/* ---------------------------------------------------------------------- 
**  Use the secant method to find a root of a function named f().
**      Figure 23.12: The secant algorithm.
**      Figure 23.13: The verbose_print() function.           
** ---------------------------------------------------------------------- 
*/
#include "tools.h"
#include "root.h"       /* Interface between roots module and main. */
#include "ffam.h"       /* Prototype for function to solve. */

extern bool verbose;    /* Imported from main. */
    
static void verbose_print( int k, 
       double x1, double y1, double x2, double  y2, double x3, double y3);

/* ---------------------------------------------------------------------- 
**  Secant root finder function. 
**      Returns 0 on success, -1 on failure. 
*/
er_type                          
secant( double x1, double x2, double *rootp )
{
    int k;                      /* the actual iteration starting from 0   */
    double x3;                  /* estimates of root value */
    double y1, y2, y3;          /* f( x) at points x1, x2, x3, resp. */
    double slope, delta;        /* line coefficients */

    if (fabs( x2 - x1 ) < EPS)  /* initial points too close together */
        return BAD_INITIAL_POINTS;
    y1 = f( x1 );  y2 = f( x2 );
    
    for (k = 0; k < MAX_ITER; k++) {
        slope = (y2 - y1) / (x2 - x1);
        if (fabs( slope ) < LIMIT)  return HORIZONTAL;

        delta = -y2 / slope;
        x3 = x2 + delta;        /* compute new estimate */
        y3 = f( x3 );
        if (verbose) verbose_print( k, x1, y1, x2, y2, x3, y3 );

        /* see if root has been found */
        if ( fabs( delta ) < EPS || fabs( y3 ) < LIMIT) { 
            *rootp = x3;        /* Store root in caller's variable  */
            return ROOT_OK;     /* and return the success code.     */
        }
    
        /* Get ready for the next iteration -------------------------- */
        x1 = x2;   y1 = y2;    /* Move old root estimate to older slot */
        x2 = x3;   y2 = y3;    /* Move new root estimate to old slot   */    
    }
    return TOO_MANY_ITERATIONS;
}

/* ---------------------------------------------------------------------- 
**  Verbose feedback.
**      Print intermediate output if user selects verbose mode.  
*/
void 
verbose_print( int k, 
    double x1, double y1, double x2, double y2, double x3, double y3 )
{
        printf( " During iteration %i:\n", k );
        printf( "    x1 = %15g, y1 = %15g\n", x1, y1 );
        printf( "    x2 = %15g, y2 = %15g\n", x2, y2 );
        printf( "    x3 = %15g, y3 = %15g\n", x3, y3 );
}