PCG.c 21.7 KB
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/*-----------------------------------------------------------------------------------------
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 * Copyright (C) 2016  For the list of authors, see file AUTHORS.
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 *
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 * This file is part of IFOS.
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 * 
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 * IFOS is free software: you can redistribute it and/or modify
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 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, version 2.0 of the License only.
 * 
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 * IFOS is distributed in the hope that it will be useful,
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 * 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
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 * along with IFOS. See file COPYING and/or <http://www.gnu.org/licenses/gpl-2.0.html>.
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-----------------------------------------------------------------------------------------*/

/*------------------------------------------------------------------------
 * Module for the Preconditioned Conjugate Gradient Method (PCG)
 * for the material parameters vp, vs, rho and lambda, mu, rho respectively
 * 
 * Daniel Koehn
 * ----------------------------------------------------------------------*/

#include "fd.h"

void PCG(float ** waveconv, float ** taper_coeff, int nsrc, float ** srcpos, int ** recpos, int ntr_glob, int iter, float C_vp, float ** gradp, int nfstart_jac, float ** waveconv_u, float C_vs, float ** gradp_u, float ** waveconv_rho, float C_rho, float ** gradp_rho, float Vs_avg, float FC){
	
	extern int NX, NY, IDX, IDY, SPATFILTER, GRAD_FILTER;
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	extern int FORWARD_ONLY, SWS_TAPER_GRAD_VERT, SWS_TAPER_GRAD_HOR, SWS_TAPER_GRAD_SOURCES, SWS_TAPER_FILE;
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	extern int POS[3], MYID, ACOUSTIC;
	extern char JACOBIAN[STRING_SIZE];
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    extern int RESTART_WORKFLOW;
    extern int VERBOSE;
    extern int start_iter;
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	char jac[225], jac2[225];
	int i, j;
	float betaz, betan, gradplastiter, gradclastiter, betar, beta;
	extern FILE *FP;
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    int use_conjugate_1=1;
    int use_conjugate_2=1;
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	FILE *FP3, *FP4, *FP6, *FP5;
	
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	/* ===================================================================================================================================================== */
	/* ===================================================== GRADIENT ZP ================================================================================== */
	/* ===================================================================================================================================================== */
	
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	if((FORWARD_ONLY==0)){
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		/* Preconditioning of the gradient */
		/* ------------------------------- */
		
		/* apply taper on the gradient */
		/* --------------------------- */
		
		if (SWS_TAPER_GRAD_VERT){   /*vertical gradient taper is applied*/
		taper_grad(waveconv,taper_coeff,srcpos,nsrc,recpos,ntr_glob,1);}
		
		if (SWS_TAPER_GRAD_HOR){   /*horizontal gradient taper is applied*/
		taper_grad(waveconv,taper_coeff,srcpos,nsrc,recpos,ntr_glob,2);}
		
		if (SWS_TAPER_GRAD_SOURCES){   /*cylindrical taper around sources is applied*/
		taper_grad(waveconv,taper_coeff,srcpos,nsrc,recpos,ntr_glob,3);}
		
		if (SWS_TAPER_FILE){   /* read taper from BIN-File*/
		taper_grad(waveconv,taper_coeff,srcpos,nsrc,recpos,ntr_glob,4);}
		
		/* save gradient */
		sprintf(jac,"%s_g.old.%i.%i",JACOBIAN,POS[1],POS[2]);
		FP3=fopen(jac,"wb");
		
		for (i=1;i<=NX;i=i+IDX){
		for (j=1;j<=NY;j=j+IDY){
			fwrite(&waveconv[j][i],sizeof(float),1,FP3);
		}
		}
			
		fclose(FP3);
		
		MPI_Barrier(MPI_COMM_WORLD);
			
