Actual source code: superlu.c

      2: /*  --------------------------------------------------------------------

      4:      This file implements a subclass of the SeqAIJ matrix class that uses
      5:      the SuperLU sparse solver.
      6: */

      8: /*
      9:      Defines the data structure for the base matrix type (SeqAIJ)
     10: */
     11: #include <../src/mat/impls/aij/seq/aij.h>

     13: /*
     14:      SuperLU include files
     15: */
     16: EXTERN_C_BEGIN
     17: #if defined(PETSC_USE_COMPLEX)
     18: #if defined(PETSC_USE_REAL_SINGLE)
     19: #include <slu_cdefs.h>
     20: #else
     21: #include <slu_zdefs.h>
     22: #endif
     23: #else
     24: #if defined(PETSC_USE_REAL_SINGLE)
     25: #include <slu_sdefs.h>
     26: #else
     27: #include <slu_ddefs.h>
     28: #endif
     29: #endif
     30: #include <slu_util.h>
     31: EXTERN_C_END

     33: /*
     34:      This is the data that defines the SuperLU factored matrix type
     35: */
     36: typedef struct {
     37:   SuperMatrix       A,L,U,B,X;
     38:   superlu_options_t options;
     39:   PetscInt          *perm_c; /* column permutation vector */
     40:   PetscInt          *perm_r; /* row permutations from partial pivoting */
     41:   PetscInt          *etree;
     42:   PetscReal         *R, *C;
     43:   char              equed[1];
     44:   PetscInt          lwork;
     45:   void              *work;
     46:   PetscReal         rpg, rcond;
     47:   mem_usage_t       mem_usage;
     48:   MatStructure      flg;
     49:   SuperLUStat_t     stat;
     50:   Mat               A_dup;
     51:   PetscScalar       *rhs_dup;
     52:   GlobalLU_t        Glu;
     53:   PetscBool         needconversion;

     55:   /* Flag to clean up (non-global) SuperLU objects during Destroy */
     56:   PetscBool CleanUpSuperLU;
     57: } Mat_SuperLU;

     59: /*
     60:     Utility function
     61: */
     62: static PetscErrorCode MatView_Info_SuperLU(Mat A,PetscViewer viewer)
     63: {
     64:   Mat_SuperLU       *lu= (Mat_SuperLU*)A->data;
     65:   PetscErrorCode    ierr;
     66:   superlu_options_t options;

     69:   options = lu->options;

     71:   PetscViewerASCIIPrintf(viewer,"SuperLU run parameters:\n");
     72:   PetscViewerASCIIPrintf(viewer,"  Equil: %s\n",(options.Equil != NO) ? "YES" : "NO");
     73:   PetscViewerASCIIPrintf(viewer,"  ColPerm: %D\n",options.ColPerm);
     74:   PetscViewerASCIIPrintf(viewer,"  IterRefine: %D\n",options.IterRefine);
     75:   PetscViewerASCIIPrintf(viewer,"  SymmetricMode: %s\n",(options.SymmetricMode != NO) ? "YES" : "NO");
     76:   PetscViewerASCIIPrintf(viewer,"  DiagPivotThresh: %g\n",options.DiagPivotThresh);
     77:   PetscViewerASCIIPrintf(viewer,"  PivotGrowth: %s\n",(options.PivotGrowth != NO) ? "YES" : "NO");
     78:   PetscViewerASCIIPrintf(viewer,"  ConditionNumber: %s\n",(options.ConditionNumber != NO) ? "YES" : "NO");
     79:   PetscViewerASCIIPrintf(viewer,"  RowPerm: %D\n",options.RowPerm);
     80:   PetscViewerASCIIPrintf(viewer,"  ReplaceTinyPivot: %s\n",(options.ReplaceTinyPivot != NO) ? "YES" : "NO");
     81:   PetscViewerASCIIPrintf(viewer,"  PrintStat: %s\n",(options.PrintStat != NO) ? "YES" : "NO");
     82:   PetscViewerASCIIPrintf(viewer,"  lwork: %D\n",lu->lwork);
     83:   if (A->factortype == MAT_FACTOR_ILU) {
     84:     PetscViewerASCIIPrintf(viewer,"  ILU_DropTol: %g\n",options.ILU_DropTol);
     85:     PetscViewerASCIIPrintf(viewer,"  ILU_FillTol: %g\n",options.ILU_FillTol);
     86:     PetscViewerASCIIPrintf(viewer,"  ILU_FillFactor: %g\n",options.ILU_FillFactor);
     87:     PetscViewerASCIIPrintf(viewer,"  ILU_DropRule: %D\n",options.ILU_DropRule);
     88:     PetscViewerASCIIPrintf(viewer,"  ILU_Norm: %D\n",options.ILU_Norm);
     89:     PetscViewerASCIIPrintf(viewer,"  ILU_MILU: %D\n",options.ILU_MILU);
     90:   }
     91:   return(0);
     92: }

     94: PetscErrorCode MatSolve_SuperLU_Private(Mat A,Vec b,Vec x)
     95: {
     96:   Mat_SuperLU       *lu = (Mat_SuperLU*)A->data;
     97:   const PetscScalar *barray;
     98:   PetscScalar       *xarray;
     99:   PetscErrorCode    ierr;
    100:   PetscInt          info,i,n;
    101:   PetscReal         ferr,berr;
    102:   static PetscBool  cite = PETSC_FALSE;

