Functions.hpp
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	#ifndef FUNCTIONSHEADERREF
	#define FUNCTIONSHEADERREF


	class LU_matrices{
	public:
	double** U_matrix;
	double** L_matrix;
	double* b_star_vector;
	};

	class Cholesky_matrices{
	public:
	double** L_matrix;
	double** L_T_matrix;
	double* b_star_vector;
	};

	double** Initialize(int size);
	double Copy(double A,int size);
	double** AllocateMemory(int rows, int cols);
	void SubstractRows (double** A,int scalar,int row_1, int row_2, int size);
	double Normalize (double** A,int row, int size);
	LU_matrices Pivot(double** A,double* b,int size);
	double* AllocateMemory(int rows);
	void FreeMemory(double** A,int rows);
	void FreeMemory(double* u);
	int FindMax (double** A,int col,int size);
	void SwapRows (double** A,int last_index, int new_index, int size);
	void TerminalPrint(double** A,int rows, int cols);
	void TerminalPrint(double* u,int size);
	double Multiply(double A,double** B,int rowsA, int colsA, int rowsB, int colsB);
	double* Multiply(double** A,double* u,int rowsA, int colsA, int rowsU);
	double* Multiply(double* u,double** A,int rowsA, int colsA, int rowsU);
	double Multiply(double A,double scalar, int rowsA, int colsA);
	double* Multiply(double* u,double scalar, int rowsU);
	void ReduceMatrix(double A,int size,int col, double &A_hat);
	double Determinant(double** A,int size);
	double Generate_L(double L,LU_matrices out,int size);
	double* Up(double** U, double* b_star, int size);
	Cholesky_matrices Cholesky_L(double** A,double* b,int size);

	#endif