paso/src/Solver_AMG.c


/*******************************************************
*
* Copyright (c) 2003-2009 by University of Queensland
* Earth Systems Science Computational Center (ESSCC)
* http://www.uq.edu.au/esscc
*
* Primary Business: Queensland, Australia
* Licensed under the Open Software License version 3.0
* http://www.opensource.org/licenses/osl-3.0.php
*
*******************************************************/


/**************************************************************/

/* Paso: AMG preconditioner                                  */

/**************************************************************/

/* Author: artak@uq.edu.au                                */

/**************************************************************/

#include "Paso.h"
#include "Solver.h"
#include "Options.h"
#include "PasoUtil.h"
#include "UMFPACK.h"
#include "MKL.h"
#include "SystemMatrix.h"
#include "Pattern_coupling.h"

/**************************************************************/

/* free all memory used by AMG                                */

void Paso_Solver_AMG_System_free(Paso_Solver_AMG_System * in) {
     dim_t i;
     if (in!=NULL) {
        for (i=0;i<in->block_size;++i) {
          Paso_Solver_AMG_free(in->amgblock[i]);
          Paso_SparseMatrix_free(in->block[i]);
        }
        MEMFREE(in);
     }
}


/* free all memory used by AMG                                */

void Paso_Solver_AMG_free(Paso_Solver_AMG * in) {
     if (in!=NULL) {
        Paso_Solver_Jacobi_free(in->GS);
        MEMFREE(in->inv_A_FF);
        MEMFREE(in->A_FF_pivot);
        Paso_SparseMatrix_free(in->A_FC);
        Paso_SparseMatrix_free(in->A_CF);
        Paso_SparseMatrix_free(in->A);
        MEMFREE(in->rows_in_F);
        MEMFREE(in->rows_in_C);
        MEMFREE(in->mask_F);
        MEMFREE(in->mask_C);
        MEMFREE(in->x_F);
        MEMFREE(in->b_F);
        MEMFREE(in->x_C);
        MEMFREE(in->b_C);
        #ifdef UMFPACK
        Paso_UMFPACK1_free((Paso_UMFPACK_Handler*)(in->solver));
        #endif
        in->solver=NULL;
        Paso_Solver_AMG_free(in->AMG_of_Schur);
        MEMFREE(in->b_C);
        MEMFREE(in);
     }
}

/**************************************************************/

/*   constructs the block-block factorization of 

        [ A_FF A_FC ]
   A_p= 
        [ A_CF A_FF ]

to 

  [      I         0  ]  [ A_FF 0 ] [ I    invA_FF*A_FF ]  
  [ A_CF*invA_FF   I  ]  [   0  S ] [ 0          I      ] 


   where S=A_FF-ACF*invA_FF*A_FC within the shape of S

   then AMG is applied to S again until S becomes empty 

*/
Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,dim_t level,Paso_Options* options) {
  Paso_Solver_AMG* out=NULL;
  Paso_Pattern* temp1=NULL;
  Paso_Pattern* temp2=NULL;
  bool_t verbose=options->verbose;
  dim_t n=A_p->numRows;
  dim_t n_block=A_p->row_block_size;
  index_t* mis_marker=NULL;  
  index_t* counter=NULL;
  index_t iPtr,*index, *where_p, iPtr_s;
  dim_t i,j;
  Paso_SparseMatrix * schur=NULL;
  Paso_SparseMatrix * schur_withFillIn=NULL;
  double S=0;
  
  /*Make sure we have block sizes 1*/
  if (A_p->col_block_size>1) {
     Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires column block size 1.");
     return NULL;
  }
  if (A_p->row_block_size>1) {
     Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires row block size 1.");
     return NULL;
  }
  out=MEMALLOC(1,Paso_Solver_AMG);
  /* identify independend set of rows/columns */
  mis_marker=TMPMEMALLOC(n,index_t);
  counter=TMPMEMALLOC(n,index_t);
  if ( !( Paso_checkPtr(mis_marker) || Paso_checkPtr(counter) || Paso_checkPtr(out)) ) {
     out->AMG_of_Schur=NULL;
     out->inv_A_FF=NULL;
     out->A_FF_pivot=NULL;
     out->A_FC=NULL;
     out->A_CF=NULL;
     out->rows_in_F=NULL;
     out->rows_in_C=NULL;
     out->mask_F=NULL;
     out->mask_C=NULL;
     out->x_F=NULL;
     out->b_F=NULL;
     out->x_C=NULL;
     out->b_C=NULL;
     out->GS=NULL;
     out->A=Paso_SparseMatrix_getReference(A_p);
     out->GS=NULL;
     out->solver=NULL;
     /*out->GS=Paso_Solver_getGS(A_p,verbose);*/
     out->level=level;
     out->n=n;
     out->n_F=0;
     out->n_block=n_block;
     