		/* merge gradient file */ 
		sprintf(jac,"%s_g.old",JACOBIAN);
		if (MYID==0) mergemod(jac,3);
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		MPI_Barrier(MPI_COMM_WORLD);
        sprintf(jac,"%s_g.old.%i.%i",JACOBIAN,POS[1],POS[2]);
        remove(jac);
        
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		/* Normalize gradient to maximum value */
		/*norm(waveconv,iter,1);*/
		
		/* apply spatial wavelength filter */
		if(SPATFILTER==1){
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			if (MYID==0&&VERBOSE){
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			fprintf(FP,"\n Spatial filter is applied to gradient (written by PE %d)\n",MYID);}
			spat_filt(waveconv,iter,1);}
		
		/* apply 2D-Gaussian filter*/
		if(GRAD_FILTER==1){smooth(waveconv,1,1,Vs_avg,FC);}
		
		/* output of the preconditioned gradient */
		for (i=1;i<=NX;i=i+IDX){
		for (j=1;j<=NY;j=j+IDY){
			waveconv[j][i] = C_vp * waveconv[j][i];
			gradp[j][i]=waveconv[j][i];
		}
		}
		
		/* save gradient for output as inversion result */
		if(iter==nfstart_jac){
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			sprintf(jac,"%s_p_it%d.old.%i.%i",JACOBIAN,iter,POS[1],POS[2]);
			FP3=fopen(jac,"wb");
			
			for (i=1;i<=NX;i=i+IDX){
			for (j=1;j<=NY;j=j+IDY){
				fwrite(&waveconv[j][i],sizeof(float),1,FP3);
			}
			}
			
			fclose(FP3);
			
			MPI_Barrier(MPI_COMM_WORLD);
			
			/* merge gradient file */ 
			sprintf(jac,"%s_p_it%d.old",JACOBIAN,iter);
			if (MYID==0) mergemod(jac,3);
			MPI_Barrier(MPI_COMM_WORLD);
			sprintf(jac,"%s_p_it%d.old.%i.%i",JACOBIAN,iter,POS[1],POS[2]);
			remove(jac);
		}
		
		/* calculate conjugate gradient direction, if iter > 1 (after Mora 1987) */
		/* --------------------------------------------------------------------- */
		
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		if((iter>1)&&(use_conjugate_1)){
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			sprintf(jac,"%s_p.old.%i.%i",JACOBIAN,POS[1],POS[2]);
			FP6=fopen(jac,"rb");
			
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			if((iter>2)&&(use_conjugate_2)){
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				sprintf(jac2,"%s_c.old.%i.%i",JACOBIAN,POS[1],POS[2]);
				FP5=fopen(jac2,"rb");
			}
			
			/* apply scalar product to obtain the coefficient beta */
			betaz = 0.0;
			betan = 0.0;
			for (i=1;i<=NX;i=i+IDX){
			for (j=1;j<=NY;j=j+IDY){
				
				fread(&gradplastiter,sizeof(float),1,FP6);
				
				/*if(gradglastiter==gradg[j][i]) err("TEST1");*/
				/*if (MYID==10)  printf("TEST beta (MYID=%d) bei (j,i)=(%i,%i): gradg(k-1) = %e, gradg(k) = %e\n",MYID,j,i,gradglastiter,gradg[j][i]);*/
				
				/*
				betaz += (1e5*gradp[j][i]) * ( (1e5*gradg[j][i]) - (1e5*gradglastiter) );
				betan += (1e5*gradplastiter) * (1e5*gradglastiter);
				*/
				
				/* Polak and Ribiere */
				/*betaz += (gradp[j][i]) * ( (gradg[j][i]) - (gradglastiter) );
				betan += (gradplastiter) * (gradglastiter);*/
				
				/* Polak and Ribiere */
				betaz += (gradp[j][i]) * ( (gradp[j][i]) - (gradplastiter) );
				betan += (gradplastiter) * (gradplastiter);
				
