Actual source code: matscalapack.c
petsc-3.15.0 2021-03-30
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      1: #include <petsc/private/petscscalapack.h>

      3: #define DEFAULT_BLOCKSIZE 64

      5: /*
      6:     The variable Petsc_ScaLAPACK_keyval is used to indicate an MPI attribute that
      7:   is attached to a communicator, in this case the attribute is a Mat_ScaLAPACK_Grid
      8: */
      9: static PetscMPIInt Petsc_ScaLAPACK_keyval = MPI_KEYVAL_INVALID;

     11: static PetscErrorCode Petsc_ScaLAPACK_keyval_free(void)
     12: {

     16:   PetscInfo(NULL,"Freeing Petsc_ScaLAPACK_keyval\n");
     17:   MPI_Comm_free_keyval(&Petsc_ScaLAPACK_keyval);
     18:   return(0);
     19: }

     21: static PetscErrorCode MatView_ScaLAPACK(Mat A,PetscViewer viewer)
     22: {
     23:   PetscErrorCode    ierr;
     24:   Mat_ScaLAPACK     *a = (Mat_ScaLAPACK*)A->data;
     25:   PetscBool         iascii;
     26:   PetscViewerFormat format;
     27:   Mat               Adense;

     30:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
     31:   if (iascii) {
     32:     PetscViewerGetFormat(viewer,&format);
     33:     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
     34:       PetscViewerASCIIPrintf(viewer,"block sizes: %d,%d\n",(int)a->mb,(int)a->nb);
     35:       PetscViewerASCIIPrintf(viewer,"grid height=%d, grid width=%d\n",(int)a->grid->nprow,(int)a->grid->npcol);
     36:       PetscViewerASCIIPrintf(viewer,"coordinates of process owning first row and column: (%d,%d)\n",(int)a->rsrc,(int)a->csrc);
     37:       PetscViewerASCIIPrintf(viewer,"dimension of largest local matrix: %d x %d\n",(int)a->locr,(int)a->locc);
     38:       return(0);
     39:     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
     40:       return(0);
     41:     }
     42:   }
     43:   /* convert to dense format and call MatView() */
     44:   MatConvert(A,MATDENSE,MAT_INITIAL_MATRIX,&Adense);
     45:   MatView(Adense,viewer);
     46:   MatDestroy(&Adense);
     47:   return(0);
     48: }

     50: static PetscErrorCode MatGetInfo_ScaLAPACK(Mat A,MatInfoType flag,MatInfo *info)
     51: {
     53:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data;
     54:   PetscLogDouble isend[2],irecv[2];

     57:   info->block_size = 1.0;

     59:   isend[0] = a->lld*a->locc;     /* locally allocated */
     60:   isend[1] = a->locr*a->locc;    /* used submatrix */
     61:   if (flag == MAT_LOCAL || flag == MAT_GLOBAL_MAX) {
     62:     info->nz_allocated   = isend[0];
     63:     info->nz_used        = isend[1];
     64:   } else if (flag == MAT_GLOBAL_MAX) {
     65:     MPIU_Allreduce(isend,irecv,2,MPIU_PETSCLOGDOUBLE,MPIU_MAX,PetscObjectComm((PetscObject)A));
     66:     info->nz_allocated   = irecv[0];
     67:     info->nz_used        = irecv[1];
     68:   } else if (flag == MAT_GLOBAL_SUM) {
     69:     MPIU_Allreduce(isend,irecv,2,MPIU_PETSCLOGDOUBLE,MPIU_SUM,PetscObjectComm((PetscObject)A));
     70:     info->nz_allocated   = irecv[0];
     71:     info->nz_used        = irecv[1];
     72:   }

     74:   info->nz_unneeded       = 0;
     75:   info->assemblies        = A->num_ass;
     76:   info->mallocs           = 0;
     77:   info->memory            = ((PetscObject)A)->mem;
     78:   info->fill_ratio_given  = 0;
     79:   info->fill_ratio_needed = 0;
     80:   info->factor_mallocs    = 0;
     81:   return(0);
     82: }

     84: PetscErrorCode MatSetOption_ScaLAPACK(Mat A,MatOption op,PetscBool flg)
     85: {
     87:   switch (op) {
     88:     case MAT_NEW_NONZERO_LOCATIONS:
     89:     case MAT_NEW_NONZERO_LOCATION_ERR:
     90:     case MAT_NEW_NONZERO_ALLOCATION_ERR:
     91:     case MAT_SYMMETRIC:
     92:     case MAT_SORTED_FULL:
     93:     case MAT_HERMITIAN:
     94:       break;
     95:     default:
     96:       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported option %s",MatOptions[op]);
     97:   }
     98:   return(0);
     99: }

    101: static PetscErrorCode MatSetValues_ScaLAPACK(Mat A,PetscInt nr,const PetscInt *rows,PetscInt nc,const PetscInt *cols,const PetscScalar *vals,InsertMode imode)
    102: {
    103:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data;
    105:   PetscInt       i,j;
    106:   PetscBLASInt   gridx,gcidx,lridx,lcidx,rsrc,csrc;

    109:   for (i=0;i<nr;i++) {
    110:     if (rows[i] < 0) continue;
    111:     PetscBLASIntCast(rows[i]+1,&gridx);
    112:     for (j=0;j<nc;j++) {
    113:       if (cols[j] < 0) continue;
    114:       PetscBLASIntCast(cols[j]+1,&gcidx);
    115:       PetscStackCallBLAS("SCALAPACKinfog2l",SCALAPACKinfog2l_(&gridx,&gcidx,a->desc,&a->grid->nprow,&a->grid->npcol,&a->grid->myrow,&a->grid->mycol,&lridx,&lcidx,&rsrc,&csrc));
    116:       if (rsrc==a->grid->myrow && csrc==a->grid->mycol) {
    117:         switch (imode) {
    118:           case INSERT_VALUES: a->loc[lridx-1+(lcidx-1)*a->lld] = vals[i*nc+j]; break;
    119:           case ADD_VALUES: a->loc[lridx-1+(lcidx-1)*a->lld] += vals[i*nc+j]; break;
    120:           default: SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"No support for InsertMode %d",(int)imode);
    121:         }
    122:       } else {
    123:         if (A->nooffprocentries) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Setting off process entry even though MatSetOption(,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) was set");
    124:         A->assembled = PETSC_FALSE;
    125:         MatStashValuesRow_Private(&A->stash,rows[i],1,cols+j,vals+i*nc+j,(PetscBool)(imode==ADD_VALUES));
    126:       }
    127:     }
    128:   }
    129:   return(0);
    130: }

    132: static PetscErrorCode MatMultXXXYYY_ScaLAPACK(Mat A,PetscBool transpose,PetscScalar beta,const PetscScalar *x,PetscScalar *y)
    133: {
    135:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data;
    136:   PetscScalar    *x2d,*y2d,alpha=1.0;
    137:   const PetscInt *ranges;
    138:   PetscBLASInt   xdesc[9],ydesc[9],x2desc[9],y2desc[9],mb,nb,lszx,lszy,zero=0,one=1,xlld,ylld,info;

    141:   if (transpose) {

    143:     /* create ScaLAPACK descriptors for vectors (1d block distribution) */
    144:     PetscLayoutGetRanges(A->rmap,&ranges);
    145:     PetscBLASIntCast(ranges[1],&mb);  /* x block size */
    146:     xlld = PetscMax(1,A->rmap->n);
    147:     PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(xdesc,&a->M,&one,&mb,&one,&zero,&zero,&a->grid->ictxcol,&xlld,&info));
    149:     PetscLayoutGetRanges(A->cmap,&ranges);
    150:     PetscBLASIntCast(ranges[1],&nb);  /* y block size */
    151:     ylld = 1;
    152:     PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(ydesc,&one,&a->N,&one,&nb,&zero,&zero,&a->grid->ictxrow,&ylld,&info));

    155:     /* allocate 2d vectors */
    156:     lszx = SCALAPACKnumroc_(&a->M,&a->mb,&a->grid->myrow,&a->rsrc,&a->grid->nprow);
    157:     lszy = SCALAPACKnumroc_(&a->N,&a->nb,&a->grid->mycol,&a->csrc,&a->grid->npcol);
    158:     PetscMalloc2(lszx,&x2d,lszy,&y2d);
    159:     xlld = PetscMax(1,lszx);