     if (level==0 || n<=options->min_coarse_matrix_size) {
         out->coarsest_level=TRUE;
         #ifdef UMFPACK 
         #else
            #ifdef MKL 
            #else 
                out->GS=Paso_Solver_getJacobi(A_p);
            #endif
         #endif
     } else {
         out->coarsest_level=FALSE;
         out->GS=Paso_Solver_getJacobi(A_p);
 
         /* identify independend set of rows/columns */
         #pragma omp parallel for private(i) schedule(static)
         for (i=0;i<n;++i) mis_marker[i]=-1;

         if (options->coarsening_method == PASO_YAIR_SHAPIRA_COARSENING) {
              Paso_Pattern_YS(A_p,mis_marker,options->coarsening_threshold);
         }
         else if (options->coarsening_method == PASO_RUGE_STUEBEN_COARSENING) {
              Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
         }
         else if (options->coarsening_method == PASO_AGGREGATION_COARSENING) {
             Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);
        }
        else {
           /*Default coarseneing*/
            Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
            /*Paso_Pattern_YS(A_p,mis_marker,options->coarsening_threshold);*/
             /*Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);*/
        }
        
        #pragma omp parallel for private(i) schedule(static)
        for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
        out->n_F=Paso_Util_cumsum(n,counter);
        
        if (out->n_F==n) {
           out->coarsest_level=TRUE;
           if (verbose) { 
               printf("AMG coarsening eliminates all unknowns, switching to Jacobi preconditioner.\n");
           }
        } else {
     
              if (Paso_noError()) {
                 
                 /*#pragma omp parallel for private(i) schedule(static)
                 for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
                 out->n_F=Paso_Util_cumsum(n,counter);
                 */
                 out->mask_F=MEMALLOC(n,index_t);
                 out->rows_in_F=MEMALLOC(out->n_F,index_t);
                 out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
                 out->A_FF_pivot=NULL; /* later use for block size>3 */
                 if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
                    /* creates an index for F from mask */
                    #pragma omp parallel for private(i) schedule(static)
                    for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
                    #pragma omp parallel for private(i) schedule(static)
                    for (i = 0; i < n; ++i) {
                       if  (mis_marker[i]) {
                              out->rows_in_F[counter[i]]=i;
                              out->mask_F[i]=counter[i];
                       } else {
                              out->mask_F[i]=-1;
                       }
                    }
                    
                    /* Compute row-sum for getting rs(A_FF)^-1*/
                    #pragma omp parallel for private(i,iPtr,j,S) schedule(static)
                    for (i = 0; i < out->n_F; ++i) {
                      S=0;
      /*printf("[%d ]: [%d] -> ",i, out->rows_in_F[i]);*/
                      for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
                       j=A_p->pattern->index[iPtr];
      /*if (j==out->rows_in_F[i]) printf("diagonal %e",A_p->val[iPtr]);*/
                       if (mis_marker[j])
                           S+=A_p->val[iPtr];
                      }
      /*printf("-> %e \n",S);*/
                      out->inv_A_FF[i]=1./S;
                    }
                 }
              }
      
              /*check whether coarsening process actually makes sense to continue.
              if coarse matrix at least smaller by 30% then continue, otherwise we stop.*/
              if ((out->n_F*100/n)<30) {
                    level=1;
                }
             
              if ( Paso_noError()) {
                    /* if there are no nodes in the coarse level there is no more work to do */
                    out->n_C=n-out->n_F;
                   
