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_free(Paso_Solver_AMG * in) {
     if (in!=NULL) {
        Paso_Solver_AMG_free(in->AMG_of_Schur);
        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 MKL
        #else 
           #ifdef UMFPACK
           Paso_UMFPACK1_free((Paso_UMFPACK_Handler*)(in->solver));
           #endif
        #endif
        in->solver=NULL;
        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,k,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;
     
     if (level==0 || n<=options->min_coarse_matrix_size) {
         out->coarsest_level=TRUE;
         #ifdef MKL
         #else
            #ifdef UMFPACK 
            #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_coup(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_Aggregiation(A_p,mis_marker,options->coarsening_threshold);*/
        }
     
        if (Paso_noError()) {
           #pragma omp parallel for private(i) schedule(static)
           for (i = 0; i < n; ++i) counter[i]=mis_marker[i];

           out->n=n;
           out->n_block=n_block;
           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] && j==out->rows_in_F[i])
                     S=A_p->val[iPtr];
                }
/*printf("-> %e\n",S);*/
                out->inv_A_FF[i]=1./S;
              }
           }
        }

        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];
                   schur_withFillIn->val[iPtr]=0.;
                   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,k) schedule(static)
                       for (i = 0; i < out->n_F; ++i) {
                            for (k=0; k<n_block;++k) {
                                   out->x_F[i*n_block+k]=0.;
                                   out->b_F[i*n_block+k]=0.;
                            }
                        }
                        #pragma omp parallel for private(i,k) schedule(static)
                        for (i = 0; i < out->n_C; ++i) {
                           for (k=0; k<n_block;++k) {
                               out->x_C[i*n_block+k]=0.;
                               out->b_C[i*n_block+k]=0.;
                           }
                        }
                   }
        }
     }
  }
  TMPMEMFREE(mis_marker);
  TMPMEMFREE(counter);
  Paso_SparseMatrix_free(schur);
  Paso_SparseMatrix_free(schur_withFillIn);
  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 MKL
        Paso_SparseMatrix *temp=NULL;
     #else
        #ifdef UMFPACK 
           Paso_UMFPACK_Handler * ptr=NULL;
        #endif
     #endif
     r=MEMALLOC(amg->n,double);
     x0=MEMALLOC(amg->n,double);
     
     if (amg->coarsest_level) {
      
      time0=Paso_timer();
       #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_MKL1(temp,x,b,0);
        Paso_SparseMatrix_free(temp);
       #else
          #ifdef UMFPACK
             ptr=(Paso_UMFPACK_Handler *)(amg->solver);
             Paso_UMFPACK1(&ptr,amg->A,x,b,0);
             amg->solver=(void*) ptr;
          #else
             Paso_Solver_solveJacobi(amg->GS,x,b);
          #endif
       #endif
       time0=Paso_timer()-time0;
       if (verbose) fprintf(stderr,"timing: DIRECT SOLVER: %e\n\n\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_free(Paso_Solver_AMG * in) {
39	if (in!=NULL) {
40	Paso_Solver_AMG_free(in->AMG_of_Schur);
41	Paso_Solver_Jacobi_free(in->GS);
42	MEMFREE(in->inv_A_FF);
43	MEMFREE(in->A_FF_pivot);
44	Paso_SparseMatrix_free(in->A_FC);
45	Paso_SparseMatrix_free(in->A_CF);
46	Paso_SparseMatrix_free(in->A);
47	MEMFREE(in->rows_in_F);
48	MEMFREE(in->rows_in_C);
49	MEMFREE(in->mask_F);
50	MEMFREE(in->mask_C);
51	MEMFREE(in->x_F);
52	MEMFREE(in->b_F);
53	MEMFREE(in->x_C);
54	MEMFREE(in->b_C);
55	#ifdef MKL
56	#else
57	#ifdef UMFPACK
58	Paso_UMFPACK1_free((Paso_UMFPACK_Handler*)(in->solver));
59	#endif
60	#endif
61	in->solver=NULL;
62	MEMFREE(in->b_C);
63	MEMFREE(in);
64	}
65	}
66
67	/**************************************************************/
