#include <stdlib.h>
#include <stdio.h>
#include <malloc.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_eigen.h>

#define TOLERANCE 1e-4
#define MAX_ITRN 20

struct Vector
{
	int n;		//dimension (number of items)
	float *p;	//values
};
typedef struct Vector Vec;

struct Matrix
{
	int n;		//# of rows
	int m;		//# of columns
	float *p;	//values
};
typedef struct Matrix Mat;

//  vector/matrix allocation and resources free
Vec * createVec(int n);
void destroyVec(Vec * vecP);
Mat * createMat(int n, int m);
void destroyMat(Mat * matP);

//  Vector/Matrix io
Vec * readVec(FILE * vecInFile);
void writeVec(Vec * vecWriteP, FILE * outFile);
Mat * readMat(FILE * matInFile);
void writeMat(Mat * matP, FILE * outFile);

//computes the eigenvalues of A, return the ordered (from largest
// to smallest) eigenvalues in v, with a maximum of n iterations,
// untill it satisfies some error estimate less than Tol
int QREvals(Mat * A,  Vec  * v, int n, float Tol);

//function used by qsort for to compare two vectors of type Vec
int vecCompare(const void * a, const void * b);
//gsl function used by qsort to compare two vectors of type gsl_vector
int gslVecCompare(const void * a, const void * b);
//max, min functions
double max(double a, double b);
double min(double a, double b);

//check if Matrix of type Mat is symmetric
int isMatSymm(const Mat * A);