                   /*if (out->n_F>500) */
                    out->rows_in_C=MEMALLOC(out->n_C,index_t);
                    out->mask_C=MEMALLOC(n,index_t);
                    if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
                         /* creates an index for C from mask */
                         #pragma omp parallel for private(i) schedule(static)
                         for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
                         Paso_Util_cumsum(n,counter);
                         #pragma omp parallel for private(i) schedule(static)
                         for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
                         #pragma omp parallel for private(i) schedule(static)
                         for (i = 0; i < n; ++i) {
                                  if  (! mis_marker[i]) {
                                      out->rows_in_C[counter[i]]=i;
                                      out->mask_C[i]=counter[i];
                                   } else {
                                      out->mask_C[i]=-1;
                                   }
                         }
                    }
              } 
              if ( Paso_noError()) {
                      /* get A_CF block: */
                      out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
                      /* get A_FC block: */
                      out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
                      /* get A_CC block: */
                      schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
      
              }
              if ( Paso_noError()) {
                     /*find the pattern of the schur complement with fill in*/
                    temp1=Paso_Pattern_multiply(PATTERN_FORMAT_DEFAULT,out->A_CF->pattern,out->A_FC->pattern);
                    temp2=Paso_Pattern_binop(PATTERN_FORMAT_DEFAULT, schur->pattern, temp1);
                    schur_withFillIn=Paso_SparseMatrix_alloc(A_p->type,temp2,1,1, TRUE);
                    Paso_Pattern_free(temp1);
                    Paso_Pattern_free(temp2);
              }
              if ( Paso_noError()) {
                    /* copy values over*/ 
                    #pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static)
                    for (i = 0; i < schur_withFillIn->numRows; ++i) {
                      for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
                         j=schur_withFillIn->pattern->index[iPtr];
                         iPtr_s=schur->pattern->ptr[i];
                         index=&(schur->pattern->index[iPtr_s]);
                         where_p=(index_t*)bsearch(&j,
                                              index,
                                              schur->pattern->ptr[i + 1]-schur->pattern->ptr[i],
                                              sizeof(index_t),
                                              Paso_comparIndex);
                         if (where_p!=NULL) {
                                schur_withFillIn->val[iPtr]=schur->val[iPtr_s+(index_t)(where_p-index)];
                         }
                       }
                    }
                    Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
                    out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,level-1,options);
              }
              /* allocate work arrays for AMG application */
              if (Paso_noError()) {
                         out->x_F=MEMALLOC(n_block*out->n_F,double);
                         out->b_F=MEMALLOC(n_block*out->n_F,double);
                         out->x_C=MEMALLOC(n_block*out->n_C,double);
                         out->b_C=MEMALLOC(n_block*out->n_C,double);
      
                         if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
                             #pragma omp parallel for private(i) schedule(static)
                             for (i = 0; i < out->n_F; ++i) {
                                         out->x_F[i]=0.;
                                         out->b_F[i]=0.;
                              }
                              #pragma omp parallel for private(i) schedule(static)
                              for (i = 0; i < out->n_C; ++i) {
                                     out->x_C[i]=0.;
                                     out->b_C[i]=0.;
                              }
                         }
              }
            Paso_SparseMatrix_free(schur);
            Paso_SparseMatrix_free(schur_withFillIn);
         }
     }
  }
  TMPMEMFREE(mis_marker);
  TMPMEMFREE(counter);

  if (Paso_noError()) {
      if (verbose && level>0 && !out->coarsest_level) {
         printf("AMG: level: %d: %d unknowns eliminated. %d left.\n",level, out->n_F,out->n_C);
     }
     return out;
  } else  {
     Paso_Solver_AMG_free(out);
     return NULL;
  }
}

/**************************************************************/

/* apply AMG precondition b-> x                               

     in fact it solves 

  [      I         0  ]  [ A_FF 0 ] [ I    invA_FF*A_FC ]  [ x_F ]  = [b_F]
  [ A_CF*invA_FF   I  ]  [   0  S ] [ 0          I      ]  [ x_C ]  = [b_C]

 in the form 

   b->[b_F,b_C] 
   x_F=invA_FF*b_F
   b_C=b_C-A_CF*x_F
   x_C=AMG(b_C)
   b_F=b_F-A_FC*x_C
   x_F=invA_FF*b_F
   x<-[x_F,x_C]

 should be called within a parallel region                                              
 barrier synconization should be performed to make sure that the input vector available 