    105:   if (lu->lwork == -1) return(0);
    106:   PetscCitationsRegister("@article{superlu99,\n  author  = {James W. Demmel and Stanley C. Eisenstat and\n             John R. Gilbert and Xiaoye S. Li and Joseph W. H. Liu},\n  title = {A supernodal approach to sparse partial pivoting},\n  journal = {SIAM J. Matrix Analysis and Applications},\n  year = {1999},\n  volume  = {20},\n  number = {3},\n  pages = {720-755}\n}\n",&cite);

    108:   VecGetLocalSize(x,&n);
    109:   lu->B.ncol = 1;   /* Set the number of right-hand side */
    110:   if (lu->options.Equil && !lu->rhs_dup) {
    111:     /* superlu overwrites b when Equil is used, thus create rhs_dup to keep user's b unchanged */
    112:     PetscMalloc1(n,&lu->rhs_dup);
    113:   }
    114:   if (lu->options.Equil) {
    115:     /* Copy b into rsh_dup */
    116:     VecGetArrayRead(b,&barray);
    117:     PetscArraycpy(lu->rhs_dup,barray,n);
    118:     VecRestoreArrayRead(b,&barray);
    119:     barray = lu->rhs_dup;
    120:   } else {
    121:     VecGetArrayRead(b,&barray);
    122:   }
    123:   VecGetArray(x,&xarray);

    125: #if defined(PETSC_USE_COMPLEX)
    126: #if defined(PETSC_USE_REAL_SINGLE)
    127:   ((DNformat*)lu->B.Store)->nzval = (singlecomplex*)barray;
    128:   ((DNformat*)lu->X.Store)->nzval = (singlecomplex*)xarray;
    129: #else
    130:   ((DNformat*)lu->B.Store)->nzval = (doublecomplex*)barray;
    131:   ((DNformat*)lu->X.Store)->nzval = (doublecomplex*)xarray;
    132: #endif
    133: #else
    134:   ((DNformat*)lu->B.Store)->nzval = (void*)barray;
    135:   ((DNformat*)lu->X.Store)->nzval = xarray;
    136: #endif

    138:   lu->options.Fact = FACTORED; /* Indicate the factored form of A is supplied. */
    139:   if (A->factortype == MAT_FACTOR_LU) {
    140: #if defined(PETSC_USE_COMPLEX)
    141: #if defined(PETSC_USE_REAL_SINGLE)
    142:     PetscStackCall("SuperLU:cgssvx",cgssvx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
    143:                                      &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond, &ferr, &berr,
    144:                                      &lu->Glu, &lu->mem_usage, &lu->stat, &info));
    145: #else
    146:     PetscStackCall("SuperLU:zgssvx",zgssvx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
    147:                                      &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond, &ferr, &berr,
    148:                                      &lu->Glu, &lu->mem_usage, &lu->stat, &info));
    149: #endif
    150: #else
    151: #if defined(PETSC_USE_REAL_SINGLE)
    152:     PetscStackCall("SuperLU:sgssvx",sgssvx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
    153:                                      &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond, &ferr, &berr,
    154:                                      &lu->Glu, &lu->mem_usage, &lu->stat, &info));
    155: #else
    156:     PetscStackCall("SuperLU:dgssvx",dgssvx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
    157:                                      &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond, &ferr, &berr,
    158:                                      &lu->Glu,&lu->mem_usage, &lu->stat, &info));
    159: #endif
    160: #endif
    161:   } else if (A->factortype == MAT_FACTOR_ILU) {
    162: #if defined(PETSC_USE_COMPLEX)
    163: #if defined(PETSC_USE_REAL_SINGLE)
    164:     PetscStackCall("SuperLU:cgsisx",cgsisx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
    165:                                      &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond,
    166:                                      &lu->Glu, &lu->mem_usage, &lu->stat, &info));
    167: #else
    168:     PetscStackCall("SuperLU:zgsisx",zgsisx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
    169:                                      &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond,
    170:                                      &lu->Glu, &lu->mem_usage, &lu->stat, &info));
    171: #endif
    172: #else
    173: #if defined(PETSC_USE_REAL_SINGLE)
    174:     PetscStackCall("SuperLU:sgsisx",sgsisx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
    175:                                      &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond,
    176:                                      &lu->Glu, &lu->mem_usage, &lu->stat, &info));
    177: #else
    178:     PetscStackCall("SuperLU:dgsisx",dgsisx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
    179:                                      &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond,
    180:                                      &lu->Glu, &lu->mem_usage, &lu->stat, &info));
    181: #endif
    182: #endif
    183:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported");
    184:   if (!lu->options.Equil) {
    185:     VecRestoreArrayRead(b,&barray);
    186:   }
    187:   VecRestoreArray(x,&xarray);