68
69	/* constructs the block-block factorization of
70
71	[ A_FF A_FC ]
72	A_p=
73	[ A_CF A_FF ]
74
75	to
76
77	[ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
78	[ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
79
80
81	where S=A_FF-ACFinvA_FFA_FC within the shape of S
82
83	then AMG is applied to S again until S becomes empty
84
85	*/
86	Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix A_p,dim_t level,Paso_Options options) {
87	Paso_Solver_AMG* out=NULL;
88	Paso_Pattern* temp1=NULL;
89	Paso_Pattern* temp2=NULL;
90	bool_t verbose=options->verbose;
91	dim_t n=A_p->numRows;
92	dim_t n_block=A_p->row_block_size;
93	index_t* mis_marker=NULL;
94	index_t* counter=NULL;
95	index_t iPtr,index, where_p, iPtr_s;
96	dim_t i,k,j;
97	Paso_SparseMatrix * schur=NULL;
98	Paso_SparseMatrix * schur_withFillIn=NULL;
99	double S=0;
100
101	/Make sure we have block sizes 1/
102	if (A_p->col_block_size>1) {
103	Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires column block size 1.");
104	return NULL;
105	}
106	if (A_p->row_block_size>1) {
107	Paso_setError(TYPE_ERROR,"Paso_Solver_getAMG: AMG requires row block size 1.");
108	return NULL;
109	}
110	out=MEMALLOC(1,Paso_Solver_AMG);
111	/* identify independend set of rows/columns */
112	mis_marker=TMPMEMALLOC(n,index_t);
113	counter=TMPMEMALLOC(n,index_t);
114	if ( !( Paso_checkPtr(mis_marker) \|\| Paso_checkPtr(counter) \|\| Paso_checkPtr(out)) ) {
115	out->AMG_of_Schur=NULL;
116	out->inv_A_FF=NULL;
117	out->A_FF_pivot=NULL;
118	out->A_FC=NULL;
119	out->A_CF=NULL;
120	out->rows_in_F=NULL;
121	out->rows_in_C=NULL;
122	out->mask_F=NULL;
123	out->mask_C=NULL;
124	out->x_F=NULL;
125	out->b_F=NULL;
126	out->x_C=NULL;
127	out->b_C=NULL;
128	out->GS=NULL;
129	out->A=Paso_SparseMatrix_getReference(A_p);
130	out->GS=NULL;
131	out->solver=NULL;
132	/out->GS=Paso_Solver_getGS(A_p,verbose);/
133	out->level=level;
134
135	if (level==0 \|\| n<=options->min_coarse_matrix_size) {
136	out->coarsest_level=TRUE;
137	#ifdef MKL
138	#else
139	#ifdef UMFPACK
140	#else
141	out->GS=Paso_Solver_getJacobi(A_p);
142	#endif
143	#endif
144	} else {
145	out->coarsest_level=FALSE;
146	out->GS=Paso_Solver_getJacobi(A_p);
147
148	/* identify independend set of rows/columns */
149	#pragma omp parallel for private(i) schedule(static)
150	for (i=0;i<n;++i) mis_marker[i]=-1;
151
152	if (options->coarsening_method == PASO_YAIR_SHAPIRA_COARSENING) {
153	Paso_Pattern_coup(A_p,mis_marker,options->coarsening_threshold);
154	}
155	else if (options->coarsening_method == PASO_RUGE_STUEBEN_COARSENING) {
156	Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
157	}
158	else if (options->coarsening_method == PASO_AGGREGATION_COARSENING) {
159	Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);
160	}
161	else {
162	/Default coarseneing/
163	Paso_Pattern_RS(A_p,mis_marker,options->coarsening_threshold);
164
165	/Paso_Pattern_Aggregiation(A_p,mis_marker,options->coarsening_threshold);/
166	}
167
168	if (Paso_noError()) {
169	#pragma omp parallel for private(i) schedule(static)
170	for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
171
172	out->n=n;
173	out->n_block=n_block;
174	out->n_F=Paso_Util_cumsum(n,counter);
175	out->mask_F=MEMALLOC(n,index_t);
176	out->rows_in_F=MEMALLOC(out->n_F,index_t);
177	out->inv_A_FF=MEMALLOC(n_blockn_blockout->n_F,double);
178	out->A_FF_pivot=NULL; /* later use for block size>3 */
179	if (! (Paso_checkPtr(out->mask_F) \|\| Paso_checkPtr(out->inv_A_FF) \|\| Paso_checkPtr(out->rows_in_F) ) ) {
180	/* creates an index for F from mask */
181	#pragma omp parallel for private(i) schedule(static)
182	for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
183	#pragma omp parallel for private(i) schedule(static)
184	for (i = 0; i < n; ++i) {
185	if (mis_marker[i]) {
186	out->rows_in_F[counter[i]]=i;
187	out->mask_F[i]=counter[i];
188	} else {
189	out->mask_F[i]=-1;
190	}
191	}
192
193	/* Compute row-sum for getting rs(A_FF)^-1*/