*/

void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
     dim_t i;
     double time0=0;
     double *r=NULL, *x0=NULL;
     bool_t verbose=0;
     #ifdef UMFPACK 
          Paso_UMFPACK_Handler * ptr=NULL;
     #else     
        #ifdef MKL
          Paso_SparseMatrix *temp=NULL;
        #endif
     #endif
     r=MEMALLOC(amg->n,double);
     x0=MEMALLOC(amg->n,double);
     
     if (amg->coarsest_level) {
      
      time0=Paso_timer();
      /*If all unknown are eliminated then Jacobi is the best preconditioner*/
      if (amg->n_F==amg->n) {
        Paso_Solver_solveJacobi(amg->GS,x,b);
      }
       else {
       #ifdef UMFPACK
             ptr=(Paso_UMFPACK_Handler *)(amg->solver);
             Paso_UMFPACK1(&ptr,amg->A,x,b,verbose);
             amg->solver=(void*) ptr;
       #else      
         #ifdef MKL
          temp=Paso_SparseMatrix_alloc(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, amg->A->pattern,1,1, FALSE);
          #pragma omp parallel for private(i) schedule(static)
          for (i=0;i<amg->A->len;++i) {
               temp->val[i]=amg->A->val[i];
          }
          Paso_SparseMatrix_free(temp);
         #else
          Paso_Solver_solveJacobi(amg->GS,x,b);
         #endif
       #endif
       }
       time0=Paso_timer()-time0;
       if (verbose) fprintf(stderr,"timing: DIRECT SOLVER: %e\n",time0);
       
     } else {
        /* presmoothing */
         time0=Paso_timer();
         Paso_Solver_solveJacobi(amg->GS,x,b);
         time0=Paso_timer()-time0;
         if (verbose) fprintf(stderr,"timing: Presmooting: %e\n",time0);
        /* end of presmoothing */
        
        
         time0=Paso_timer();
         #pragma omp parallel for private(i) schedule(static)
         for (i=0;i<amg->n;++i) r[i]=b[i];
         
         /*r=b-Ax*/ 
         Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
       
        /* b->[b_F,b_C]     */
        #pragma omp parallel for private(i) schedule(static)
        for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
        
        #pragma omp parallel for private(i) schedule(static)
        for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];

        /* x_F=invA_FF*b_F  */
        Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
        
        /* b_C=b_C-A_CF*x_F */
        Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
        
        time0=Paso_timer()-time0;
        if (verbose) fprintf(stderr,"timing: Before next level: %e\n",time0);
        
        /* x_C=AMG(b_C)     */
        Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
        
        time0=Paso_timer();
        /* b_F=b_F-A_FC*x_C */
        Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
        /* x_F=invA_FF*b_F  */
        Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
        /* x<-[x_F,x_C]     */

        #pragma omp parallel for private(i) schedule(static)
        for (i=0;i<amg->n;++i) {
            if (amg->mask_C[i]>-1) {
                 x[i]=amg->x_C[amg->mask_C[i]];
            } else {
                 x[i]=amg->x_F[amg->mask_F[i]];
            }
        }
        
        time0=Paso_timer()-time0;
        if (verbose) fprintf(stderr,"timing: After next level: %e\n",time0);

     /*postsmoothing*/
     time0=Paso_timer();
     #pragma omp parallel for private(i) schedule(static)
     for (i=0;i<amg->n;++i) r[i]=b[i];
     
     /*r=b-Ax */
     Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
     Paso_Solver_solveJacobi(amg->GS,x0,r);
     
     #pragma omp parallel for private(i) schedule(static)
     for (i=0;i<amg->n;++i) x[i]+=x0[i];
     
     time0=Paso_timer()-time0;
     if (verbose) fprintf(stderr,"timing: Postsmoothing: %e\n",time0);