    189:   if (!info || info == lu->A.ncol+1) {
    190:     if (lu->options.IterRefine) {
    191:       PetscPrintf(PETSC_COMM_SELF,"Iterative Refinement:\n");
    192:       PetscPrintf(PETSC_COMM_SELF,"  %8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
    193:       for (i = 0; i < 1; ++i) {
    194:         PetscPrintf(PETSC_COMM_SELF,"  %8d%8d%16e%16e\n", i+1, lu->stat.RefineSteps, ferr, berr);
    195:       }
    196:     }
    197:   } else if (info > 0) {
    198:     if (lu->lwork == -1) {
    199:       PetscPrintf(PETSC_COMM_SELF,"  ** Estimated memory: %D bytes\n", info - lu->A.ncol);
    200:     } else {
    201:       PetscPrintf(PETSC_COMM_SELF,"  Warning: gssvx() returns info %D\n",info);
    202:     }
    203:   } else if (info < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB, "info = %D, the %D-th argument in gssvx() had an illegal value", info,-info);

    205:   if (lu->options.PrintStat) {
    206:     PetscPrintf(PETSC_COMM_SELF,"MatSolve__SuperLU():\n");
    207:     PetscStackCall("SuperLU:StatPrint",StatPrint(&lu->stat));
    208:   }
    209:   return(0);
    210: }

    212: PetscErrorCode MatSolve_SuperLU(Mat A,Vec b,Vec x)
    213: {
    214:   Mat_SuperLU    *lu = (Mat_SuperLU*)A->data;

    218:   if (A->factorerrortype) {
    219:     PetscInfo(A,"MatSolve is called with singular matrix factor, skip\n");
    220:     VecSetInf(x);
    221:     return(0);
    222:   }

    224:   lu->options.Trans = TRANS;
    225:   MatSolve_SuperLU_Private(A,b,x);
    226:   return(0);
    227: }

    229: PetscErrorCode MatSolveTranspose_SuperLU(Mat A,Vec b,Vec x)
    230: {
    231:   Mat_SuperLU    *lu = (Mat_SuperLU*)A->data;

    235:   if (A->factorerrortype) {
    236:     PetscInfo(A,"MatSolve is called with singular matrix factor, skip\n");
    237:     VecSetInf(x);
    238:     return(0);
    239:   }

    241:   lu->options.Trans = NOTRANS;
    242:   MatSolve_SuperLU_Private(A,b,x);
    243:   return(0);
    244: }

    246: static PetscErrorCode MatLUFactorNumeric_SuperLU(Mat F,Mat A,const MatFactorInfo *info)
    247: {
    248:   Mat_SuperLU    *lu = (Mat_SuperLU*)F->data;
    249:   Mat_SeqAIJ     *aa;
    251:   PetscInt       sinfo;
    252:   PetscReal      ferr, berr;
    253:   NCformat       *Ustore;
    254:   SCformat       *Lstore;

    257:   if (lu->flg == SAME_NONZERO_PATTERN) { /* successing numerical factorization */
    258:     lu->options.Fact = SamePattern;
    259:     /* Ref: ~SuperLU_3.0/EXAMPLE/dlinsolx2.c */
    260:     Destroy_SuperMatrix_Store(&lu->A);
    261:     if (lu->A_dup) {
    262:       MatCopy_SeqAIJ(A,lu->A_dup,SAME_NONZERO_PATTERN);
    263:     }

    265:     if (lu->lwork >= 0) {
    266:       PetscStackCall("SuperLU:Destroy_SuperNode_Matrix",Destroy_SuperNode_Matrix(&lu->L));
    267:       PetscStackCall("SuperLU:Destroy_CompCol_Matrix",Destroy_CompCol_Matrix(&lu->U));
    268:       lu->options.Fact = SamePattern;
    269:     }
    270:   }

    272:   /* Create the SuperMatrix for lu->A=A^T:
    273:        Since SuperLU likes column-oriented matrices,we pass it the transpose,
    274:        and then solve A^T X = B in MatSolve(). */
    275:   if (lu->A_dup) {
    276:     aa = (Mat_SeqAIJ*)(lu->A_dup)->data;
    277:   } else {
    278:     aa = (Mat_SeqAIJ*)(A)->data;
    279:   }
    280: #if defined(PETSC_USE_COMPLEX)
    281: #if defined(PETSC_USE_REAL_SINGLE)
    282:   PetscStackCall("SuperLU:cCreate_CompCol_Matrix",cCreate_CompCol_Matrix(&lu->A,A->cmap->n,A->rmap->n,aa->nz,(singlecomplex*)aa->a,aa->j,aa->i,SLU_NC,SLU_C,SLU_GE));
    283: #else
    284:   PetscStackCall("SuperLU:zCreate_CompCol_Matrix",zCreate_CompCol_Matrix(&lu->A,A->cmap->n,A->rmap->n,aa->nz,(doublecomplex*)aa->a,aa->j,aa->i,SLU_NC,SLU_Z,SLU_GE));
    285: #endif
    286: #else
    287: #if defined(PETSC_USE_REAL_SINGLE)
    288:   PetscStackCall("SuperLU:sCreate_CompCol_Matrix",sCreate_CompCol_Matrix(&lu->A,A->cmap->n,A->rmap->n,aa->nz,aa->a,aa->j,aa->i,SLU_NC,SLU_S,SLU_GE));
    289: #else
    290:   PetscStackCall("SuperLU:dCreate_CompCol_Matrix",dCreate_CompCol_Matrix(&lu->A,A->cmap->n,A->rmap->n,aa->nz,aa->a,aa->j,aa->i,SLU_NC,SLU_D,SLU_GE));
    291: #endif
    292: #endif