				/* Fletcher and Reeves */
				/*betaz += (gradp[j][i]) * (gradg[j][i]);
				betan += (gradplastiter) * (gradglastiter);*/
				
			}
			}
			
			/*printf("TEST: vor exchange (MYID=%d): beta = betaz/betan = %e/%e = %e\n",MYID,betaz,betan,betaz/betan);*/
			
			/*betaz = exchange_L2(betaz,1,1);
			betan = exchange_L2(betan,1,1);*/
			
			betar = 0.0;
			MPI_Allreduce(&betaz,&betar,1,MPI_FLOAT,MPI_SUM,MPI_COMM_WORLD);
			betaz = betar;
			
			betar = 0.0;
			MPI_Allreduce(&betan,&betar,1,MPI_FLOAT,MPI_SUM,MPI_COMM_WORLD);
			betan = betar;
			
// 			beta = betaz/betan;
			beta = 0.0f;
			if(betan !=0.0f) beta = betaz/betan;
			
			/* direction reset */
			if(beta<0.0){beta = 0.0;}
			
			/*betaVp = beta;*/
			
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			/*printf("\n\nTEST: nach exchange (MYID=%d): beta = %e / %e = %e\n",MYID,betaz,betan,beta);*/
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			fseek(FP6,0,SEEK_SET);
			
			for (i=1;i<=NX;i=i+IDX){
			for (j=1;j<=NY;j=j+IDY){
				
				if(iter==2){
					fread(&gradplastiter,sizeof(float),1,FP6);
					waveconv[j][i] = gradp[j][i] + gradplastiter * beta;
				}
				
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				if((iter>2)&&(use_conjugate_2)){
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					fread(&gradclastiter,sizeof(float),1,FP5);
					waveconv[j][i] = gradp[j][i] + gradclastiter * beta;
				}
				
				/*if (iter >= 2){
					if (isnan(waveconv[j][i]) || isinf(waveconv[j][i])){
						sum = 0.0;
						h = 0;
						for (ii=-1;ii<=1;ii++){
						for (jj=-1;jj<=1;jj++){
							if (isnan(waveconv[j+jj][i+ii]) || isinf(waveconv[j+jj][i+ii])) continue;
							sum += waveconv[j+jj][i+ii];
							h++;
						}
						}
						if (h>0) waveconv[j][i] = sum / h;
						else waveconv[j][i] = 0.0;
					}
				}*/
			}
			}
			
			fclose(FP6);
			
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			if((iter>2)&&(use_conjugate_2)){fclose(FP5);}
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		}
		
		/* output of the conjugate gradient */
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		if((iter>1)&&(use_conjugate_1)){
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			sprintf(jac2,"%s_c.old.%i.%i",JACOBIAN,POS[1],POS[2]);
			FP5=fopen(jac2,"wb");
			
			for (i=1;i<=NX;i=i+IDX){
			for (j=1;j<=NY;j=j+IDY){
				fwrite(&waveconv[j][i],sizeof(float),1,FP5);
			}
			}
			
			fclose(FP5);
			
			MPI_Barrier(MPI_COMM_WORLD);
			
			/* merge gradient file */ 
			sprintf(jac2,"%s_c.old",JACOBIAN);
			if (MYID==0) mergemod(jac2,3);
		}
		
		/* output of preconditioned gradient */
		sprintf(jac,"%s_p.old.%i.%i",JACOBIAN,POS[1],POS[2]);
		FP4=fopen(jac,"wb");
		
		/* output of the preconditioned gradient */
		for (i=1;i<=NX;i=i+IDX){
		for (j=1;j<=NY;j=j+IDY){
			/*fwrite(&waveconv[j][i],sizeof(float),1,FP4);*/
			fwrite(&gradp[j][i],sizeof(float),1,FP4);
		}
		}
		
		fclose(FP4);
		
		MPI_Barrier(MPI_COMM_WORLD);
		
