NumPy

Objective

In this lesson, you will learn all you need to know to get moving with numpy. ie:

• What is Numpy
• Inspecting Numpy arrays
• Performing array mathematics
• Subsetting, Slicing and Indexing arrays
• Array manipulation

What is Numpy

Numpy is a python package used for scientific computing

Numpy provides arrays which are greater and faster alternatives to traditional python lists. An array is a group of elements of the same data type

A standard numpy array is required to have elements of the same data type.

# Uncomment and run this cell to install numpy
# !pip install numpy

Inspecting our arrays

To use numpy, we'll first import it (you must have it installed for this to work)

# import numpy module
import numpy as np

We can check the version we'll be using by using the __version__ method

# checking the numpy version
np.__version__

'1.26.3'

Numpy gives us a more powerful Python List alternative data structure called a Numpy ndarray, we creat it using the array() from numpy

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

The object that's created by array() is called ndarray. This can be shown by checking the type of the object using type()

# Checking type of object
type(num_arr)

numpy.ndarray

Data Types

The table below describes some of the most common data types we use in numpy

We can check the shape of a numpy array by using the shape attribute as demonstrated below

# shape of array
num_arr.shape

(4,)

Dimensions

Similarly, we find the the number of dimensions in our array using the ndim attribute. A dimension in NumPy refers to the number of axes or levels of depth in an array, determining its shape (e.g., 2D for a matrix, 3D for a tensor).

# finding the number of dimensions
num_arr.ndim

1

Length

In NumPy, the length refers to the size of the first axis (dimension) of an array, which is the number of elements along that axis. We can use the len() method to find the length.

# number of elements in array
len(num_arr)

4

Size

Size in NumPy refers to the total number of elements in an array across all dimensions. We can use the size of a numpy array using the size attribute

# another way to get the number of elements
num_arr.size

4

Data Type(dtype)

dtype in NumPy refers to the data type of the elements stored in an array, such as int, float, bool, etc.

# finding data type of array elements
print(num_arr.dtype.name)

int64

Converting Array Data Types

We cas use astype() method to convert an array from one type to another.

# converting an array
float_arr = np.array([1.2, 3.5, 7.0])

# use astype() to convert to a specific
int_arr = float_arr.astype(int)

print(f'Array: {float_arr}, Data Type: {float_arr.dtype}')
print(f'Array: {int_arr}, Data Type: {int_arr.dtype}')

Array: [1.2 3.5 7. ], Data Type: float64
Array: [1 3 7], Data Type: int64

Ask for help

np.info(np.ndarray.shape)

?np.ndarray.shape

Array mathematics

Numpy has out of the box tools to help us perform some import mathematical operations

Arithmetic Operations

Arithmetic operations in NumPy are element-wise operations like addition, subtraction, multiplication, and division that can be performed directly between arrays or between an array and a scalar.

# creating arrays
array1 = np.array([1, 4, 6, 7])
array2 = np.array([3, 5, 3, 1])

# subtract
difference1 = array2 - array1
print('difference1 =', difference1)

# another way
difference2 = np.subtract(array2, array1)
print('difference2 =', difference2)

As we may notice, numpy does element-wise operations for ordinary arithmetic operations

# sum
summation1 = array1 + array2
print('summation1 =', summation1)

# another way
summation2 = np.add(array1, array2)
print('summation2 =', summation2)

Trigonometric operations

Trigonometric operations in NumPy are functions like np.sin(), np.cos(), and np.tan() that perform element-wise trigonometric calculations on arrays.

# sin
print('sin(array1) =', np.sin(array1))
# cos
print('cos(array1) =', np.cos(array1))
# log
print('log(array1) =', np.log(array1))

# dot product
array1.dot(array2)

Given matrices A and B, the dot operation mulitiplies A with the transpose of B

Research:

another way to dot matrices (arrays)

Comparison

In NumPy, comparison operators perform element-wise comparisons on arrays and return boolean arrays of the same shape, where each element indicates True or False based on the corresponding element-wise comparison.

array1 == array2

array1 > 3

Aggregate functions

NumPy provides several aggregate functions that perform operations across the elements of an array and return a single scalar value.