    161:     /* create ScaLAPACK descriptors for vectors (2d block distribution) */
    162:     PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(x2desc,&a->M,&one,&a->mb,&one,&zero,&zero,&a->grid->ictxt,&xlld,&info));
    164:     PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(y2desc,&one,&a->N,&one,&a->nb,&zero,&zero,&a->grid->ictxt,&ylld,&info));

    167:     /* redistribute x as a column of a 2d matrix */
    168:     PetscStackCallBLAS("SCALAPACKgemr2d",SCALAPACKgemr2d_(&a->M,&one,(PetscScalar*)x,&one,&one,xdesc,x2d,&one,&one,x2desc,&a->grid->ictxcol));

    170:     /* redistribute y as a row of a 2d matrix */
    171:     if (beta!=0.0) PetscStackCallBLAS("SCALAPACKgemr2d",SCALAPACKgemr2d_(&one,&a->N,y,&one,&one,ydesc,y2d,&one,&one,y2desc,&a->grid->ictxrow));

    173:     /* call PBLAS subroutine */
    174:     PetscStackCallBLAS("PBLASgemv",PBLASgemv_("T",&a->M,&a->N,&alpha,a->loc,&one,&one,a->desc,x2d,&one,&one,x2desc,&one,&beta,y2d,&one,&one,y2desc,&one));

    176:     /* redistribute y from a row of a 2d matrix */
    177:     PetscStackCallBLAS("SCALAPACKgemr2d",SCALAPACKgemr2d_(&one,&a->N,y2d,&one,&one,y2desc,y,&one,&one,ydesc,&a->grid->ictxrow));

    179:   } else {   /* non-transpose */

    181:     /* create ScaLAPACK descriptors for vectors (1d block distribution) */
    182:     PetscLayoutGetRanges(A->cmap,&ranges);
    183:     PetscBLASIntCast(ranges[1],&nb);  /* x block size */
    184:     xlld = 1;
    185:     PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(xdesc,&one,&a->N,&one,&nb,&zero,&zero,&a->grid->ictxrow,&xlld,&info));
    187:     PetscLayoutGetRanges(A->rmap,&ranges);
    188:     PetscBLASIntCast(ranges[1],&mb);  /* y block size */
    189:     ylld = PetscMax(1,A->rmap->n);
    190:     PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(ydesc,&a->M,&one,&mb,&one,&zero,&zero,&a->grid->ictxcol,&ylld,&info));

    193:     /* allocate 2d vectors */
    194:     lszy = SCALAPACKnumroc_(&a->M,&a->mb,&a->grid->myrow,&a->rsrc,&a->grid->nprow);
    195:     lszx = SCALAPACKnumroc_(&a->N,&a->nb,&a->grid->mycol,&a->csrc,&a->grid->npcol);
    196:     PetscMalloc2(lszx,&x2d,lszy,&y2d);
    197:     ylld = PetscMax(1,lszy);

    199:     /* create ScaLAPACK descriptors for vectors (2d block distribution) */
    200:     PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(x2desc,&one,&a->N,&one,&a->nb,&zero,&zero,&a->grid->ictxt,&xlld,&info));
    202:     PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(y2desc,&a->M,&one,&a->mb,&one,&zero,&zero,&a->grid->ictxt,&ylld,&info));

    205:     /* redistribute x as a row of a 2d matrix */
    206:     PetscStackCallBLAS("SCALAPACKgemr2d",SCALAPACKgemr2d_(&one,&a->N,(PetscScalar*)x,&one,&one,xdesc,x2d,&one,&one,x2desc,&a->grid->ictxrow));

    208:     /* redistribute y as a column of a 2d matrix */
    209:     if (beta!=0.0) PetscStackCallBLAS("SCALAPACKgemr2d",SCALAPACKgemr2d_(&a->M,&one,y,&one,&one,ydesc,y2d,&one,&one,y2desc,&a->grid->ictxcol));

    211:     /* call PBLAS subroutine */
    212:     PetscStackCallBLAS("PBLASgemv",PBLASgemv_("N",&a->M,&a->N,&alpha,a->loc,&one,&one,a->desc,x2d,&one,&one,x2desc,&one,&beta,y2d,&one,&one,y2desc,&one));

    214:     /* redistribute y from a column of a 2d matrix */
    215:     PetscStackCallBLAS("SCALAPACKgemr2d",SCALAPACKgemr2d_(&a->M,&one,y2d,&one,&one,y2desc,y,&one,&one,ydesc,&a->grid->ictxcol));

    217:   }
    218:   PetscFree2(x2d,y2d);
    219:   return(0);
    220: }

    222: static PetscErrorCode MatMult_ScaLAPACK(Mat A,Vec x,Vec y)
    223: {
    224:   PetscErrorCode    ierr;
    225:   const PetscScalar *xarray;
    226:   PetscScalar       *yarray;

    229:   VecGetArrayRead(x,&xarray);
    230:   VecGetArray(y,&yarray);
    231:   MatMultXXXYYY_ScaLAPACK(A,PETSC_FALSE,0.0,xarray,yarray);
    232:   VecRestoreArrayRead(x,&xarray);
    233:   VecRestoreArray(y,&yarray);
    234:   return(0);
    235: }

    237: static PetscErrorCode MatMultTranspose_ScaLAPACK(Mat A,Vec x,Vec y)
    238: {
    239:   PetscErrorCode    ierr;
    240:   const PetscScalar *xarray;
    241:   PetscScalar       *yarray;

    244:   VecGetArrayRead(x,&xarray);
    245:   VecGetArray(y,&yarray);
    246:   MatMultXXXYYY_ScaLAPACK(A,PETSC_TRUE,0.0,xarray,yarray);
    247:   VecRestoreArrayRead(x,&xarray);
    248:   VecRestoreArray(y,&yarray);
    249:   return(0);
    250: }

    252: static PetscErrorCode MatMultAdd_ScaLAPACK(Mat A,Vec x,Vec y,Vec z)
    253: {
    254:   PetscErrorCode    ierr;
    255:   const PetscScalar *xarray;
    256:   PetscScalar       *zarray;

    259:   if (y != z) { VecCopy(y,z); }
    260:   VecGetArrayRead(x,&xarray);
    261:   VecGetArray(z,&zarray);
    262:   MatMultXXXYYY_ScaLAPACK(A,PETSC_FALSE,1.0,xarray,zarray);
    263:   VecRestoreArrayRead(x,&xarray);
    264:   VecRestoreArray(z,&zarray);
    265:   return(0);
    266: }

    268: static PetscErrorCode MatMultTransposeAdd_ScaLAPACK(Mat A,Vec x,Vec y,Vec z)
    269: {
    270:   PetscErrorCode    ierr;
    271:   const PetscScalar *xarray;
    272:   PetscScalar       *zarray;

    275:   if (y != z) { VecCopy(y,z); }
    276:   VecGetArrayRead(x,&xarray);
    277:   VecGetArray(z,&zarray);
    278:   MatMultXXXYYY_ScaLAPACK(A,PETSC_TRUE,1.0,xarray,zarray);
    279:   VecRestoreArrayRead(x,&xarray);
    280:   VecRestoreArray(z,&zarray);
    281:   return(0);
    282: }

    284: PetscErrorCode MatMatMultNumeric_ScaLAPACK(Mat A,Mat B,Mat C)
    285: {
    286:   Mat_ScaLAPACK *a = (Mat_ScaLAPACK*)A->data;
    287:   Mat_ScaLAPACK *b = (Mat_ScaLAPACK*)B->data;
    288:   Mat_ScaLAPACK *c = (Mat_ScaLAPACK*)C->data;
    289:   PetscScalar   sone=1.0,zero=0.0;
    290:   PetscBLASInt  one=1;

    293:   PetscStackCallBLAS("PBLASgemm",PBLASgemm_("N","N",&a->M,&b->N,&a->N,&sone,a->loc,&one,&one,a->desc,b->loc,&one,&one,b->desc,&zero,c->loc,&one,&one,c->desc));
    294:   C->assembled = PETSC_TRUE;
    295:   return(0);
    296: }

    298: PetscErrorCode MatMatMultSymbolic_ScaLAPACK(Mat A,Mat B,PetscReal fill,Mat C)
    299: {

    303:   MatSetSizes(C,A->rmap->n,B->cmap->n,PETSC_DECIDE,PETSC_DECIDE);
    304:   MatSetType(C,MATSCALAPACK);
    305:   MatSetUp(C);
    306:   C->ops->matmultnumeric = MatMatMultNumeric_ScaLAPACK;
    307:   return(0);
    308: }

