1458 lines
28 KiB
Plaintext
1458 lines
28 KiB
Plaintext
< q1
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Import the numpy package under the name `np` (★☆☆)
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< h1
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hint: import … as
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< a1
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import numpy as np
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< q2
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Print the numpy version and the configuration (★☆☆)
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< h2
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hint: np.__version__, np.show_config)
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< a2
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print(np.__version__)
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np.show_config()
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< q3
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Create a null vector of size 10 (★☆☆)
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< h3
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hint: np.zeros
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< a3
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Z = np.zeros(10)
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print(Z)
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< q4
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How to find the memory size of any array (★☆☆)
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< h4
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hint: size, itemsize
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< a4
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Z = np.zeros((10,10))
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print("%d bytes" % (Z.size * Z.itemsize))
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< q5
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How to get the documentation of the numpy add function from the command line? (★☆☆)
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< h5
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hint: np.info
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< a5
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%run `python -c "import numpy; numpy.info(numpy.add)"`
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< q6
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Create a null vector of size 10 but the fifth value which is 1 (★☆☆)
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< h6
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hint: array[4]
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< a6
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Z = np.zeros(10)
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Z[4] = 1
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print(Z)
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< q7
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Create a vector with values ranging from 10 to 49 (★☆☆)
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< h7
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hint: arange
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< a7
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Z = np.arange(10,50)
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print(Z)
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< q8
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Reverse a vector (first element becomes last) (★☆☆)
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< h8
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hint: array[::-1]
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< a8
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Z = np.arange(50)
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Z = Z[::-1]
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print(Z)
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< q9
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Create a 3x3 matrix with values ranging from 0 to 8 (★☆☆)
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< h9
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hint: reshape
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< a9
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Z = np.arange(9).reshape(3, 3)
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print(Z)
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< q10
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Find indices of non-zero elements from [1,2,0,0,4,0] (★☆☆)
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< h10
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hint: np.nonzero
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< a10
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nz = np.nonzero([1,2,0,0,4,0])
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print(nz)
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< q11
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Create a 3x3 identity matrix (★☆☆)
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< h11
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hint: np.eye
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< a11
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Z = np.eye(3)
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print(Z)
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< q12
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Create a 3x3x3 array with random values (★☆☆)
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< h12
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hint: np.random.random
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< a12
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Z = np.random.random((3,3,3))
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print(Z)
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< q13
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Create a 10x10 array with random values and find the minimum and maximum values (★☆☆)
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< h13
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hint: min, max
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< a13
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Z = np.random.random((10,10))
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Zmin, Zmax = Z.min(), Z.max()
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print(Zmin, Zmax)
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< q14
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Create a random vector of size 30 and find the mean value (★☆☆)
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< h14
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hint: mean
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< a14
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Z = np.random.random(30)
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m = Z.mean()
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print(m)
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< q15
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Create a 2d array with 1 on the border and 0 inside (★☆☆)
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< h15
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hint: array[1:-1, 1:-1]
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< a15
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Z = np.ones((10,10))
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Z[1:-1,1:-1] = 0
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print(Z)
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< q16
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How to add a border (filled with 0's) around an existing array? (★☆☆)
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< h16
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hint: np.pad
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< a16
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Z = np.ones((5,5))
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Z = np.pad(Z, pad_width=1, mode='constant', constant_values=0)
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print(Z)
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< q17
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What is the result of the following expression? (★☆☆)
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```python
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0 * np.nan
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np.nan == np.nan
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np.inf > np.nan
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np.nan - np.nan
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np.nan in set([np.nan])
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0.3 == 3 * 0.1
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```
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< h17
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hint: NaN = not a number, inf = infinity
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< a17
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print(0 * np.nan)
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print(np.nan == np.nan)
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print(np.inf > np.nan)
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print(np.nan - np.nan)
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print(np.nan in set([np.nan]))
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print(0.3 == 3 * 0.1)
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< q18
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Create a 5x5 matrix with values 1,2,3,4 just below the diagonal (★☆☆)
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< h18
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hint: np.diag
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< a18
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Z = np.diag(1+np.arange(4),k=-1)
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print(Z)
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< q19
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Create a 8x8 matrix and fill it with a checkerboard pattern (★☆☆)
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< h19
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hint: array[::2]
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< a19
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Z = np.array([[(i + j) % 2 for j in range(8)] for i in range(8)])
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print(Z)
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< q20
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Consider a (6,7,8) shape array, what is the index (x,y,z) of the 100th element?
