Mathematical Operations on Arrays in Python

NumPy, a popular library in Python, provides powerful tools for performing mathematical operations on arrays. These operations can be applied element-wise, across specific axes, or on the entire array. This article covers various mathematical operations that can be performed on NumPy arrays.

Importing NumPy

Before performing mathematical operations, you need to import the NumPy library:

    import numpy as np
        

Basic Arithmetic Operations

NumPy allows you to perform basic arithmetic operations like addition, subtraction, multiplication, and division directly on arrays.

    # Creating arrays
    array1 = np.array([1, 2, 3])
    array2 = np.array([4, 5, 6])

    # Element-wise addition
    add_result = array1 + array2
    print("Addition:", add_result)  # Output: [5 7 9]

    # Element-wise subtraction
    sub_result = array1 - array2
    print("Subtraction:", sub_result)  # Output: [-3 -3 -3]

    # Element-wise multiplication
    mul_result = array1 * array2
    print("Multiplication:", mul_result)  # Output: [4 10 18]

    # Element-wise division
    div_result = array1 / array2
    print("Division:", div_result)  # Output: [0.25 0.4  0.5]
        

Mathematical Functions

NumPy provides several mathematical functions that can be applied to arrays.

    # Creating an array
    array = np.array([1, 4, 9, 16])

    # Square root
    sqrt_result = np.sqrt(array)
    print("Square Root:", sqrt_result)  # Output: [1. 2. 3. 4.]

    # Exponential
    exp_result = np.exp(array)
    print("Exponential:", exp_result)

    # Logarithm
    log_result = np.log(array)
    print("Logarithm:", log_result)
        

Aggregate Functions

Aggregate functions operate on the entire array or along specific axes to compute summary statistics.

    # Creating an array
    array = np.array([[1, 2, 3], [4, 5, 6]])

    # Sum of all elements
    sum_result = np.sum(array)
    print("Sum:", sum_result)  # Output: 21

    # Mean of all elements
    mean_result = np.mean(array)
    print("Mean:", mean_result)  # Output: 3.5

    # Maximum and minimum
    max_result = np.max(array)
    min_result = np.min(array)
    print("Max:", max_result)  # Output: 6
    print("Min:", min_result)  # Output: 1
        

Trigonometric Functions

NumPy supports trigonometric functions like sine, cosine, and tangent.

    # Creating an array of angles in radians
    angles = np.array([0, np.pi / 2, np.pi])

    # Sine function
    sin_result = np.sin(angles)
    print("Sine:", sin_result)  # Output: [0. 1. 0.]

    # Cosine function
    cos_result = np.cos(angles)
    print("Cosine:", cos_result)  # Output: [1. 0. -1.]

    # Tangent function
    tan_result = np.tan(angles)
    print("Tangent:", tan_result)
        

Linear Algebra Operations

NumPy also provides support for linear algebra operations such as dot products and matrix multiplication.

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

    # Dot product
    dot_result = np.dot(matrix1, matrix2)
    print("Dot Product:\n", dot_result)

    # Determinant
    det_result = np.linalg.det(matrix1)
    print("Determinant:", det_result)
        

Broadcasting

NumPy supports broadcasting, which allows arithmetic operations between arrays of different shapes.

    # Creating arrays
    array = np.array([1, 2, 3])
    scalar = 5

    # Adding a scalar to an array
    broadcast_result = array + scalar
    print("Broadcasting Result:", broadcast_result)  # Output: [6 7 8]
        

Conclusion

NumPy provides a comprehensive set of tools for performing mathematical operations on arrays, making it an essential library for numerical computing. By mastering these operations, you can efficiently manipulate and analyze data in Python.