		/* merge gradient file */ 
		sprintf(jac,"%s_p.old",JACOBIAN);
		if (MYID==0) mergemod(jac,3);
	}
	
	/* ===================================================================================================================================================== */
	/* ===================================================== GRADIENT Zs ================================================================================== */
	/* ===================================================================================================================================================== */
	
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	if((FORWARD_ONLY==0)&&(!ACOUSTIC)){
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		/* Preconditioning of the gradient */
		/* ------------------------------- */
		
		/* apply taper on the gradient */
		/* --------------------------- */
		if (SWS_TAPER_GRAD_VERT){   /*vertical gradient taper is applied*/
		taper_grad(waveconv_u,taper_coeff,srcpos,nsrc,recpos,ntr_glob,1);}
		
		if (SWS_TAPER_GRAD_HOR){   /*horizontal gradient taper is applied*/
		taper_grad(waveconv_u,taper_coeff,srcpos,nsrc,recpos,ntr_glob,2);}
		
		if (SWS_TAPER_GRAD_SOURCES){   /*cylindrical taper around sources is applied*/
		taper_grad(waveconv_u,taper_coeff,srcpos,nsrc,recpos,ntr_glob,3);}
		
		if (SWS_TAPER_FILE){   /* read taper from BIN-File*/                          
		taper_grad(waveconv_u,taper_coeff,srcpos,nsrc,recpos,ntr_glob,5);}
		
		/* save gradient */
		sprintf(jac,"%s_g_u.old.%i.%i",JACOBIAN,POS[1],POS[2]);
		FP3=fopen(jac,"wb");
		
		for (i=1;i<=NX;i=i+IDX){
		for (j=1;j<=NY;j=j+IDY){
			fwrite(&waveconv_u[j][i],sizeof(float),1,FP3);
		}
		}
			
		fclose(FP3);
		
		MPI_Barrier(MPI_COMM_WORLD);
			
		/* merge gradient file */ 
		sprintf(jac,"%s_g_u.old",JACOBIAN);
		if (MYID==0) mergemod(jac,3);
		
		/* Normalize gradient to maximum value */
		/*norm(waveconv_u,iter,2);*/
		
		/* apply spatial wavelength filter */
		if(SPATFILTER==1){
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			if (MYID==0&&VERBOSE){
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			fprintf(FP,"\n Spatial filter is applied to gradient (written by PE %d)\n",MYID);}
		spat_filt(waveconv_u,iter,2);}
		
		/* apply 2D-Gaussian filter*/
		if(GRAD_FILTER==1){smooth(waveconv_u,2,1,Vs_avg,FC);}
		
		/* output of the preconditioned gradient */
		for (i=1;i<=NX;i=i+IDX){
		for (j=1;j<=NY;j=j+IDY){
			waveconv_u[j][i] = C_vs * waveconv_u[j][i];
			gradp_u[j][i]=waveconv_u[j][i];
		}
		}
		
		/* save gradient for output as inversion result */
		if(iter==nfstart_jac){
			sprintf(jac,"%s_p_u_it%d.old.%i.%i",JACOBIAN,iter,POS[1],POS[2]);
			FP3=fopen(jac,"wb");
			
			for (i=1;i<=NX;i=i+IDX){
			for (j=1;j<=NY;j=j+IDY){
				fwrite(&waveconv_u[j][i],sizeof(float),1,FP3);
			}
			}
			
			fclose(FP3);
			
			MPI_Barrier(MPI_COMM_WORLD);
			
			/* merge gradient file */ 
			sprintf(jac,"%s_p_u_it%d.old",JACOBIAN,iter);
			if (MYID==0) mergemod(jac,3);
			MPI_Barrier(MPI_COMM_WORLD);
			sprintf(jac,"%s_p_u_it%d.old.%i.%i",JACOBIAN,iter,POS[1],POS[2]);
			remove(jac);
		}
		