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< h20
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hint: np.unravel_index
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< a20
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print(np.unravel_index(99,(6,7,8)))
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< q21
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Create a checkerboard 8x8 matrix using the tile function (★☆☆)
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< h21
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hint: np.tile
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< a21
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Z = np.tile( np.array([[0,1],[1,0]]), (4,4))
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print(Z)
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< q22
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Normalize a 5x5 random matrix (★☆☆)
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< h22
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hint: (x -mean)/std
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< a22
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Z = np.random.random((5,5))
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Z = (Z - np.mean (Z)) / (np.std (Z))
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print(Z)
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< q23
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Create a custom dtype that describes a color as four unsigned bytes (RGBA) (★☆☆)
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< h23
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hint: np.dtype
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< a23
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color = np.dtype([("r", np.ubyte, 1),
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("g", np.ubyte, 1),
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("b", np.ubyte, 1),
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("a", np.ubyte, 1)])
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< q24
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Multiply a 5x3 matrix by a 3x2 matrix (real matrix product) (★☆☆)
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< h24
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hint:
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< a24
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Z = np.dot(np.ones((5,3)), np.ones((3,2)))
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print(Z)
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# Alternative solution, in Python 3.5 and above
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Z = np.ones((5,3)) @ np.ones((3,2))
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print(Z)
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< q25
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Given a 1D array, negate all elements which are between 3 and 8, in place. (★☆☆)
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< h25
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hint: >, <
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< a25
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# Author: Evgeni Burovski
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Z = np.arange(11)
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Z[(3 < Z) & (Z <= 8)] *= -1
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print(Z)
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< q26
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What is the output of the following script? (★☆☆)
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```python
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# Author: Jake VanderPlas
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print(sum(range(5),-1))
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from numpy import *
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print(sum(range(5),-1))
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```
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< h26
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hint: np.sum
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< a26
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# Author: Jake VanderPlas
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print(sum(range(5),-1))
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from numpy import *
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print(sum(range(5),-1))
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< q27
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Consider an integer vector Z, which of these expressions are legal? (★☆☆)
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```python
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Z**Z
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2 << Z >> 2
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Z <- Z
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1j*Z
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Z/1/1
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Z<Z>Z
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```
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< h27
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No hints provided...
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< a27
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Z**Z
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2 << Z >> 2
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Z <- Z
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1j*Z
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Z/1/1
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Z<Z>Z
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< q28
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What are the result of the following expressions?
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```python
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np.array(0) / np.array(0)
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np.array(0) // np.array(0)
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np.array([np.nan]).astype(int).astype(float)
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```
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< h28
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No hints provided...
