Lecture 3 : Scientific computing with Python (Correction)

November, 2021 - François HU

Master of Science in Artificial Intelligence Systems - EPITA

This lecture is available here: https://curiousml.github.io/

import numpy as np

Exercice 1

generate arr1:

[[ 0  4  8 12 16]
 [ 1  5  9 13 17]
 [ 2  6 10 14 18]
 [ 3  7 11 15 19]]

arr = np.arange(0, 20)
arr1 = arr.reshape((4, 5), order='F')
print(arr1)

[[ 0  4  8 12 16]
 [ 1  5  9 13 17]
 [ 2  6 10 14 18]
 [ 3  7 11 15 19]]

generate arr2

[[ 0  1  4  9 16]
 [ 1  4  9 16 25]
 [ 4  9 16 25 36]
 [ 9 16 25 36 49]]

# method 1: with a single for loop

arr2 = np.empty((4, 5), dtype=int)
for i in range(4):
    arr2[i] = np.arange(0+i, 5+i)**2

print(arr2)

[[ 0  1  4  9 16]
 [ 1  4  9 16 25]
 [ 4  9 16 25 36]
 [ 9 16 25 36 49]]

# method 2: tile method

A = np.tile(np.arange(5), (4,1))
B = np.tile(np.arange(4), (5,1)).T
arr2 = (A+B)**2
print(arr2)

[[ 0  1  4  9 16]
 [ 1  4  9 16 25]
 [ 4  9 16 25 36]
 [ 9 16 25 36 49]]

# method 3: with mgrid method

A, B = np.mgrid[0:4, 0:5]
arr2 = (A+B)**2
print(arr2)

[[ 0  1  4  9 16]
 [ 1  4  9 16 25]
 [ 4  9 16 25 36]
 [ 9 16 25 36 49]]

generate arr3

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

arr = [[0, 1], [1, 0]]

arr3 = np.tile(arr, (3, 3))
print(arr3)

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

Exercice 3

extract from arr1

[[ 6 18 10]
 [ 7 19 11]
 [ 5 17  9]]

print(arr1)

[[ 0  4  8 12 16]
 [ 1  5  9 13 17]
 [ 2  6 10 14 18]
 [ 3  7 11 15 19]]

arr = arr1[[2, 3, 1], :]
arr = arr[:, [1, 4, 2]]
print(arr)

[[ 6 18 10]
 [ 7 19 11]
 [ 5 17  9]]

Exercice 4.

Replace all the items with value 0 of arr3 by -1

print(arr3)

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

arr3[arr3 == 0] = -1
print(arr3)

[[-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]]

Exercice 4 bis

Create a random vector of size 20 (all values between $[0, 1)$) and replace:

• the maximum value by $-1$
• and the second maximum value by $-2$

arr = np.random.rand(20)
print(arr)
arr[np.argmax(arr)] = -1
arr[np.argmax(arr)] = -2
print(arr)

[0.45872932 0.02738977 0.50322762 0.60618899 0.08398527 0.15019626
 0.72605628 0.99079127 0.63991756 0.68164655 0.12079612 0.93871948
 0.63168153 0.03420702 0.48203706 0.80210342 0.46730872 0.60330258
 0.10317196 0.73161766]
[ 0.45872932  0.02738977  0.50322762  0.60618899  0.08398527  0.15019626
  0.72605628 -1.          0.63991756  0.68164655  0.12079612 -2.
  0.63168153  0.03420702  0.48203706  0.80210342  0.46730872  0.60330258
  0.10317196  0.73161766]