		/* calculate conjugate gradient direction, if iter > 1 (after Mora 1987) */
		/* --------------------------------------------------------------------- */
		
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		if((iter>1)&&(use_conjugate_1)){
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			sprintf(jac,"%s_p_u.old.%i.%i",JACOBIAN,POS[1],POS[2]);
			FP6=fopen(jac,"rb");
			
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			if((iter>2)&&(use_conjugate_2)){
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				sprintf(jac2,"%s_c_u.old.%i.%i",JACOBIAN,POS[1],POS[2]);
				FP5=fopen(jac2,"rb");
			}
			
				/* apply scalar product to obtain the coefficient beta */
			betaz = 0.0;
			betan = 0.0;
			for (i=1;i<=NX;i=i+IDX){
			for (j=1;j<=NY;j=j+IDY){
				
				fread(&gradplastiter,sizeof(float),1,FP6);
				/*if(gradglastiter==gradg[j][i]) err("TEST1");*/
				/*if (MYID==10)  printf("TEST beta (MYID=%d) bei (j,i)=(%i,%i): gradg(k-1) = %e, gradg(k) = %e\n",MYID,j,i,gradglastiter,gradg[j][i]);*/
				
				/*
				betaz += (1e5*gradp[j][i]) * ( (1e5*gradg[j][i]) - (1e5*gradglastiter) );
				betan += (1e5*gradplastiter) * (1e5*gradglastiter);
				*/
				
				/* Polak and Ribiere */
				/*betaz += (gradp_u[j][i]) * ( (gradg_u[j][i]) - (gradglastiter) );
				betan += (gradplastiter) * (gradglastiter);*/
				
				/* Polak and Ribiere */
				betaz += (gradp_u[j][i]) * ( (gradp_u[j][i]) - (gradplastiter) );
				betan += (gradplastiter) * (gradplastiter);
				
				/* Fletcher and Reeves */
				/*betaz += (gradp[j][i]) * (gradg[j][i]);
				betan += (gradplastiter) * (gradglastiter);*/
				
			}
			}
			
			/*printf("TEST: vor exchange (MYID=%d): beta = betaz/betan = %e/%e = %e\n",MYID,betaz,betan,betaz/betan);*/
			
			/*betaz = exchange_L2(betaz,1,1);
			betan = exchange_L2(betan,1,1);*/
			
			betar = 0.0;
			MPI_Allreduce(&betaz,&betar,1,MPI_FLOAT,MPI_SUM,MPI_COMM_WORLD);
			betaz = betar;
			
			betar = 0.0;
			MPI_Allreduce(&betan,&betar,1,MPI_FLOAT,MPI_SUM,MPI_COMM_WORLD);
			betan = betar;
			
// 			beta = betaz/betan;
			beta = 0.0f;
			if(betan !=0.0f) beta = betaz/betan;
			
			/* direction reset */
			if(beta<0.0){beta = 0.0;}
			
			/*betaVs = beta;*/
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			//printf("\n\nTEST: nach exchange (MYID=%d): beta = %e / %e = %e\n",MYID,betaz,betan,beta);
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			fseek(FP6,0,SEEK_SET);
			
			for (i=1;i<=NX;i=i+IDX){
			for (j=1;j<=NY;j=j+IDY){
				
				if(iter==2){
					fread(&gradplastiter,sizeof(float),1,FP6);
					waveconv_u[j][i] = gradp_u[j][i] + gradplastiter * beta;
				}
				
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				if((iter>2)&&(use_conjugate_2)){
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					fread(&gradclastiter,sizeof(float),1,FP5);
					waveconv_u[j][i] = gradp_u[j][i] + gradclastiter * beta;
				}
				
