OO.dtype)] )
PP = np.unique(PP)
print(PP)

[( 2,  2) ( 2, 39) ( 3, 25) ( 3, 93) ( 5, 88) ( 5, 89) ( 9, 83) ( 9, 97)
 (10, 47) (10, 90) (12, 14) (12, 64) (14, 64) (25, 93) (34, 50) (34, 52)
 (45, 49) (45, 91) (47, 90) (49, 91) (50, 52) (50, 91) (50, 95) (75, 77)
 (75, 96) (77, 96) (83, 97) (88, 89) (91, 95)]

74. Given a sorted array C that corresponds to a bincount, how to produce an array A such that np.bincount(A) == C? (★★★)

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. How to compute averages using a sliding window over an array? (★★★)

def averages(a, n=3):
    ret = np.cumsum(a, dtype=float)
    ret[n:] = ret[n:] - ret[:-n]
    return ret[n - 1:] / n
QQ = np.arange(20)
print(averages(QQ, n=3))

[ 1.  2.  3.  4.  5.  6.  7.  8.  9. 10. 11. 12. 13. 14. 15. 16. 17. 18.]

76. Consider a one-dimensional array Z, build a two-dimensional array whose first row is (Z[0],Z[1],Z[2]) and each subsequent row is shifted by 1 (last row should be (Z[-3],Z[-2],Z[-1]) (★★★)

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)
RR = rolling(np.arange(10), 3)
print(RR)

[[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. How to negate a boolean, or to change the sign of a float inplace? (★★★)

SS = np.random.uniform(-1.0,1.0,100)
print(np.negative(SS, out=SS)) #negate

SS = np.random.randint(0,2,100)
print(np.logical_not(SS, out=SS)) #change sign

[-0.43142588  0.59859061  0.99627396  0.5061813   0.2986948  -0.75969152
  0.09852039  0.87043876  0.13050159 -0.26983961  0.29544981  0.19388506
 -0.88774356  0.84948479  0.12381086 -0.86133151  0.81037492 -0.1238283
 -0.59918499  0.52416698  0.18695595 -0.47251299 -0.92117043 -0.59976303
  0.71169079 -0.2194166  -0.25086565  0.97415259 -0.45587028 -0.0324917
  0.90116924  0.2811058  -0.64532039  0.20115784 -0.69115601  0.14410459
  0.24122662 -0.79970774 -0.76669329  0.818251   -0.59007297  0.70438253
 -0.11152939 -0.27525082  0.54086191  0.1070056  -0.0055339  -0.2172159
 -0.17467491  0.0604967   0.16020891  0.1573619  -0.52369539  0.7920129
 -0.62214378  0.52645377 -0.53538175 -0.23886017  0.36976027  0.50107766
  0.09816686 -0.33300007  0.45323223  0.90179019 -0.61841695  0.43110295
  0.59279946  0.52638756 -0.15583409  0.25777017 -0.86229103  0.18841807
  0.2287678   0.05469322  0.85113725 -0.20106931  0.31634615  0.843137
 -0.8115738   0.94390636  0.58514223 -0.46873879  0.32093915  0.56064315
 -0.25036866 -0.87978798 -0.16159554 -0.4467953  -0.06028119  0.23601978
  0.5767654   0.26049789  0.1563624  -0.39939618 -0.44685844 -0.19481331
 -0.08709067 -0.27862611  0.52935558 -0.84561232]
[1 0 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 0 1 0
 0 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 0 1
 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 0]

78. Consider 2 sets of points P0,P1 describing lines (2d) and a point p, how to compute distance from p to each line i (P0[i],P1[i])? (★★★)

def distance(P0, P1, p):
    T = P1 - P0
    L = (T**2).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((D**2).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 from p to (PO, P1):", [x for x in distance(P0, P1, p)])

Distance from p to (PO, P1): [1.8313287239123373, 2.5640799000521093, 5.099403702870596, 7.142537274796611, 6.469783494437534, 2.080045169655839, 10.956626653403658, 1.1927409378556184, 5.977329582321501, 4.483721602433141]