     /*end of postsmoothing*/
     
     }
     MEMFREE(r);
     MEMFREE(x0);
     return;
}
1
2	/*******************************************************
3	*
4	* Copyright (c) 2003-2009 by University of Queensland
5	* Earth Systems Science Computational Center (ESSCC)
6	* http://www.uq.edu.au/esscc
7	*
8	* Primary Business: Queensland, Australia
9	* Licensed under the Open Software License version 3.0
10	* http://www.opensource.org/licenses/osl-3.0.php
11	*
12	*******************************************************/
13
14
15	/**************************************************************/
16
17	/* Paso: AMG preconditioner */
18
19	/**************************************************************/
20
21	/* Author: artak@uq.edu.au */
22
23	/**************************************************************/
24
25	#include "Paso.h"
26	#include "Solver.h"
27	#include "Options.h"
28	#include "PasoUtil.h"
29	#include "UMFPACK.h"
30	#include "MKL.h"
31	#include "SystemMatrix.h"
32	#include "Pattern_coupling.h"
33
34	/**************************************************************/
35
36	/* free all memory used by AMG */
37
38	void Paso_Solver_AMG_System_free(Paso_Solver_AMG_System * in) {
39	dim_t i;
40	if (in!=NULL) {
41	for (i=0;i<in->block_size;++i) {
42	Paso_Solver_AMG_free(in->amgblock[i]);
43	Paso_SparseMatrix_free(in->block[i]);
44	}
45	MEMFREE(in);
46	}
47	}
48
49
50	/* free all memory used by AMG */
51
52	void Paso_Solver_AMG_free(Paso_Solver_AMG * in) {
53	if (in!=NULL) {
54	Paso_Solver_Jacobi_free(in->GS);
55	MEMFREE(in->inv_A_FF);
56	MEMFREE(in->A_FF_pivot);
57	Paso_SparseMatrix_free(in->A_FC);
58	Paso_SparseMatrix_free(in->A_CF);
59	Paso_SparseMatrix_free(in->A);
60	MEMFREE(in->rows_in_F);
61	MEMFREE(in->rows_in_C);
62	MEMFREE(in->mask_F);
63	MEMFREE(in->mask_C);
64	MEMFREE(in->x_F);
65	MEMFREE(in->b_F);
66	MEMFREE(in->x_C);
67	MEMFREE(in->b_C);
68	#ifdef UMFPACK
69	Paso_UMFPACK1_free((Paso_UMFPACK_Handler*)(in->solver));
70	#endif
71	in->solver=NULL;
72	Paso_Solver_AMG_free(in->AMG_of_Schur);
73	MEMFREE(in->b_C);
74	MEMFREE(in);
75	}
76	}
77
78	/**************************************************************/
79
80	/* constructs the block-block factorization of
81
82	[ A_FF A_FC ]
83	A_p=
84	[ A_CF A_FF ]
85
86	to
87
88	[ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
89	[ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
90
91
92	where S=A_FF-ACFinvA_FFA_FC within the shape of S
93
94	then AMG is applied to S again until S becomes empty
95
96	*/
97	Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix A_p,dim_t level,Paso_Options options) {
98	Paso_Solver_AMG* out=NULL;
99	Paso_Pattern* temp1=NULL;
100	Paso_Pattern* temp2=NULL;
101	bool_t verbose=options->verbose;
102	dim_t n=A_p->numRows;
103	dim_t n_block=A_p->row_block_size;
104	index_t* mis_marker=NULL;
105	index_t* counter=NULL;
106	index_t iPtr,index, where_p, iPtr_s;
107	dim_t i,j;
108	Paso_SparseMatrix * schur=NULL;
109	Paso_SparseMatrix * schur_withFillIn=NULL;
110	double S=0;
111
112	/Make sure we have block sizes 1/
113	if (A_p->col_block_size>1) {
114	Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires column block size 1.");
115	return NULL;
116	}
117	if (A_p->row_block_size>1) {
118	Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires row block size 1.");
119	return NULL;
120	}
121	out=MEMALLOC(1,Paso_Solver_AMG);
122	/* identify independend set of rows/columns */
123	mis_marker=TMPMEMALLOC(n,index_t);
124	counter=TMPMEMALLOC(n,index_t);
125	if ( !( Paso_checkPtr(mis_marker) \|\| Paso_checkPtr(counter) \|\| Paso_checkPtr(out)) ) {
126	out->AMG_of_Schur=NULL;
127	out->inv_A_FF=NULL;
