// lsfit.h  1, 2, 3, 4, 5, 6, 7 dimensions
//          6, 6, 6, 6, 6, 6, 4 maximum power
//          Compute a multiple dimensional polynomial
//          that is a least square fit of some data.
//          Evaluate the polynomial at desired points.
// use:   fit_init(n,m); n is number of dimensions
//                       m is highest power
// provide data
//
// 3D example                                                                
//    fit_init(3,6); // 3D to 6th power u = poly(x,y,z)                     
//    last = false;
//    for(i=0; i<n; i++){ // must provide enough independent data
//      if(i==n-1) last = true;
//      fit3_data(x, y, z, u, last); } // now have fit
//
// use fit polynomial to evaluate at various points
//                    usually not accurate outside data range
//  val = eval2_poly(x, y) 
//
// special use for fitting 2D
//        fit2_bpoly(nx, ny, xg, yg, u) build coefficients
//                   nx number of x coordinates i=0,nx-1
//                   ny number of y coordinates j=0,ny-1
//                   xg array of x coordinate values
//                   yg array of y coordinate values
//                   u[i*ny+j] value at point i,j
// function prototypes
void fit_init(int n, int m); // only one fit at a time, n variable, m power
void fit_free();             // optional, free allocated ram
                             // after use and before next fit
int  get_fitnnn();       // needed for get_fit nnn, allocate CC[nnn] double
                         // allocate pwr[n*nnn] int
void get_fit(double CC[], int pwr[]); // index pwr i*n+variable, i=0,nnn-1
void write_fit7(char* fname);         

void fit1_data(double x, double u, int last);
void fit2_data(double x, double y, double u, int last);
void fit3_data(double x, double y, double z, double u, int last);
void fit4_data(double x, double y, double z, double t, double u, int last);
void fit5_data(double x, double y, double z, double t, double u, double w,
               int last);
void fit6_data(double x, double y, double z, double t, double u, double v,
               double w, int last);
void fit7_data(double x, double y, double z, double t, double u, double v,
               double w, double val, int last);

void fit2_bpoly(int nx, int ny, double x[], double y[], double u[]);

double eval1_poly(double x);
double eval2_poly(double x, double y);
double eval3_poly(double x, double y, double z);
double eval4_poly(double x, double y, double z, double t);
double eval5_poly(double x, double y, double z, double t, double u);
double eval6_poly(double x, double y, double z, double t, double u,
                  double v);
double eval7_poly(double x, double y, double z, double t, double u,
                  double v, double w);