79. Consider 2 sets of points P0,P1 describing lines (2d) and a set of points P, how to compute distance from each point j (P[j]) to each line i (P0[i],P1[i])? (★★★)

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("Distance from p to (PO, P1):", np.array([distance(P0,P1,P_j) for P_j in P]))

Distance from p to (PO, P1): [[ 4.29916349  4.23818085  8.03233455  6.6405848   8.71025014  3.18622955
   3.9033785  10.72694093  1.42601259  0.18769035]
 [12.28269988  7.45993477  0.42597785  1.27891201  0.1327635   2.0244737
   3.20704788 16.55014636  7.53225981  6.51210984]
 [ 2.01866776  8.64473252  6.01658513  3.25237841 11.95744441 14.59577906
   9.39764654  0.01900807 10.21144718  9.82550706]
 [ 6.17706285  2.15642733  3.64946483  1.49487768  5.71967553  3.96273991
   0.06692718 10.42050327  6.60443098  0.29905605]
 [11.4834466   0.34026901  5.30804075  7.48274352  1.33751753  3.28982012
   5.83492792 11.9548802  15.87844125  2.58455606]
 [10.51736023  2.35087248  2.26130727  3.55010431  0.52294888  2.22780331
   2.53278978 12.66719162 11.97610471  2.98268618]
 [ 2.84661972  2.9788588   3.98254353  1.45488219  7.99883084  8.80968331
   4.8587401   5.75330625  9.05341657  4.17680613]
 [12.5804987   4.20244099  3.58830069  3.54171873  1.3445298   0.16274503
   1.34676222 14.77354974 12.21124597  5.11094778]
 [ 1.78826947  9.78092657  4.73649841  5.08861028 11.28873682 15.31208779
  11.06547106  0.53850886 12.00751364 10.23873834]
 [10.9819553   7.75975908  1.64723933  3.28071894  1.81287162  1.75702387
   4.42607988 16.08821801  5.45050815  5.88141323]]

80. Consider an arbitrary array, write a function that extract a subpart with a fixed shape and centered on a given element (pad with a `fill` value when necessary) (★★★)

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


C:\anaconda\envs\test3\lib\site-packages\ipykernel_launcher.py:23: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.

81. Consider an array Z = [1,2,3,4,5,6,7,8,9,10,11,12,13,14], how to generate an array R = [[1,2,3,4], [2,3,4,5], [3,4,5,6], …, [11,12,13,14]]? (★★★)

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. Compute a matrix rank (★★★)

TT = np.random.uniform(0,1,(10,10))
U,S,V = np.linalg.svd(TT)
rank = np.sum(S>1e-10)
print(rank)

83. How to find the most frequent value in an array?

UU = np.random.randint(0,10,50)
print(np.bincount(UU).argmax())

84. Extract all the contiguous 3x3 blocks from a random 10x10 matrix (★★★)

VV = np.random.randint(0,5,(10,10))
n = 3
i = 1+(VV.shape[0]-3)
j = 1+(VV.shape[1]-3)
C = stride_tricks.as_strided(VV, shape=(i,j,n,n), strides=VV.strides+VV.strides)
print(C)

[[[[4 4 0]
   [0 3 0]
   [3 3 0]]

  [[4 0 1]
   [3 0 1]
   [3 0 0]]

  [[0 1 4]
   [0 1 0]
   [0 0 4]]

  [[1 4 2]
   [1 0 3]
   [0 4 4]]

  [[4 2 0]
   [0 3 0]
   [4 4 2]]

  [[2 0 3]
   [3 0 0]
   [4 2 2]]

  [[0 3 3]
   [0 0 0]
   [2 2 0]]

  [[3 3 4]
   [0 0 1]
   [2 0 4]]]


 [[[0 3 0]
   [3 3 0]
   [2 2 4]]

  [[3 0 1]
   [3 0 0]
   [2 4 2]]

  [[0 1 0]
   [0 0 4]
   [4 2 2]]

  [[1 0 3]
   [0 4 4]
   [2 2 3]]

