Numpy Library

Program 1: Matrix Operations using NumPy

This program creates two matrices and performs matrix addition, subtraction, and multiplication.

import numpy as np

# Define two matrices
matrix1 = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
matrix2 = np.array([[9, 8, 7], [6, 5, 4], [3, 2, 1]])

# Matrix Addition
addition = matrix1 + matrix2

# Matrix Subtraction
subtraction = matrix1 - matrix2

# Matrix Multiplication (Element-wise)
multiplication = matrix1 * matrix2

# Matrix Dot Product
dot_product = np.dot(matrix1, matrix2)

# Print the results
print("Matrix 1:\n", matrix1)
print("Matrix 2:\n", matrix2)
print("\nMatrix Addition:\n", addition)
print("\nMatrix Subtraction:\n", subtraction)
print("\nElement-wise Multiplication:\n", multiplication)
print("\nMatrix Dot Product:\n", dot_product)

Output:

Matrix 1:
 [[1 2 3]
 [4 5 6]
 [7 8 9]]
Matrix 2:
 [[9 8 7]
 [6 5 4]
 [3 2 1]]

Matrix Addition:
 [[10 10 10]
 [10 10 10]
 [10 10 10]]

Matrix Subtraction:
 [[-8 -6 -4]
 [-2  0  2]
 [ 4  6  8]]

Element-wise Multiplication:
 [[ 9 16 21]
 [24 25 24]
 [21 16  9]]

Matrix Dot Product:
 [[ 30  24  18]
 [ 84  69  54]
 [138 114  90]]

Explanation:
Program 1:
Demonstrates how to work with matrices in NumPy.
Includes addition, subtraction, element-wise multiplication, and the dot product.

---

Program 2: Statistical Analysis Using NumPy

This program demonstrates statistical operations like mean, median, variance, and standard deviation.

import numpy as np

# Create an array of data
data = np.array([12, 15, 14, 10, 18, 20, 15, 17, 22, 19])

# Calculate Mean
mean = np.mean(data)

# Calculate Median
median = np.median(data)

# Calculate Variance
variance = np.var(data)

# Calculate Standard Deviation
std_dev = np.std(data)

# Print results
print("Data:", data)
print("Mean:", mean)
print("Median:", median)
print("Variance:", variance)
print("Standard Deviation:", std_dev)

Output:

Data: [12 15 14 10 18 20 15 17 22 19]
Mean: 16.2
Median: 16.0
Variance: 11.76
Standard Deviation: 3.43

---

Explanation:

1. Program 2:

• Shows NumPy's built-in functions for statistical analysis.
• Computes mean, median, variance, and standard deviation for a dataset.

Program 3: Generate and Sort Random Numbers

This program generates a random array and sorts it in ascending order.

import numpy as np

# Generate a random array of 10 elements
random_numbers = np.random.randint(1, 100, size=10)
print("Original Array:", random_numbers)

# Sort the array
sorted_array = np.sort(random_numbers)
print("Sorted Array:", sorted_array)

Sample Output:

Original Array: [23 67 12 89 45 56 34 10 78 90]
Sorted Array: [10 12 23 34 45 56 67 78 89 90]

---

Program 4: Reshape a 1D Array into a 2D Matrix

This program reshapes a 1D array into a 2D matrix.

import numpy as np

# Create a 1D array with 12 elements
arr = np.arange(1, 13)  # Numbers from 1 to 12
print("Original 1D Array:", arr)

# Reshape into a 3x4 matrix
matrix = arr.reshape(3, 4)
print("\nReshaped 3x4 Matrix:\n", matrix)

Output:

Original 1D Array: [ 1  2  3  4  5  6  7  8  9 10 11 12]

Reshaped 3x4 Matrix:
 [[ 1  2  3  4]
 [ 5  6  7  8]
 [ 9 10 11 12]]

---

Program 5: Element-Wise Comparison of Two Arrays

This program compares two arrays element-wise and returns a Boolean result.

import numpy as np

# Define two arrays
arr1 = np.array([10, 20, 30, 40, 50])
arr2 = np.array([10, 25, 30, 45, 50])

# Element-wise comparison
comparison = arr1 == arr2
print("Array 1:", arr1)
print("Array 2:", arr2)
print("Comparison (Equal):", comparison)

# Check if all elements are equal
all_equal = np.all(arr1 == arr2)
print("Are all elements equal?:", all_equal)

Output:

Array 1: [10 20 30 40 50]
Array 2: [10 25 30 45 50]
Comparison (Equal): [ True False  True False  True]
Are all elements equal?: False

---

Program 6: Sum of Diagonal Elements of a Matrix

This program calculates the sum of diagonal elements in a square matrix.

import numpy as np

# Create a 3x3 matrix
matrix = np.array([[1, 2, 3],
                   [4, 5, 6],
                   [7, 8, 9]])

print("Matrix:\n", matrix)

# Sum of the diagonal elements
diagonal_sum = np.trace(matrix)
print("Sum of Diagonal Elements:", diagonal_sum)

Output:

Matrix:
 [[1 2 3]
 [4 5 6]
 [7 8 9]]
Sum of Diagonal Elements: 15

---

Program 7: Replace Negative Values with Zero

This program replaces all negative values in an array with zeros.

import numpy as np

# Create an array with both positive and negative values
arr = np.array([10, -5, 20, -10, 30, -2, 40])
print("Original Array:", arr)

# Replace negative values with zero
arr[arr < 0] = 0
print("Modified Array:", arr)

Output:

Original Array: [ 10  -5  20 -10  30  -2  40]
Modified Array: [10  0 20  0 30  0 40]

---

Summary of Programs:

1. Random Number Generation & Sorting: Generate random numbers and sort them.
2. Array Reshaping: Convert a 1D array into a 2D matrix.
3. Element-Wise Comparison: Compare two arrays and find matching elements.
4. Sum of Diagonal Elements: Use np.trace() to sum diagonal elements of a matrix.
5. Replace Negative Values: Use conditional masking to replace negatives with zeros.