    310: static PetscErrorCode MatMatTransposeMultNumeric_ScaLAPACK(Mat A,Mat B,Mat C)
    311: {
    312:   Mat_ScaLAPACK *a = (Mat_ScaLAPACK*)A->data;
    313:   Mat_ScaLAPACK *b = (Mat_ScaLAPACK*)B->data;
    314:   Mat_ScaLAPACK *c = (Mat_ScaLAPACK*)C->data;
    315:   PetscScalar   sone=1.0,zero=0.0;
    316:   PetscBLASInt  one=1;

    319:   PetscStackCallBLAS("PBLASgemm",PBLASgemm_("N","T",&a->M,&b->M,&a->N,&sone,a->loc,&one,&one,a->desc,b->loc,&one,&one,b->desc,&zero,c->loc,&one,&one,c->desc));
    320:   C->assembled = PETSC_TRUE;
    321:   return(0);
    322: }

    324: static PetscErrorCode MatMatTransposeMultSymbolic_ScaLAPACK(Mat A,Mat B,PetscReal fill,Mat C)
    325: {

    329:   MatSetSizes(C,A->rmap->n,B->rmap->n,PETSC_DECIDE,PETSC_DECIDE);
    330:   MatSetType(C,MATSCALAPACK);
    331:   MatSetUp(C);
    332:   return(0);
    333: }

    335: /* --------------------------------------- */
    336: static PetscErrorCode MatProductSetFromOptions_ScaLAPACK_AB(Mat C)
    337: {
    339:   C->ops->matmultsymbolic = MatMatMultSymbolic_ScaLAPACK;
    340:   C->ops->productsymbolic = MatProductSymbolic_AB;
    341:   return(0);
    342: }

    344: static PetscErrorCode MatProductSetFromOptions_ScaLAPACK_ABt(Mat C)
    345: {
    347:   C->ops->mattransposemultsymbolic = MatMatTransposeMultSymbolic_ScaLAPACK;
    348:   C->ops->productsymbolic          = MatProductSymbolic_ABt;
    349:   return(0);
    350: }

    352: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_ScaLAPACK(Mat C)
    353: {
    355:   Mat_Product    *product = C->product;

    358:   switch (product->type) {
    359:     case MATPRODUCT_AB:
    360:       MatProductSetFromOptions_ScaLAPACK_AB(C);
    361:       break;
    362:     case MATPRODUCT_ABt:
    363:       MatProductSetFromOptions_ScaLAPACK_ABt(C);
    364:       break;
    365:     default: SETERRQ1(PetscObjectComm((PetscObject)C),PETSC_ERR_SUP,"MatProduct type %s is not supported for ScaLAPACK and ScaLAPACK matrices",MatProductTypes[product->type]);
    366:   }
    367:   return(0);
    368: }
    369: /* --------------------------------------- */

    371: static PetscErrorCode MatGetDiagonal_ScaLAPACK(Mat A,Vec D)
    372: {
    373:   PetscErrorCode    ierr;
    374:   Mat_ScaLAPACK     *a = (Mat_ScaLAPACK*)A->data;
    375:   PetscScalar       *darray,*d2d,v;
    376:   const PetscInt    *ranges;
    377:   PetscBLASInt      j,ddesc[9],d2desc[9],mb,nb,lszd,zero=0,one=1,dlld,info;

    380:   VecGetArray(D,&darray);

    382:   if (A->rmap->N<=A->cmap->N) {   /* row version */

    384:     /* create ScaLAPACK descriptor for vector (1d block distribution) */
    385:     PetscLayoutGetRanges(A->rmap,&ranges);
    386:     PetscBLASIntCast(ranges[1],&mb);  /* D block size */
    387:     dlld = PetscMax(1,A->rmap->n);
    388:     PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(ddesc,&a->M,&one,&mb,&one,&zero,&zero,&a->grid->ictxcol,&dlld,&info));

    391:     /* allocate 2d vector */
    392:     lszd = SCALAPACKnumroc_(&a->M,&a->mb,&a->grid->myrow,&a->rsrc,&a->grid->nprow);
    393:     PetscCalloc1(lszd,&d2d);
    394:     dlld = PetscMax(1,lszd);

    396:     /* create ScaLAPACK descriptor for vector (2d block distribution) */
    397:     PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(d2desc,&a->M,&one,&a->mb,&one,&zero,&zero,&a->grid->ictxt,&dlld,&info));

    400:     /* collect diagonal */
    401:     for (j=1;j<=a->M;j++) {
    402:       PetscStackCallBLAS("SCALAPACKelget",SCALAPACKelget_("R"," ",&v,a->loc,&j,&j,a->desc));
    403:       PetscStackCallBLAS("SCALAPACKelset",SCALAPACKelset_(d2d,&j,&one,d2desc,&v));
    404:     }

    406:     /* redistribute d from a column of a 2d matrix */
    407:     PetscStackCallBLAS("SCALAPACKgemr2d",SCALAPACKgemr2d_(&a->M,&one,d2d,&one,&one,d2desc,darray,&one,&one,ddesc,&a->grid->ictxcol));
    408:     PetscFree(d2d);

    410:   } else {   /* column version */

    412:     /* create ScaLAPACK descriptor for vector (1d block distribution) */
    413:     PetscLayoutGetRanges(A->cmap,&ranges);
    414:     PetscBLASIntCast(ranges[1],&nb);  /* D block size */
    415:     dlld = 1;
    416:     PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(ddesc,&one,&a->N,&one,&nb,&zero,&zero,&a->grid->ictxrow,&dlld,&info));

    419:     /* allocate 2d vector */
    420:     lszd = SCALAPACKnumroc_(&a->N,&a->nb,&a->grid->mycol,&a->csrc,&a->grid->npcol);
    421:     PetscCalloc1(lszd,&d2d);

    423:     /* create ScaLAPACK descriptor for vector (2d block distribution) */
    424:     PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(d2desc,&one,&a->N,&one,&a->nb,&zero,&zero,&a->grid->ictxt,&dlld,&info));

    427:     /* collect diagonal */
    428:     for (j=1;j<=a->N;j++) {
    429:       PetscStackCallBLAS("SCALAPACKelget",SCALAPACKelget_("C"," ",&v,a->loc,&j,&j,a->desc));
    430:       PetscStackCallBLAS("SCALAPACKelset",SCALAPACKelset_(d2d,&one,&j,d2desc,&v));
    431:     }

    433:     /* redistribute d from a row of a 2d matrix */
    434:     PetscStackCallBLAS("SCALAPACKgemr2d",SCALAPACKgemr2d_(&one,&a->N,d2d,&one,&one,d2desc,darray,&one,&one,ddesc,&a->grid->ictxrow));
    435:     PetscFree(d2d);
    436:   }

    438:   VecRestoreArray(D,&darray);
    439:   VecAssemblyBegin(D);
    440:   VecAssemblyEnd(D);
    441:   return(0);
    442: }

    444: static PetscErrorCode MatDiagonalScale_ScaLAPACK(Mat A,Vec L,Vec R)
    445: {
    446:   PetscErrorCode    ierr;
    447:   Mat_ScaLAPACK     *a = (Mat_ScaLAPACK*)A->data;
    448:   const PetscScalar *d;
    449:   const PetscInt    *ranges;
    450:   PetscScalar       *d2d;
    451:   PetscBLASInt      i,j,ddesc[9],d2desc[9],mb,nb,lszd,zero=0,one=1,dlld,info;

    454:   if (R) {
    455:     VecGetArrayRead(R,(const PetscScalar **)&d);
    456:     /* create ScaLAPACK descriptor for vector (1d block distribution) */
    457:     PetscLayoutGetRanges(A->cmap,&ranges);
    458:     PetscBLASIntCast(ranges[1],&nb);  /* D block size */
    459:     dlld = 1;
    460:     PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(ddesc,&one,&a->N,&one,&nb,&zero,&zero,&a->grid->ictxrow,&dlld,&info));

    463:     /* allocate 2d vector */
    464:     lszd = SCALAPACKnumroc_(&a->N,&a->nb,&a->grid->mycol,&a->csrc,&a->grid->npcol);
    465:     PetscCalloc1(lszd,&d2d);

    467:     /* create ScaLAPACK descriptor for vector (2d block distribution) */
    468:     PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(d2desc,&one,&a->N,&one,&a->nb,&zero,&zero,&a->grid->ictxt,&dlld,&info));

    471:     /* redistribute d to a row of a 2d matrix */
    472:     PetscStackCallBLAS("SCALAPACKgemr2d",SCALAPACKgemr2d_(&one,&a->N,(PetscScalar*)d,&one,&one,ddesc,d2d,&one,&one,d2desc,&a->grid->ictxrow));