    294:   /* Numerical factorization */
    295:   lu->B.ncol = 0;  /* Indicate not to solve the system */
    296:   if (F->factortype == MAT_FACTOR_LU) {
    297: #if defined(PETSC_USE_COMPLEX)
    298: #if defined(PETSC_USE_REAL_SINGLE)
    299:     PetscStackCall("SuperLU:cgssvx",cgssvx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
    300:                                      &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond, &ferr, &berr,
    301:                                      &lu->Glu, &lu->mem_usage, &lu->stat, &sinfo));
    302: #else
    303:     PetscStackCall("SuperLU:zgssvx",zgssvx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
    304:                                      &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond, &ferr, &berr,
    305:                                      &lu->Glu, &lu->mem_usage, &lu->stat, &sinfo));
    306: #endif
    307: #else
    308: #if defined(PETSC_USE_REAL_SINGLE)
    309:     PetscStackCall("SuperLU:sgssvx",sgssvx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
    310:                                      &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond, &ferr, &berr,
    311:                                      &lu->Glu, &lu->mem_usage, &lu->stat, &sinfo));
    312: #else
    313:     PetscStackCall("SuperLU:dgssvx",dgssvx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
    314:                                      &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond, &ferr, &berr,
    315:                                      &lu->Glu,&lu->mem_usage, &lu->stat, &sinfo));
    316: #endif
    317: #endif
    318:   } else if (F->factortype == MAT_FACTOR_ILU) {
    319:     /* Compute the incomplete factorization, condition number and pivot growth */
    320: #if defined(PETSC_USE_COMPLEX)
    321: #if defined(PETSC_USE_REAL_SINGLE)
    322:     PetscStackCall("SuperLU:cgsisx",cgsisx(&lu->options, &lu->A, lu->perm_c, lu->perm_r,lu->etree, lu->equed, lu->R, lu->C,
    323:                                      &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond,
    324:                                      &lu->Glu, &lu->mem_usage, &lu->stat, &sinfo));
    325: #else
    326:     PetscStackCall("SuperLU:zgsisx",zgsisx(&lu->options, &lu->A, lu->perm_c, lu->perm_r,lu->etree, lu->equed, lu->R, lu->C,
    327:                                      &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond,
    328:                                      &lu->Glu, &lu->mem_usage, &lu->stat, &sinfo));
    329: #endif
    330: #else
    331: #if defined(PETSC_USE_REAL_SINGLE)
    332:     PetscStackCall("SuperLU:sgsisx",sgsisx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
    333:                                      &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond,
    334:                                      &lu->Glu, &lu->mem_usage, &lu->stat, &sinfo));
    335: #else
    336:     PetscStackCall("SuperLU:dgsisx",dgsisx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
    337:                                      &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond,
    338:                                      &lu->Glu, &lu->mem_usage, &lu->stat, &sinfo));
    339: #endif
    340: #endif
    341:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported");
    342:   if (!sinfo || sinfo == lu->A.ncol+1) {
    343:     if (lu->options.PivotGrowth) {
    344:       PetscPrintf(PETSC_COMM_SELF,"  Recip. pivot growth = %e\n", lu->rpg);
    345:     }
    346:     if (lu->options.ConditionNumber) {
    347:       PetscPrintf(PETSC_COMM_SELF,"  Recip. condition number = %e\n", lu->rcond);
    348:     }
    349:   } else if (sinfo > 0) {
    350:     if (A->erroriffailure) {
    351:       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot in row %D",sinfo);
    352:     } else {
    353:       if (sinfo <= lu->A.ncol) {
    354:         if (lu->options.ILU_FillTol == 0.0) {
    355:           F->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    356:         }
    357:         PetscInfo2(F,"Number of zero pivots %D, ILU_FillTol %g\n",sinfo,lu->options.ILU_FillTol);
    358:       } else if (sinfo == lu->A.ncol + 1) {
    359:         /*
    360:          U is nonsingular, but RCOND is less than machine
    361:                       precision, meaning that the matrix is singular to
    362:                       working precision. Nevertheless, the solution and
    363:                       error bounds are computed because there are a number
    364:                       of situations where the computed solution can be more
    365:                       accurate than the value of RCOND would suggest.
    366:          */
    367:         PetscInfo1(F,"Matrix factor U is nonsingular, but is singular to working precision. The solution is computed. info %D",sinfo);
    368:       } else { /* sinfo > lu->A.ncol + 1 */
    369:         F->factorerrortype = MAT_FACTOR_OUTMEMORY;
    370:         PetscInfo1(F,"Number of bytes allocated when memory allocation fails %D\n",sinfo);
    371:       }
    372:     }
    373:   } else SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB, "info = %D, the %D-th argument in gssvx() had an illegal value", sinfo,-sinfo);

