LA Namespace Reference

Functions
std::vector< double >	ROOTEquationSolver (const double &m1, const double &b1, const double &m2, const double &b2, const double &m3, const double &b3, bool debugMode)
void	GaussianElimination (std::vector< std::vector< double >> &mat, bool debugMode=false)
int	GetMatrixRank (const std::vector< std::vector< double >> &mat)
int	CheckSolutions (const std::vector< std::vector< double >> &mat, std::vector< double > &solution)
bool	ValidateSolution (const std::vector< std::vector< double >> &origMat, const std::vector< double > &solution, bool debugMode)
bool	IsSlopeUndefined (double slope)
std::vector< double >	SolveSystemOfThreeEquations (const double &m1, const double &b1, const double &m2, const double &b2, const double &m3, const double &b3, bool debugMode)

Function Documentation

CheckSolutions()

int LA::CheckSolutions	(	const std::vector< std::vector< double >> &	mat,
		std::vector< double > &	solution
	)

Function to check the type of solution

Create the augmented matrix by copying the original matrix and adding a column of constants

Remove the solution column to get the coefficient matrix

No solution

Infinite solutions

Perform back substitution to find the solution

No solution

Unique solution

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GaussianElimination()

void LA::GaussianElimination	(	std::vector< std::vector< double >> &	mat,
		bool	debugMode = false
	)

Function to perform Gaussian elimination. converts the matrix to an upper triangular form.

Find pivot for column i

If the pivot is zero, skip this column

Scale pivot row

Eliminate below

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GetMatrixRank()

int LA::GetMatrixRank

(

const std::vector< std::vector< double >> &

mat

)

Function to determine the rank of the matrix

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IsSlopeUndefined()

bool LA::IsSlopeUndefined

(

double

slope

)

A helper function to check if a slope is undefined.

ROOTEquationSolver()

std::vector<double> LA::ROOTEquationSolver	(	const double &	m1,
		const double &	b1,
		const double &	m2,
		const double &	b2,
		const double &	m3,
		const double &	b3,
		bool	debugMode
	)

uses TDecompSVD, which performs a singular value decomposition to solve the linear system

Solution vector

Solve the system

Handle the error by returning an empty vector.

If is_good_solution is true, convert solution into an std::vector and return it.

Parameters

m2	XZ projection: z = m1*x + b1
m3	YZ projection: z = m2*y + b2
debugMode	XY projection: y = m3*x + b3

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SolveSystemOfThreeEquations()

std::vector<double> LA::SolveSystemOfThreeEquations	(	const double &	m1,
		const double &	b1,
		const double &	m2,
		const double &	b2,
		const double &	m3,
		const double &	b3,
		bool	debugMode
	)

To solve Augmented matrix representation of the system of equations Form: ax + by + cz = d

Parameters

m2	XZ projection: z = m1*x + b1
m3	YZ projection: z = m2*y + b2
debugMode	XY projection: y = m3*x + b3

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ValidateSolution()

bool LA::ValidateSolution	(	const std::vector< std::vector< double >> &	origMat,
		const std::vector< double > &	solution,
		bool	debugMode
	)

The solution does not satisfy the equation

The solution satisfies all equations

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