				
				/*if (iter >= 2){
					if (isnan(waveconv_u[j][i]) || isinf(waveconv_u[j][i])){
						sum = 0.0;
						h = 0;
						for (ii=-1;ii<=1;ii++){
						for (jj=-1;jj<=1;jj++){
							if (isnan(waveconv_u[j+jj][i+ii]) || isinf(waveconv_u[j+jj][i+ii])) continue;
							sum += waveconv_u[j+jj][i+ii];
							h++;
						}
						}
						if (h>0) waveconv_u[j][i] = sum / h;
						else waveconv_u[j][i] = 0.0;
					}
				}*/
			}
			}
			
			fclose(FP6);
			
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			if((iter>2)&&(use_conjugate_2)){fclose(FP5);}
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		}
		
		/* output of the conjugate gradient */
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		if((iter>1)&&(use_conjugate_1)){
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			sprintf(jac2,"%s_c_u.old.%i.%i",JACOBIAN,POS[1],POS[2]);
			FP5=fopen(jac2,"wb");
			
			for (i=1;i<=NX;i=i+IDX){
			for (j=1;j<=NY;j=j+IDY){
				fwrite(&waveconv_u[j][i],sizeof(float),1,FP5);
			}
			}
			
			fclose(FP5);
			
			MPI_Barrier(MPI_COMM_WORLD);
			
			/* merge gradient file */ 
			sprintf(jac2,"%s_c_u.old",JACOBIAN);
			if (MYID==0) mergemod(jac2,3);  
		}
		
		sprintf(jac,"%s_p_u.old.%i.%i",JACOBIAN,POS[1],POS[2]);
		FP4=fopen(jac,"wb");
		
		/* output of the preconditioned gradient */
		for (i=1;i<=NX;i=i+IDX){
		for (j=1;j<=NY;j=j+IDY){
			/*fwrite(&waveconv_u[j][i],sizeof(float),1,FP4);*/
			fwrite(&gradp_u[j][i],sizeof(float),1,FP4);
		}
		}
		
		fclose(FP4);
		
		MPI_Barrier(MPI_COMM_WORLD);
		
		/* merge gradient file */ 
		sprintf(jac,"%s_p_u.old",JACOBIAN);
		if (MYID==0) mergemod(jac,3);
		
	}
	
	/* ===================================================================================================================================================== */
	/* ===================================================== GRADIENT rho ================================================================================== */
	/* ===================================================================================================================================================== */
	
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	if((FORWARD_ONLY==0)){
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		/* Preconditioning of the gradient */
		/* ------------------------------- */
		if (SWS_TAPER_GRAD_VERT){   /*vertical gradient taper is applied*/
		taper_grad(waveconv_rho,taper_coeff,srcpos,nsrc,recpos,ntr_glob,1);}
		
		if (SWS_TAPER_GRAD_HOR){   /*horizontal gradient taper is applied*/
		taper_grad(waveconv_rho,taper_coeff,srcpos,nsrc,recpos,ntr_glob,2);}
		
		if (SWS_TAPER_GRAD_SOURCES){   /*cylindrical taper around sources is applied*/
		taper_grad(waveconv_rho,taper_coeff,srcpos,nsrc,recpos,ntr_glob,3);}
		
		if (SWS_TAPER_FILE){   /* read taper from BIN-File*/                          
		taper_grad(waveconv_rho,taper_coeff,srcpos,nsrc,recpos,ntr_glob,6);}
		
		/* save gradient */
		sprintf(jac,"%s_g_rho.old.%i.%i",JACOBIAN,POS[1],POS[2]);
		FP3=fopen(jac,"wb");
		
		for (i=1;i<=NX;i=i+IDX){
		for (j=1;j<=NY;j=j+IDY){
			fwrite(&waveconv_rho[j][i],sizeof(float),1,FP3);
		}
		}
			
		fclose(FP3);
		
		MPI_Barrier(MPI_COMM_WORLD);
			
		/* merge gradient file */ 
		sprintf(jac,"%s_g_rho.old",JACOBIAN);
		if (MYID==0) mergemod(jac,3);
		