194	#pragma omp parallel for private(i,iPtr,j,S) schedule(static)
195	for (i = 0; i < out->n_F; ++i) {
196	S=0;
197	/printf("%d : %d -> ",i, out->rows_in_F[i]);/
198	for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
199	j=A_p->pattern->index[iPtr];
200	/if (j==out->rows_in_F[i]) printf("diagonal %e",A_p->val[iPtr]);/
201	if (mis_marker[j] && j==out->rows_in_F[i])
202	S=A_p->val[iPtr];
203	}
204	/printf("-> %e\n",S);/
205	out->inv_A_FF[i]=1./S;
206	}
207	}
208	}
209
210	if ( Paso_noError()) {
211	/* if there are no nodes in the coarse level there is no more work to do */
212	out->n_C=n-out->n_F;
213
214	/if (out->n_F>500) /
215	out->rows_in_C=MEMALLOC(out->n_C,index_t);
216	out->mask_C=MEMALLOC(n,index_t);
217	if (! (Paso_checkPtr(out->mask_C) \|\| Paso_checkPtr(out->rows_in_C) ) ) {
218	/* creates an index for C from mask */
219	#pragma omp parallel for private(i) schedule(static)
220	for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
221	Paso_Util_cumsum(n,counter);
222	#pragma omp parallel for private(i) schedule(static)
223	for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
224	#pragma omp parallel for private(i) schedule(static)
225	for (i = 0; i < n; ++i) {
226	if (! mis_marker[i]) {
227	out->rows_in_C[counter[i]]=i;
228	out->mask_C[i]=counter[i];
229	} else {
230	out->mask_C[i]=-1;
231	}
232	}
233	}
234	}
235	if ( Paso_noError()) {
236	/* get A_CF block: */
237	out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
238	/* get A_FC block: */
239	out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
240	/* get A_CC block: */
241	schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
242
243	}
244	if ( Paso_noError()) {
245	/find the pattern of the schur complement with fill in/
246	temp1=Paso_Pattern_multiply(PATTERN_FORMAT_DEFAULT,out->A_CF->pattern,out->A_FC->pattern);
247	temp2=Paso_Pattern_binop(PATTERN_FORMAT_DEFAULT, schur->pattern, temp1);
248	schur_withFillIn=Paso_SparseMatrix_alloc(A_p->type,temp2,1,1, TRUE);
249	Paso_Pattern_free(temp1);
250	Paso_Pattern_free(temp2);
251	}
252	if ( Paso_noError()) {
253	/* copy values over*/
254	#pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static)
255	for (i = 0; i < schur_withFillIn->numRows; ++i) {
256	for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
257	j=schur_withFillIn->pattern->index[iPtr];
258	iPtr_s=schur->pattern->ptr[i];
259	schur_withFillIn->val[iPtr]=0.;
260	index=&(schur->pattern->index[iPtr_s]);
261	where_p=(index_t*)bsearch(&j,
262	index,
263	schur->pattern->ptr[i + 1]-schur->pattern->ptr[i],
264	sizeof(index_t),
265	Paso_comparIndex);
266	if (where_p!=NULL) {
267	schur_withFillIn->val[iPtr]=schur->val[iPtr_s+(index_t)(where_p-index)];
268	}
269	}
270	}
271	Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
272	out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,level-1,options);
273	}
274	/* allocate work arrays for AMG application */
275	if (Paso_noError()) {
276	out->x_F=MEMALLOC(n_block*out->n_F,double);
277	out->b_F=MEMALLOC(n_block*out->n_F,double);
278	out->x_C=MEMALLOC(n_block*out->n_C,double);
279	out->b_C=MEMALLOC(n_block*out->n_C,double);
280
281	if (! (Paso_checkPtr(out->x_F) \|\| Paso_checkPtr(out->b_F) \|\| Paso_checkPtr(out->x_C) \|\| Paso_checkPtr(out->b_C) ) ) {
282	#pragma omp parallel for private(i,k) schedule(static)
283	for (i = 0; i < out->n_F; ++i) {
284	for (k=0; k<n_block;++k) {
285	out->x_F[i*n_block+k]=0.;
286	out->b_F[i*n_block+k]=0.;
287	}
288	}
289	#pragma omp parallel for private(i,k) schedule(static)
290	for (i = 0; i < out->n_C; ++i) {
291	for (k=0; k<n_block;++k) {
292	out->x_C[i*n_block+k]=0.;
293	out->b_C[i*n_block+k]=0.;
294	}
295	}
296	}
297	}
298	}
299	}
300	TMPMEMFREE(mis_marker);
301	TMPMEMFREE(counter);
302	Paso_SparseMatrix_free(schur);
303	Paso_SparseMatrix_free(schur_withFillIn);
304	if (Paso_noError()) {
305	if (verbose && level>0 && !out->coarsest_level) {
