paso/src/AMLI.c


/*******************************************************
*
* Copyright (c) 2003-2010 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: AMLI preconditioner                                  */

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

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

/**************************************************************/
   
#include "Paso.h"
#include "Preconditioner.h"
#include "Options.h"
#include "PasoUtil.h"
#include "UMFPACK.h"
#include "MKL.h"
#include "SystemMatrix.h"
#include "Coarsening.h"
#include "BlockOps.h"

/*************************************************************,amli->b_F*/

/* free all memory used by AMLI                                */

void Paso_Solver_AMLI_System_free(Paso_Solver_AMLI_System * in) {
     dim_t i;
     if (in!=NULL) {
        for (i=0;i<in->block_size;++i) {
          Paso_Solver_AMLI_free(in->amliblock[i]);
          Paso_SparseMatrix_free(in->block[i]);
        }
        MEMFREE(in);
     }
}


/* free all memory used by AMLI                                */

void Paso_Solver_AMLI_free(Paso_Solver_AMLI * in) {
     if (in!=NULL) {
    Paso_Preconditioner_LocalSmoother_free(in->Smoother);
    
        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);
        if(in->coarsest_level==TRUE) {
        #ifdef MKL
          Paso_MKL_free1(in->AOffset1);
          Paso_SparseMatrix_free(in->AOffset1);
        #else
          #ifdef UMFPACK
          Paso_UMFPACK1_free((Paso_UMFPACK_Handler*)(in->solver));
          #endif
        #endif
        }
        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);
        in->solver=NULL;
        Paso_Solver_AMLI_free(in->AMLI_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 AMLI is applied to S again until S becomes empty 

*/
Paso_Solver_AMLI* Paso_Solver_getAMLI(Paso_SparseMatrix *A_p,dim_t level,Paso_Options* options) {
  Paso_Solver_AMLI* 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;
  
  
 /* char filename[8];
  sprintf(filename,"AMLILevel%d",level);
  
 Paso_SparseMatrix_saveMM(A_p,filename);
  */
  
  /*Make sure we have block sizes 1*/
  if (A_p->col_block_size>1) {
     Esys_setError(TYPE_ERROR,"Paso_Solver_getAMLI: AMLI requires column block size 1.");
     return NULL;
  }
  if (A_p->row_block_size>1) {
     Esys_setError(TYPE_ERROR,"Paso_Solver_getAMLI: AMLI requires row block size 1.");
     return NULL;
  }
  out=MEMALLOC(1,Paso_Solver_AMLI);
  /* identify independend set of rows/columns */
  mis_marker=TMPMEMALLOC(n,index_t);
  counter=TMPMEMALLOC(n,index_t);
  if ( !( Esys_checkPtr(mis_marker) || Esys_checkPtr(counter) || Esys_checkPtr(out)) ) {
     out->AMLI_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->A=Paso_SparseMatrix_getReference(A_p);
     out->Smoother=NULL;
     out->solver=NULL;
     /*out->GS=Paso_Solver_getGS(A_p,verbose);*/
     out->level=level;
     out->n=n;
     out->n_F=n+1;
     out->n_block=n_block;
     out->post_sweeps=options->post_sweeps;
     out->pre_sweeps=options->pre_sweeps;
     
     if (level==0 || n<=options->min_coarse_matrix_size) {
         out->coarsest_level=TRUE;
         #ifdef MKL
                  out->AOffset1=Paso_SparseMatrix_alloc(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, out->A->pattern,1,1, FALSE);
                  #pragma omp parallel for private(i) schedule(static)
                  for (i=0;i<out->A->len;++i) {
                       out->AOffset1->val[i]=out->A->val[i];
                  }
         #else
            #ifdef UMFPACK 
            #else
            out->Smoother=Paso_Preconditioner_LocalSmoother_alloc(A_p,TRUE,verbose);
            #endif
         #endif
     } else {
         out->coarsest_level=FALSE;
     out->Smoother=Paso_Preconditioner_LocalSmoother_alloc(A_p,TRUE,verbose);
 
