FtfUtilities.cxx

//:>------------------------------------------------------------------
//: FILE:       FTF_Utilities.cxx
//: HISTORY:
//:             28oct1996 version 1.00
//:<------------------------------------------------------------------
//:>------------------------------------------------------------------
//: FUNCTIONS:   Standalone functions
//: DESCRIPTION: Generic functions used in tracking
//: AUTHOR:      ppy - Pablo Yepes, yepes@physics.rice.edu
//:>------------------------------------------------------------------
#include <stdio.h>
#include <math.h>

//void invert_matrix ( int n, double *h ) ;
//void matrix_diagonal ( double *h, double *h11, double *h22, double *h33 ) ;
//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
//   Invert matrix h of dimension n
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
//
//
//   Originally written in FORTRAN by Jawluen Tang, Physics department , UT-Austin 
//              modified and translated to C by Pablo Yepes, Rice U. 
//                               
//     The following routine is to invert a square symmetric matrix 
//     (in our case,it is a 3x3 matrix,so NOD=3)and calculate its 
//     determinant,substituting the inverse matrix into the same array 
//     of the original matrix H. 
//     See Philip R. Bevington,"Data reduction and error analysis for 
//     the physical science",p302 
//
void ftfInvertMatrix ( int n, double *h )  {
        static double detm, dmax_, temp;
    static int i, j, k, l;
        static int ik[3], jk[3];

    detm = 1.F ;
    
    for (k = 0 ; k < n ; ++k) {
        dmax_ = (double)0.;
        j = -1 ;
        while(j < k) {
            i = -1 ;
            while(i < k) {
                
                for (i = k; i < n; ++i) {
                    
                    for (j = k; j < n; ++j) {
                        if (fabs(dmax_) <= fabs(h[i+j*3])) 
                                {
                            dmax_ = h[i + j * 3];
                            ik[k] = i;
                            jk[k] = j;
                        }
                    }
                }
                if (dmax_ == (double)0.) {
                    //printf ( "Determinant is ZERO!" );
                    return ;
                }
                i = ik[k];
            }
            if (i > k) {
                
                for (j = 0 ; j < n; ++j) {
                    temp = h[k + j * 3];
                    h[k + j * 3] = h[i + j * 3];
                    h[i + j * 3] = -(double)temp;
                }
            }
            j = jk[k];
        }
        if (j != k) {
            
            for (i = 0 ; i < n; ++i) {
                temp = h[i + k * 3];
                h[i + k * 3] = h[i + j * 3];
                h[i + j * 3] = -(double)temp;
            }
        }
        
        for (i = 0 ; i < n; ++i) {
            if (i != k) {
                h[i + k * 3] = -(double)h[i + k * 3] / dmax_;
            }
        }
        
        for (i = 0; i < n; ++i) {
            
            for (j = 0; j < n; ++j) {
                if (i != k && j != k) {
                       h[i + j * 3] += h[i + k * 3] * h[k + j * 3];
                    }
            }
        }
        for (j = 0; j < n; ++j) {
            if (j != k) {
                h[k + j * 3] /= dmax_;
            }
        }
        h[k + k * 3] = 1.F / dmax_;
        detm *= dmax_;
    }
    for (l = 0; l < n; ++l) {
        k = n - l -1 ;
            j = ik[k];
            if (j > k) {
               for (i = 0; i < n; ++i) {
                      temp = h[i + k * 3];
                      h[i + k * 3] = -(double)h[i + j * 3];
                      h[i + j * 3] = temp;
               }
           }
           i = jk[k];
           if (i > k) {
              for (j = 0; j < n; ++j) {
                temp = h[k + j * 3];
                    h[k + j * 3] = -(double)h[i + j * 3];
                    h[i + j * 3] = temp;
              }
           }
    }
    return ;
} 
//+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
//    Function to give the diagonal elements (h11,h22,h33)
//    of the inverse symmetric 3x3 matrix of h
//    Calculation by Geary Eppley (Rice University)
//    coded by Pablo Yepes        (Rice University)
//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
void ftfMatrixDiagonal ( double *h, double &h11, double &h22, double &h33 ){
        double f1, f2, f3 ;

        f1 = h[5]*h[6]-h[8]*h[1] ;
        f2 = h[4]*h[8]-h[5]*h[5] ;
        f3 = h[8]*h[0]-h[2]*h[2] ;
        h11 = double(h[8] / ( f3 - f1 * f1 / f2 )) ;

        f1 = h[2]*h[1]-h[0]*h[5] ;
        f2 = h[8]*h[0]-h[2]*h[2] ;
        f3 = h[0]*h[4]-h[1]*h[1] ;
        h22 = double(h[0] / ( f3 - f1 * f1 / f2 )) ;

        f1 = h[1]*h[5]-h[4]*h[2] ;
        f2 = h[0]*h[4]-h[1]*h[1] ;
        f3 = h[4]*h[8]-h[7]*h[7] ;
        h33 = double(h[4] / ( f3 - f1 * f1 / f2 )) ;
}