128	out->A_FF_pivot=NULL;
129	out->A_FC=NULL;
130	out->A_CF=NULL;
131	out->rows_in_F=NULL;
132	out->rows_in_C=NULL;
133	out->mask_F=NULL;
134	out->mask_C=NULL;
135	out->x_F=NULL;
136	out->b_F=NULL;
137	out->x_C=NULL;
138	out->b_C=NULL;
139	out->GS=NULL;
140	out->A=Paso_SparseMatrix_getReference(A_p);
141	out->GS=NULL;
142	out->solver=NULL;
143	/out->GS=Paso_Solver_getGS(A_p,verbose);/
144	out->level=level;
145	out->n=n;
146	out->n_F=0;
147	out->n_block=n_block;
148
149	if (level==0 \|\| n<=options->min_coarse_matrix_size) {
150	out->coarsest_level=TRUE;
151	#ifdef UMFPACK
152	#else
153	#ifdef MKL
154	#else
155	out->GS=Paso_Solver_getJacobi(A_p);
156	#endif
157	#endif
158	} else {
159	out->coarsest_level=FALSE;
160	out->GS=Paso_Solver_getJacobi(A_p);
161
162	/* identify independend set of rows/columns */
163	#pragma omp parallel for private(i) schedule(static)
164	for (i=0;i<n;++i) mis_marker[i]=-1;
165
166	if (options->coarsening_method == PASO_YAIR_SHAPIRA_COARSENING) {
167	Paso_Pattern_YS(A_p,mis_marker,options->coarsening_threshold);
168	}
169	else if (options->coarsening_method == PASO_RUGE_STUEBEN_COARSENING) {
170	Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
171	}
172	else if (options->coarsening_method == PASO_AGGREGATION_COARSENING) {
173	Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);
174	}
175	else {
176	/Default coarseneing/
177	Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
178	/Paso_Pattern_YS(A_p,mis_marker,options->coarsening_threshold);/
179	/Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);/
180	}
181
182	#pragma omp parallel for private(i) schedule(static)
183	for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
184	out->n_F=Paso_Util_cumsum(n,counter);
185
186	if (out->n_F==n) {
187	out->coarsest_level=TRUE;
188	if (verbose) {
189	printf("AMG coarsening eliminates all unknowns, switching to Jacobi preconditioner.\n");
190	}
191	} else {
192
193	if (Paso_noError()) {
194
195	/*#pragma omp parallel for private(i) schedule(static)
196	for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
197	out->n_F=Paso_Util_cumsum(n,counter);
198	*/
199	out->mask_F=MEMALLOC(n,index_t);
200	out->rows_in_F=MEMALLOC(out->n_F,index_t);
201	out->inv_A_FF=MEMALLOC(n_blockn_blockout->n_F,double);
202	out->A_FF_pivot=NULL; /* later use for block size>3 */
203	if (! (Paso_checkPtr(out->mask_F) \|\| Paso_checkPtr(out->inv_A_FF) \|\| Paso_checkPtr(out->rows_in_F) ) ) {
204	/* creates an index for F from mask */
205	#pragma omp parallel for private(i) schedule(static)
206	for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
207	#pragma omp parallel for private(i) schedule(static)
208	for (i = 0; i < n; ++i) {
209	if (mis_marker[i]) {
210	out->rows_in_F[counter[i]]=i;
211	out->mask_F[i]=counter[i];
212	} else {
213	out->mask_F[i]=-1;
214	}
215	}
216
217	/* Compute row-sum for getting rs(A_FF)^-1*/
218	#pragma omp parallel for private(i,iPtr,j,S) schedule(static)
219	for (i = 0; i < out->n_F; ++i) {
220	S=0;
221	/printf("[%d ]: [%d] -> ",i, out->rows_in_F[i]);/
222	for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
223	j=A_p->pattern->index[iPtr];
224	/if (j==out->rows_in_F[i]) printf("diagonal %e",A_p->val[iPtr]);/
225	if (mis_marker[j])
226	S+=A_p->val[iPtr];
227	}
228	/printf("-> %e \n",S);/
229	out->inv_A_FF[i]=1./S;
230	}
231	}
232	}
233
234	/*check whether coarsening process actually makes sense to continue.
235	if coarse matrix at least smaller by 30% then continue, otherwise we stop.*/
236	if ((out->n_F*100/n)<30) {
237	level=1;
238	}
239
240	if ( Paso_noError()) {
241	/* if there are no nodes in the coarse level there is no more work to do */