     Paso_Coarsening_Local(mis_marker,A_p, options->coarsening_threshold, options->coarsening_method);
             
        #pragma omp parallel for private(i) schedule(static)
        for (i = 0; i < n; ++i) {
       mis_marker[i]=(mis_marker[i]== PASO_COARSENING_IN_F);
       counter[i]=mis_marker[i];
        
        }
        
        out->n_F=Paso_Util_cumsum(n,counter);
        
        if (out->n_F==0) {
           out->coarsest_level=TRUE;
           level=0;
           if (verbose) { 
               /*printf("AMLI coarsening eliminates all unknowns, switching to Jacobi preconditioner.\n");*/
               printf("AMLI coarsening does not eliminate any of the unknowns, switching to Jacobi preconditioner.\n");
           }
        }
        else if (out->n_F==n) {
          out->coarsest_level=TRUE;
           level=0;
           if (verbose) { 
               /*printf("AMLI coarsening eliminates all unknowns, switching to Jacobi preconditioner.\n");*/
               printf("AMLI coarsening eliminates all of the unknowns, switching to Jacobi preconditioner.\n");
          
            }
        } else {
     
              if (Esys_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);
                 */
                 
                 /*if(level==3) {
                   printf("##TOTAL: %d, ELIMINATED: %d\n",n,out->n_F);
                   for (i = 0; i < n; ++i) {
                    printf("##%d %d\n",i,mis_marker[i]);
                   }
                 }*/
                 
                 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 (! (Esys_checkPtr(out->mask_F) || Esys_checkPtr(out->inv_A_FF) || Esys_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 ( Esys_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 (! (Esys_checkPtr(out->mask_C) || Esys_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 ( Esys_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 ( Esys_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 ( Esys_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->AMLI_of_Schur=Paso_Solver_getAMLI(schur_withFillIn,level-1,options);
              }
              /* allocate work arrays for AMLI application */
              if (Esys_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 (! (Esys_checkPtr(out->x_F) || Esys_checkPtr(out->b_F) || Esys_checkPtr(out->x_C) || Esys_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 (Esys_noError()) {
      if (verbose && level>0 && !out->coarsest_level) {
         printf("AMLI: level: %d: %d unknowns eliminated. %d left.\n",level, out->n_F,out->n_C);
     }
     return out;
  } else  {
     Paso_Solver_AMLI_free(out);
     return NULL;
  }
}

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

/* apply AMLI 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=AMLI(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_solveAMLI(Paso_Solver_AMLI * amli, double * x, double * b) {
     dim_t i;
     double time0=0;
     double *r=NULL, *x0=NULL,*x_F_temp=NULL;
     bool_t verbose=0;
     
     dim_t post_sweeps=amli->post_sweeps;
     dim_t pre_sweeps=amli->pre_sweeps;
     
     #ifdef UMFPACK 
          Paso_UMFPACK_Handler * ptr=NULL;
     #endif
     
     r=MEMALLOC(amli->n,double);
     x0=MEMALLOC(amli->n,double);
     x_F_temp=MEMALLOC(amli->n_F,double);
     
     if (amli->coarsest_level) {
      
      time0=Esys_timer();
      /*If all unknown are eliminated then Jacobi is the best preconditioner*/
      if (amli->n_F==0 || amli->n_F==amli->n) {
     Paso_Preconditioner_LocalSmoother_solve(amli->A, amli->Smoother,x,b,1,FALSE);
      }
       else {
       #ifdef MKL
          Paso_MKL1(amli->AOffset1,x,b,verbose);
       #else
          #ifdef UMFPACK
             ptr=(Paso_UMFPACK_Handler *)(amli->solver);
             Paso_UMFPACK1(&ptr,amli->A,x,b,verbose);
             amli->solver=(void*) ptr;
          #else      
          Paso_Preconditioner_LocalSmoother_solve(amli->A,amli->Smoother,x,b,1,FALSE);
         #endif
       #endif
       }
       time0=Esys_timer()-time0;
       if (verbose) fprintf(stderr,"timing: DIRECT SOLVER: %e\n",time0);
       