		/* Normalize gradient to maximum value */
		/*norm(waveconv_rho,iter,3);*/
		
		/* apply spatial wavelength filter */
		if(SPATFILTER==1){
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			if (MYID==0&&VERBOSE){
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			fprintf(FP,"\n Spatial filter is applied to gradient (written by PE %d)\n",MYID);}
		spat_filt(waveconv_rho,iter,3);}
		
		/* apply 2D-Gaussian filter*/
		if(GRAD_FILTER==1){smooth(waveconv_rho,3,1,Vs_avg,FC);}
		
		/* output of the preconditioned gradient */
		for (i=1;i<=NX;i=i+IDX){
		for (j=1;j<=NY;j=j+IDY){
		waveconv_rho[j][i] = C_rho * waveconv_rho[j][i];
			gradp_rho[j][i]=waveconv_rho[j][i];
		}
		}
		
		/* save gradient for output as inversion result */
		if(iter==nfstart_jac){
			sprintf(jac,"%s_p_rho_it%d.old.%i.%i",JACOBIAN,iter,POS[1],POS[2]);
			FP3=fopen(jac,"wb");
			
			for (i=1;i<=NX;i=i+IDX){
			for (j=1;j<=NY;j=j+IDY){
				fwrite(&waveconv_rho[j][i],sizeof(float),1,FP3);
			}
			}
			
			fclose(FP3);
			
			MPI_Barrier(MPI_COMM_WORLD);
			
			/* merge gradient file */ 
			sprintf(jac,"%s_p_rho_it%d.old",JACOBIAN,iter);
			if (MYID==0) mergemod(jac,3);
			MPI_Barrier(MPI_COMM_WORLD);
			sprintf(jac,"%s_p_rho_it%d.old.%i.%i",JACOBIAN,iter,POS[1],POS[2]);
			remove(jac);
		}
		
		/* calculate conjugate gradient direction, if iter > 1 (after Mora 1987) */
		/* --------------------------------------------------------------------- */
		
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		if((iter>1)&&(use_conjugate_1)){
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			sprintf(jac,"%s_p_rho.old.%i.%i",JACOBIAN,POS[1],POS[2]);
			FP6=fopen(jac,"rb");
			
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				sprintf(jac2,"%s_c_rho.old.%i.%i",JACOBIAN,POS[1],POS[2]);
				FP5=fopen(jac2,"rb");
			}
			
			/* apply scalar product to obtain the coefficient beta */
			betaz = 0.0;
			betan = 0.0;
			for (i=1;i<=NX;i=i+IDX){
			for (j=1;j<=NY;j=j+IDY){
				
				fread(&gradplastiter,sizeof(float),1,FP6);
				
				/*if(gradglastiter==gradg[j][i]) err("TEST1");*/
				/*if (MYID==10)  printf("TEST beta (MYID=%d) bei (j,i)=(%i,%i): gradg(k-1) = %e, gradg(k) = %e\n",MYID,j,i,gradglastiter,gradg[j][i]);*/
				
				/*
				betaz += (1e5*gradp[j][i]) * ( (1e5*gradg[j][i]) - (1e5*gradglastiter) );
				betan += (1e5*gradplastiter) * (1e5*gradglastiter);
				*/
				
				/* Polak and Ribiere */
				/*betaz += (gradp_rho[j][i]) * ( (gradg_rho[j][i]) - (gradglastiter) );
				betan += (gradplastiter) * (gradglastiter);*/
				
				/* Polak and Ribiere */
				betaz += (gradp_rho[j][i]) * ( (gradp_rho[j][i]) - (gradplastiter) );
				betan += (gradplastiter) * (gradplastiter);
				
				/* Fletcher and Reeves */
				/*betaz += (gradp[j][i]) * (gradg[j][i]);
				betan += (gradplastiter) * (gradglastiter);*/
				