    474:     /* broadcast along process columns */
    475:     if (!a->grid->myrow) Cdgebs2d(a->grid->ictxt,"C"," ",1,lszd,d2d,dlld);
    476:     else Cdgebr2d(a->grid->ictxt,"C"," ",1,lszd,d2d,dlld,0,a->grid->mycol);

    478:     /* local scaling */
    479:     for (j=0;j<a->locc;j++) for (i=0;i<a->locr;i++) a->loc[i+j*a->lld] *= d2d[j];

    481:     PetscFree(d2d);
    482:     VecRestoreArrayRead(R,(const PetscScalar **)&d);
    483:   }
    484:   if (L) {
    485:     VecGetArrayRead(L,(const PetscScalar **)&d);
    486:     /* create ScaLAPACK descriptor for vector (1d block distribution) */
    487:     PetscLayoutGetRanges(A->rmap,&ranges);
    488:     PetscBLASIntCast(ranges[1],&mb);  /* D block size */
    489:     dlld = PetscMax(1,A->rmap->n);
    490:     PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(ddesc,&a->M,&one,&mb,&one,&zero,&zero,&a->grid->ictxcol,&dlld,&info));

    493:     /* allocate 2d vector */
    494:     lszd = SCALAPACKnumroc_(&a->M,&a->mb,&a->grid->myrow,&a->rsrc,&a->grid->nprow);
    495:     PetscCalloc1(lszd,&d2d);
    496:     dlld = PetscMax(1,lszd);

    498:     /* create ScaLAPACK descriptor for vector (2d block distribution) */
    499:     PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(d2desc,&a->M,&one,&a->mb,&one,&zero,&zero,&a->grid->ictxt,&dlld,&info));

    502:     /* redistribute d to a column of a 2d matrix */
    503:     PetscStackCallBLAS("SCALAPACKgemr2d",SCALAPACKgemr2d_(&a->M,&one,(PetscScalar*)d,&one,&one,ddesc,d2d,&one,&one,d2desc,&a->grid->ictxcol));

    505:     /* broadcast along process rows */
    506:     if (!a->grid->mycol) Cdgebs2d(a->grid->ictxt,"R"," ",lszd,1,d2d,dlld);
    507:     else Cdgebr2d(a->grid->ictxt,"R"," ",lszd,1,d2d,dlld,a->grid->myrow,0);

    509:     /* local scaling */
    510:     for (i=0;i<a->locr;i++) for (j=0;j<a->locc;j++) a->loc[i+j*a->lld] *= d2d[i];

    512:     PetscFree(d2d);
    513:     VecRestoreArrayRead(L,(const PetscScalar **)&d);
    514:   }
    515:   return(0);
    516: }

    518: static PetscErrorCode MatMissingDiagonal_ScaLAPACK(Mat A,PetscBool *missing,PetscInt *d)
    519: {
    521:   *missing = PETSC_FALSE;
    522:   return(0);
    523: }

    525: static PetscErrorCode MatScale_ScaLAPACK(Mat X,PetscScalar a)
    526: {
    527:   Mat_ScaLAPACK *x = (Mat_ScaLAPACK*)X->data;
    528:   PetscBLASInt  n,one=1;

    531:   n = x->lld*x->locc;
    532:   PetscStackCallBLAS("BLASscal",BLASscal_(&n,&a,x->loc,&one));
    533:   return(0);
    534: }

    536: static PetscErrorCode MatShift_ScaLAPACK(Mat X,PetscScalar alpha)
    537: {
    538:   Mat_ScaLAPACK *x = (Mat_ScaLAPACK*)X->data;
    539:   PetscBLASInt  i,n;
    540:   PetscScalar   v;

    543:   n = PetscMin(x->M,x->N);
    544:   for (i=1;i<=n;i++) {
    545:     PetscStackCallBLAS("SCALAPACKelget",SCALAPACKelget_("-"," ",&v,x->loc,&i,&i,x->desc));
    546:     v += alpha;
    547:     PetscStackCallBLAS("SCALAPACKelset",SCALAPACKelset_(x->loc,&i,&i,x->desc,&v));
    548:   }
    549:   return(0);
    550: }

    552: static PetscErrorCode MatAXPY_ScaLAPACK(Mat Y,PetscScalar alpha,Mat X,MatStructure str)
    553: {
    555:   Mat_ScaLAPACK  *x = (Mat_ScaLAPACK*)X->data;
    556:   Mat_ScaLAPACK  *y = (Mat_ScaLAPACK*)Y->data;
    557:   PetscBLASInt   one=1;
    558:   PetscScalar    beta=1.0;

    561:   MatScaLAPACKCheckDistribution(Y,1,X,3);
    562:   PetscStackCallBLAS("SCALAPACKmatadd",SCALAPACKmatadd_(&x->M,&x->N,&alpha,x->loc,&one,&one,x->desc,&beta,y->loc,&one,&one,y->desc));
    563:   PetscObjectStateIncrease((PetscObject)Y);
    564:   return(0);
    565: }

    567: static PetscErrorCode MatCopy_ScaLAPACK(Mat A,Mat B,MatStructure str)
    568: {
    570:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data;
    571:   Mat_ScaLAPACK  *b = (Mat_ScaLAPACK*)B->data;

    574:   PetscArraycpy(b->loc,a->loc,a->lld*a->locc);
    575:   PetscObjectStateIncrease((PetscObject)B);
    576:   return(0);
    577: }

    579: static PetscErrorCode MatDuplicate_ScaLAPACK(Mat A,MatDuplicateOption op,Mat *B)
    580: {
    581:   Mat            Bs;
    582:   MPI_Comm       comm;
    583:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data,*b;

    587:   PetscObjectGetComm((PetscObject)A,&comm);
    588:   MatCreate(comm,&Bs);
    589:   MatSetSizes(Bs,A->rmap->n,A->cmap->n,PETSC_DECIDE,PETSC_DECIDE);
    590:   MatSetType(Bs,MATSCALAPACK);
    591:   b = (Mat_ScaLAPACK*)Bs->data;
    592:   b->M    = a->M;
    593:   b->N    = a->N;
    594:   b->mb   = a->mb;
    595:   b->nb   = a->nb;
    596:   b->rsrc = a->rsrc;
    597:   b->csrc = a->csrc;
    598:   MatSetUp(Bs);
    599:   *B = Bs;
    600:   if (op == MAT_COPY_VALUES) {
    601:     PetscArraycpy(b->loc,a->loc,a->lld*a->locc);
    602:   }
    603:   Bs->assembled = PETSC_TRUE;
    604:   return(0);
    605: }

    607: static PetscErrorCode MatTranspose_ScaLAPACK(Mat A,MatReuse reuse,Mat *B)
    608: {
    610:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data, *b;
    611:   Mat            Bs = *B;
    612:   PetscBLASInt   one=1;
    613:   PetscScalar    sone=1.0,zero=0.0;
    614: #if defined(PETSC_USE_COMPLEX)
    615:   PetscInt       i,j;
    616: #endif

    619:   if (reuse == MAT_INITIAL_MATRIX) {
    620:     MatCreateScaLAPACK(PetscObjectComm((PetscObject)A),a->nb,a->mb,a->N,a->M,a->csrc,a->rsrc,&Bs);
    621:     *B = Bs;
    622:   } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Only MAT_INITIAL_MATRIX supported");
    623:   b = (Mat_ScaLAPACK*)Bs->data;
    624:   PetscStackCallBLAS("PBLAStran",PBLAStran_(&a->N,&a->M,&sone,a->loc,&one,&one,a->desc,&zero,b->loc,&one,&one,b->desc));
    625: #if defined(PETSC_USE_COMPLEX)
    626:   /* undo conjugation */
    627:   for (i=0;i<b->locr;i++) for (j=0;j<b->locc;j++) b->loc[i+j*b->lld] = PetscConj(b->loc[i+j*b->lld]);
    628: #endif
    629:   Bs->assembled = PETSC_TRUE;
    630:   return(0);
    631: }

    633: static PetscErrorCode MatConjugate_ScaLAPACK(Mat A)
    634: {
    635:   Mat_ScaLAPACK *a = (Mat_ScaLAPACK*)A->data;
    636:   PetscInt      i,j;

    639:   for (i=0;i<a->locr;i++) for (j=0;j<a->locc;j++) a->loc[i+j*a->lld] = PetscConj(a->loc[i+j*a->lld]);
    640:   return(0);
    641: }