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< a28
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print(np.array(0) / np.array(0))
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print(np.array(0) // np.array(0))
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print(np.array([np.nan]).astype(int).astype(float))
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< q29
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How to round away from zero a float array ? (★☆☆)
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< h29
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hint: np.uniform, np.copysign, np.ceil, np.abs
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< a29
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# Author: Charles R Harris
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Z = np.random.uniform(-10,+10,10)
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print (np.copysign(np.ceil(np.abs(Z)), Z))
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< q30
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How to find common values between two arrays? (★☆☆)
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< h30
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hint: np.intersect1d
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< a30
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Z1 = np.random.randint(0,10,10)
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Z2 = np.random.randint(0,10,10)
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print(np.intersect1d(Z1,Z2))
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< q31
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How to ignore all numpy warnings (not recommended)? (★☆☆)
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< h31
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hint: np.seterr, np.errstate
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< a31
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# Suicide mode on
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defaults = np.seterr(all="ignore")
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Z = np.ones(1) / 0
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# Back to sanity
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_ = np.seterr(**defaults)
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# Equivalently with a context manager
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nz = np.nonzero([1,2,0,0,4,0])
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print(nz)
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< q32
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Is the following expressions true? (★☆☆)
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```python
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np.sqrt(-1) == np.emath.sqrt(-1)
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```
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< h32
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hint: imaginary number
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< a32
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np.sqrt(-1) == np.emath.sqrt(-1)
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< q33
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How to get the dates of yesterday, today and tomorrow? (★☆☆)
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< h33
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hint: np.datetime64, np.timedelta64
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< a33
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yesterday = np.datetime64('today', 'D') - np.timedelta64(1, 'D')
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today = np.datetime64('today', 'D')
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tomorrow = np.datetime64('today', 'D') + np.timedelta64(1, 'D')
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< q34
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How to get all the dates corresponding to the month of July 2016? (★★☆)
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< h34
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hint: np.arange(dtype=datetime64['D'])
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< a34
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Z = np.arange('2016-07', '2016-08', dtype='datetime64[D]')
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print(Z)
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< q35
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How to compute ((A+B)*(-A/2)) in place (without copy)? (★★☆)
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< h35
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hint: np.add(out=), np.negative(out=), np.multiply(out=), np.divide(out=)
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< a35
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A = np.ones(3)*1
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B = np.ones(3)*2
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C = np.ones(3)*3
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np.add(A,B,out=B)
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np.divide(A,2,out=A)
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np.negative(A,out=A)
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np.multiply(A,B,out=A)
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< q36
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Extract the integer part of a random array of positive numbers using 4 different methods (★★☆)
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< h36
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hint: %, np.floor, astype, np.trunc
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< a36
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Z = np.random.uniform(0,10,10)
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print (Z - Z%1)
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print (np.floor(Z))
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print (Z.astype(int))
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print (np.trunc(Z))
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< q37
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Create a 5x5 matrix with row values ranging from 0 to 4 (★★☆)
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< h37
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hint: np.arange
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< a37
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Z = np.zeros((5,5))
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Z += np.arange(5)
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print(Z)
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< q38
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Consider a generator function that generates 10 integers and use it to build an array (★☆☆)
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< h38
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hint: np.fromiter
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< a38
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def generate():
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for x in range(10):
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yield x
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Z = np.fromiter(generate(),dtype=float,count=-1)
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print(Z)
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< q39
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Create a vector of size 10 with values ranging from 0 to 1, both excluded (★★☆)
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< h39
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hint: np.linspace
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< a39
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Z = np.linspace(0,1,11,endpoint=False)[1:]
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print(Z)
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< q40
