Mat.cpp

A matrix library written in c++ for educational purposes

Matrix Library

Overview

This library provides a Matrix class with various operations for matrix manipulation, including addition, subtraction, multiplication, inversion, and more. Utility functions for matrix computations are also included.

Class: Matrix

Private Members

• int rows: Number of rows in the matrix.
• int columns: Number of columns in the matrix.
• vector<vector<double>> elements: Stores matrix elements.
• void verifyIndex(int& row, int& column): Ensures the given indices are within valid bounds.

Public Methods

Constructor

• Matrix(int rows, int columns): Initializes a matrix with given dimensions.

  Matrix mat(3, 3);

Element Access

• int get(int row, int column): Returns the value at a specific position.

  int val = mat.get(1, 2);

• double& at(int row, int column): Provides a reference to an element.

  mat.at(0, 1) = 5.0;

• void set(vector<vector<double>> elements): Sets matrix elements and adjusts size.

  mat.set({{1, 2}, {3, 4}});

• vector<double> getCol(int col): Returns a column as a vector.

  vector<double> colVec = mat.getCol(1);

• void setCol(int col, vector<double> colvec): Replaces a column with a new vector.

  mat.setCol(1, {5, 6, 7});

Basic Operations

• void print(): Prints the matrix.

  mat.print();

• Matrix operator+(Matrix& matrix2): Adds two matrices.

  Matrix sum = mat1 + mat2;

• Matrix operator-(Matrix& matrix): Subtracts two matrices.

  Matrix diff = mat1 - mat2;

• Matrix operator*(Matrix& m2): Multiplies two matrices.

  Matrix product = mat1 * mat2;

• Matrix operator*(double scaler): Multiplies a matrix by a scalar.

  Matrix scaled = mat * 2.0;

• Matrix operator/(double scaler): Divides a matrix by a scalar.

  Matrix divided = mat / 2.0;

• bool operator==(Matrix& matrix): Checks if two matrices are equal.

  bool isEqual = (mat1 == mat2);

Matrix Properties

• int getRows(): Returns number of rows.

  int rows = mat.getRows();

• int getColumns(): Returns number of columns.

  int cols = mat.getColumns();

• void transpose(): Transposes the matrix.

  mat.transpose();

• double determinant(): Computes determinant.

  double det = mat.determinant();

• void resize(int row, int col): Resizes the matrix.

  mat.resize(4, 4);

• void swapRows(int row1, int row2): Swaps two rows.

  mat.swapRows(0, 1);

• void swapColumns(int col1, int col2): Swaps two columns.

  mat.swapColumns(0, 1);

• void invert(): Computes the inverse of the matrix.

  mat.invert();

• double trace(): Computes trace of the matrix.

  double tr = mat.trace();

• int rank(): Computes the rank of the matrix.

  int r = mat.rank();

• vector<double> getEigenValues(): Returns eigenvalues.

  vector<double> eigenvalues = mat.getEigenValues();

Utility Functions (Defined in MatrixUtils.cpp)

• void verifyEqualDimension(Matrix& m1, Matrix& m2): Ensures matrices have the same dimensions.

  verifyEqualDimension(mat1, mat2);

• void verifySquareMatrix(Matrix& m1): Ensures a matrix is square.

  verifySquareMatrix(mat);

• void setMinorMatrix(Matrix& m, int row, int col, Matrix& minorMatrix): Creates a minor matrix.

  setMinorMatrix(mat, 1, 1, minorMat);

• double getDeterminant(int size, Matrix& m): Computes determinant.

  double det = getDeterminant(3, mat);

• Matrix createIdentityMatrix(int n): Returns an identity matrix.

  Matrix identity = createIdentityMatrix(3);

• void reduceToREF(Matrix& m): Converts to Row Echelon Form (REF).

  reduceToREF(mat);

• bool verifyDiagonalMatrix(Matrix m): Checks if a matrix is diagonal.

  bool isDiagonal = verifyDiagonalMatrix(mat);

• double getNormOfCol(Matrix m, int col): Computes the norm of a column.

  double norm = getNormOfCol(mat, 1);

• void gramSchmidt(Matrix m, Matrix& result): Applies Gram-Schmidt orthogonalization.

  gramSchmidt(mat, result);

License

This project is open-source and free to use.

Todo

Basic Operations:

• Implement matrix creation (e.g., from an array or zeros)
• Implement matrix printing (output in a readable format)
• Implement matrix addition (element-wise)
• Implement matrix subtraction (element-wise)
• Implement matrix scalar multiplication (multiply each element by a constant)
• Implement matrix scalar division (divide each element by a constant)
• Implement matrix transposition (swap rows and columns)
• Implement matrix equality check (compare if two matrices are equal)
• Implement matrix resizing (expand or shrink the matrix)
• Implement matrix determinant calculation (for small square matrices, e.g., 2x2 and 3x3)

Intermediate Operations:

• Implement matrix multiplication (standard matrix product)
• Implement matrix inversion (for invertible square matrices)
• Implement matrix rank (using Gaussian elimination or similar techniques)
• Implement matrix trace (sum of diagonal elements)
• Implement matrix diagonalization (for certain square matrices)
• Implement matrix identity creation (returning an identity matrix of size n)
• Implement matrix row and column operations (e.g., swapping rows/columns, scaling rows/columns)
• Implement Matrix eigen values (for smaller square matrix such as 2 , 3, 4)