242	out->n_C=n-out->n_F;
243
244	/if (out->n_F>500) /
245	out->rows_in_C=MEMALLOC(out->n_C,index_t);
246	out->mask_C=MEMALLOC(n,index_t);
247	if (! (Paso_checkPtr(out->mask_C) \|\| Paso_checkPtr(out->rows_in_C) ) ) {
248	/* creates an index for C from mask */
249	#pragma omp parallel for private(i) schedule(static)
250	for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
251	Paso_Util_cumsum(n,counter);
252	#pragma omp parallel for private(i) schedule(static)
253	for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
254	#pragma omp parallel for private(i) schedule(static)
255	for (i = 0; i < n; ++i) {
256	if (! mis_marker[i]) {
257	out->rows_in_C[counter[i]]=i;
258	out->mask_C[i]=counter[i];
259	} else {
260	out->mask_C[i]=-1;
261	}
262	}
263	}
264	}
265	if ( Paso_noError()) {
266	/* get A_CF block: */
267	out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
268	/* get A_FC block: */
269	out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
270	/* get A_CC block: */
271	schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
272
273	}
274	if ( Paso_noError()) {
275	/find the pattern of the schur complement with fill in/
276	temp1=Paso_Pattern_multiply(PATTERN_FORMAT_DEFAULT,out->A_CF->pattern,out->A_FC->pattern);
277	temp2=Paso_Pattern_binop(PATTERN_FORMAT_DEFAULT, schur->pattern, temp1);
278	schur_withFillIn=Paso_SparseMatrix_alloc(A_p->type,temp2,1,1, TRUE);
279	Paso_Pattern_free(temp1);
280	Paso_Pattern_free(temp2);
281	}
282	if ( Paso_noError()) {
283	/* copy values over*/
284	#pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static)
285	for (i = 0; i < schur_withFillIn->numRows; ++i) {
286	for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
287	j=schur_withFillIn->pattern->index[iPtr];
288	iPtr_s=schur->pattern->ptr[i];
289	index=&(schur->pattern->index[iPtr_s]);
290	where_p=(index_t*)bsearch(&j,
291	index,
292	schur->pattern->ptr[i + 1]-schur->pattern->ptr[i],
293	sizeof(index_t),
294	Paso_comparIndex);
295	if (where_p!=NULL) {
296	schur_withFillIn->val[iPtr]=schur->val[iPtr_s+(index_t)(where_p-index)];
297	}
298	}
299	}
300	Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
301	out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,level-1,options);
302	}
303	/* allocate work arrays for AMG application */
304	if (Paso_noError()) {
305	out->x_F=MEMALLOC(n_block*out->n_F,double);
306	out->b_F=MEMALLOC(n_block*out->n_F,double);
307	out->x_C=MEMALLOC(n_block*out->n_C,double);
308	out->b_C=MEMALLOC(n_block*out->n_C,double);
309
310	if (! (Paso_checkPtr(out->x_F) \|\| Paso_checkPtr(out->b_F) \|\| Paso_checkPtr(out->x_C) \|\| Paso_checkPtr(out->b_C) ) ) {
311	#pragma omp parallel for private(i) schedule(static)
312	for (i = 0; i < out->n_F; ++i) {
313	out->x_F[i]=0.;
314	out->b_F[i]=0.;
315	}
316	#pragma omp parallel for private(i) schedule(static)
317	for (i = 0; i < out->n_C; ++i) {
318	out->x_C[i]=0.;
319	out->b_C[i]=0.;
320	}
321	}
322	}
323	Paso_SparseMatrix_free(schur);
324	Paso_SparseMatrix_free(schur_withFillIn);
325	}
326	}
327	}
328	TMPMEMFREE(mis_marker);
329	TMPMEMFREE(counter);
330
331	if (Paso_noError()) {
332	if (verbose && level>0 && !out->coarsest_level) {
333	printf("AMG: level: %d: %d unknowns eliminated. %d left.\n",level, out->n_F,out->n_C);
334	}
335	return out;
336	} else {
337	Paso_Solver_AMG_free(out);
338	return NULL;
339	}
340	}
341
342	/**************************************************************/
343
344	/* apply AMG precondition b-> x
345
346	in fact it solves
347
348	[ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FC ] [ x_F ] = [b_F]
349	[ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
350
351	in the form
352
