Python NumPy¶

NumPy is the fundamental package for numerical computing in Python. It provides support for large, multi-dimensional arrays and matrices, along with a collection of mathematical functions to operate on these arrays.

Table of Contents¶

1. Basic Concepts
2. Advanced Concepts
3. Exercises
4. Real-World Applications

1. Basic Concepts ¶

1.1 NumPy Arrays¶

In [1]:

import numpy as np

# Creating arrays
arr1 = np.array([1, 2, 3])
arr2 = np.array([[1, 2], [3, 4]])

print("arr1:", arr1)
print("arr2:\n", arr2)
print("Shape of arr2:", arr2.shape)

import numpy as np # Creating arrays arr1 = np.array([1, 2, 3]) arr2 = np.array([[1, 2], [3, 4]]) print("arr1:", arr1) print("arr2:\n", arr2) print("Shape of arr2:", arr2.shape)

arr1: [1 2 3]
arr2:
 [[1 2]
 [3 4]]
Shape of arr2: (2, 2)

1.2 Array Operations¶

NumPy allows element-wise operations for arithmetic, comparisons, etc.

In [2]:

arr3 = np.array([10, 20, 30])

# Element-wise arithmetic
print("arr1 + arr3 =", arr1 + arr3)

# Scalar operations
print("arr1 * 2 =", arr1 * 2)

# Comparison
print("arr3 > 15?", arr3 > 15)

arr3 = np.array([10, 20, 30]) # Element-wise arithmetic print("arr1 + arr3 =", arr1 + arr3) # Scalar operations print("arr1 * 2 =", arr1 * 2) # Comparison print("arr3 > 15?", arr3 > 15)

arr1 + arr3 = [11 22 33]
arr1 * 2 = [2 4 6]
arr3 > 15? [False  True  True]

1.3 Slicing and Indexing¶

In [3]:

arr4 = np.array([10, 11, 12, 13, 14, 15])
print("arr4[1:4] =", arr4[1:4])
arr5 = np.array([[1,2,3],[4,5,6],[7,8,9]])
print("\n", arr5)
print("arr5[0, 1] =", arr5[0, 1])
print("arr5[:, 1] =", arr5[:, 1])

arr4 = np.array([10, 11, 12, 13, 14, 15]) print("arr4[1:4] =", arr4[1:4]) arr5 = np.array([[1,2,3],[4,5,6],[7,8,9]]) print("\n", arr5) print("arr5[0, 1] =", arr5[0, 1]) print("arr5[:, 1] =", arr5[:, 1])

arr4[1:4] = [11 12 13]

 [[1 2 3]
 [4 5 6]
 [7 8 9]]
arr5[0, 1] = 2
arr5[:, 1] = [2 5 8]

2. Advanced Concepts ¶

2.1 Broadcasting¶

NumPy can automatically expand array dimensions to match shapes during operations.

In [4]:

arr6 = np.array([[1, 2, 3], [4, 5, 6]])
arr7 = np.array([10, 20, 30])
# arr6 is (2,3) and arr7 is (3,)

result = arr6 + arr7  # Broadcasting adds arr7 to each row of arr6
print(result)

arr6 = np.array([[1, 2, 3], [4, 5, 6]]) arr7 = np.array([10, 20, 30]) # arr6 is (2,3) and arr7 is (3,) result = arr6 + arr7 # Broadcasting adds arr7 to each row of arr6 print(result)

[[11 22 33]
 [14 25 36]]

2.2 Reshaping and Transposing¶

In [5]:

arr8 = np.arange(1, 7)
print("Original:", arr8)
arr8_reshaped = arr8.reshape(2, 3)
print("\nReshaped to (2,3):\n", arr8_reshaped)

# Transpose
print("\nTransposed:\n", arr8_reshaped.T)

arr8 = np.arange(1, 7) print("Original:", arr8) arr8_reshaped = arr8.reshape(2, 3) print("\nReshaped to (2,3):\n", arr8_reshaped) # Transpose print("\nTransposed:\n", arr8_reshaped.T)

Original: [1 2 3 4 5 6]

Reshaped to (2,3):
 [[1 2 3]
 [4 5 6]]

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

2.3 Mathematical and Statistical Functions¶

NumPy provides a variety of built-in functions for computations like sum, mean, std, etc.

In [6]:

arr9 = np.array([1, 2, 3, 4, 5])
print("Sum:", np.sum(arr9))
print("Mean:", np.mean(arr9))
print("Standard Deviation:", np.std(arr9))

arr9 = np.array([1, 2, 3, 4, 5]) print("Sum:", np.sum(arr9)) print("Mean:", np.mean(arr9)) print("Standard Deviation:", np.std(arr9))

Sum: 15
Mean: 3.0
Standard Deviation: 1.4142135623730951

2.4 Random Module¶

Useful for generating random numbers, random samples, etc.

In [7]:

random_arr = np.random.rand(3, 3)  # uniform distribution
print("Random Array:\n", random_arr)

randint_arr = np.random.randint(0, 10, size=(2, 5))
print("\nRandom Integers:\n", randint_arr)

random_arr = np.random.rand(3, 3) # uniform distribution print("Random Array:\n", random_arr) randint_arr = np.random.randint(0, 10, size=(2, 5)) print("\nRandom Integers:\n", randint_arr)

Random Array:
 [[0.16558855 0.99591053 0.75989262]
 [0.00898257 0.12894033 0.74504858]
 [0.60349745 0.82211221 0.25542086]]

Random Integers:
 [[6 6 1 6 5]
 [3 5 8 0 6]]

3. Exercises ¶

Exercise 1: Basic Array Operations¶

1. Create a NumPy array of shape (4,4) with numbers from 1 to 16.
2. Print the slice containing the second row.
3. Multiply the entire array by 2.

In [8]:

# Your code here

# Your code here

Exercise 2: Reshaping and Broadcasting¶

1. Create a 1D array with numbers from 1 to 9.
2. Reshape it into (3,3).
3. Add a 1D array [10,10,10] to it using broadcasting.

In [9]:

# Your code here

# Your code here

Exercise 3: Statistical Functions¶

1. Generate an array of 100 random numbers (using np.random.randn()).
2. Compute the mean and standard deviation.
3. Print the values.

In [10]:

# Your code here

# Your code here

4. Real-World Applications ¶

Machine Learning¶

• NumPy arrays are the foundation for libraries like scikit-learn, TensorFlow, and PyTorch.

Linear Algebra¶

• Operations like matrix multiplication, decompositions, etc. are common in ML and data analysis.

Signal Processing, Simulations¶

• Researchers often use NumPy for large-scale numerical simulations, random processes, or DSP tasks.

NumPy is indispensable for scientific computing in Python, serving as the backbone for almost every advanced data library!