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Create a random vector of size 10 and sort it (★★☆)
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< h40
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hint: sort
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< a40
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Z = np.random.random(10)
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Z.sort()
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print(Z)
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< q41
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How to sum a small array faster than np.sum? (★★☆)
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< h41
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hint: np.add.reduce
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< a41
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# Author: Evgeni Burovski
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Z = np.arange(10)
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np.add.reduce(Z)
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< q42
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Consider two random array A and B, check if they are equal (★★☆)
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< h42
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hint: np.allclose, np.array_equal
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< a42
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A = np.random.randint(0,2,5)
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B = np.random.randint(0,2,5)
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# Assuming identical shape of the arrays and a tolerance for the comparison of values
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equal = np.allclose(A,B)
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print(equal)
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# Checking both the shape and the element values, no tolerance (values have to be exactly equal)
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equal = np.array_equal(A,B)
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print(equal)
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< q43
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Make an array immutable (read-only) (★★☆)
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< h43
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hint: flags.writeable
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< a43
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Z = np.zeros(10)
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Z.flags.writeable = False
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Z[0] = 1
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< q44
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Consider a random 10x2 matrix representing cartesian coordinates, convert them to polar coordinates (★★☆)
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< h44
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hint: np.sqrt, np.arctan2
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< a44
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Z = np.random.random((10,2))
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X,Y = Z[:,0], Z[:,1]
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R = np.sqrt(X**2+Y**2)
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T = np.arctan2(Y,X)
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print(R)
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print(T)
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< q45
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Create random vector of size 10 and replace the maximum value by 0 (★★☆)
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< h45
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hint: argmax
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< a45
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Z = np.random.random(10)
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Z[Z.argmax()] = 0
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print(Z)
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< q46
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Create a structured array with `x` and `y` coordinates covering the [0,1]x[0,1] area (★★☆)
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< h46
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hint: np.meshgrid
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< a46
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Z = np.zeros((5,5), [('x',float),('y',float)])
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Z['x'], Z['y'] = np.meshgrid(np.linspace(0,1,5),
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np.linspace(0,1,5))
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print(Z)
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< q47
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Given two arrays, X and Y, construct the Cauchy matrix C (Cij =1/(xi - yj))
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< h47
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hint: np.subtract.outer
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< a47
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# Author: Evgeni Burovski
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X = np.arange(8)
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Y = X + 0.5
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C = 1.0 / np.subtract.outer(X, Y)
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print(np.linalg.det(C))
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< q48
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Print the minimum and maximum representable value for each numpy scalar type (★★☆)
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< h48
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hint: np.iinfo, np.finfo, eps
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< a48
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for dtype in [np.int8, np.int32, np.int64]:
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print(np.iinfo(dtype).min)
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print(np.iinfo(dtype).max)
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for dtype in [np.float32, np.float64]:
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print(np.finfo(dtype).min)
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print(np.finfo(dtype).max)
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print(np.finfo(dtype).eps)
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< q49
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How to print all the values of an array? (★★☆)
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< h49
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hint: np.set_printoptions
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< a49
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np.set_printoptions(threshold=np.nan)
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Z = np.zeros((16,16))
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|
print(Z)
|
|
|
|
< q50
|
|
How to find the closest value (to a given scalar) in a vector? (★★☆)
|
|
|
|
< h50
|
|
hint: argmin
|
|
|
|
< a50
|
|
Z = np.arange(100)
|
|
v = np.random.uniform(0,100)
|
|
index = (np.abs(Z-v)).argmin()
|
|
print(Z[index])
|
|
|
|
< q51
|
|
Create a structured array representing a position (x,y) and a color (r,g,b) (★★☆)
|
|
|
|
< h51
|
|
hint: dtype
|
|
|
|
< a51
|
|
Z = np.zeros(10, [ ('position', [ ('x', float, 1),
|
|
('y', float, 1)]),
|
|
('color', [ ('r', float, 1),
|
|
('g', float, 1),
|
|
('b', float, 1)])])
|
|
print(Z)
|
|
|
|
< q52
|
|
Consider a random vector with shape (100,2) representing coordinates, find point by point distances (★★☆)
|
|
|
|
< h52
|
|
hint: np.atleast_2d, T, np.sqrt
|
|
|
|
< a52
|
|
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)
|
|
|
|
< q53
|
|
How to convert a float (32 bits) array into an integer (32 bits) in place?