     } else {
        /* presmoothing */
         time0=Esys_timer();
     Paso_Preconditioner_LocalSmoother_solve(amli->A,amli->Smoother,x,b,pre_sweeps,FALSE);
         time0=Esys_timer()-time0;
         if (verbose) fprintf(stderr,"timing: Presmooting: %e\n",time0);
        /* end of presmoothing */
        
        
         time0=Esys_timer();
         #pragma omp parallel for private(i) schedule(static)
         for (i=0;i<amli->n;++i) r[i]=b[i];
         
         /*r=b-Ax*/ 
         Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amli->A,x,1.,r);
       
        /* r->[b_F,b_C]     */
        #pragma omp parallel for private(i) schedule(static)
        for (i=0;i<amli->n_F;++i) amli->b_F[i]=r[amli->rows_in_F[i]];
        
        #pragma omp parallel for private(i) schedule(static)
        for (i=0;i<amli->n_C;++i) amli->b_C[i]=r[amli->rows_in_C[i]];

        /* x_F=invA_FF*b_F  */
    Paso_Copy(amli->n_F, amli->x_F,amli->b_F);
        Paso_BlockOps_allMV(1,amli->n_F,amli->inv_A_FF,amli->A_FF_pivot,amli->x_F);
        
        /* b_C=b_C-A_CF*x_F */
        Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amli->A_CF,amli->x_F,1.,amli->b_C);
        
        time0=Esys_timer()-time0;
        if (verbose) fprintf(stderr,"timing: Before next level: %e\n",time0);
        
        /* x_C=AMLI(b_C)     */
        Paso_Solver_solveAMLI(amli->AMLI_of_Schur,amli->x_C,amli->b_C);
        
        time0=Esys_timer();
        
        /* b_F=-A_FC*x_C */ 
        Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amli->A_FC,amli->x_C,0.,amli->b_F);
        /* x_F_temp=invA_FF*b_F  */
    Paso_Copy(amli->n_F, x_F_temp,amli->b_F);
        Paso_BlockOps_allMV(1,amli->n_F,amli->inv_A_FF,amli->A_FF_pivot,x_F_temp);
        
        #pragma omp parallel for private(i) schedule(static)
        for (i=0;i<amli->n_F;++i) {
                 amli->x_F[i]+=x_F_temp[i];
        }
        
        /* x<-[x_F,x_C]     */
        #pragma omp parallel for private(i) schedule(static)
        for (i=0;i<amli->n;++i) {
            if (amli->mask_C[i]>-1) {
                 x[i]+=amli->x_C[amli->mask_C[i]];
            } else {
                 x[i]+=amli->x_F[amli->mask_F[i]];
            }
        }
        
        time0=Esys_timer()-time0;
        if (verbose) fprintf(stderr,"timing: After next level: %e\n",time0);

     /*postsmoothing*/
     time0=Esys_timer();
     Paso_Preconditioner_LocalSmoother_solve(amli->A,amli->Smoother,x,b,post_sweeps,TRUE);     
     time0=Esys_timer()-time0;
     if (verbose) fprintf(stderr,"timing: Postsmoothing: %e\n",time0);