353	b->[b_F,b_C]
354	x_F=invA_FF*b_F
355	b_C=b_C-A_CF*x_F
356	x_C=AMG(b_C)
357	b_F=b_F-A_FC*x_C
358	x_F=invA_FF*b_F
359	x<-[x_F,x_C]
360
361	should be called within a parallel region
362	barrier synconization should be performed to make sure that the input vector available
363
364	*/
365
366	void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
367	dim_t i;
368	double time0=0;
369	double r=NULL, x0=NULL;
370	bool_t verbose=0;
371	#ifdef UMFPACK
372	Paso_UMFPACK_Handler * ptr=NULL;
373	#else
374	#ifdef MKL
375	Paso_SparseMatrix *temp=NULL;
376	#endif
377	#endif
378	r=MEMALLOC(amg->n,double);
379	x0=MEMALLOC(amg->n,double);
380
381	if (amg->coarsest_level) {
382
383	time0=Paso_timer();
384	/If all unknown are eliminated then Jacobi is the best preconditioner/
385	if (amg->n_F==amg->n) {
386	Paso_Solver_solveJacobi(amg->GS,x,b);
387	}
388	else {
389	#ifdef UMFPACK
390	ptr=(Paso_UMFPACK_Handler *)(amg->solver);
391	Paso_UMFPACK1(&ptr,amg->A,x,b,verbose);
392	amg->solver=(void*) ptr;
393	#else
394	#ifdef MKL
395	temp=Paso_SparseMatrix_alloc(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, amg->A->pattern,1,1, FALSE);
396	#pragma omp parallel for private(i) schedule(static)
397	for (i=0;i<amg->A->len;++i) {
398	temp->val[i]=amg->A->val[i];
399	}
400	Paso_SparseMatrix_free(temp);
401	#else
402	Paso_Solver_solveJacobi(amg->GS,x,b);
403	#endif
404	#endif
405	}
406	time0=Paso_timer()-time0;
407	if (verbose) fprintf(stderr,"timing: DIRECT SOLVER: %e\n",time0);
408
409	} else {
410	/* presmoothing */
411	time0=Paso_timer();
412	Paso_Solver_solveJacobi(amg->GS,x,b);
413	time0=Paso_timer()-time0;
414	if (verbose) fprintf(stderr,"timing: Presmooting: %e\n",time0);
415	/* end of presmoothing */
416
417
418	time0=Paso_timer();
419	#pragma omp parallel for private(i) schedule(static)
420	for (i=0;i<amg->n;++i) r[i]=b[i];
421
422	/r=b-Ax/
423	Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
424
425	/* b->[b_F,b_C] */
426	#pragma omp parallel for private(i) schedule(static)
427	for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
428
429	#pragma omp parallel for private(i) schedule(static)
430	for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
431
432	/* x_F=invA_FFb_F /
433	Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
434
435	/* b_C=b_C-A_CFx_F /
436	Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
437
438	time0=Paso_timer()-time0;
439	if (verbose) fprintf(stderr,"timing: Before next level: %e\n",time0);
440
441	/* x_C=AMG(b_C) */
442	Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
443
444	time0=Paso_timer();
445	/* b_F=b_F-A_FCx_C /
446	Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
447	/* x_F=invA_FFb_F /
448	Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
449	/* x<-[x_F,x_C] */
450
451	#pragma omp parallel for private(i) schedule(static)
452	for (i=0;i<amg->n;++i) {
453	if (amg->mask_C[i]>-1) {
454	x[i]=amg->x_C[amg->mask_C[i]];
455	} else {
456	x[i]=amg->x_F[amg->mask_F[i]];
457	}
458	}
459
460	time0=Paso_timer()-time0;
461	if (verbose) fprintf(stderr,"timing: After next level: %e\n",time0);
462
463	/postsmoothing/
464	time0=Paso_timer();
465	#pragma omp parallel for private(i) schedule(static)
466	for (i=0;i<amg->n;++i) r[i]=b[i];
467
468	/r=b-Ax /
469	Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
470	Paso_Solver_solveJacobi(amg->GS,x0,r);
471
472	#pragma omp parallel for private(i) schedule(static)
473	for (i=0;i<amg->n;++i) x[i]+=x0[i];
474
475	time0=Paso_timer()-time0;
476	if (verbose) fprintf(stderr,"timing: Postsmoothing: %e\n",time0);
477
478	/end of postsmoothing/
479
480	}
481	MEMFREE(r);
482	MEMFREE(x0);
483	return;
484	}