    375:   if (lu->options.PrintStat) {
    376:     PetscPrintf(PETSC_COMM_SELF,"MatLUFactorNumeric_SuperLU():\n");
    377:     PetscStackCall("SuperLU:StatPrint",StatPrint(&lu->stat));
    378:     Lstore = (SCformat*) lu->L.Store;
    379:     Ustore = (NCformat*) lu->U.Store;
    380:     PetscPrintf(PETSC_COMM_SELF,"  No of nonzeros in factor L = %D\n", Lstore->nnz);
    381:     PetscPrintf(PETSC_COMM_SELF,"  No of nonzeros in factor U = %D\n", Ustore->nnz);
    382:     PetscPrintf(PETSC_COMM_SELF,"  No of nonzeros in L+U = %D\n", Lstore->nnz + Ustore->nnz - lu->A.ncol);
    383:     PetscPrintf(PETSC_COMM_SELF,"  L\\U MB %.3f\ttotal MB needed %.3f\n",
    384:                          lu->mem_usage.for_lu/1e6, lu->mem_usage.total_needed/1e6);
    385:   }

    387:   lu->flg                = SAME_NONZERO_PATTERN;
    388:   F->ops->solve          = MatSolve_SuperLU;
    389:   F->ops->solvetranspose = MatSolveTranspose_SuperLU;
    390:   F->ops->matsolve       = NULL;
    391:   return(0);
    392: }

    394: static PetscErrorCode MatDestroy_SuperLU(Mat A)
    395: {
    397:   Mat_SuperLU    *lu=(Mat_SuperLU*)A->data;

    400:   if (lu->CleanUpSuperLU) { /* Free the SuperLU datastructures */
    401:     PetscStackCall("SuperLU:Destroy_SuperMatrix_Store",Destroy_SuperMatrix_Store(&lu->A));
    402:     PetscStackCall("SuperLU:Destroy_SuperMatrix_Store",Destroy_SuperMatrix_Store(&lu->B));
    403:     PetscStackCall("SuperLU:Destroy_SuperMatrix_Store",Destroy_SuperMatrix_Store(&lu->X));
    404:     PetscStackCall("SuperLU:StatFree",StatFree(&lu->stat));
    405:     if (lu->lwork >= 0) {
    406:       PetscStackCall("SuperLU:Destroy_SuperNode_Matrix",Destroy_SuperNode_Matrix(&lu->L));
    407:       PetscStackCall("SuperLU:Destroy_CompCol_Matrix",Destroy_CompCol_Matrix(&lu->U));
    408:     }
    409:   }
    410:   PetscFree(lu->etree);
    411:   PetscFree(lu->perm_r);
    412:   PetscFree(lu->perm_c);
    413:   PetscFree(lu->R);
    414:   PetscFree(lu->C);
    415:   PetscFree(lu->rhs_dup);
    416:   MatDestroy(&lu->A_dup);
    417:   PetscFree(A->data);

    419:   /* clear composed functions */
    420:   PetscObjectComposeFunction((PetscObject)A,"MatFactorGetSolverType_C",NULL);
    421:   PetscObjectComposeFunction((PetscObject)A,"MatSuperluSetILUDropTol_C",NULL);
    422:   return(0);
    423: }

    425: static PetscErrorCode MatView_SuperLU(Mat A,PetscViewer viewer)
    426: {
    427:   PetscErrorCode    ierr;
    428:   PetscBool         iascii;
    429:   PetscViewerFormat format;

    432:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    433:   if (iascii) {
    434:     PetscViewerGetFormat(viewer,&format);
    435:     if (format == PETSC_VIEWER_ASCII_INFO) {
    436:       MatView_Info_SuperLU(A,viewer);
    437:     }
    438:   }
    439:   return(0);
    440: }

    442: PetscErrorCode MatMatSolve_SuperLU(Mat A,Mat B,Mat X)
    443: {
    444:   Mat_SuperLU    *lu = (Mat_SuperLU*)A->data;
    445:   PetscBool      flg;

    449:   PetscObjectTypeCompareAny((PetscObject)B,&flg,MATSEQDENSE,MATMPIDENSE,NULL);
    450:   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Matrix B must be MATDENSE matrix");
    451:   PetscObjectTypeCompareAny((PetscObject)X,&flg,MATSEQDENSE,MATMPIDENSE,NULL);
    452:   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Matrix X must be MATDENSE matrix");
    453:   lu->options.Trans = TRANS;
    454:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatMatSolve_SuperLU() is not implemented yet");
    455:   return(0);
    456: }

    458: /*
    459:    Note the r permutation is ignored
    460: */
    461: static PetscErrorCode MatLUFactorSymbolic_SuperLU(Mat F,Mat A,IS r,IS c,const MatFactorInfo *info)
    462: {
    463:   Mat_SuperLU    *lu = (Mat_SuperLU*)(F->data);

    467:   lu->flg                 = DIFFERENT_NONZERO_PATTERN;
    468:   lu->CleanUpSuperLU      = PETSC_TRUE;
    469:   F->ops->lufactornumeric = MatLUFactorNumeric_SuperLU;

    471:   /* if we are here, the nonzero pattern has changed unless the user explicitly called MatLUFactorSymbolic */
    472:   MatDestroy(&lu->A_dup);
    473:   if (lu->needconversion) {
    474:     MatConvert(A,MATSEQAIJ,MAT_INITIAL_MATRIX,&lu->A_dup);
    475:   }
    476:   if (lu->options.Equil == YES && !lu->A_dup) { /* superlu overwrites input matrix and rhs when Equil is used, thus create A_dup to keep user's A unchanged */
    477:     MatDuplicate_SeqAIJ(A,MAT_COPY_VALUES,&lu->A_dup);
    478:   }
    479:   return(0);
    480: }

