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import numpy as np
1. Write a function to generate square arrays of size $n \times n$ that increment by one in layers. For example, for n=11, we have
array([[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
[1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1],
[1, 2, 3, 3, 3, 3, 3, 3, 3, 2, 1],
[1, 2, 3, 4, 4, 4, 4, 4, 3, 2, 1],
[1, 2, 3, 4, 5, 5, 5, 4, 3, 2, 1],
[1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1],
[1, 2, 3, 4, 5, 5, 5, 4, 3, 2, 1],
[1, 2, 3, 4, 4, 4, 4, 4, 3, 2, 1],
[1, 2, 3, 3, 3, 3, 3, 3, 3, 2, 1],
[1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1],
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]])Generate a $13 \times 13$ square.
In [31]:
def f(n):
x = np.ones((n, n)).astype('int')
for i in range(1, (n+1)//2):
x[i:-i, i:-i] += 1
return x
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f(13)
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2. Generate the following array starting from np.arange(1, 25)
array([[ 1, 5, 9, 13, 17, 21],
[ 2, 6, 10, 14, 18, 22],
[ 3, 7, 11, 15, 19, 23],
[ 4, 8, 12, 16, 20, 24]])
In [38]:
x = np.arange(1, 25)
x = x.reshape((6,4)).T
x
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x.sum(axis=1)
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x.sum(axis=0)
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xn = x/x.sum(axis=1)[:, np.newaxis]
np.sum(xn, axis=1)
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x % 12
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x[1:3, 1:5]
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3. Create the $12 \times 12$ multiplicaiton table below using the vector np.arange(1, 13) and broadcasting.
array([[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12],
[ 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24],
[ 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36],
[ 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48],
[ 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60],
[ 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72],
[ 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84],
[ 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96],
[ 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108],
[ 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120],
[ 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132],
[ 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144]])
In [69]:
x = np.arange(1, 13)
x[:, np.newaxis] * x[np.newaxis, :]
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4. Calculate the pairwise distance matrix between the column vectors of the following array (use Euclidean distance). This should be a $6 \times 6$ array. Try to calculate the distance matrix using different approaches (e.g. loops, broadcasting, scipy funcitons).
array([[ 1, 5, 9, 13, 17, 21],
[ 2, 6, 10, 14, 18, 22],
[ 3, 7, 11, 15, 19, 23],
[ 4, 8, 12, 16, 20, 24]])Plot the resulting distance matrix as a "heatmap" using matlplotlib.
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x = np.arange(1, 25).reshape((6,4))
x
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np.sqrt(np.sum((x[np.newaxis, :, :] - x[:, np.newaxis, :])**2, -1))
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In [75]:
from scipy.spatial import distance_matrix
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distance_matrix(x, x)
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