/*
 *  Ricciflowcode.h
 *  
 *
 *  Created by Christopher Herzog on 11/24/06.
 *  Copyright 2006. All rights reserved.
 *
 */

#define NMAX_DEFAULT 10 /* The grid size */
#define WIDTH_DEFAULT 1.2 /* The grid width */
#define DEFAULT_OUT "garbage.txt" /* default output file */
#define DIFF_ERROR_RAW 1E-16 /* min average change of gridpoint per iteration */
#define MAX_LOOPS_DEFAULT 10 /* how many times steps to run */
#define MY_PRINT_DEFAULT 2 /* displays output every 2 iterations */
#define FLOW_PARAM_DEFAULT 0.1 /* controls Ricci flow time step size */
#define ROOT_ERROR 1E-10 /* root finding error */



/* global variable defining grid width */ 

int NMAX;

/*global variable defining grid spacing */

double DELTA;

/* controls speed of Ricci-flow */

double FLOW_PARAM;

/* Updates the boundary conditions
 */
 
void boundaryupdate(double **tf);

/* Updates the lattice
 */ 
 
double Fijupdate(double **tf, double **newfunct, double *oldshift);

/* Interpolates values in the lattice for boundaryupdate()
 */
 
double planarinterp(double x, double y, double **tf);


/* Computes Guillemin's trial potential
 */
 
double Fpottest(double xi, double eta);
 
/* Functions converting grid position to xi and eta coordinates
 */
 
 double xicoord(int i);
 double etacoord(int j);
 
/* computes volume of space using Riemann sums*/ 
 
double volcomp(double **tf, double fshift);
 
/* computes the value of hdot */ 
 
double discfunct(int i, int j, int flag, double **tf);

/* calculates an error measure in satisfying hdot = 0 */

double calcdiscerror(double **tf, double oldshift);

/* bicubic interpolation routines from numerical recipes
 */

void bcucof(double *y, double *y1, double *y2, double *y12, double d1, double d2, double **c);

void bcuint(double *y, double *y1, double *y2, double *y12, double x1l, double x1u, double x2l, double
x2u, double x1, double x2, double *ansy, double *ansy1, double *ansy2);

void free_matrix(double **c, int imin, int imax, int jmin, int jmax);

double **matrix(int imin, int imax, int jmin, int jmax);