    482: static PetscErrorCode MatSuperluSetILUDropTol_SuperLU(Mat F,PetscReal dtol)
    483: {
    484:   Mat_SuperLU *lu= (Mat_SuperLU*)F->data;

    487:   lu->options.ILU_DropTol = dtol;
    488:   return(0);
    489: }

    491: /*@
    492:   MatSuperluSetILUDropTol - Set SuperLU ILU drop tolerance
    493:    Logically Collective on Mat

    495:    Input Parameters:
    496: +  F - the factored matrix obtained by calling MatGetFactor() from PETSc-SuperLU interface
    497: -  dtol - drop tolerance

    499:   Options Database:
    500: .   -mat_superlu_ilu_droptol <dtol>

    502:    Level: beginner

    504:    References:
    505: .      SuperLU Users' Guide

    507: .seealso: MatGetFactor()
    508: @*/
    509: PetscErrorCode MatSuperluSetILUDropTol(Mat F,PetscReal dtol)
    510: {

    516:   PetscTryMethod(F,"MatSuperluSetILUDropTol_C",(Mat,PetscReal),(F,dtol));
    517:   return(0);
    518: }

    520: PetscErrorCode MatFactorGetSolverType_seqaij_superlu(Mat A,MatSolverType *type)
    521: {
    523:   *type = MATSOLVERSUPERLU;
    524:   return(0);
    525: }

    527: /*MC
    528:   MATSOLVERSUPERLU = "superlu" - A solver package providing solvers LU and ILU for sequential matrices
    529:   via the external package SuperLU.

    531:   Use ./configure --download-superlu to have PETSc installed with SuperLU

    533:   Use -pc_type lu -pc_factor_mat_solver_type superlu to use this direct solver

    535:   Options Database Keys:
    536: + -mat_superlu_equil <FALSE>            - Equil (None)
    537: . -mat_superlu_colperm <COLAMD>         - (choose one of) NATURAL MMD_ATA MMD_AT_PLUS_A COLAMD
    538: . -mat_superlu_iterrefine <NOREFINE>    - (choose one of) NOREFINE SINGLE DOUBLE EXTRA
    539: . -mat_superlu_symmetricmode: <FALSE>   - SymmetricMode (None)
    540: . -mat_superlu_diagpivotthresh <1>      - DiagPivotThresh (None)
    541: . -mat_superlu_pivotgrowth <FALSE>      - PivotGrowth (None)
    542: . -mat_superlu_conditionnumber <FALSE>  - ConditionNumber (None)
    543: . -mat_superlu_rowperm <NOROWPERM>      - (choose one of) NOROWPERM LargeDiag
    544: . -mat_superlu_replacetinypivot <FALSE> - ReplaceTinyPivot (None)
    545: . -mat_superlu_printstat <FALSE>        - PrintStat (None)
    546: . -mat_superlu_lwork <0>                - size of work array in bytes used by factorization (None)
    547: . -mat_superlu_ilu_droptol <0>          - ILU_DropTol (None)
    548: . -mat_superlu_ilu_filltol <0>          - ILU_FillTol (None)
    549: . -mat_superlu_ilu_fillfactor <0>       - ILU_FillFactor (None)
    550: . -mat_superlu_ilu_droprull <0>         - ILU_DropRule (None)
    551: . -mat_superlu_ilu_norm <0>             - ILU_Norm (None)
    552: - -mat_superlu_ilu_milu <0>             - ILU_MILU (None)

    554:    Notes:
    555:     Do not confuse this with MATSOLVERSUPERLU_DIST which is for parallel sparse solves

    557:     Cannot currently use ordering provided by PETSc.

    559:    Level: beginner

    561: .seealso: PCLU, PCILU, MATSOLVERSUPERLU_DIST, MATSOLVERMUMPS, PCFactorSetMatSolverType(), MatSolverType
    562: M*/

    564: static PetscErrorCode MatGetFactor_seqaij_superlu(Mat A,MatFactorType ftype,Mat *F)
    565: {
    566:   Mat            B;
    567:   Mat_SuperLU    *lu;
    569:   PetscInt       indx,m=A->rmap->n,n=A->cmap->n;
    570:   PetscBool      flg,set;
    571:   PetscReal      real_input;
    572:   const char     *colperm[]   ={"NATURAL","MMD_ATA","MMD_AT_PLUS_A","COLAMD"}; /* MY_PERMC - not supported by the petsc interface yet */
    573:   const char     *iterrefine[]={"NOREFINE", "SINGLE", "DOUBLE", "EXTRA"};
    574:   const char     *rowperm[]   ={"NOROWPERM", "LargeDiag"}; /* MY_PERMC - not supported by the petsc interface yet */

    577:   MatCreate(PetscObjectComm((PetscObject)A),&B);
    578:   MatSetSizes(B,A->rmap->n,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);
    579:   PetscStrallocpy("superlu",&((PetscObject)B)->type_name);
    580:   MatSetUp(B);
    581:   if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU) {
    582:     B->ops->lufactorsymbolic  = MatLUFactorSymbolic_SuperLU;
    583:     B->ops->ilufactorsymbolic = MatLUFactorSymbolic_SuperLU;
    584:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported");