     /*end of postsmoothing*/
     
     }
     MEMFREE(r);
     MEMFREE(x0);
     MEMFREE(x_F_temp);
     return;
}
1
2	/*******************************************************
3	*
4	* Copyright (c) 2003-2010 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: AMLI preconditioner */
18
19	/**************************************************************/
20
21	/* Author: artak@uq.edu.au */
22
23	/**************************************************************/
24
25	#include "Paso.h"
26	#include "Preconditioner.h"
27	#include "Options.h"
28	#include "PasoUtil.h"
29	#include "UMFPACK.h"
30	#include "MKL.h"
31	#include "SystemMatrix.h"
32	#include "Coarsening.h"
33	#include "BlockOps.h"
34
35	/************************************************************,amli->b_F/
36
37	/* free all memory used by AMLI */
38
39	void Paso_Solver_AMLI_System_free(Paso_Solver_AMLI_System * in) {
40	dim_t i;
41	if (in!=NULL) {
42	for (i=0;i<in->block_size;++i) {
43	Paso_Solver_AMLI_free(in->amliblock[i]);
44	Paso_SparseMatrix_free(in->block[i]);
45	}
46	MEMFREE(in);
47	}
48	}
49
50
51	/* free all memory used by AMLI */
52
53	void Paso_Solver_AMLI_free(Paso_Solver_AMLI * in) {
54	if (in!=NULL) {
55	Paso_Preconditioner_LocalSmoother_free(in->Smoother);
56
57	MEMFREE(in->inv_A_FF);
58	MEMFREE(in->A_FF_pivot);
59	Paso_SparseMatrix_free(in->A_FC);
60	Paso_SparseMatrix_free(in->A_CF);
61	Paso_SparseMatrix_free(in->A);
62	if(in->coarsest_level==TRUE) {
63	#ifdef MKL
64	Paso_MKL_free1(in->AOffset1);
65	Paso_SparseMatrix_free(in->AOffset1);
66	#else
67	#ifdef UMFPACK
68	Paso_UMFPACK1_free((Paso_UMFPACK_Handler*)(in->solver));
69	#endif
70	#endif
71	}
72	MEMFREE(in->rows_in_F);
73	MEMFREE(in->rows_in_C);
74	MEMFREE(in->mask_F);
75	MEMFREE(in->mask_C);
76	MEMFREE(in->x_F);
77	MEMFREE(in->b_F);
78	MEMFREE(in->x_C);
79	MEMFREE(in->b_C);
80	in->solver=NULL;
81	Paso_Solver_AMLI_free(in->AMLI_of_Schur);
82	MEMFREE(in->b_C);
83	MEMFREE(in);
84	}
85	}
86
87	/**************************************************************/
88
89	/* constructs the block-block factorization of
90
91	[ A_FF A_FC ]
92	A_p=
93	[ A_CF A_FF ]
94
95	to
96
97	[ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
98	[ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
99
100
101	where S=A_FF-ACFinvA_FFA_FC within the shape of S
102
103	then AMLI is applied to S again until S becomes empty
104
105	*/
106	Paso_Solver_AMLI* Paso_Solver_getAMLI(Paso_SparseMatrix A_p,dim_t level,Paso_Options options) {
107	Paso_Solver_AMLI* out=NULL;
108	Paso_Pattern* temp1=NULL;
109	Paso_Pattern* temp2=NULL;
110	bool_t verbose=options->verbose;
111	dim_t n=A_p->numRows;
112	dim_t n_block=A_p->row_block_size;
113	index_t* mis_marker=NULL;
114	index_t* counter=NULL;
115	index_t iPtr,index, where_p, iPtr_s;
116	dim_t i,j;
117	Paso_SparseMatrix * schur=NULL;
118	Paso_SparseMatrix * schur_withFillIn=NULL;
119	double S=0;
120
121
122	/* char filename[8];
123	sprintf(filename,"AMLILevel%d",level);
124
125	Paso_SparseMatrix_saveMM(A_p,filename);
126	*/
127