306	printf("AMG: level: %d: %d unknowns eliminated. %d left.\n",level, out->n_F,out->n_C);
307	}
308	return out;
309	} else {
310	Paso_Solver_AMG_free(out);
311	return NULL;
312	}
313	}
314
315	/**************************************************************/
316
317	/* apply AMG precondition b-> x
318
319	in fact it solves
320
321	[ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FC ] [ x_F ] = [b_F]
322	[ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
323
324	in the form
325
326	b->[b_F,b_C]
327	x_F=invA_FF*b_F
328	b_C=b_C-A_CF*x_F
329	x_C=AMG(b_C)
330	b_F=b_F-A_FC*x_C
331	x_F=invA_FF*b_F
332	x<-[x_F,x_C]
333
334	should be called within a parallel region
335	barrier synconization should be performed to make sure that the input vector available
336
337	*/
338
339	void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
340	dim_t i;
341	double time0=0;
342	double r=NULL, x0=NULL;
343	bool_t verbose=0;
344	#ifdef MKL
345	Paso_SparseMatrix *temp=NULL;
346	#else
347	#ifdef UMFPACK
348	Paso_UMFPACK_Handler * ptr=NULL;
349	#endif
350	#endif
351	r=MEMALLOC(amg->n,double);
352	x0=MEMALLOC(amg->n,double);
353
354	if (amg->coarsest_level) {
355
356	time0=Paso_timer();
357	#ifdef MKL
358	temp=Paso_SparseMatrix_alloc(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, amg->A->pattern,1,1, FALSE);
359	#pragma omp parallel for private(i) schedule(static)
360	for (i=0;i<amg->A->len;++i) {
361	temp->val[i]=amg->A->val[i];
362	}
363	Paso_MKL1(temp,x,b,0);
364	Paso_SparseMatrix_free(temp);
365	#else
366	#ifdef UMFPACK
367	ptr=(Paso_UMFPACK_Handler *)(amg->solver);
368	Paso_UMFPACK1(&ptr,amg->A,x,b,0);
369	amg->solver=(void*) ptr;
370	#else
371	Paso_Solver_solveJacobi(amg->GS,x,b);
372	#endif
373	#endif
374	time0=Paso_timer()-time0;
375	if (verbose) fprintf(stderr,"timing: DIRECT SOLVER: %e\n\n\n",time0);
376
377	} else {
378	/* presmoothing */
379	time0=Paso_timer();
380	Paso_Solver_solveJacobi(amg->GS,x,b);
381	time0=Paso_timer()-time0;
382	if (verbose) fprintf(stderr,"timing: Presmooting: %e\n",time0);
383	/* end of presmoothing */
384
385
386	time0=Paso_timer();
387	#pragma omp parallel for private(i) schedule(static)
388	for (i=0;i<amg->n;++i) r[i]=b[i];
389
390	/r=b-Ax/
391	Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
392
393	/* b->[b_F,b_C] */
394	#pragma omp parallel for private(i) schedule(static)
395	for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
396
397	#pragma omp parallel for private(i) schedule(static)
398	for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
399
400	/* x_F=invA_FFb_F /
401	Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
402
403	/* b_C=b_C-A_CFx_F /
404	Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
405
406	time0=Paso_timer()-time0;
407	if (verbose) fprintf(stderr,"timing: Before next level: %e\n",time0);
408
409	/* x_C=AMG(b_C) */
410	Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
411
412	time0=Paso_timer();
413	/* b_F=b_F-A_FCx_C /
414	Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
415	/* x_F=invA_FFb_F /
416	Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
417	/* x<-[x_F,x_C] */
418
419	#pragma omp parallel for private(i) schedule(static)
420	for (i=0;i<amg->n;++i) {
421	if (amg->mask_C[i]>-1) {
422	x[i]=amg->x_C[amg->mask_C[i]];
423	} else {
424	x[i]=amg->x_F[amg->mask_F[i]];
425	}
426	}
427
428	time0=Paso_timer()-time0;
429	if (verbose) fprintf(stderr,"timing: After next level: %e\n",time0);
430
431	/postsmoothing/
432	time0=Paso_timer();
433	#pragma omp parallel for private(i) schedule(static)
434	for (i=0;i<amg->n;++i) r[i]=b[i];
435
436	/r=b-Ax /
437	Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
438	Paso_Solver_solveJacobi(amg->GS,x0,r);
439
440	#pragma omp parallel for private(i) schedule(static)
441	for (i=0;i<amg->n;++i) x[i]+=x0[i];
442
443	time0=Paso_timer()-time0;
444	if (verbose) fprintf(stderr,"timing: Postsmoothing: %e\n",time0);
445
446	/end of postsmoothing/
447
448	}
449	MEMFREE(r);
450	MEMFREE(x0);
451	return;
452	}