  [[0 3 0]
   [4 4 2]
   [2 3 2]]

  [[3 0 0]
   [4 2 2]
   [3 2 3]]

  [[0 0 0]
   [2 2 0]
   [2 3 1]]

  [[0 0 1]
   [2 0 4]
   [3 1 4]]]


 [[[3 3 0]
   [2 2 4]
   [2 3 1]]

  [[3 0 0]
   [2 4 2]
   [3 1 2]]

  [[0 0 4]
   [4 2 2]
   [1 2 2]]

  [[0 4 4]
   [2 2 3]
   [2 2 4]]

  [[4 4 2]
   [2 3 2]
   [2 4 3]]

  [[4 2 2]
   [3 2 3]
   [4 3 2]]

  [[2 2 0]
   [2 3 1]
   [3 2 2]]

  [[2 0 4]
   [3 1 4]
   [2 2 3]]]


 [[[2 2 4]
   [2 3 1]
   [3 2 1]]

  [[2 4 2]
   [3 1 2]
   [2 1 4]]

  [[4 2 2]
   [1 2 2]
   [1 4 4]]

  [[2 2 3]
   [2 2 4]
   [4 4 3]]

  [[2 3 2]
   [2 4 3]
   [4 3 3]]

  [[3 2 3]
   [4 3 2]
   [3 3 0]]

  [[2 3 1]
   [3 2 2]
   [3 0 3]]

  [[3 1 4]
   [2 2 3]
   [0 3 2]]]


 [[[2 3 1]
   [3 2 1]
   [2 0 3]]

  [[3 1 2]
   [2 1 4]
   [0 3 3]]

  [[1 2 2]
   [1 4 4]
   [3 3 4]]

  [[2 2 4]
   [4 4 3]
   [3 4 0]]

  [[2 4 3]
   [4 3 3]
   [4 0 4]]

  [[4 3 2]
   [3 3 0]
   [0 4 1]]

  [[3 2 2]
   [3 0 3]
   [4 1 0]]

  [[2 2 3]
   [0 3 2]
   [1 0 4]]]


 [[[3 2 1]
   [2 0 3]
   [0 2 4]]

  [[2 1 4]
   [0 3 3]
   [2 4 4]]

  [[1 4 4]
   [3 3 4]
   [4 4 0]]

  [[4 4 3]
   [3 4 0]
   [4 0 4]]

  [[4 3 3]
   [4 0 4]
   [0 4 2]]

  [[3 3 0]
   [0 4 1]
   [4 2 3]]

  [[3 0 3]
   [4 1 0]
   [2 3 0]]

  [[0 3 2]
   [1 0 4]
   [3 0 0]]]


 [[[2 0 3]
   [0 2 4]
   [0 0 0]]

  [[0 3 3]
   [2 4 4]
   [0 0 0]]

  [[3 3 4]
   [4 4 0]
   [0 0 4]]

  [[3 4 0]
   [4 0 4]
   [0 4 1]]

  [[4 0 4]
   [0 4 2]
   [4 1 3]]

  [[0 4 1]
   [4 2 3]
   [1 3 0]]

  [[4 1 0]
   [2 3 0]
   [3 0 1]]

  [[1 0 4]
   [3 0 0]
   [0 1 3]]]


 [[[0 2 4]
   [0 0 0]
   [4 4 1]]

  [[2 4 4]
   [0 0 0]
   [4 1 4]]

  [[4 4 0]
   [0 0 4]
   [1 4 2]]

  [[4 0 4]
   [0 4 1]
   [4 2 2]]

  [[0 4 2]
   [4 1 3]
   [2 2 4]]

  [[4 2 3]
   [1 3 0]
   [2 4 2]]

  [[2 3 0]
   [3 0 1]
   [4 2 0]]

  [[3 0 0]
   [0 1 3]
   [2 0 0]]]]

85. Create a 2D array subclass such that Z[i,j] == Z[j,i] (★★★)

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(WW):
    return np.asarray(WW + WW.T - np.diag(WW.diagonal())).view(Symetric)