    643: static PetscErrorCode MatHermitianTranspose_ScaLAPACK(Mat A,MatReuse reuse,Mat *B)
    644: {
    646:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data, *b;
    647:   Mat            Bs = *B;
    648:   PetscBLASInt   one=1;
    649:   PetscScalar    sone=1.0,zero=0.0;

    652:   if (reuse == MAT_INITIAL_MATRIX) {
    653:     MatCreateScaLAPACK(PetscObjectComm((PetscObject)A),a->nb,a->mb,a->N,a->M,a->csrc,a->rsrc,&Bs);
    654:     *B = Bs;
    655:   } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Only MAT_INITIAL_MATRIX supported");
    656:   b = (Mat_ScaLAPACK*)Bs->data;
    657:   PetscStackCallBLAS("PBLAStran",PBLAStran_(&a->N,&a->M,&sone,a->loc,&one,&one,a->desc,&zero,b->loc,&one,&one,b->desc));
    658:   Bs->assembled = PETSC_TRUE;
    659:   return(0);
    660: }

    662: static PetscErrorCode MatSolve_ScaLAPACK(Mat A,Vec B,Vec X)
    663: {
    665:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data;
    666:   PetscScalar    *x,*x2d;
    667:   const PetscInt *ranges;
    668:   PetscBLASInt   xdesc[9],x2desc[9],mb,lszx,zero=0,one=1,xlld,nrhs=1,info;

    671:   VecCopy(B,X);
    672:   VecGetArray(X,&x);

    674:   /* create ScaLAPACK descriptor for a vector (1d block distribution) */
    675:   PetscLayoutGetRanges(A->rmap,&ranges);
    676:   PetscBLASIntCast(ranges[1],&mb);  /* x block size */
    677:   xlld = PetscMax(1,A->rmap->n);
    678:   PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(xdesc,&a->M,&one,&mb,&one,&zero,&zero,&a->grid->ictxcol,&xlld,&info));

    681:   /* allocate 2d vector */
    682:   lszx = SCALAPACKnumroc_(&a->M,&a->mb,&a->grid->myrow,&a->rsrc,&a->grid->nprow);
    683:   PetscMalloc1(lszx,&x2d);
    684:   xlld = PetscMax(1,lszx);

    686:   /* create ScaLAPACK descriptor for a vector (2d block distribution) */
    687:   PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(x2desc,&a->M,&one,&a->mb,&one,&zero,&zero,&a->grid->ictxt,&xlld,&info));

    690:   /* redistribute x as a column of a 2d matrix */
    691:   PetscStackCallBLAS("SCALAPACKgemr2d",SCALAPACKgemr2d_(&a->M,&one,x,&one,&one,xdesc,x2d,&one,&one,x2desc,&a->grid->ictxcol));

    693:   /* call ScaLAPACK subroutine */
    694:   switch (A->factortype) {
    695:     case MAT_FACTOR_LU:
    696:       PetscStackCallBLAS("SCALAPACKgetrs",SCALAPACKgetrs_("N",&a->M,&nrhs,a->loc,&one,&one,a->desc,a->pivots,x2d,&one,&one,x2desc,&info));
    698:       break;
    699:     case MAT_FACTOR_CHOLESKY:
    700:       PetscStackCallBLAS("SCALAPACKpotrs",SCALAPACKpotrs_("L",&a->M,&nrhs,a->loc,&one,&one,a->desc,x2d,&one,&one,x2desc,&info));
    702:       break;
    703:     default:
    704:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unfactored Matrix or Unsupported MatFactorType");
    705:   }

    707:   /* redistribute x from a column of a 2d matrix */
    708:   PetscStackCallBLAS("SCALAPACKgemr2d",SCALAPACKgemr2d_(&a->M,&one,x2d,&one,&one,x2desc,x,&one,&one,xdesc,&a->grid->ictxcol));

    710:   PetscFree(x2d);
    711:   VecRestoreArray(X,&x);
    712:   return(0);
    713: }

    715: static PetscErrorCode MatSolveAdd_ScaLAPACK(Mat A,Vec B,Vec Y,Vec X)
    716: {

    720:   MatSolve_ScaLAPACK(A,B,X);
    721:   VecAXPY(X,1,Y);
    722:   return(0);
    723: }

    725: static PetscErrorCode MatMatSolve_ScaLAPACK(Mat A,Mat B,Mat X)
    726: {
    728:   Mat_ScaLAPACK *a = (Mat_ScaLAPACK*)A->data,*b,*x;
    729:   PetscBool      flg1,flg2;
    730:   PetscBLASInt   one=1,info;

    733:   PetscObjectTypeCompare((PetscObject)B,MATSCALAPACK,&flg1);
    734:   PetscObjectTypeCompare((PetscObject)X,MATSCALAPACK,&flg2);
    735:   if (!(flg1 && flg2)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Both B and X must be of type MATSCALAPACK");
    736:   MatScaLAPACKCheckDistribution(B,1,X,2);
    737:   b = (Mat_ScaLAPACK*)B->data;
    738:   x = (Mat_ScaLAPACK*)X->data;
    739:   PetscArraycpy(x->loc,b->loc,b->lld*b->locc);

    741:   switch (A->factortype) {
    742:     case MAT_FACTOR_LU:
    743:       PetscStackCallBLAS("SCALAPACKgetrs",SCALAPACKgetrs_("N",&a->M,&x->N,a->loc,&one,&one,a->desc,a->pivots,x->loc,&one,&one,x->desc,&info));
    745:       break;
    746:     case MAT_FACTOR_CHOLESKY:
    747:       PetscStackCallBLAS("SCALAPACKpotrs",SCALAPACKpotrs_("L",&a->M,&x->N,a->loc,&one,&one,a->desc,x->loc,&one,&one,x->desc,&info));
    749:       break;
    750:     default:
    751:       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unfactored Matrix or Unsupported MatFactorType");
    752:   }
    753:   return(0);
    754: }

    756: static PetscErrorCode MatLUFactor_ScaLAPACK(Mat A,IS row,IS col,const MatFactorInfo *factorinfo)
    757: {
    759:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data;
    760:   PetscBLASInt   one=1,info;

    763:   if (!a->pivots) {
    764:     PetscMalloc1(a->locr+a->mb,&a->pivots);
    765:     PetscLogObjectMemory((PetscObject)A,a->locr*sizeof(PetscBLASInt));
    766:   }
    767:   PetscStackCallBLAS("SCALAPACKgetrf",SCALAPACKgetrf_(&a->M,&a->N,a->loc,&one,&one,a->desc,a->pivots,&info));
    769:   A->factortype = MAT_FACTOR_LU;
    770:   A->assembled  = PETSC_TRUE;

    772:   PetscFree(A->solvertype);
    773:   PetscStrallocpy(MATSOLVERSCALAPACK,&A->solvertype);
    774:   return(0);
    775: }

    777: static PetscErrorCode MatLUFactorNumeric_ScaLAPACK(Mat F,Mat A,const MatFactorInfo *info)
    778: {

    782:   MatCopy(A,F,SAME_NONZERO_PATTERN);
    783:   MatLUFactor_ScaLAPACK(F,0,0,info);
    784:   return(0);
    785: }

    787: static PetscErrorCode MatLUFactorSymbolic_ScaLAPACK(Mat F,Mat A,IS r,IS c,const MatFactorInfo *info)
    788: {
    790:   /* F is created and allocated by MatGetFactor_scalapack_petsc(), skip this routine. */
    791:   return(0);
    792: }

    794: static PetscErrorCode MatCholeskyFactor_ScaLAPACK(Mat A,IS perm,const MatFactorInfo *factorinfo)
    795: {
    797:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data;
    798:   PetscBLASInt   one=1,info;

    801:   PetscStackCallBLAS("SCALAPACKpotrf",SCALAPACKpotrf_("L",&a->M,a->loc,&one,&one,a->desc,&info));
    803:   A->factortype = MAT_FACTOR_CHOLESKY;
    804:   A->assembled  = PETSC_TRUE;

    806:   PetscFree(A->solvertype);
    807:   PetscStrallocpy(MATSOLVERSCALAPACK,&A->solvertype);
    808:   return(0);
    809: }

    811: static PetscErrorCode MatCholeskyFactorNumeric_ScaLAPACK(Mat F,Mat A,const MatFactorInfo *info)
    812: {

    816:   MatCopy(A,F,SAME_NONZERO_PATTERN);
    817:   MatCholeskyFactor_ScaLAPACK(F,0,info);
    818:   return(0);
    819: }

