methods.h File Reference

Core computational functions for solving linear systems. More...

#include <vector>
#include <string>

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Functions
int	GaussianElimination (std::vector< std::vector< double > > &m, int rows, int cols)
	Performs Gaussian elimination on the augmented matrix with partial pivoting.
int	DetermineRank (const std::vector< std::vector< double > > &m, int rows, int cols)
	Determines the rank of the coefficient matrix A (excluding augmented column).
bool	BackSubstitution (const std::vector< std::vector< double > > &m, int rows, int cols, std::vector< double > &solution)
	Performs back-substitution to find the solution vector.
void	ShowGeneralSolution (const std::vector< std::vector< double > > &m, int rows, int cols, int rank)
	Displays the general solution for systems with infinitely many solutions.
std::vector< int >	IdentifyPivots (const std::vector< std::vector< double > > &m, int rows, int cols)
	Identifies the pivot columns in the matrix.

Detailed Description

Core computational functions for solving linear systems.

Author

Gilbert Young

Date

2024/09/25

This header declares functions for Gaussian elimination with partial pivoting, back-substitution, rank determination, and displaying general solutions.

Definition in file methods.h.

Function Documentation

BackSubstitution()

bool BackSubstitution	(	const std::vector< std::vector< double > > &	m,
		int	rows,
		int	cols,
		std::vector< double > &	solution )

Performs back-substitution to find the solution vector.

Parameters

m	The upper triangular matrix after Gaussian elimination.
rows	Number of rows in the matrix.
cols	Number of columns in the matrix (including augmented column).
solution	Reference to store the solution vector.

Returns

true If a unique solution exists.

false If the system is inconsistent.

DetermineRank()

int DetermineRank	(	const std::vector< std::vector< double > > &	m,
		int	rows,
		int	cols )

Determines the rank of the coefficient matrix A (excluding augmented column).

Parameters

m	The augmented matrix [A|b].
rows	Number of rows in the matrix.
cols	Number of columns in the matrix (including augmented column).

Returns

int The rank of the matrix A.

GaussianElimination()

int GaussianElimination	(	std::vector< std::vector< double > > &	m,
		int	rows,
		int	cols )

Performs Gaussian elimination on the augmented matrix with partial pivoting.

Parameters

m	Reference to the augmented matrix [A|b] to be modified.
rows	Number of rows in the matrix.
cols	Number of columns in the matrix (including augmented column).

Returns

int Number of row exchanges performed during elimination.

IdentifyPivots()

std::vector< int > IdentifyPivots	(	const std::vector< std::vector< double > > &	m,
		int	rows,
		int	cols )

Identifies the pivot columns in the matrix.

Parameters

m	The matrix after Gaussian elimination.
rows	Number of rows in the matrix.
cols	Number of columns in the matrix (including augmented column).

Returns

std::vector<int> A vector containing the indices of the pivot columns.

ShowGeneralSolution()

void ShowGeneralSolution	(	const std::vector< std::vector< double > > &	m,
		int	rows,
		int	cols,
		int	rank )

Displays the general solution for systems with infinitely many solutions.

Parameters

m	The matrix after Gaussian elimination.
rows	Number of rows in the matrix.
cols	Number of columns in the matrix (including augmented column).
rank	The rank of the coefficient matrix A.