NumPy

The NumPy modul offers lot of possibilities in handling list, vectors, matrices, hypermatrices...

import numpy as np

Let us start with lists.

# Create 2 lists
lst1 = [2, 3, 5, 1, 8]
lst2 = [2.2, 4.5, 3, 6.7, 5]

# Convert them into numpy arrays
np_l1 = np.array(lst1)
np_l2 = np.array(lst2)

print(type(np_l1))
print(np_l2)

<class 'numpy.ndarray'>
[2.2 4.5 3.  6.7 5. ]

# Elementwise operations
l1_squared_per_l2 = np_l1**2 / np_l2
print(l1_squared_per_l2)

[ 1.81818182  2.          8.33333333  0.14925373 12.8       ]

# Elemenwise boolean operation
l1_squared_per_l2 < 2

array([ True, False, False,  True, False])

# Choose the elements
l1_squared_per_l2[l1_squared_per_l2 < 2]

array([1.81818182, 0.14925373])

# Construct an equaly spaced array
np.linspace(0, 10, 11)

array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.])

Using NumPy in plotting

import matplotlib.pyplot as plt

x = np.linspace(0, 2*np.pi, 100)
s = np.sin(x)
plt.plot(x, s)

[<matplotlib.lines.Line2D at 0x7effb56e3d30>]

Matrices

# Construct matrices
m1 = np.array([(1,2,3), (4,5,6)])
print(m1)

[[1 2 3]
 [4 5 6]]

m2 = np.arange(1, 7).reshape(2, 3)
print(m2)

[[1 2 3]
 [4 5 6]]

m1.dtype

dtype('int64')

m3 = np.arange(1, 6, .9).reshape(2, 3)
print(m3)

[[1.  1.9 2.8]
 [3.7 4.6 5.5]]

m3.dtype

dtype('float64')

print(m3.size) 
print(m3.shape)

6
(2, 3)

m4 = np.arange(8).reshape(2, 2, 2)
print(m4)

[[[0 1]
  [2 3]]

 [[4 5]
  [6 7]]]

m4.shape

(2, 2, 2)

# Unit matrix
u = np.eye(2)  # eye pronounced as I
print(u)

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

# Zero matrix
z = np.zeros((2, 3))
print(z)

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

# Matrix of ones
o = np.ones((2, 3))
print(o)

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

a = np.array([[1, 2], [3, 4]])
b = np.array([[1, 0], [2, 1]])
print(a)
print(b)

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

# Elemenwise product
c = a*b
print(c)

[[1 0]
 [6 4]]

# Matrix product
d1 = a@b
# or
d2 = a.dot(b)
print(d1)
print(d2)

[[ 5  2]
 [11  4]]
[[ 5  2]
 [11  4]]

Random numbers

rng = np.random.default_rng(1)     # random number generator

m = rng.random((2,3))
print(m)

[[0.51182162 0.9504637  0.14415961]
 [0.94864945 0.31183145 0.42332645]]

m.sum()

3.290252281866131

m.min()

0.14415961271963373

m.max()

0.9504636963259353

Universal functions

# Elementwise evaluation
np.sin(m)

array([[0.48976625, 0.81368514, 0.14366081],
       [0.81262917, 0.30680228, 0.41079554]])

np.exp(m)

array([[1.6683275 , 2.58690892, 1.15506846],
       [2.58221988, 1.36592445, 1.52703271]])