# average
mean = array1.mean()
print('Mean: ', mean)

# min
minimum = array1.min()
print('Minimum: ', minimum)

# max
maximum = array1.max()
print('Maximum: ', maximum)

# corrcoef
correlation_coefficient = np.corrcoef(array1, array2)
print('Correlation Coefficient: ', correlation_coefficient)

standard_deviation = np.std(array1)
print('Standard Deviation: ', standard_deviation)

Research:

copying arrays (you might meet view(), copy())

Subsetting, Slicing and Indexing

Indexing is the technique we use to access individual elements in an array. 0 represents the first element, 1 the represents second element and so on.

Slicing is used to access elements of an array using a range of two indexes. The first index is the start of the range while the second index is the end of the range. The indexes are separated by a colon ie [start:end]

# Creating numpy arrays of different dimension
# 1D array
arr1 = np.array([1, 4, 6, 7])
print('Array1 (1D): \n', arr1)

# 2D array
arr2 = np.array([[1.5, 2, 3], [4, 5, 6]]) 
print('Array2 (2D): \n', arr2)

#3D array
arr3 = np.array([[[1, 2, 3], [4, 5, 6], [7, 8, 9]], 
                 [[10, 11, 12], [13, 14, 15], [16, 17, 18]]]) 
print('Array3 (3D): \n', arr3)

Array1 (1D): 
 [1 4 6 7]
Array2 (2D): 
 [[1.5 2.  3. ]
 [4.  5.  6. ]]
Array3 (3D): 
 [[[ 1  2  3]
  [ 4  5  6]
  [ 7  8  9]]

 [[10 11 12]
  [13 14 15]
  [16 17 18]]]

# find the dimensions of an array
print('Array1 (1D):', arr1.shape)
print('Array2 (2D):', arr2.shape)
print('Array3 (3D):', arr3.shape)

Array1 (1D): (4,)
Array2 (2D): (2, 3)
Array3 (3D): (2, 3, 3)

Indexing

# accessing items in a 1D array
arr1[2]

6

# accessing items in 2D array
arr2[1, 2]

6.0

# accessing in a 3D array
arr3[0, 1, 2]

6

slicing

# slicing 1D array
arr1[0:3]

array([1, 4, 6])

# slicing a 2D array
arr2[1, 1:]

array([5., 6.])

# slicing a 3D array
first = arr3[0, 2]
second = arr3[1, 0]

np.concatenate((first, second))

array([ 7,  8,  9, 10, 11, 12])

Boolean Indexing

Boolean indexing in NumPy allows you to select elements from an array based on a boolean condition or a boolean array of the same shape. The elements corresponding to True values in the boolean array/condition are selected, while those corresponding to False are discarded.

# boolean indexing
arr1[arr1 < 5]

Research:

Fancy Indexing

Array manipulation

NumPy provides a wide range of functions that allow you to change the shape, dimensions, and structure of arrays to suit your needs

print(arr2)

[[1.5 2.  3. ]
 [4.  5.  6. ]]

# transpose
arr2_transpose1 = np.transpose(arr2) 
print('Transpose1: \n', arr2_transpose1)

# another way
arr2_transpose2 = arr2.T
print('Transpose2: \n', arr2_transpose2)

Transpose1: 
 [[1.5 4. ]
 [2.  5. ]
 [3.  6. ]]
Transpose2: 
 [[1.5 4. ]
 [2.  5. ]
 [3.  6. ]]

# combining arrays
first = arr3[0, 2]
second = arr3[1, 0]

np.concatenate((first, second))

array([ 7,  8,  9, 10, 11, 12])

test_arr1 = np.array([[7, 8, 9], [10, 11, 12]])
test_arr2 = np.array([[1, 2, 3], [4, 5, 6]])

np.concatenate((test_arr1, test_arr2), axis=1)

array([[ 7,  8,  9,  1,  2,  3],
       [10, 11, 12,  4,  5,  6]])

Some homework

Research:

Adding/Removing Elements resize()

append()

insert()

delete()

Changing array shape ravel()

reshape()

# stacking 
# np.vstack((a,b))
# np.hstack((a,b))
# np.column_stack((a,b))
# np.c_[a, b]

# splitting arrays
# np.hsplit()
# np.vsplit()

What's on your mind? Put it in the comments!