S = symetric(np.random.randint(0,10,(5,5)))
S[2,3] = 42
print(S)

[[ 7  7  7 11  2]
 [ 7  8  6  4  8]
 [ 7  6  8 42  7]
 [11  4 42  7  8]
 [ 2  8  7  8  1]]

86. Consider a set of p matrices wich shape (n,n) and a set of p vectors with shape (n,1). How to compute the sum of of the p matrix products at once? (result has shape (n,1)) (★★★)

p = 10
n = 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)

[[200.]
 [200.]
 [200.]
 [200.]
 [200.]
 [200.]
 [200.]
 [200.]
 [200.]
 [200.]
 [200.]
 [200.]
 [200.]
 [200.]
 [200.]
 [200.]
 [200.]
 [200.]
 [200.]
 [200.]]

87. Consider a 16x16 array, how to get the block-sum (block size is 4x4)? (★★★)

WW = np.ones((16,16))
k = 4
b_s = np.add.reduceat(np.add.reduceat(WW, np.arange(0, WW.shape[0], k), axis=0),
                                          np.arange(0, WW.shape[1], k), axis=1)
print(b_s)

[[16. 16. 16. 16.]
 [16. 16. 16. 16.]
 [16. 16. 16. 16.]
 [16. 16. 16. 16.]]

88. How to implement the Game of Life using numpy arrays? (★★★)

def iterate(X):
    N = (X[0:-2,0:-2] + X[0:-2,1:-1] + X[0:-2,2:] +
         X[1:-1,0:-2]                + X[1:-1,2:] +
         X[2:  ,0:-2] + X[2:  ,1:-1] + X[2:  ,2:])

    birth = (N==3) & (X[1:-1,1:-1]==0)
    survive = ((N==2) | (N==3)) & (X[1:-1,1:-1]==1)
    X[...] = 0
    X[1:-1,1:-1][birth | survive] = 1
    return X

XX = np.random.randint(0,2,(50,50))
for i in range(100): XX = iterate(XX)
print(XX)

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

89. How to get the n largest values of an array (★★★)

YY = np.arange(10000)
np.random.shuffle(YY)
n = 5

print(YY[np.argsort(YY)[-n:]])

[9995 9996 9997 9998 9999]

90. Given an arbitrary number of vectors, build the cartesian product (every combinations of every item) (★★★)

def cartesian_product(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_product(([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. How to create a record array from a regular array? (★★★)

ZZ = np.array([("Hello", 2.5, 3),
               ("World", 3.6, 2)])
regular= np.core.records.fromarrays(ZZ.T,
                                    names='col1, col2, col3',
                                    formats='S8, f8, i8')
print(regular)

[(b'Hello', 2.5, 3) (b'World', 3.6, 2)]

92. Consider a large vector Z, compute Z to the power of 3 using 3 different methods (★★★)

Z = np.random.rand(int(5e7))

%timeit np.power(Z,3)
%timeit Z*Z*Z
%timeit np.einsum('i,i,i->i',Z,Z,Z)

6 s ± 193 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
ms ± 16.4 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)
ms ± 19.9 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

93. Consider two arrays A and B of shape (8,3) and (2,2). How to find rows of A that contain elements of each row of B regardless of the order of the elements in B? (★★★)

A = np.random.randint(0,5,(8,3))
B = np.random.randint(0,5,(2,2))

C = (A[..., np.newaxis, np.newaxis] == B)
row = np.where(C.any((3,1)).all(1))[0]
print(row)

[0 2 3 6 7]

94. Considering a 10x3 matrix, extract rows with unequal values (e.g. [2,2,3]) (★★★)

Z = np.random.randint(0,5,(10,3))
print(Z)

E = np.all(Z[:,1:] == Z[:,:-1], axis=1)
U = Z[~E]
print(U)

U = Z[Z.max(axis=1) != Z.min(axis=1),:]
print(U)