|
|
|
|
< h53
|
|
hint: view and [:] =
|
|
|
|
< a53
|
|
# Thanks Vikas (https://stackoverflow.com/a/10622758/5989906)
|
|
# & unutbu (https://stackoverflow.com/a/4396247/5989906)
|
|
Z = (np.random.rand(10)*100).astype(np.float32)
|
|
Y = Z.view(np.int32)
|
|
Y[:] = Z
|
|
print(Y)
|
|
|
|
< q54
|
|
How to read the following file? (★★☆)
|
|
```
|
|
1, 2, 3, 4, 5
|
|
6, , , 7, 8
|
|
, , 9,10,11
|
|
```
|
|
|
|
< h54
|
|
hint: np.genfromtxt
|
|
|
|
< a54
|
|
from io import StringIO
|
|
|
|
# Fake file
|
|
s = StringIO('''1, 2, 3, 4, 5
|
|
|
|
6, , , 7, 8
|
|
|
|
, , 9,10,11
|
|
''')
|
|
Z = np.genfromtxt(s, delimiter=",", dtype=np.int)
|
|
print(Z)
|
|
|
|
< q55
|
|
What is the equivalent of enumerate for numpy arrays? (★★☆)
|
|
|
|
< h55
|
|
hint: np.ndenumerate, np.ndindex
|
|
|
|
< a55
|
|
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])
|
|
|
|
< q56
|
|
Generate a generic 2D Gaussian-like array (★★☆)
|
|
|
|
< h56
|
|
hint: np.meshgrid, np.exp
|
|
|
|
< a56
|
|
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 * sigma**2 ) ) )
|
|
print(G)
|
|
|
|
< q57
|
|
How to randomly place p elements in a 2D array? (★★☆)
|
|
|
|
< h57
|
|
hint: np.put, np.random.choice
|
|
|
|
< a57
|
|
# 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)
|
|
|
|
< q58
|
|
Subtract the mean of each row of a matrix (★★☆)
|
|
|
|
< h58
|
|
hint: mean(axis=,keepdims=)
|
|
|
|
< a58
|
|
# 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)
|
|
|
|
< q59
|
|
How to sort an array by the nth column? (★★☆)
|
|
|
|
< h59
|
|
hint: argsort
|
|
|
|
< a59
|
|
# Author: Steve Tjoa
|
|
|
|
Z = np.random.randint(0,10,(3,3))
|
|
print(Z)
|
|
print(Z[Z[:,1].argsort()])
|
|
|
|
< q60
|
|
How to tell if a given 2D array has null columns? (★★☆)
|
|
|
|
< h60
|
|
hint: any, ~
|
|
|
|
< a60
|
|
# Author: Warren Weckesser
|
|
|
|
Z = np.random.randint(0,3,(3,10))
|
|
print((~Z.any(axis=0)).any())
|
|
|
|
< q61
|
|
Find the nearest value from a given value in an array (★★☆)
|
|
|
|
< h61
|
|
hint: np.abs, argmin, flat
|
|
|
|
< a61
|
|
Z = np.random.uniform(0,1,10)
|
|
z = 0.5
|
|
m = Z.flat[np.abs(Z - z).argmin()]
|
|
print(m)
|
|
|
|
< q62
|
|
Considering two arrays with shape (1,3) and (3,1), how to compute their sum using an iterator? (★★☆)
|
|
|
|
< h62
|
|
hint: np.nditer
|
|
|
|
< a62
|
|
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])
|
|
|
|
< q63
|
|
Create an array class that has a name attribute (★★☆)
|
|
|
|
< h63
|
|
hint: class method
|
|
|
|
< a63
|
|
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)
|
|
|
|
< q64
|
|
Consider a given vector, how to add 1 to each element indexed by a second vector (be careful with repeated indices)? (★★★)
|
|
|
|
< h64
|
|
hint: np.bincount | np.add.at
|
|
|
|
< a64
|
|
# 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)
|
|
|
|
< q65
|
|
How to accumulate elements of a vector (X) to an array (F) based on an index list (I)? (★★★)
|
|
|
|
< h65
|
|
hint: np.bincount
|
|
|
|
< a65
|
|
# 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)
|
|
|
|
< q66
|
|
Considering a (w,h,3) image of (dtype=ubyte), compute the number of unique colors (★★★)
|
|
|
|
< h66
|
|
hint: np.unique
|
|
|
|
< a66
|
|
# Author: Nadav Horesh
|
|
|
|
w,h = 16,16
|
|
I = np.random.randint(0,2,(h,w,3)).astype(np.ubyte)
|
|
F = I[...,0]*256*256 + I[...,1]*256 +I[...,2]
|
|
n = len(np.unique(F))
|
|
print(np.unique(I))
|
|
|
|
< q67
|
|
Considering a four dimensions array, how to get sum over the last two axis at once? (★★★)
