map_af_integ.C

/*
 *  Method of the class Map_af for computing the integral of a Cmp over
 *  all space.
 */

/*
 *   Copyright (c) 1999-2003 Eric Gourgoulhon
 *
 *   This file is part of LORENE.
 *
 *   LORENE is free software; you can redistribute it and/or modify
 *   it under the terms of the GNU General Public License as published by
 *   the Free Software Foundation; either version 2 of the License, or
 *   (at your option) any later version.
 *
 *   LORENE is distributed in the hope that it will be useful,
 *   but WITHOUT ANY WARRANTY; without even the implied warranty of
 *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *   GNU General Public License for more details.
 *
 *   You should have received a copy of the GNU General Public License
 *   along with LORENE; if not, write to the Free Software
 *   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 *
 */


char map_af_integ_C[] = "$Header: /cvsroot/Lorene/C++/Source/Map/map_af_integ.C,v 1.7 2009/10/08 16:20:47 j_novak Exp $" ;

/*
 * $Id: map_af_integ.C,v 1.7 2009/10/08 16:20:47 j_novak Exp $
 * $Log: map_af_integ.C,v $
 * Revision 1.7  2009/10/08 16:20:47  j_novak
 * Addition of new bases T_COS and T_SIN.
 *
 * Revision 1.6  2008/08/27 08:48:05  jl_cornou
 * Added R_JACO02 case
 *
 * Revision 1.5  2007/10/05 15:56:19  j_novak
 * Addition of new bases for the non-symmetric case in theta.
 *
 * Revision 1.4  2003/12/19 16:21:43  j_novak
 * Shadow hunt
 *
 * Revision 1.3  2003/10/19 19:58:15  e_gourgoulhon
 * Access to Base_val::b now via Base_val::get_b().
 *
 * Revision 1.2  2003/10/15 10:35:27  e_gourgoulhon
 * Changed cast (double *) into static_cast<double*>.
 *
 * Revision 1.1.1.1  2001/11/20 15:19:27  e_gourgoulhon
 * LORENE
 *
 * Revision 1.2  2000/01/28  16:09:37  eric
 * Remplacement du ci.get_dzpuis() == 4 par ci.check_dzpuis(4).
 *
 * Revision 1.1  1999/12/09  10:45:43  eric
 * Initial revision
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Map/map_af_integ.C,v 1.7 2009/10/08 16:20:47 j_novak Exp $
 *
 */

// Headers C
#include <stdlib.h>
#include <math.h>


// Headers Lorene
#include "map.h"
#include "cmp.h"

Tbl* Map_af::integrale(const Cmp& ci) const {

    static double* cx_tcp = 0 ;     // Coefficients theta, dev. en cos(2l theta)
    static double* cx_rrp = 0 ;     // Coefficients r rare, dev. en T_{2i}
    static double* cx_rf_x2 = 0 ;   // Coefficients r fin, int. en r^2
    static double* cx_rf_x = 0 ;    // Coefficients r fin, int en r
    static double* cx_rf = 0 ;      // Coefficients r fin, int en cst.

    static int nt_cp_pre = 0 ;
    static int nr_p_pre = 0 ;
    static int nr_f_pre = 0 ;

    assert(ci.get_etat() != ETATNONDEF) ; 

    int nz = mg->get_nzone() ; 
    
    Tbl* resu = new Tbl(nz) ;
    
    if (ci.get_etat() == ETATZERO) {
    resu->annule_hard() ; 
    return resu ; 
    }
    
    assert( ci.get_etat() == ETATQCQ ) ; 
    