    821: static PetscErrorCode MatCholeskyFactorSymbolic_ScaLAPACK(Mat F,Mat A,IS perm,const MatFactorInfo *info)
    822: {
    824:   /* F is created and allocated by MatGetFactor_scalapack_petsc(), skip this routine. */
    825:   return(0);
    826: }

    828: PetscErrorCode MatFactorGetSolverType_scalapack_scalapack(Mat A,MatSolverType *type)
    829: {
    831:   *type = MATSOLVERSCALAPACK;
    832:   return(0);
    833: }

    835: static PetscErrorCode MatGetFactor_scalapack_scalapack(Mat A,MatFactorType ftype,Mat *F)
    836: {
    837:   Mat            B;
    838:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data;

    842:   /* Create the factorization matrix */
    843:   MatCreateScaLAPACK(PetscObjectComm((PetscObject)A),a->mb,a->nb,a->M,a->N,a->rsrc,a->csrc,&B);
    844:   B->factortype = ftype;
    845:   PetscFree(B->solvertype);
    846:   PetscStrallocpy(MATSOLVERSCALAPACK,&B->solvertype);

    848:   PetscObjectComposeFunction((PetscObject)B,"MatFactorGetSolverType_C",MatFactorGetSolverType_scalapack_scalapack);
    849:   *F = B;
    850:   return(0);
    851: }

    853: PETSC_EXTERN PetscErrorCode MatSolverTypeRegister_ScaLAPACK(void)
    854: {

    858:   MatSolverTypeRegister(MATSOLVERSCALAPACK,MATSCALAPACK,MAT_FACTOR_LU,MatGetFactor_scalapack_scalapack);
    859:   MatSolverTypeRegister(MATSOLVERSCALAPACK,MATSCALAPACK,MAT_FACTOR_CHOLESKY,MatGetFactor_scalapack_scalapack);
    860:   return(0);
    861: }

    863: static PetscErrorCode MatNorm_ScaLAPACK(Mat A,NormType type,PetscReal *nrm)
    864: {
    866:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data;
    867:   PetscBLASInt   one=1,lwork=0;
    868:   const char     *ntype;
    869:   PetscScalar    *work=NULL,dummy;

    872:   switch (type){
    873:     case NORM_1:
    874:       ntype = "1";
    875:       lwork = PetscMax(a->locr,a->locc);
    876:       break;
    877:     case NORM_FROBENIUS:
    878:       ntype = "F";
    879:       work  = &dummy;
    880:       break;
    881:     case NORM_INFINITY:
    882:       ntype = "I";
    883:       lwork = PetscMax(a->locr,a->locc);
    884:       break;
    885:     default:
    886:       SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Unsupported norm type");
    887:   }
    888:   if (lwork) { PetscMalloc1(lwork,&work); }
    889:   *nrm = SCALAPACKlange_(ntype,&a->M,&a->N,a->loc,&one,&one,a->desc,work);
    890:   if (lwork) { PetscFree(work); }
    891:   return(0);
    892: }

    894: static PetscErrorCode MatZeroEntries_ScaLAPACK(Mat A)
    895: {
    896:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data;

    900:   PetscArrayzero(a->loc,a->lld*a->locc);
    901:   return(0);
    902: }

    904: static PetscErrorCode MatGetOwnershipIS_ScaLAPACK(Mat A,IS *rows,IS *cols)
    905: {
    906:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data;
    908:   PetscInt       i,n,nb,isrc,nproc,iproc,*idx;

    911:   if (rows) {
    912:     n     = a->locr;
    913:     nb    = a->mb;
    914:     isrc  = a->rsrc;
    915:     nproc = a->grid->nprow;
    916:     iproc = a->grid->myrow;
    917:     PetscMalloc1(n,&idx);
    918:     for (i=0;i<n;i++) idx[i] = nproc*nb*(i/nb) + i%nb + ((nproc+iproc-isrc)%nproc)*nb;
    919:     ISCreateGeneral(PETSC_COMM_SELF,n,idx,PETSC_OWN_POINTER,rows);
    920:   }
    921:   if (cols) {
    922:     n     = a->locc;
    923:     nb    = a->nb;
    924:     isrc  = a->csrc;
    925:     nproc = a->grid->npcol;
    926:     iproc = a->grid->mycol;
    927:     PetscMalloc1(n,&idx);
    928:     for (i=0;i<n;i++) idx[i] = nproc*nb*(i/nb) + i%nb + ((nproc+iproc-isrc)%nproc)*nb;
    929:     ISCreateGeneral(PETSC_COMM_SELF,n,idx,PETSC_OWN_POINTER,cols);
    930:   }
    931:   return(0);
    932: }

    934: static PetscErrorCode MatConvert_ScaLAPACK_Dense(Mat A,MatType newtype,MatReuse reuse,Mat *B)
    935: {
    937:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data;
    938:   Mat            Bmpi;
    939:   MPI_Comm       comm;
    940:   PetscInt       i,M=A->rmap->N,N=A->cmap->N,m,n,rstart,rend,nz;
    941:   const PetscInt *ranges,*branges,*cwork;
    942:   const PetscScalar *vwork;
    943:   PetscBLASInt   bdesc[9],bmb,zero=0,one=1,lld,info;
    944:   PetscScalar    *barray;
    945:   PetscBool      differ=PETSC_FALSE;
    946:   PetscMPIInt    size;

    949:   PetscObjectGetComm((PetscObject)A,&comm);
    950:   PetscLayoutGetRanges(A->rmap,&ranges);

    952:   if (reuse == MAT_REUSE_MATRIX) { /* check if local sizes differ in A and B */
    953:     MPI_Comm_size(comm,&size);
    954:     PetscLayoutGetRanges((*B)->rmap,&branges);
    955:     for (i=0;i<size;i++) if (ranges[i+1]!=branges[i+1]) { differ=PETSC_TRUE; break; }
    956:   }

    958:   if (reuse == MAT_REUSE_MATRIX && differ) { /* special case, use auxiliary dense matrix */
    959:     MatCreate(comm,&Bmpi);
    960:     m = PETSC_DECIDE;
    961:     PetscSplitOwnershipEqual(comm,&m,&M);
    962:     n = PETSC_DECIDE;
    963:     PetscSplitOwnershipEqual(comm,&n,&N);
    964:     MatSetSizes(Bmpi,m,n,M,N);
    965:     MatSetType(Bmpi,MATDENSE);
    966:     MatSetUp(Bmpi);

    968:     /* create ScaLAPACK descriptor for B (1d block distribution) */
    969:     PetscBLASIntCast(ranges[1],&bmb);  /* row block size */
    970:     lld = PetscMax(A->rmap->n,1);  /* local leading dimension */
    971:     PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(bdesc,&a->M,&a->N,&bmb,&a->N,&zero,&zero,&a->grid->ictxcol,&lld,&info));

    974:     /* redistribute matrix */
    975:     MatDenseGetArray(Bmpi,&barray);
    976:     PetscStackCallBLAS("SCALAPACKgemr2d",SCALAPACKgemr2d_(&a->M,&a->N,a->loc,&one,&one,a->desc,barray,&one,&one,bdesc,&a->grid->ictxcol));
    977:     MatDenseRestoreArray(Bmpi,&barray);
    978:     MatAssemblyBegin(Bmpi,MAT_FINAL_ASSEMBLY);
    979:     MatAssemblyEnd(Bmpi,MAT_FINAL_ASSEMBLY);

    981:     /* transfer rows of auxiliary matrix to the final matrix B */
    982:     MatGetOwnershipRange(Bmpi,&rstart,&rend);
    983:     for (i=rstart;i<rend;i++) {
    984:       MatGetRow(Bmpi,i,&nz,&cwork,&vwork);
    985:       MatSetValues(*B,1,&i,nz,cwork,vwork,INSERT_VALUES);
    986:       MatRestoreRow(Bmpi,i,&nz,&cwork,&vwork);
    987:     }
    988:     MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);
    989:     MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);
    990:     MatDestroy(&Bmpi);

    992:   } else {  /* normal cases */

    994:     if (reuse == MAT_REUSE_MATRIX) Bmpi = *B;
    995:     else {
    996:       MatCreate(comm,&Bmpi);
    997:       m = PETSC_DECIDE;
    998:       PetscSplitOwnershipEqual(comm,&m,&M);
    999:       n = PETSC_DECIDE;
    1000:       PetscSplitOwnershipEqual(comm,&n,&N);
    1001:       MatSetSizes(Bmpi,m,n,M,N);
    1002:       MatSetType(Bmpi,MATDENSE);
    1003:       MatSetUp(Bmpi);
    1004:     }