|
|
|
|
< h67
|
|
hint: sum(axis=(-2,-1))
|
|
|
|
< a67
|
|
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)
|
|
|
|
< q68
|
|
Considering a one-dimensional vector D, how to compute means of subsets of D using a vector S of same size describing subset indices? (★★★)
|
|
|
|
< h68
|
|
hint: np.bincount
|
|
|
|
< a68
|
|
# 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())
|
|
|
|
< q69
|
|
How to get the diagonal of a dot product? (★★★)
|
|
|
|
< h69
|
|
hint: np.diag
|
|
|
|
< a69
|
|
# 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)
|
|
|
|
< q70
|
|
Consider the vector [1, 2, 3, 4, 5], how to build a new vector with 3 consecutive zeros interleaved between each value? (★★★)
|
|
|
|
< h70
|
|
hint: array[::4]
|
|
|
|
< a70
|
|
# 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)
|
|
|
|
< q71
|
|
Consider an array of dimension (5,5,3), how to mulitply it by an array with dimensions (5,5)? (★★★)
|
|
|
|
< h71
|
|
hint: array[:, :, None]
|
|
|
|
< a71
|
|
A = np.ones((5,5,3))
|
|
B = 2*np.ones((5,5))
|
|
print(A * B[:,:,None])
|
|
|
|
< q72
|
|
How to swap two rows of an array? (★★★)
|
|
|
|
< h72
|
|
hint: array[[]] = array[[]]
|
|
|
|
< a72
|
|
# Author: Eelco Hoogendoorn
|
|
|
|
A = np.arange(25).reshape(5,5)
|
|
A[[0,1]] = A[[1,0]]
|
|
print(A)
|
|
|
|
< q73
|
|
Consider a set of 10 triplets describing 10 triangles (with shared vertices), find the set of unique line segments composing all the triangles (★★★)
|
|
|
|
< h73
|
|
hint: repeat, np.roll, np.sort, view, np.unique
|
|
|
|
< a73
|
|
# 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)
|
|
|
|
< q74
|
|
Given an array C that is a bincount, how to produce an array A such that np.bincount(A) == C? (★★★)
|
|
|
|
< h74
|
|
hint: np.repeat
|
|
|
|
< a74
|
|
# 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)
|
|
|
|
< q75
|
|
How to compute averages using a sliding window over an array? (★★★)
|
|
|
|
< h75
|
|
hint: np.cumsum
|
|
|
|
< a75
|
|
# 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))
|
|
|
|
< q76
|
|
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]) (★★★)
|
|
|
|
< h76
|
|
hint: from numpy.lib import stride_tricks
|
|
|
|
< a76
|
|
# 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)
|
|
|
|
< q77
|
|
How to negate a boolean, or to change the sign of a float inplace? (★★★)
|
|
|
|
< h77
|
|
hint: np.logical_not, np.negative
|
|
|
|
< a77
|
|
# 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)
|
|
|
|
< q78
|
|
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])? (★★★)
|
|
|
|
< h78
|
|
No hints provided...
|
|
|
|
< a78
|
|
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(P0, P1, p))
|
|
|
|
< q79
|
|
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])? (★★★)
|
|
|
|
< h79
|
|
No hints provided...
|
|
|
|
< a79
|
|
# 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]))
|
|
|
|
< q80
|
|
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) (★★★)
|
|
|
|
< h80
|
|
hint: minimum maximum
|
|
|
|
< a80
|
|
# 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)
|
|
|
|
< q81
|
|
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]]? (★★★)
|
|
|
|
< h81
|
|
hint: stride_tricks.as_strided
|
|
|
|
< a81
|
|
# 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)
|
|
|
|
< q82
|
|
Compute a matrix rank (★★★)
|
|
|
|
< h82
|
|
hint: np.linalg.svd
|
|
|
|
< a82
|
|
# 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)
|
|
|
|
< q83
|
|
How to find the most frequent value in an array?