    586:   PetscFree(B->solvertype);
    587:   PetscStrallocpy(MATSOLVERSUPERLU,&B->solvertype);

    589:   B->ops->getinfo     = MatGetInfo_External;
    590:   B->ops->destroy     = MatDestroy_SuperLU;
    591:   B->ops->view        = MatView_SuperLU;
    592:   B->factortype       = ftype;
    593:   B->assembled        = PETSC_TRUE;           /* required by -ksp_view */
    594:   B->preallocated     = PETSC_TRUE;

    596:   PetscNewLog(B,&lu);

    598:   if (ftype == MAT_FACTOR_LU) {
    599:     set_default_options(&lu->options);
    600:     /* Comments from SuperLU_4.0/SRC/dgssvx.c:
    601:       "Whether or not the system will be equilibrated depends on the
    602:        scaling of the matrix A, but if equilibration is used, A is
    603:        overwritten by diag(R)*A*diag(C) and B by diag(R)*B
    604:        (if options->Trans=NOTRANS) or diag(C)*B (if options->Trans = TRANS or CONJ)."
    605:      We set 'options.Equil = NO' as default because additional space is needed for it.
    606:     */
    607:     lu->options.Equil = NO;
    608:   } else if (ftype == MAT_FACTOR_ILU) {
    609:     /* Set the default input options of ilu: */
    610:     PetscStackCall("SuperLU:ilu_set_default_options",ilu_set_default_options(&lu->options));
    611:   }
    612:   lu->options.PrintStat = NO;

    614:   /* Initialize the statistics variables. */
    615:   PetscStackCall("SuperLU:StatInit",StatInit(&lu->stat));
    616:   lu->lwork = 0;   /* allocate space internally by system malloc */

    618:   PetscOptionsBegin(PetscObjectComm((PetscObject)A),((PetscObject)A)->prefix,"SuperLU Options","Mat");
    619:   PetscOptionsBool("-mat_superlu_equil","Equil","None",(PetscBool)lu->options.Equil,(PetscBool*)&lu->options.Equil,NULL);
    620:   PetscOptionsEList("-mat_superlu_colperm","ColPerm","None",colperm,4,colperm[3],&indx,&flg);
    621:   if (flg) lu->options.ColPerm = (colperm_t)indx;
    622:   PetscOptionsEList("-mat_superlu_iterrefine","IterRefine","None",iterrefine,4,iterrefine[0],&indx,&flg);
    623:   if (flg) lu->options.IterRefine = (IterRefine_t)indx;
    624:   PetscOptionsBool("-mat_superlu_symmetricmode","SymmetricMode","None",(PetscBool)lu->options.SymmetricMode,&flg,&set);
    625:   if (set && flg) lu->options.SymmetricMode = YES;
    626:   PetscOptionsReal("-mat_superlu_diagpivotthresh","DiagPivotThresh","None",lu->options.DiagPivotThresh,&real_input,&flg);
    627:   if (flg) lu->options.DiagPivotThresh = (double) real_input;
    628:   PetscOptionsBool("-mat_superlu_pivotgrowth","PivotGrowth","None",(PetscBool)lu->options.PivotGrowth,&flg,&set);
    629:   if (set && flg) lu->options.PivotGrowth = YES;
    630:   PetscOptionsBool("-mat_superlu_conditionnumber","ConditionNumber","None",(PetscBool)lu->options.ConditionNumber,&flg,&set);
    631:   if (set && flg) lu->options.ConditionNumber = YES;
    632:   PetscOptionsEList("-mat_superlu_rowperm","rowperm","None",rowperm,2,rowperm[lu->options.RowPerm],&indx,&flg);
    633:   if (flg) lu->options.RowPerm = (rowperm_t)indx;
    634:   PetscOptionsBool("-mat_superlu_replacetinypivot","ReplaceTinyPivot","None",(PetscBool)lu->options.ReplaceTinyPivot,&flg,&set);
    635:   if (set && flg) lu->options.ReplaceTinyPivot = YES;
    636:   PetscOptionsBool("-mat_superlu_printstat","PrintStat","None",(PetscBool)lu->options.PrintStat,&flg,&set);
    637:   if (set && flg) lu->options.PrintStat = YES;
    638:   PetscOptionsInt("-mat_superlu_lwork","size of work array in bytes used by factorization","None",lu->lwork,&lu->lwork,NULL);
    639:   if (lu->lwork > 0) {
    640:     /* lwork is in bytes, hence PetscMalloc() is used here, not PetscMalloc1()*/
    641:     PetscMalloc(lu->lwork,&lu->work);
    642:   } else if (lu->lwork != 0 && lu->lwork != -1) {
    643:     PetscPrintf(PETSC_COMM_SELF,"   Warning: lwork %D is not supported by SUPERLU. The default lwork=0 is used.\n",lu->lwork);
    644:     lu->lwork = 0;
    645:   }
    646:   /* ilu options */
    647:   PetscOptionsReal("-mat_superlu_ilu_droptol","ILU_DropTol","None",lu->options.ILU_DropTol,&real_input,&flg);
    648:   if (flg) lu->options.ILU_DropTol = (double) real_input;
    649:   PetscOptionsReal("-mat_superlu_ilu_filltol","ILU_FillTol","None",lu->options.ILU_FillTol,&real_input,&flg);
    650:   if (flg) lu->options.ILU_FillTol = (double) real_input;
    651:   PetscOptionsReal("-mat_superlu_ilu_fillfactor","ILU_FillFactor","None",lu->options.ILU_FillFactor,&real_input,&flg);
    652:   if (flg) lu->options.ILU_FillFactor = (double) real_input;
    653:   PetscOptionsInt("-mat_superlu_ilu_droprull","ILU_DropRule","None",lu->options.ILU_DropRule,&lu->options.ILU_DropRule,NULL);
    654:   PetscOptionsInt("-mat_superlu_ilu_norm","ILU_Norm","None",lu->options.ILU_Norm,&indx,&flg);
    655:   if (flg) lu->options.ILU_Norm = (norm_t)indx;
    656:   PetscOptionsInt("-mat_superlu_ilu_milu","ILU_MILU","None",lu->options.ILU_MILU,&indx,&flg);
    657:   if (flg) lu->options.ILU_MILU = (milu_t)indx;
    658:   PetscOptionsEnd();