128	/Make sure we have block sizes 1/
129	if (A_p->col_block_size>1) {
130	Esys_setError(TYPE_ERROR,"Paso_Solver_getAMLI: AMLI requires column block size 1.");
131	return NULL;
132	}
133	if (A_p->row_block_size>1) {
134	Esys_setError(TYPE_ERROR,"Paso_Solver_getAMLI: AMLI requires row block size 1.");
135	return NULL;
136	}
137	out=MEMALLOC(1,Paso_Solver_AMLI);
138	/* identify independend set of rows/columns */
139	mis_marker=TMPMEMALLOC(n,index_t);
140	counter=TMPMEMALLOC(n,index_t);
141	if ( !( Esys_checkPtr(mis_marker) \|\| Esys_checkPtr(counter) \|\| Esys_checkPtr(out)) ) {
142	out->AMLI_of_Schur=NULL;
143	out->inv_A_FF=NULL;
144	out->A_FF_pivot=NULL;
145	out->A_FC=NULL;
146	out->A_CF=NULL;
147	out->rows_in_F=NULL;
148	out->rows_in_C=NULL;
149	out->mask_F=NULL;
150	out->mask_C=NULL;
151	out->x_F=NULL;
152	out->b_F=NULL;
153	out->x_C=NULL;
154	out->b_C=NULL;
155	out->A=Paso_SparseMatrix_getReference(A_p);
156	out->Smoother=NULL;
157	out->solver=NULL;
158	/out->GS=Paso_Solver_getGS(A_p,verbose);/
159	out->level=level;
160	out->n=n;
161	out->n_F=n+1;
162	out->n_block=n_block;
163	out->post_sweeps=options->post_sweeps;
164	out->pre_sweeps=options->pre_sweeps;
165
166	if (level==0 \|\| n<=options->min_coarse_matrix_size) {
167	out->coarsest_level=TRUE;
168	#ifdef MKL
169	out->AOffset1=Paso_SparseMatrix_alloc(MATRIX_FORMAT_BLK1 + MATRIX_FORMAT_OFFSET1, out->A->pattern,1,1, FALSE);
170	#pragma omp parallel for private(i) schedule(static)
171	for (i=0;i<out->A->len;++i) {
172	out->AOffset1->val[i]=out->A->val[i];
173	}
174	#else
175	#ifdef UMFPACK
176	#else
177	out->Smoother=Paso_Preconditioner_LocalSmoother_alloc(A_p,TRUE,verbose);
178	#endif
179	#endif
180	} else {
181	out->coarsest_level=FALSE;
182	out->Smoother=Paso_Preconditioner_LocalSmoother_alloc(A_p,TRUE,verbose);
183
184	Paso_Coarsening_Local(mis_marker,A_p, options->coarsening_threshold, options->coarsening_method);
185
186	#pragma omp parallel for private(i) schedule(static)
187	for (i = 0; i < n; ++i) {
188	mis_marker[i]=(mis_marker[i]== PASO_COARSENING_IN_F);
189	counter[i]=mis_marker[i];
190
191	}
192
193	out->n_F=Paso_Util_cumsum(n,counter);
194
195	if (out->n_F==0) {
196	out->coarsest_level=TRUE;
197	level=0;
198	if (verbose) {
199	/printf("AMLI coarsening eliminates all unknowns, switching to Jacobi preconditioner.\n");/
200	printf("AMLI coarsening does not eliminate any of the unknowns, switching to Jacobi preconditioner.\n");
201	}
202	}
203	else if (out->n_F==n) {
204	out->coarsest_level=TRUE;
205	level=0;
206	if (verbose) {
207	/printf("AMLI coarsening eliminates all unknowns, switching to Jacobi preconditioner.\n");/
208	printf("AMLI coarsening eliminates all of the unknowns, switching to Jacobi preconditioner.\n");
209
210	}
211	} else {
212
213	if (Esys_noError()) {
214
215	/*#pragma omp parallel for private(i) schedule(static)
216	for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
217	out->n_F=Paso_Util_cumsum(n,counter);
218	*/
219
220	/*if(level==3) {
221	printf("##TOTAL: %d, ELIMINATED: %d\n",n,out->n_F);
