C++ Matrix Library

Overview

This library provides robust classes and functions to work with matrices and fractions in C++. It is designed to facilitate complex mathematical computations and ease the process of handling matrices and fractions. The library includes comprehensive features for matrix operations, file I/O for CSV files, and various utility functions for diverse mathematical computations.

Features

Fraction Class

Constructors

• Fraction()
  • Default constructor.
• Fraction(int num, int den)
  • Parameterized constructor with numerator (num) and denominator (den).

Setter Functions

• void setNumerator(int num)
  • Set numerator to num.
• void setDenominator(int den)
  • Set denominator to den.
• void setFraction(int num, int den)
  • Set both numerator and denominator.

Getter Functions

• int getNumerator() const
  • Get the numerator.
• int getDenominator() const
  • Get the denominator.
• std::pair<int, int> getFraction() const
  • Get the fraction as a pair.

Utility Functions

• int gcd(int a, int b) const
  • Calculate the greatest common divisor (GCD).
• void simplify()
  • Simplify the fraction to its simplest form.

Display Function

• void display() const
  • Display the fraction in numerator/denominator format.

Operations

• Fraction inverse() const
  • Get the inverse of the fraction.

Operator Overloading

• Fraction operator+(const Fraction& other) const
  • Addition with another fraction.
• Fraction operator-(const Fraction& other) const
  • Subtraction with another fraction.
• Fraction operator*(const Fraction& other) const
  • Multiplication with another fraction.
• Fraction operator/(const Fraction& other) const
  • Division with another fraction.
• Fraction operator+(int value) const
  • Addition with an integer.
• Fraction operator-(int value) const
  • Subtraction with an integer.
• Fraction operator*(int value) const
  • Multiplication with an integer.
• Fraction operator/(int value) const
  • Division with an integer.
• Fraction operator-() const
  • Unary negation.
• friend std::ostream& operator<<(std::ostream& os, const Fraction& fraction)
  • Output stream operator.
• friend std::istream& operator>>(std::istream& is, Fraction& fraction)
  • Input stream operator.

Matrix Class

Constructors

• Matrix()
  • Default constructor.
• Matrix(int rows, int cols)
  • Parameterized constructor with number of rows (rows) and columns (cols).
• Matrix(int size, const Fraction& diagonalValue)
  • Parameterized constructor for diagonal scalar matrix.
• Matrix(int rows, int cols, const std::vector<std::vector<Fraction>>& elements)
  • Parameterized constructor with elements from an array.
• Matrix(const Matrix& other)
  • Copy constructor.

Destructor

• ~Matrix()
  • Properly deallocates memory.

Display Function

• void display() const
  • Display the matrix.

Set and Get Functions

• void setElement(int row, int col, const Fraction& value)
  • Set the element at row and col to value.
• Fraction getElement(int row, int col) const
  • Get the element at row and col.

In-Built Functions

• Fraction trace() const
  • Calculate the trace of the matrix.
• Fraction determinant() const
  • Calculate the determinant of the matrix.
• int rowMajorOrder(int row, int col) const
  • Calculate the position in row-major order.
• int columnMajorOrder(int row, int col) const
  • Calculate the position in column-major order.
• Matrix power(int exponent) const
  • Raise the matrix to a power of exponent.
• Matrix reshape(int newRows, int newCols) const
  • Reshape the matrix to newRows x newCols.
• Matrix transpose() const
  • Transpose the matrix.
• Matrix concatenateRows(const Matrix& other) const
  • Concatenate with another matrix along rows.
• Matrix concatenateColumns(const Matrix& other) const
  • Concatenate with another matrix along columns.
• std::vector<Fraction> characteristicPolynomial() const
  • Calculate the characteristic polynomial of the matrix.

Operator Overloading

• Matrix operator*(const Fraction& value) const
  • Multiplication by a fraction.
• Matrix operator+(const Matrix& other) const
  • Addition with another matrix.
• Matrix operator-(const Matrix& other) const
  • Subtraction with another matrix.
• Matrix operator*(const Matrix& other) const
  • Multiplication with another matrix.
• Matrix& operator=(const Matrix& other)
  • Assignment operator.
• std::vector<Fraction>& operator[](int index)
  • Subscript operator for accessing rows.
• friend std::ostream& operator<<(std::ostream& os, const Matrix& matrix)
  • Output stream operator.

File I/O

• void readCSV(const std::string& filename)
  • Reads a matrix from a CSV file.
• void writeCSV(const std::string& filename) const
  • Writes a matrix and its properties (trace, determinant, transpose, characteristic polynomial) to a CSV file.

Usage

• Create or import matrices.
• Perform various matrix operations.
• Read and write matrices to and from CSV files.

Authors

• Himanshu Dania GitHub
• Kanav Goyal GitHub