    (ci.va).coef() ;    // The spectral coefficients are required
    
    const Mtbl_cf* p_mti = (ci.va).c_cf ; 

    assert( ci.check_dzpuis(4) ) ;      // dzpuis must be equal to 4  
    
    assert(p_mti->get_etat() == ETATQCQ) ; 

    resu->set_etat_qcq() ;  // Allocates the memory for the array of double

    // Loop of the various domains
    // ---------------------------
    for (int l=0 ; l<nz ; l++) {
    
    const Tbl* p_tbi = p_mti->t[l] ; 
    
    if ( p_tbi->get_etat() == ETATZERO ) {
        resu->t[l] = 0 ; 
    }
    else {      // Case where the computation must be done
    
        assert( p_tbi->get_etat() == ETATQCQ ) ; 
    
        int nt = mg->get_nt(l) ; 
        int nr = mg->get_nr(l) ;
        
        int base = (p_mti->base).get_b(l) ; 
        int base_r = base & MSQ_R ;
        int base_t = base & MSQ_T ;
        int base_p = base & MSQ_P ;
        
        // ----------------------------------
        // Integration on theta -> array in r
        // ----------------------------------

        double* s_tr = new double[nr] ; // Partial integral on theta 
        double* x_spec = p_tbi->t ; // Pointer on the spectral coefficients
        
        switch (base_t) {
        
        case T_COS_P: case T_COSSIN_CP: {
            if (nt > nt_cp_pre) {  // Initialization of factors for summation
            nt_cp_pre = nt ;
            cx_tcp 
                = static_cast<double*>(realloc(cx_tcp, nt*sizeof(double))) ;
            for (int j=0 ; j<nt ; j++) {
                cx_tcp[j] = 2./(1. - 4.*j*j) ;  // Factor 2 symmetry
            }
            }
            
            // Summation : 
            for (int i=0 ; i<nr ; i++) s_tr[i] = 0 ;
            for (int j=0 ; j<nt ; j++) {
            for (int i=0 ; i<nr ; i++) {
                s_tr[i] += cx_tcp[j] * x_spec[i] ;
            }
            x_spec += nr ;  // Next theta
            }
            break ;
        }
        case T_COSSIN_C: case T_COS: {
            // Summation : 
            for (int i=0 ; i<nr ; i++) s_tr[i] = 0 ;
            for (int j=0 ; j<nt ; j++) {
            if ((j%2)==0)
                for (int i=0 ; i<nr ; i++) {
                s_tr[i] += (2. / (1.-j*j)) * x_spec[i] ;
                }
            x_spec += nr ;  // Next theta
            }
            break ;         
        }
        default: {
            cout << "Map_af::integrale: unknown theta basis ! " << endl ;
            abort () ;
            break ;
        }
            
        }   // End of the various cases on base_t

        // ----------------
        // Integration on r
        // ----------------

        double som = 0 ;
        double som_x2 = 0;
        double som_x = 0 ;
        double som_c = 0 ;
    
        switch(base_r) {
        case R_CHEBP: case R_CHEBPIM_P: case R_CHEBPI_P :{
        assert(beta[l] == 0) ;
        if (nr > nr_p_pre) {  // Initialization of factors for summation
            nr_p_pre = nr ;
            cx_rrp = static_cast<double*>(realloc(cx_rrp, nr*sizeof(double))) ;
            for (int i=0 ; i<nr ; i++) {
            cx_rrp[i] = (3. - 4.*i*i) / 
                    (9. - 40. * i*i + 16. * i*i*i*i) ;
            }
        }
        
        for (int i=0 ; i<nr ; i++) {
            som += cx_rrp[i] * s_tr[i] ;
        }
        double rmax = alpha[l] ;
        som *= rmax*rmax*rmax ;
        break ;
        }
        
        case R_CHEB: {
        if (nr > nr_f_pre) {  // Initialization of factors for summation
            nr_f_pre = nr ;
            cx_rf_x2 = static_cast<double*>(realloc(cx_rf_x2, nr*sizeof(double))) ;
            cx_rf_x  = static_cast<double*>(realloc(cx_rf_x, nr*sizeof(double))) ;
            cx_rf    = static_cast<double*>(realloc(cx_rf, nr*sizeof(double))) ;
            for (int i=0 ; i<nr ; i +=2 ) {
            cx_rf_x2[i] = 2.*(3. - i*i)/(9. - 10. * i*i + i*i*i*i) ;
            cx_rf_x[i] = 0 ;
            cx_rf[i] = 2./(1. - i*i) ;
            }
            for (int i=1 ; i<nr ; i +=2 ) {
            cx_rf_x2[i] = 0 ;
            cx_rf_x[i] = 2./(4. - i*i) ;
            cx_rf[i] = 0 ;
            }
        }
        