222	for (i = 0; i < n; ++i) {
223	printf("##%d %d\n",i,mis_marker[i]);
224	}
225	}*/
226
227	out->mask_F=MEMALLOC(n,index_t);
228	out->rows_in_F=MEMALLOC(out->n_F,index_t);
229	out->inv_A_FF=MEMALLOC(n_blockn_blockout->n_F,double);
230	out->A_FF_pivot=NULL; /* later use for block size>3 */
231	if (! (Esys_checkPtr(out->mask_F) \|\| Esys_checkPtr(out->inv_A_FF) \|\| Esys_checkPtr(out->rows_in_F) ) ) {
232	/* creates an index for F from mask */
233	#pragma omp parallel for private(i) schedule(static)
234	for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
235	#pragma omp parallel for private(i) schedule(static)
236	for (i = 0; i < n; ++i) {
237	if (mis_marker[i]) {
238	out->rows_in_F[counter[i]]=i;
239	out->mask_F[i]=counter[i];
240	} else {
241	out->mask_F[i]=-1;
242	}
243	}
244
245	/* Compute row-sum for getting rs(A_FF)^-1*/
246	#pragma omp parallel for private(i,iPtr,j,S) schedule(static)
247	for (i = 0; i < out->n_F; ++i) {
248	S=0;
249	/printf("[%d ]: [%d] -> ",i, out->rows_in_F[i]);/
250	for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
251	j=A_p->pattern->index[iPtr];
252	/if (j==out->rows_in_F[i]) printf("diagonal %e",A_p->val[iPtr]);/
253	if (mis_marker[j])
254	S+=A_p->val[iPtr];
255	}
256	/printf("-> %e \n",S);/
257	out->inv_A_FF[i]=1./S;
258	}
259	}
260	}
261
262	/*check whether coarsening process actually makes sense to continue.
263	if coarse matrix at least smaller by 30% then continue, otherwise we stop.*/
264	if ((out->n_F*100/n)<30) {
265	level=1;
266	}
267
268	if ( Esys_noError()) {
269	/* if there are no nodes in the coarse level there is no more work to do */
270	out->n_C=n-out->n_F;
271
272	/if (out->n_F>500) /
273	out->rows_in_C=MEMALLOC(out->n_C,index_t);
274	out->mask_C=MEMALLOC(n,index_t);
275	if (! (Esys_checkPtr(out->mask_C) \|\| Esys_checkPtr(out->rows_in_C) ) ) {
276	/* creates an index for C from mask */
277	#pragma omp parallel for private(i) schedule(static)
278	for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
279	Paso_Util_cumsum(n,counter);
280	#pragma omp parallel for private(i) schedule(static)
281	for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
282	#pragma omp parallel for private(i) schedule(static)
283	for (i = 0; i < n; ++i) {
284	if (! mis_marker[i]) {
285	out->rows_in_C[counter[i]]=i;
286	out->mask_C[i]=counter[i];
287	} else {
288	out->mask_C[i]=-1;
289	}
290	}
291	}
292	}
293	if ( Esys_noError()) {
294	/* get A_CF block: */
295	out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
296	/* get A_FC block: */
297	out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
298	/* get A_CC block: */
299	schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
300
301	}
302	if ( Esys_noError()) {
303	/find the pattern of the schur complement with fill in/
304	temp1=Paso_Pattern_multiply(PATTERN_FORMAT_DEFAULT,out->A_CF->pattern,out->A_FC->pattern);
305	temp2=Paso_Pattern_binop(PATTERN_FORMAT_DEFAULT, schur->pattern, temp1);
306	schur_withFillIn=Paso_SparseMatrix_alloc(A_p->type,temp2,1,1, TRUE);
307	Paso_Pattern_free(temp1);