[[2 2 3]
 [2 1 1]
 [4 4 3]
 [3 3 2]
 [3 3 0]
 [2 0 3]
 [4 4 4]
 [1 4 0]
 [3 1 2]
 [3 3 1]]
[[2 2 3]
 [2 1 1]
 [4 4 3]
 [3 3 2]
 [3 3 0]
 [2 0 3]
 [1 4 0]
 [3 1 2]
 [3 3 1]]
[[2 2 3]
 [2 1 1]
 [4 4 3]
 [3 3 2]
 [3 3 0]
 [2 0 3]
 [1 4 0]
 [3 1 2]
 [3 3 1]]

95. Convert a vector of ints into a matrix binary representation (★★★)

I = np.array([0, 1, 2, 3, 15, 16, 32, 64, 128])
binary = ((I.reshape(-1,1) & (2**np.arange(8))) != 0).astype(int)
print(binary[:,::-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]]

96. Given a two dimensional array, how to extract unique rows? (★★★)

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

97. Considering 2 vectors A & B, write the einsum equivalent of inner, outer, sum, and mul function (★★★)

A = np.random.uniform(0,1,10)
B = np.random.uniform(0,1,10)

print(np.einsum('i->', A))
print(np.einsum('i,i->i', A, B))
print(np.einsum('i,i', A, B))
print(np.einsum('i,j->ij', A, B))

4.075983517837068
[0.11852559 0.97144867 0.29852673 0.00153444 0.01007951 0.09154318
 0.02183748 0.05792591 0.31107278 0.07007961]
1.9525738919183642
[[0.11852559 0.22352757 0.08831299 0.01113801 0.03249977 0.04809327
  0.13463387 0.022667   0.07743695 0.22089436]
 [0.51511109 0.97144867 0.3838074  0.04840568 0.14124367 0.2090129
  0.58511752 0.09851057 0.33654025 0.96000479]
 [0.40065518 0.75559613 0.29852673 0.0376501  0.10985981 0.16257095
  0.45510643 0.07662187 0.26176217 0.74669505]
 [0.0163288  0.03079451 0.01216653 0.00153444 0.00447736 0.00662562
  0.01854798 0.00312274 0.01066818 0.03043175]
 [0.03675965 0.06932508 0.02738949 0.00345435 0.01007951 0.0149157
  0.04175549 0.00702997 0.02401638 0.06850842]
 [0.22560763 0.42547372 0.16809943 0.02120065 0.0618617  0.09154318
  0.25626895 0.04314552 0.14739743 0.42046155]
 [0.01922474 0.03625595 0.01432428 0.00180657 0.00527143 0.00780068
  0.02183748 0.00367657 0.0125602  0.03582885]
 [0.30289416 0.57122849 0.22568534 0.02846337 0.0830537  0.12290317
  0.34405914 0.05792591 0.19789144 0.56449929]
 [0.47613038 0.8979349  0.35476302 0.04474261 0.13055514 0.19319598
  0.54083912 0.09105585 0.31107278 0.88735703]
 [0.03760271 0.070915   0.02801764 0.00353358 0.01031068 0.01525778
  0.04271313 0.0071912  0.02456718 0.07007961]]

98. Considering a path described by two vectors (X,Y), how to sample it using equidistant samples (★★★)?

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
r = np.zeros_like(X)
r[1:] = np.cumsum(dr)
r_int = np.linspace(0, r.max(), 200)
X_int = np.interp(r_int, r, X)
Y_int = np.interp(r_int, r, Y)

99. Given an integer n and a 2D array X, select from X the rows which can be interpreted as draws from a multinomial distribution with n degrees, i.e., the rows which only contain integers and which sum to n. (★★★)

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. Compute bootstrapped 95% confidence intervals for the mean of a 1D array X (i.e., resample the elements of an array with replacement N times, compute the mean of each sample, and then compute percentiles over the means). (★★★)

X = np.random.randn(100)
N = 1000

ind = np.random.randint(0, X.size, (N, X.size))
means = X[ind].mean(axis=1)
conf = np.percentile(means, [2.5, 97.5])
print(conf)

[-0.1795802   0.19789334]

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조문선 (Munsun Jo)