Numpy - Exercises

Here is a series of tests to check your knowledge in Numpy. The goal is for this library and the vectorized programming it implies to become natural. You should forget about classic programming with loops (do not use a for loop or anything else in this notebook except for list comprehension).

Functions should never modify their arguments.

The exercises indicate the number of lines in the answer. This includes the function header when there is one.

Remember to test your results.

import numpy as np
rand = np.random.RandomState(123)

A = np.arange(12).reshape(3,4)
B = rand.randint(-10, 10, size=(5,5))
print(A, '\n')
print(B)

[[ 0  1  2  3]
 [ 4  5  6  7]
 [ 8  9 10 11]] 

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

Square Matrix

Create the 5x5 square matrix containing the first 25 integers, from 1 to 25.

1 line

array([[ 1,  2,  3,  4,  5],
       [ 6,  7,  8,  9, 10],
       [11, 12, 13, 14, 15],
       [16, 17, 18, 19, 20],
       [21, 22, 23, 24, 25]])

Vector Norm

Return the Euclidean norm of a vector without using the norm function.

2 lines

def norm(v):
    

Sub-Matrix

Extract the sub-matrix of size (n-2)x(m-2) that removes the borders of the nxm matrix A.

2 lines

def submat(A):

Random Vector

Create a function that takes a size n and returns a random integer vector of size n between -a and +a and centered as close as possible to 0.

3 lines

def rand_vec(n, a):

Trace

Return the trace of a matrix without using the trace function (you have to find the missing elements yourself).

2 lines

def trace(A):
 

Matrix of Multiples of 3

Round the given matrix to the nearest multiple of 3 (for each value).

2 lines

def round3(A):

Count of 9s

Count the number of 9s in an integer matrix A given as a parameter.

2 lines

def nb9(A):

Column with the Smallest Average

Return the index of the column of a matrix with the smallest average.

2 lines

def min_col_mean(A):

ChessSum

We consider the matrix as a chessboard with alternating white and black squares. The square at [0,0] is black. Calculate the sum of the values on the white squares.

2 lines

def chess_sum(A):

2 Minimums

Return the 2 smallest values of a matrix using a method with linear complexity. Note that if the matrix has its minimum value duplicated, the answer is twice this minimum value.

6 lines

def mins(A):

Rows in Order

Sort the rows of a matrix in ascending order of their average.

2 lines

def sort_lines(A):

Unique Values

Provide the list of unique values (appearing only once) in a numpy array (the unique function will be useful).

3 lines

def val_unique(A):

Magic Tensor

Construct a 3D tensor of size nxnxn using n times the first n² integers and such that the sum of the elements of each plane (slice) is always the same.

3 lines

def mk_magic_tensor(n):

Tensor Slices

Extract all the slices of a 3D tensor. We return a list of arrays.

5 lines (2 lines with the take function)

def extract_planes(T):