308	Paso_Pattern_free(temp2);
309	}
310	if ( Esys_noError()) {
311	/* copy values over*/
312	#pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static)
313	for (i = 0; i < schur_withFillIn->numRows; ++i) {
314	for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
315	j=schur_withFillIn->pattern->index[iPtr];
316	iPtr_s=schur->pattern->ptr[i];
317	index=&(schur->pattern->index[iPtr_s]);
318	where_p=(index_t*)bsearch(&j,
319	index,
320	schur->pattern->ptr[i + 1]-schur->pattern->ptr[i],
321	sizeof(index_t),
322	Paso_comparIndex);
323	if (where_p!=NULL) {
324	schur_withFillIn->val[iPtr]=schur->val[iPtr_s+(index_t)(where_p-index)];
325	}
326	}
327	}
328	Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
329	out->AMLI_of_Schur=Paso_Solver_getAMLI(schur_withFillIn,level-1,options);
330	}
331	/* allocate work arrays for AMLI application */
332	if (Esys_noError()) {
333	out->x_F=MEMALLOC(n_block*out->n_F,double);
334	out->b_F=MEMALLOC(n_block*out->n_F,double);
335	out->x_C=MEMALLOC(n_block*out->n_C,double);
336	out->b_C=MEMALLOC(n_block*out->n_C,double);
337
338	if (! (Esys_checkPtr(out->x_F) \|\| Esys_checkPtr(out->b_F) \|\| Esys_checkPtr(out->x_C) \|\| Esys_checkPtr(out->b_C) ) ) {
339	#pragma omp parallel for private(i) schedule(static)
340	for (i = 0; i < out->n_F; ++i) {
341	out->x_F[i]=0.;
342	out->b_F[i]=0.;
343	}
344	#pragma omp parallel for private(i) schedule(static)
345	for (i = 0; i < out->n_C; ++i) {
346	out->x_C[i]=0.;
347	out->b_C[i]=0.;
348	}
349	}
350	}
351	Paso_SparseMatrix_free(schur);
352	Paso_SparseMatrix_free(schur_withFillIn);
353	}
354	}
355	}
356	TMPMEMFREE(mis_marker);
357	TMPMEMFREE(counter);
358
359	if (Esys_noError()) {
360	if (verbose && level>0 && !out->coarsest_level) {
361	printf("AMLI: level: %d: %d unknowns eliminated. %d left.\n",level, out->n_F,out->n_C);
362	}
363	return out;
364	} else {
365	Paso_Solver_AMLI_free(out);
366	return NULL;
367	}
368	}
369
370	/**************************************************************/
371
372	/* apply AMLI precondition b-> x
373
374	in fact it solves
375
376	[ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FC ] [ x_F ] = [b_F]
377	[ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
378
379	in the form
380
381	b->[b_F,b_C]
382	x_F=invA_FF*b_F
383	b_C=b_C-A_CF*x_F
384	x_C=AMLI(b_C)
385	b_F=b_F-A_FC*x_C
386	x_F=invA_FF*b_F
387	x<-[x_F,x_C]
388
389	should be called within a parallel region
390	barrier synconization should be performed to make sure that the input vector available
391
392	*/
393
394	void Paso_Solver_solveAMLI(Paso_Solver_AMLI * amli, double * x, double * b) {
395	dim_t i;
396	double time0=0;
397	double r=NULL, x0=NULL,*x_F_temp=NULL;
398	bool_t verbose=0;
399
400	dim_t post_sweeps=amli->post_sweeps;
401	dim_t pre_sweeps=amli->pre_sweeps;
402
403	#ifdef UMFPACK
404	Paso_UMFPACK_Handler * ptr=NULL;
405	#endif
406
407	r=MEMALLOC(amli->n,double);
408	x0=MEMALLOC(amli->n,double);
409	x_F_temp=MEMALLOC(amli->n_F,double);
410
411	if (amli->coarsest_level) {
412
413	time0=Esys_timer();
