NTDS’17 demo 3: Numpy

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Copyright © Code Fetcher 2022

Hermina Petric Maretic, EPFL LTS4

NumPy is the fundamental package for scientific computing with Python. It contains among other things:

a powerful N-dimensional array object
sophisticated (broadcasting) functions
tools for integrating C/C++ and Fortran code
useful linear algebra, Fourier transform, and random number capabilities

Besides its obvious scientific uses, NumPy can also be used as an efficient multi-dimensional container of generic data. Arbitrary data-types can be defined. This allows NumPy to seamlessly and speedily integrate with a wide variety of databases.

In [1]:

import numpy as np

In [2]:

#create a numpy array
a = np.array([1,2,3,4])
a

Out[2]:

array([1, 2, 3, 4])

In [3]:

#or a 2 dimensional array
m = np.array([[1,2],[3,4]])
m

Out[3]:

array([[1, 2],
       [3, 4]])

In [4]:

m[0,0]

Out[4]:

In [5]:

m[:,1]

Out[5]:

array([2, 4])

In [6]:

a[:2]

Out[6]:

array([1, 2])

In [7]:

a[-2] #second last element of the array

Out[7]:

In [8]:

a[-2:] #last two elements of the array

Out[8]:

array([3, 4])

Careful if you’re used to Python list

In [9]:

b = [1,2,3,4]

In [10]:

b + b
b

Out[10]:

[1, 2, 3, 4]

In [11]:

a + a
a

Out[11]:

array([1, 2, 3, 4])

In [12]:

#if you want to add elements to a
np.append(a,a)

Out[12]:

array([1, 2, 3, 4, 1, 2, 3, 4])

In [13]:

np.append(a,[1,2,3])

Out[13]:

array([1, 2, 3, 4, 1, 2, 3])

In [14]:

np.insert(a, 1, 5) #insert 5 on position number 1

Out[14]:

array([1, 5, 2, 3, 4])

Basic arithmetics with numpy arrays

In [15]:

a + 3

Out[15]:

array([4, 5, 6, 7])

In [16]:

a * 3

Out[16]:

array([ 3,  6,  9, 12])

In [17]:

a ** 3

Out[17]:

array([ 1,  8, 27, 64])

In [18]:

a * a

Out[18]:

array([ 1,  4,  9, 16])

In [19]:

a.sum()

Out[19]:

In [20]:

m * m #still elementwise multiplication

Out[20]:

array([[ 1,  4],
       [ 9, 16]])

In [21]:

np.dot(m,m) #standard matrix multiplication

Out[21]:

array([[ 7, 10],
       [15, 22]])

In [22]:

m = np.matrix(m) #there is a type matrix
m * m #for matrices, multiplication works as we're used to

Out[22]:

matrix([[ 7, 10],
        [15, 22]])

Some functions to create arrays

In [23]:

x = np.arange(0,10,2) #beginning, end, step
x

Out[23]:

array([0, 2, 4, 6, 8])

In [24]:

np.linspace(0,10,5) #beginning, end, number of variables

Out[24]:

array([  0. ,   2.5,   5. ,   7.5,  10. ])

In [25]:

np.logspace(0,10,10,base=2) #beginning, end, number of variables

Out[25]:

array([  1.00000000e+00,   2.16011948e+00,   4.66611616e+00,
         1.00793684e+01,   2.17726400e+01,   4.70315038e+01,
         1.01593667e+02,   2.19454460e+02,   4.74047853e+02,
         1.02400000e+03])

In [26]:

np.diag([1,2,3])

Out[26]:

array([[1, 0, 0],
       [0, 2, 0],
       [0, 0, 3]])

In [27]:

np.zeros(5)

Out[27]:

array([ 0.,  0.,  0.,  0.,  0.])

In [28]:

np.ones((3,3))

Out[28]:

array([[ 1.,  1.,  1.],
       [ 1.,  1.,  1.],
       [ 1.,  1.,  1.]])

In [29]:

np.random.rand(5,2)

Out[29]:

array([[ 0.95867801,  0.36665502],
       [ 0.12711337,  0.17199144],
       [ 0.06886422,  0.08173259],
       [ 0.07495435,  0.73382897],
       [ 0.49609348,  0.4109899 ]])

Some linear algebra functions

In [30]:

np.diag(m)

Out[30]:

array([1, 4])

In [31]:

np.trace(m)

Out[31]:

In [32]:

m.T

Out[32]:

matrix([[1, 3],
        [2, 4]])

In [33]:

m1 = np.linalg.inv(m)
m1

Out[33]:

matrix([[-2. ,  1. ],
        [ 1.5, -0.5]])

In [34]:

np.linalg.det(m)

Out[34]:

-2.0000000000000004

In [35]:

np.linalg.det(m1)

Out[35]:

-0.49999999999999967

In [36]:

[eival, eivec] = np.linalg.eig(m)

In [37]:

eival

Out[37]:

array([-0.37228132,  5.37228132])

In [38]:

eivec

Out[38]:

matrix([[-0.82456484, -0.41597356],
        [ 0.56576746, -0.90937671]])

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