        for (int i=0 ; i<nr ; i +=2 ) {
            som_x2 += cx_rf_x2[i] * s_tr[i] ;
        }
        for (int i=1 ; i<nr ; i +=2 ) {
            som_x += cx_rf_x[i] * s_tr[i] ;
        }
        for (int i=0 ; i<nr ; i +=2 ) {
            som_c += cx_rf[i] * s_tr[i] ;
        }
        double a = alpha[l] ;
        double b = beta[l] ;
        som = a*a*a * som_x2 + 2.*a*a*b * som_x + a*b*b * som_c ;
        break ;
        }

        case R_JACO02: {
        if (nr > nr_f_pre) {  // Initialization of factors for summation
            nr_f_pre = nr ;
            cx_rf_x2 = static_cast<double*>(realloc(cx_rf_x2, nr*sizeof(double))) ;
            cx_rf_x  = static_cast<double*>(realloc(cx_rf_x, nr*sizeof(double))) ;
            cx_rf    = static_cast<double*>(realloc(cx_rf, nr*sizeof(double))) ;
            double signe = 1 ;
            for (int i=0 ; i<nr ; i +=1 ) {
            cx_rf_x2[i] = 0 ;
            cx_rf_x[i] = 2*signe/double(i+1)/double(i+2);
            cx_rf[i] = 2*signe ;
            signe = - signe ;
            }
            cx_rf_x2[0] = double(8)/double(3) ;
        }
        
        for (int i=0 ; i<nr ; i +=1 ) {
            som_x2 += cx_rf_x2[i] * s_tr[i] ;
        }
        for (int i=1 ; i<nr ; i +=1 ) {
            som_x += cx_rf_x[i] * s_tr[i] ;
        }
        for (int i=0 ; i<nr ; i +=1 ) {
            som_c += cx_rf[i] * s_tr[i] ;
        }
        double a = alpha[l] ;
        double b = beta[l] ;
        assert(b == a) ;
        som = a*a*a * som_x2 + 2.*a*a*(b-a) * som_x + a*(b-a)*(b-a) * som_c ;
        break ;
        }
        
        case R_CHEBU: {
        assert(beta[l] == - alpha[l]) ;
        if (nr > nr_f_pre) {  // Initialization of factors for summation
            nr_f_pre = nr ;
            cx_rf    = static_cast<double*>(realloc(cx_rf, nr*sizeof(double))) ;
            for (int i=0 ; i<nr ; i +=2 ) {
            cx_rf[i] = 2./(1. - i*i) ;
            }
            for (int i=1 ; i<nr ; i +=2 ) {
            cx_rf[i] = 0 ;
            }
        }
        
        for (int i=0 ; i<nr ; i +=2 ) {
            som_c += cx_rf[i] * s_tr[i] ;
        }
        som = - alpha[l] * som_c ;
        break ;
        }


        default: {
        cout << "Map_af::integrale: unknown r basis ! " << endl ;
        abort () ;
        break ;
        }
        
        }   // End of the various cases on base_r
        
        // ------------------
        // Integration on phi
        // ------------------

        switch (base_p) {

        case P_COSSIN: {
        som *= 2. * M_PI ;
        break ;
        }
        
        case P_COSSIN_P: {
        som *= 2. * M_PI ;
        break ;
        }
        
        default: {
        cout << "Map_af::integrale: unknown phi basis ! " << endl ;
        abort () ;
        break ;
        }
        
        }   // End of the various cases on base_p

        // Final result for this domain:
        // ----------------------------
           
        resu->t[l] = som ; 
        delete [] s_tr ;

    }   // End of the case where the computation must be done
    
    
    }   // End of the loop onto the domains
        
    return resu ;
    
}

---