414	/If all unknown are eliminated then Jacobi is the best preconditioner/
415	if (amli->n_F==0 \|\| amli->n_F==amli->n) {
416	Paso_Preconditioner_LocalSmoother_solve(amli->A, amli->Smoother,x,b,1,FALSE);
417	}
418	else {
419	#ifdef MKL
420	Paso_MKL1(amli->AOffset1,x,b,verbose);
421	#else
422	#ifdef UMFPACK
423	ptr=(Paso_UMFPACK_Handler *)(amli->solver);
424	Paso_UMFPACK1(&ptr,amli->A,x,b,verbose);
425	amli->solver=(void*) ptr;
426	#else
427	Paso_Preconditioner_LocalSmoother_solve(amli->A,amli->Smoother,x,b,1,FALSE);
428	#endif
429	#endif
430	}
431	time0=Esys_timer()-time0;
432	if (verbose) fprintf(stderr,"timing: DIRECT SOLVER: %e\n",time0);
433
434	} else {
435	/* presmoothing */
436	time0=Esys_timer();
437	Paso_Preconditioner_LocalSmoother_solve(amli->A,amli->Smoother,x,b,pre_sweeps,FALSE);
438	time0=Esys_timer()-time0;
439	if (verbose) fprintf(stderr,"timing: Presmooting: %e\n",time0);
440	/* end of presmoothing */
441
442
443	time0=Esys_timer();
444	#pragma omp parallel for private(i) schedule(static)
445	for (i=0;i<amli->n;++i) r[i]=b[i];
446
447	/r=b-Ax/
448	Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amli->A,x,1.,r);
449
450	/* r->[b_F,b_C] */
451	#pragma omp parallel for private(i) schedule(static)
452	for (i=0;i<amli->n_F;++i) amli->b_F[i]=r[amli->rows_in_F[i]];
453
454	#pragma omp parallel for private(i) schedule(static)
455	for (i=0;i<amli->n_C;++i) amli->b_C[i]=r[amli->rows_in_C[i]];
456
457	/* x_F=invA_FFb_F /
458	Paso_Copy(amli->n_F, amli->x_F,amli->b_F);
459	Paso_BlockOps_allMV(1,amli->n_F,amli->inv_A_FF,amli->A_FF_pivot,amli->x_F);
460
461	/* b_C=b_C-A_CFx_F /
462	Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amli->A_CF,amli->x_F,1.,amli->b_C);
463
464	time0=Esys_timer()-time0;
465	if (verbose) fprintf(stderr,"timing: Before next level: %e\n",time0);
466
467	/* x_C=AMLI(b_C) */
468	Paso_Solver_solveAMLI(amli->AMLI_of_Schur,amli->x_C,amli->b_C);
469
470	time0=Esys_timer();
471
472	/* b_F=-A_FCx_C /
473	Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amli->A_FC,amli->x_C,0.,amli->b_F);
474	/* x_F_temp=invA_FFb_F /
475	Paso_Copy(amli->n_F, x_F_temp,amli->b_F);
476	Paso_BlockOps_allMV(1,amli->n_F,amli->inv_A_FF,amli->A_FF_pivot,x_F_temp);
477
478	#pragma omp parallel for private(i) schedule(static)
479	for (i=0;i<amli->n_F;++i) {
480	amli->x_F[i]+=x_F_temp[i];
481	}
482
483	/* x<-[x_F,x_C] */
484	#pragma omp parallel for private(i) schedule(static)
485	for (i=0;i<amli->n;++i) {
486	if (amli->mask_C[i]>-1) {
487	x[i]+=amli->x_C[amli->mask_C[i]];
488	} else {
489	x[i]+=amli->x_F[amli->mask_F[i]];
490	}
491	}
492
493	time0=Esys_timer()-time0;
494	if (verbose) fprintf(stderr,"timing: After next level: %e\n",time0);
495
496	/postsmoothing/
497	time0=Esys_timer();
498	Paso_Preconditioner_LocalSmoother_solve(amli->A,amli->Smoother,x,b,post_sweeps,TRUE);
499	time0=Esys_timer()-time0;
500	if (verbose) fprintf(stderr,"timing: Postsmoothing: %e\n",time0);
501
502	/end of postsmoothing/
503
504	}
505	MEMFREE(r);
506	MEMFREE(x0);
507	MEMFREE(x_F_temp);
508	return;
509	}