    660:   /* Allocate spaces (notice sizes are for the transpose) */
    661:   PetscMalloc1(m,&lu->etree);
    662:   PetscMalloc1(n,&lu->perm_r);
    663:   PetscMalloc1(m,&lu->perm_c);
    664:   PetscMalloc1(n,&lu->R);
    665:   PetscMalloc1(m,&lu->C);

    667:   /* create rhs and solution x without allocate space for .Store */
    668: #if defined(PETSC_USE_COMPLEX)
    669: #if defined(PETSC_USE_REAL_SINGLE)
    670:   PetscStackCall("SuperLU:cCreate_Dense_Matrix(",cCreate_Dense_Matrix(&lu->B, m, 1, NULL, m, SLU_DN, SLU_C, SLU_GE));
    671:   PetscStackCall("SuperLU:cCreate_Dense_Matrix(",cCreate_Dense_Matrix(&lu->X, m, 1, NULL, m, SLU_DN, SLU_C, SLU_GE));
    672: #else
    673:   PetscStackCall("SuperLU:zCreate_Dense_Matrix",zCreate_Dense_Matrix(&lu->B, m, 1, NULL, m, SLU_DN, SLU_Z, SLU_GE));
    674:   PetscStackCall("SuperLU:zCreate_Dense_Matrix",zCreate_Dense_Matrix(&lu->X, m, 1, NULL, m, SLU_DN, SLU_Z, SLU_GE));
    675: #endif
    676: #else
    677: #if defined(PETSC_USE_REAL_SINGLE)
    678:   PetscStackCall("SuperLU:sCreate_Dense_Matrix",sCreate_Dense_Matrix(&lu->B, m, 1, NULL, m, SLU_DN, SLU_S, SLU_GE));
    679:   PetscStackCall("SuperLU:sCreate_Dense_Matrix",sCreate_Dense_Matrix(&lu->X, m, 1, NULL, m, SLU_DN, SLU_S, SLU_GE));
    680: #else
    681:   PetscStackCall("SuperLU:dCreate_Dense_Matrix",dCreate_Dense_Matrix(&lu->B, m, 1, NULL, m, SLU_DN, SLU_D, SLU_GE));
    682:   PetscStackCall("SuperLU:dCreate_Dense_Matrix",dCreate_Dense_Matrix(&lu->X, m, 1, NULL, m, SLU_DN, SLU_D, SLU_GE));
    683: #endif
    684: #endif

    686:   PetscObjectComposeFunction((PetscObject)B,"MatFactorGetSolverType_C",MatFactorGetSolverType_seqaij_superlu);
    687:   PetscObjectComposeFunction((PetscObject)B,"MatSuperluSetILUDropTol_C",MatSuperluSetILUDropTol_SuperLU);
    688:   B->data  = lu;

    690:   *F       = B;
    691:   return(0);
    692: }

    694: static PetscErrorCode MatGetFactor_seqsell_superlu(Mat A,MatFactorType ftype,Mat *F)
    695: {
    696:   Mat_SuperLU    *lu;

    700:   MatGetFactor_seqaij_superlu(A,ftype,F);
    701:   lu   = (Mat_SuperLU*)((*F)->data);
    702:   lu->needconversion = PETSC_TRUE;
    703:   return(0);
    704: }

    706: PETSC_EXTERN PetscErrorCode MatSolverTypeRegister_SuperLU(void)
    707: {

    711:   MatSolverTypeRegister(MATSOLVERSUPERLU,MATSEQAIJ,MAT_FACTOR_LU,MatGetFactor_seqaij_superlu);
    712:   MatSolverTypeRegister(MATSOLVERSUPERLU,MATSEQAIJ,MAT_FACTOR_ILU,MatGetFactor_seqaij_superlu);
    713:   MatSolverTypeRegister(MATSOLVERSUPERLU,MATSEQSELL,MAT_FACTOR_LU,MatGetFactor_seqsell_superlu);
    714:   MatSolverTypeRegister(MATSOLVERSUPERLU,MATSEQSELL,MAT_FACTOR_ILU,MatGetFactor_seqsell_superlu);
    715:   return(0);
    716: }