Working with numpy

Index

Generate a sequence
Operations on a single vector
Basics
Calculate statistical measures
Subset a vector

Generate a matrix
Matrix operations
Subset a matrix

If you don’t know, in short - Numpy is a python library which provides support for fast computations over arrays (vectors, matrices, tensors). Its faster compared to structuring the same computation in base python because operations are vectorized & in general you end up writing code that is pretty close to mathematical notation of your operations instead of writing low level code & dealing with errors & overheads that might creep in during these operations.

Import numpy package for current session

import numpy as np

Vectors

Create vectors by generating different sequence of numbers

# sequence of integers between given bounds

w = np.arange(10,25, step=1)

# 10 random integers between given bounds

x = np.random.randint(low=0,high=10,size=10)

# 10 real numbers drawn from standard normal distribution

y = np.random.randn(10)

# A vector of length 10 with all zeroes

z = np.zeros(10)

# Another convenient way to generate a vetor or even an array of zeroes is as follows:

z = np.zeros_like(y)

# generate sequence of numbers between given bounds & fixed step

s = np.arange(start=15, stop=35, step=2)

print(x)

[8 5 8 2 2 6 1 0 2 5]

Single vector operations

Sum of a sequence : \(Sum = \displaystyle\sum_{i=1}^{n} x_i\)

x.sum()

Adding a constant to each element of vector : \(x_{i_{new}} = \displaystyle x_i+c\)

c = 2

X_new = x+c
print(X_new)

[ 2  2 11  4  5  8  7  6  3  2]

Multiplying a constant to each element of vector : \(x_{i_{new}} = \displaystyle x_i*c\)

c = 5

X_new = x*c
print(X_new)

[ 0  0 45 10 15 30 25 20  5  0]

Reverse a vector

S_new = s[::-1]
print(S_new)

[33 31 29 27 25 23 21 19 17 15]

Calculate basic statistical measures

Mean (\(\mu\))

x = np.random.randint(low=0,high=1000,size=100)

x.mean(dtype=np.float32)

475.54001

Standard deviation (\(\sigma\))

x.std(dtype=np.float32)

298.57318

Variance (\(\sigma^2\))

x.var(dtype=np.float32)

89145.938

Subset a vector

Index for maximum & minimum values in a sequence

x.argmax()

x.argmin()

Subset using index

# 2nd to 5th element (excluding 5th)

x[2:5]

array([ 31,   1, 561])

Matrices

Create a matrix

Get a matrix of particular shape by providing numbers

x = np.array([
            [1,2,3,4],
            [1,2,3,4],
            [1,2,3,4]
         ])
x

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

Transpose of a matrix

y = np.array([
            [1,2,3,4],
            [1,2,3,4],
            [1,2,3,4]
         ]).T
y

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

Get a matrix of particular shape

np.zeros(shape=(4,5))

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

np.ones(shape=(4,5))

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

np.random.rand(4,5)

array([[ 0.09429882,  0.34480325,  0.11695385,  0.96194279,  0.53927071],
       [ 0.78844899,  0.7351646 ,  0.43960103,  0.20815778,  0.50149201],
       [ 0.26338585,  0.89077065,  0.20248855,  0.90770632,  0.91826611],
       [ 0.62807109,  0.48525764,  0.55865624,  0.88327996,  0.51471048]])

np.ones_like(x)

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

Matrix operations

Multiply a matrix by constant

5 * x

array([[ 5, 10, 15, 20],
       [ 5, 10, 15, 20],
       [ 5, 10, 15, 20]])

Multiply a matrix by another

y@x  # New matrix maultiplication operator in python3.5+ !

array([[ 3,  6,  9, 12],
       [ 6, 12, 18, 24],
       [ 9, 18, 27, 36],
       [12, 24, 36, 48]])

np.dot(y,x) # numpy based dot product

array([[ 3,  6,  9, 12],
       [ 6, 12, 18, 24],
       [ 9, 18, 27, 36],
       [12, 24, 36, 48]])

x*y.T # elementwise multiplication or hadamard product of two matrices with same shape

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

Subset a matrix

x[:,:]

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

x[:,1:3]

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