    1006:     /* create ScaLAPACK descriptor for B (1d block distribution) */
    1007:     PetscBLASIntCast(ranges[1],&bmb);  /* row block size */
    1008:     lld = PetscMax(A->rmap->n,1);  /* local leading dimension */
    1009:     PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(bdesc,&a->M,&a->N,&bmb,&a->N,&zero,&zero,&a->grid->ictxcol,&lld,&info));

    1012:     /* redistribute matrix */
    1013:     MatDenseGetArray(Bmpi,&barray);
    1014:     PetscStackCallBLAS("SCALAPACKgemr2d",SCALAPACKgemr2d_(&a->M,&a->N,a->loc,&one,&one,a->desc,barray,&one,&one,bdesc,&a->grid->ictxcol));
    1015:     MatDenseRestoreArray(Bmpi,&barray);

    1017:     MatAssemblyBegin(Bmpi,MAT_FINAL_ASSEMBLY);
    1018:     MatAssemblyEnd(Bmpi,MAT_FINAL_ASSEMBLY);
    1019:     if (reuse == MAT_INPLACE_MATRIX) {
    1020:       MatHeaderReplace(A,&Bmpi);
    1021:     } else *B = Bmpi;
    1022:   }
    1023:   return(0);
    1024: }

    1026: PETSC_INTERN PetscErrorCode MatConvert_Dense_ScaLAPACK(Mat A,MatType newtype,MatReuse reuse,Mat *B)
    1027: {
    1029:   Mat_ScaLAPACK  *b;
    1030:   Mat            Bmpi;
    1031:   MPI_Comm       comm;
    1032:   PetscInt       M=A->rmap->N,N=A->cmap->N,m,n;
    1033:   const PetscInt *ranges;
    1034:   PetscBLASInt   adesc[9],amb,zero=0,one=1,lld,info;
    1035:   PetscScalar    *aarray;
    1036:   PetscInt       lda;

    1039:   PetscObjectGetComm((PetscObject)A,&comm);

    1041:   if (reuse == MAT_REUSE_MATRIX) Bmpi = *B;
    1042:   else {
    1043:     MatCreate(comm,&Bmpi);
    1044:     m = PETSC_DECIDE;
    1045:     PetscSplitOwnershipEqual(comm,&m,&M);
    1046:     n = PETSC_DECIDE;
    1047:     PetscSplitOwnershipEqual(comm,&n,&N);
    1048:     MatSetSizes(Bmpi,m,n,M,N);
    1049:     MatSetType(Bmpi,MATSCALAPACK);
    1050:     MatSetUp(Bmpi);
    1051:   }
    1052:   b = (Mat_ScaLAPACK*)Bmpi->data;

    1054:   /* create ScaLAPACK descriptor for A (1d block distribution) */
    1055:   PetscLayoutGetRanges(A->rmap,&ranges);
    1056:   PetscBLASIntCast(ranges[1],&amb);  /* row block size */
    1057:   MatDenseGetLDA(A,&lda);
    1058:   lld = PetscMax(lda,1);  /* local leading dimension */
    1059:   PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(adesc,&b->M,&b->N,&amb,&b->N,&zero,&zero,&b->grid->ictxcol,&lld,&info));

    1062:   /* redistribute matrix */
    1063:   MatDenseGetArray(A,&aarray);
    1064:   PetscStackCallBLAS("SCALAPACKgemr2d",SCALAPACKgemr2d_(&b->M,&b->N,aarray,&one,&one,adesc,b->loc,&one,&one,b->desc,&b->grid->ictxcol));
    1065:   MatDenseRestoreArray(A,&aarray);

    1067:   MatAssemblyBegin(Bmpi,MAT_FINAL_ASSEMBLY);
    1068:   MatAssemblyEnd(Bmpi,MAT_FINAL_ASSEMBLY);
    1069:   if (reuse == MAT_INPLACE_MATRIX) {
    1070:     MatHeaderReplace(A,&Bmpi);
    1071:   } else *B = Bmpi;
    1072:   return(0);
    1073: }

    1075: PETSC_INTERN PetscErrorCode MatConvert_AIJ_ScaLAPACK(Mat A,MatType newtype,MatReuse reuse,Mat *newmat)
    1076: {
    1077:   Mat               mat_scal;
    1078:   PetscErrorCode    ierr;
    1079:   PetscInt          M=A->rmap->N,N=A->cmap->N,rstart=A->rmap->rstart,rend=A->rmap->rend,m,n,row,ncols;
    1080:   const PetscInt    *cols;
    1081:   const PetscScalar *vals;

    1084:   if (reuse == MAT_REUSE_MATRIX) {
    1085:     mat_scal = *newmat;
    1086:     MatZeroEntries(mat_scal);
    1087:   } else {
    1088:     MatCreate(PetscObjectComm((PetscObject)A),&mat_scal);
    1089:     m = PETSC_DECIDE;
    1090:     PetscSplitOwnershipEqual(PetscObjectComm((PetscObject)A),&m,&M);
    1091:     n = PETSC_DECIDE;
    1092:     PetscSplitOwnershipEqual(PetscObjectComm((PetscObject)A),&n,&N);
    1093:     MatSetSizes(mat_scal,m,n,M,N);
    1094:     MatSetType(mat_scal,MATSCALAPACK);
    1095:     MatSetUp(mat_scal);
    1096:   }
    1097:   for (row=rstart;row<rend;row++) {
    1098:     MatGetRow(A,row,&ncols,&cols,&vals);
    1099:     MatSetValues(mat_scal,1,&row,ncols,cols,vals,INSERT_VALUES);
    1100:     MatRestoreRow(A,row,&ncols,&cols,&vals);
    1101:   }
    1102:   MatAssemblyBegin(mat_scal,MAT_FINAL_ASSEMBLY);
    1103:   MatAssemblyEnd(mat_scal,MAT_FINAL_ASSEMBLY);

    1105:   if (reuse == MAT_INPLACE_MATRIX) { MatHeaderReplace(A,&mat_scal); }
    1106:   else *newmat = mat_scal;
    1107:   return(0);
    1108: }

    1110: PETSC_INTERN PetscErrorCode MatConvert_SBAIJ_ScaLAPACK(Mat A, MatType newtype,MatReuse reuse,Mat *newmat)
    1111: {
    1112:   Mat               mat_scal;
    1113:   PetscErrorCode    ierr;
    1114:   PetscInt          M=A->rmap->N,N=A->cmap->N,m,n,row,ncols,j,rstart=A->rmap->rstart,rend=A->rmap->rend;
    1115:   const PetscInt    *cols;
    1116:   const PetscScalar *vals;
    1117:   PetscScalar       v;

    1120:   if (reuse == MAT_REUSE_MATRIX) {
    1121:     mat_scal = *newmat;
    1122:     MatZeroEntries(mat_scal);
    1123:   } else {
    1124:     MatCreate(PetscObjectComm((PetscObject)A),&mat_scal);
    1125:     m = PETSC_DECIDE;
    1126:     PetscSplitOwnershipEqual(PetscObjectComm((PetscObject)A),&m,&M);
    1127:     n = PETSC_DECIDE;
    1128:     PetscSplitOwnershipEqual(PetscObjectComm((PetscObject)A),&n,&N);
    1129:     MatSetSizes(mat_scal,m,n,M,N);
    1130:     MatSetType(mat_scal,MATSCALAPACK);
    1131:     MatSetUp(mat_scal);
    1132:   }
    1133:   MatGetRowUpperTriangular(A);
    1134:   for (row=rstart;row<rend;row++) {
    1135:     MatGetRow(A,row,&ncols,&cols,&vals);
    1136:     MatSetValues(mat_scal,1,&row,ncols,cols,vals,ADD_VALUES);
    1137:     for (j=0;j<ncols;j++) { /* lower triangular part */
    1138:       if (cols[j] == row) continue;
    1139:       v    = A->hermitian ? PetscConj(vals[j]) : vals[j];
    1140:       MatSetValues(mat_scal,1,&cols[j],1,&row,&v,ADD_VALUES);
    1141:     }
    1142:     MatRestoreRow(A,row,&ncols,&cols,&vals);
    1143:   }
    1144:   MatRestoreRowUpperTriangular(A);
    1145:   MatAssemblyBegin(mat_scal,MAT_FINAL_ASSEMBLY);
    1146:   MatAssemblyEnd(mat_scal,MAT_FINAL_ASSEMBLY);