|
|
|
|
< h83
|
|
hint: np.bincount, argmax
|
|
|
|
< a83
|
|
Z = np.random.randint(0,10,50)
|
|
print(np.bincount(Z).argmax())
|
|
|
|
< q84
|
|
Extract all the contiguous 3x3 blocks from a random 10x10 matrix (★★★)
|
|
|
|
< h84
|
|
hint: stride_tricks.as_strided
|
|
|
|
< a84
|
|
# 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)
|
|
|
|
< q85
|
|
Create a 2D array subclass such that Z[i,j] == Z[j,i] (★★★)
|
|
|
|
< h85
|
|
hint: class method
|
|
|
|
< a85
|
|
# 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)
|
|
|
|
< q86
|
|
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)) (★★★)
|
|
|
|
< h86
|
|
hint: np.tensordot
|
|
|
|
< a86
|
|
# 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.
|
|
|
|
< q87
|
|
Consider a 16x16 array, how to get the block-sum (block size is 4x4)? (★★★)
|
|
|
|
< h87
|
|
hint: np.add.reduceat
|
|
|
|
< a87
|
|
# 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)
|
|
|
|
< q88
|
|
How to implement the Game of Life using numpy arrays? (★★★)
|
|
|
|
< h88
|
|
No hints provided...
|
|
|
|
< a88
|
|
# 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)
|
|
|
|
< q89
|
|
How to get the n largest values of an array (★★★)
|
|
|
|
< h89
|
|
hint: np.argsort | np.argpartition
|
|
|
|
< a89
|
|
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]])
|
|
|
|
< q90
|
|
Given an arbitrary number of vectors, build the cartesian product (every combinations of every item) (★★★)
|
|
|
|
< h90
|
|
hint: np.indices
|
|
|
|
< a90
|
|
# 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])))
|
|
|
|
< q91
|
|
How to create a record array from a regular array? (★★★)
|
|
|
|
< h91
|
|
hint: np.core.records.fromarrays
|
|
|
|
< a91
|
|
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)
|
|
|
|
< q92
|
|
Consider a large vector Z, compute Z to the power of 3 using 3 different methods (★★★)
|
|
|
|
< h92
|
|
hint: np.power, *, np.einsum
|
|
|
|
< a92
|
|
# 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)
|
|
|
|
< q93
|
|
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? (★★★)
|
|
|
|
< h93
|
|
hint: np.where
|
|
|
|
< a93
|
|
# 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)
|
|
|
|
< q94
|
|
Considering a 10x3 matrix, extract rows with unequal values (e.g. [2,2,3]) (★★★)
|
|
|
|
< h94
|
|
No hints provided...
|
|
|
|
< a94
|
|
# 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)
|
|
|
|
< q95
|
|
Convert a vector of ints into a matrix binary representation (★★★)
|
|
|
|
< h95
|
|
hint: np.unpackbits
|
|
|
|
< a95
|
|
# Author: Warren Weckesser
|
|
|
|
I = np.array([0, 1, 2, 3, 15, 16, 32, 64, 128])
|
|
B = ((I.reshape(-1,1) & (2**np.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))
|
|
|
|
< q96
|
|
Given a two dimensional array, how to extract unique rows? (★★★)
|
|
|
|
< h96
|
|
hint: np.ascontiguousarray | np.unique
|
|
|
|
< a96
|
|
# 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)
|
|
|
|
# Author: Andreas Kouzelis
|
|
# NumPy >= 1.13
|
|
uZ = np.unique(Z, axis=0)
|
|
print(uZ)
|
|
|
|
< q97
|
|
Considering 2 vectors A & B, write the einsum equivalent of inner, outer, sum, and mul function (★★★)
|
|
|
|
< h97
|
|
hint: np.einsum
|
|
|
|
< a97
|
|
# 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)
|
|
|
|
< q98
|
|
Considering a path described by two vectors (X,Y), how to sample it using equidistant samples (★★★)?
|
|
|
|
< h98
|
|
hint: np.cumsum, np.interp
|
|
|
|
< a98
|
|
# 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)
|
|
|
|
< q99
|
|
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. (★★★)
|
|
|
|
< h99
|
|
hint: np.logical_and.reduce, np.mod
|
|
|
|
< a99
|
|
# 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])
|
|
|
|
< q100
|
|
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). (★★★)
|
|
|
|
< h100
|
|
hint: np.percentile
|
|
|
|
< a100
|
|
# 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)
|
|
|