2. Numpy Basics

NumPy is a powerful Python library used for numerical and scientific computing. It provides support for arrays, matrices, and functions to perform mathematical operations efficiently.

1. What is NumPy?

NumPy stands for Numerical Python and provides a high-performance multidimensional array object (ndarray) and tools for working with arrays. It’s the foundation of scientific computing in Python.

2. Installing NumPy

You can install NumPy using pip:

pip install numpy

3. Creating Arrays

The most basic object in NumPy is the ndarray. You can create arrays in multiple ways.

3.1 Using `np.array()`

You can create an array from a list or tuple using np.array().

import numpy as np

# Creating a 1D array
arr1 = np.array([1, 2, 3, 4])

# Creating a 2D array (Matrix)
arr2 = np.array([[1, 2, 3], [4, 5, 6]])

print(arr1)
print(arr2)

3.2 Array Creation Functions

NumPy provides handy functions to create arrays without needing explicit lists or tuples.

np.zeros(shape): Creates an array filled with zeros.
np.ones(shape): Creates an array filled with ones.
np.arange(start, stop, step): Creates an array with values ranging from start to stop (not inclusive) at intervals of step.
np.linspace(start, stop, num): Creates an array with num equally spaced values between start and stop.

Example:

# Creating an array of zeros
zeros_array = np.zeros((3, 3))

# Creating an array of ones
ones_array = np.ones((2, 4))

# Creating an array with a range of values
range_array = np.arange(0, 10, 2)

# Creating an array with evenly spaced values
linspace_array = np.linspace(0, 1, 5)

print(zeros_array)
print(ones_array)
print(range_array)
print(linspace_array)

4. Array Attributes

Important attributes to know about ndarray objects:

shape: The dimensions of the array.
dtype: The data type of the array elements.
size: Total number of elements in the array.
ndim: The number of dimensions (axes) of the array.

Example:

arr = np.array([[1, 2, 3], [4, 5, 6]])

print("Shape:", arr.shape)
print("Data type:", arr.dtype)
print("Number of elements:", arr.size)
print("Number of dimensions:", arr.ndim)

5. Array Indexing and Slicing

Indexing and slicing in NumPy arrays work similarly to Python lists but extend to multiple dimensions.

5.1 Indexing

arr = np.array([1, 2, 3, 4, 5])

# Accessing single elements
print(arr[0])  # First element
print(arr[-1])  # Last element

# Accessing elements in a 2D array
arr2d = np.array([[1, 2, 3], [4, 5, 6]])
print(arr2d[0, 2])  # Element at row 0, column 2

5.2 Slicing

You can slice arrays to get subarrays.

arr = np.array([1, 2, 3, 4, 5])

# Slicing 1D array
print(arr[1:4])  # Elements from index 1 to 3

# Slicing 2D array
arr2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
print(arr2d[1:, 1:])  # Slicing rows and columns

6. Array Operations

6.1 Mathematical Operations

NumPy allows element-wise operations on arrays, including addition, subtraction, multiplication, and division.

arr1 = np.array([1, 2, 3])
arr2 = np.array([4, 5, 6])

# Element-wise addition
print(arr1 + arr2)

# Element-wise multiplication
print(arr1 * arr2)

6.2 Broadcasting

When performing operations on arrays with different shapes, NumPy applies broadcasting rules to make the shapes compatible.

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

# Broadcasting a scalar
print(arr + 5)  # Adds 5 to each element

7. Array Reshaping

You can change the shape of an array using reshape().

arr = np.arange(6)  # Array with values 0 to 5
reshaped = arr.reshape((2, 3))  # Reshape to 2 rows and 3 columns
print(reshaped)

8. Stacking and Splitting Arrays

8.1 Stacking

You can stack arrays vertically or horizontally using vstack() and hstack().

arr1 = np.array([1, 2, 3])
arr2 = np.array([4, 5, 6])

# Vertical stacking
print(np.vstack((arr1, arr2)))

# Horizontal stacking
print(np.hstack((arr1, arr2)))

8.2 Splitting

You can split arrays into smaller arrays using split().

arr = np.array([1, 2, 3, 4, 5, 6])

# Split into 3 arrays
print(np.split(arr, 3))

9. Universal Functions (ufuncs)

NumPy provides universal functions (ufuncs) that operate on arrays element-wise, such as np.sqrt(), np.log(), np.exp(), np.sin(), etc.

arr = np.array([1, 4, 9, 16])

# Square root of each element
print(np.sqrt(arr))

# Natural logarithm
print(np.log(arr))

10. Linear Algebra with NumPy

NumPy provides functions to perform matrix operations, including dot products, transposition, and inversion.

A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])

# Matrix multiplication (dot product)
print(np.dot(A, B))

# Transpose of a matrix
print(A.T)

11. Random Numbers in NumPy

NumPy includes functions to generate random numbers, which are useful in simulations and probabilistic algorithms.

# Random numbers between 0 and 1
rand_arr = np.random.rand(3, 3)

# Random integers between a given range
rand_ints = np.random.randint(0, 10, size=(2, 3))

print(rand_arr)
print(rand_ints)

Important Things in NumPy:

Array Creation: np.array(), zeros(), ones(), arange(), linspace().
Array Indexing/Slicing: Retrieve and modify elements and subarrays.
Element-wise Operations: Perform math operations between arrays.
Reshaping: Change the dimensions of arrays using reshape().
Broadcasting: Perform operations on arrays of different shapes.
Stacking/Splitting: Combine and split arrays.
Linear Algebra: np.dot(), transposition, and matrix inversion.

This tutorial covers the foundational concepts of NumPy. You can dive deeper into each topic by exploring additional methods and functions.

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