			}
			}
			
			/*printf("TEST: vor exchange (MYID=%d): beta = betaz/betan = %e/%e = %e\n",MYID,betaz,betan,betaz/betan);*/
			
			/*betaz = exchange_L2(betaz,1,1);
			betan = exchange_L2(betan,1,1);*/
			
			betar = 0.0;
			MPI_Allreduce(&betaz,&betar,1,MPI_FLOAT,MPI_SUM,MPI_COMM_WORLD);
			betaz = betar;
			
			betar = 0.0;
			MPI_Allreduce(&betan,&betar,1,MPI_FLOAT,MPI_SUM,MPI_COMM_WORLD);
			betan = betar;
			
// 			beta = betaz/betan;
			beta = 0.0f;
			if(betan !=0.0f) beta = betaz/betan;
			
			/* direction reset */
			if(beta<0.0){beta = 0.0;}

			/*betarho = beta;*/
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			//printf("\n\nTEST: nach exchange (MYID=%d): beta = %e / %e = %e\n",MYID,betaz,betan,beta);
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			fseek(FP6,0,SEEK_SET);
			
			for (i=1;i<=NX;i=i+IDX){
			for (j=1;j<=NY;j=j+IDY){
				
				if(iter==2){
					fread(&gradplastiter,sizeof(float),1,FP6);
					waveconv_rho[j][i] = gradp_rho[j][i] + gradplastiter * beta;
				}
				
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				if((iter>2)&&(use_conjugate_2)){
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					fread(&gradclastiter,sizeof(float),1,FP5);
					waveconv_rho[j][i] = gradp_rho[j][i] + gradclastiter * beta;
				}
				
				/*if (iter >= 2){
					if (isnan(waveconv_u[j][i]) || isinf(waveconv_u[j][i])){
						sum = 0.0;
						h = 0;
						for (ii=-1;ii<=1;ii++){
						for (jj=-1;jj<=1;jj++){
							if (isnan(waveconv_rho[j+jj][i+ii]) || isinf(waveconv_rho[j+jj][i+ii])) continue;
							sum += waveconv_rho[j+jj][i+ii];
							h++;
						}
						}
						if (h>0) waveconv_rho[j][i] = sum / h;
						else waveconv_rho[j][i] = 0.0;
					}
				}*/
			}
			}
			
			fclose(FP6);
			
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			if((iter>2)&&(use_conjugate_2)){fclose(FP5);}
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		}
		
		/* output of the conjugate gradient */
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		if((iter>1)&&(use_conjugate_1)){
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			sprintf(jac2,"%s_c_rho.old.%i.%i",JACOBIAN,POS[1],POS[2]);
			FP5=fopen(jac2,"wb");
			
			for (i=1;i<=NX;i=i+IDX){
			for (j=1;j<=NY;j=j+IDY){
				fwrite(&waveconv_rho[j][i],sizeof(float),1,FP5);
			}
			}
			
			fclose(FP5);
			
			MPI_Barrier(MPI_COMM_WORLD);
			
			/* merge gradient file */ 
			sprintf(jac2,"%s_c_rho.old",JACOBIAN);
			if (MYID==0) mergemod(jac2,3);  
		}
		
		sprintf(jac,"%s_p_rho.old.%i.%i",JACOBIAN,POS[1],POS[2]);
		FP4=fopen(jac,"wb");
		
		/* output of the preconditioned gradient */
		for (i=1;i<=NX;i=i+IDX){
		for (j=1;j<=NY;j=j+IDY){
			/*fwrite(&waveconv_rho[j][i],sizeof(float),1,FP4);*/
			fwrite(&gradp_rho[j][i],sizeof(float),1,FP4);
		}
		}
		
		fclose(FP4);
		
		MPI_Barrier(MPI_COMM_WORLD);
		
		/* merge gradient file */ 
		sprintf(jac,"%s_p_rho.old",JACOBIAN);
		if (MYID==0) mergemod(jac,3);
	}
}