    1148:   if (reuse == MAT_INPLACE_MATRIX) { MatHeaderReplace(A,&mat_scal); }
    1149:   else *newmat = mat_scal;
    1150:   return(0);
    1151: }

    1153: static PetscErrorCode MatScaLAPACKSetPreallocation(Mat A)
    1154: {
    1155:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data;
    1157:   PetscInt       sz=0;

    1160:   PetscLayoutSetUp(A->rmap);
    1161:   PetscLayoutSetUp(A->cmap);
    1162:   if (!a->lld) a->lld = a->locr;

    1164:   PetscFree(a->loc);
    1165:   PetscIntMultError(a->lld,a->locc,&sz);
    1166:   PetscCalloc1(sz,&a->loc);
    1167:   PetscLogObjectMemory((PetscObject)A,sz*sizeof(PetscScalar));

    1169:   A->preallocated = PETSC_TRUE;
    1170:   return(0);
    1171: }

    1173: static PetscErrorCode MatDestroy_ScaLAPACK(Mat A)
    1174: {
    1175:   Mat_ScaLAPACK      *a = (Mat_ScaLAPACK*)A->data;
    1176:   PetscErrorCode     ierr;
    1177:   Mat_ScaLAPACK_Grid *grid;
    1178:   PetscBool          flg;
    1179:   MPI_Comm           icomm;

    1182:   MatStashDestroy_Private(&A->stash);
    1183:   PetscFree(a->loc);
    1184:   PetscFree(a->pivots);
    1185:   PetscCommDuplicate(PetscObjectComm((PetscObject)A),&icomm,NULL);
    1186:   MPI_Comm_get_attr(icomm,Petsc_ScaLAPACK_keyval,(void**)&grid,(int*)&flg);
    1187:   if (--grid->grid_refct == 0) {
    1188:     Cblacs_gridexit(grid->ictxt);
    1189:     Cblacs_gridexit(grid->ictxrow);
    1190:     Cblacs_gridexit(grid->ictxcol);
    1191:     PetscFree(grid);
    1192:     MPI_Comm_delete_attr(icomm,Petsc_ScaLAPACK_keyval);
    1193:   }
    1194:   PetscCommDestroy(&icomm);
    1195:   PetscObjectComposeFunction((PetscObject)A,"MatGetOwnershipIS_C",NULL);
    1196:   PetscObjectComposeFunction((PetscObject)A,"MatFactorGetSolverType_C",NULL);
    1197:   PetscObjectComposeFunction((PetscObject)A,"MatScaLAPACKSetBlockSizes_C",NULL);
    1198:   PetscObjectComposeFunction((PetscObject)A,"MatScaLAPACKGetBlockSizes_C",NULL);
    1199:   PetscFree(A->data);
    1200:   return(0);
    1201: }

    1203: PETSC_STATIC_INLINE PetscErrorCode MatScaLAPACKCheckLayout(PetscLayout map)
    1204: {
    1206:   const PetscInt *ranges;
    1207:   PetscMPIInt    size;
    1208:   PetscInt       i,n;

    1211:   MPI_Comm_size(map->comm,&size);
    1212:   if (size>2) {
    1213:     PetscLayoutGetRanges(map,&ranges);
    1214:     n = ranges[1]-ranges[0];
    1215:     for (i=1;i<size-1;i++) if (ranges[i+1]-ranges[i]!=n) break;
    1216:     if (i<size-1 && ranges[i+1]-ranges[i]!=0 && ranges[i+2]-ranges[i+1]!=0) SETERRQ(map->comm,PETSC_ERR_SUP,"MATSCALAPACK must have equal local sizes in all processes (except possibly the last one), consider using MatCreateScaLAPACK");
    1217:   }
    1218:   return(0);
    1219: }

    1221: PetscErrorCode MatSetUp_ScaLAPACK(Mat A)
    1222: {
    1223:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data;
    1225:   PetscBLASInt   info=0;

    1228:   PetscLayoutSetUp(A->rmap);
    1229:   PetscLayoutSetUp(A->cmap);

    1231:   /* check that the layout is as enforced by MatCreateScaLAPACK */
    1232:   MatScaLAPACKCheckLayout(A->rmap);
    1233:   MatScaLAPACKCheckLayout(A->cmap);

    1235:   /* compute local sizes */
    1236:   PetscBLASIntCast(A->rmap->N,&a->M);
    1237:   PetscBLASIntCast(A->cmap->N,&a->N);
    1238:   a->locr = SCALAPACKnumroc_(&a->M,&a->mb,&a->grid->myrow,&a->rsrc,&a->grid->nprow);
    1239:   a->locc = SCALAPACKnumroc_(&a->N,&a->nb,&a->grid->mycol,&a->csrc,&a->grid->npcol);
    1240:   a->lld  = PetscMax(1,a->locr);

    1242:   /* allocate local array */
    1243:   MatScaLAPACKSetPreallocation(A);

    1245:   /* set up ScaLAPACK descriptor */
    1246:   PetscStackCallBLAS("SCALAPACKdescinit",SCALAPACKdescinit_(a->desc,&a->M,&a->N,&a->mb,&a->nb,&a->rsrc,&a->csrc,&a->grid->ictxt,&a->lld,&info));
    1248:   return(0);
    1249: }

    1251: PetscErrorCode MatAssemblyBegin_ScaLAPACK(Mat A,MatAssemblyType type)
    1252: {
    1254:   PetscInt       nstash,reallocs;

    1257:   if (A->nooffprocentries) return(0);
    1258:   MatStashScatterBegin_Private(A,&A->stash,NULL);
    1259:   MatStashGetInfo_Private(&A->stash,&nstash,&reallocs);
    1260:   PetscInfo2(A,"Stash has %D entries, uses %D mallocs.\n",nstash,reallocs);
    1261:   return(0);
    1262: }

    1264: PetscErrorCode MatAssemblyEnd_ScaLAPACK(Mat A,MatAssemblyType type)
    1265: {
    1267:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data;
    1268:   PetscMPIInt    n;
    1269:   PetscInt       i,flg,*row,*col;
    1270:   PetscScalar    *val;
    1271:   PetscBLASInt   gridx,gcidx,lridx,lcidx,rsrc,csrc;

    1274:   if (A->nooffprocentries) return(0);
    1275:   while (1) {
    1276:     MatStashScatterGetMesg_Private(&A->stash,&n,&row,&col,&val,&flg);
    1277:     if (!flg) break;
    1278:     for (i=0;i<n;i++) {
    1279:       PetscBLASIntCast(row[i]+1,&gridx);
    1280:       PetscBLASIntCast(col[i]+1,&gcidx);
    1281:       PetscStackCallBLAS("SCALAPACKinfog2l",SCALAPACKinfog2l_(&gridx,&gcidx,a->desc,&a->grid->nprow,&a->grid->npcol,&a->grid->myrow,&a->grid->mycol,&lridx,&lcidx,&rsrc,&csrc));
    1282:       if (rsrc!=a->grid->myrow || csrc!=a->grid->mycol) SETERRQ(PetscObjectComm((PetscObject)A),1,"Something went wrong, received value does not belong to this process");
    1283:       switch (A->insertmode) {
    1284:         case INSERT_VALUES: a->loc[lridx-1+(lcidx-1)*a->lld] = val[i]; break;
    1285:         case ADD_VALUES: a->loc[lridx-1+(lcidx-1)*a->lld] += val[i]; break;
    1286:         default: SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"No support for InsertMode %d",(int)A->insertmode);
    1287:       }
    1288:     }
    1289:   }
    1290:   MatStashScatterEnd_Private(&A->stash);
    1291:   return(0);
    1292: }

    1294: PetscErrorCode MatLoad_ScaLAPACK(Mat newMat,PetscViewer viewer)
    1295: {
    1297:   Mat            Adense,As;
    1298:   MPI_Comm       comm;

    1301:   PetscObjectGetComm((PetscObject)newMat,&comm);
    1302:   MatCreate(comm,&Adense);
    1303:   MatSetType(Adense,MATDENSE);
    1304:   MatLoad(Adense,viewer);
    1305:   MatConvert(Adense,MATSCALAPACK,MAT_INITIAL_MATRIX,&As);
    1306:   MatDestroy(&Adense);
    1307:   MatHeaderReplace(newMat,&As);
    1308:   return(0);
    1309: }

    1311: /* -------------------------------------------------------------------*/
    1312: static struct _MatOps MatOps_Values = {
    1313:        MatSetValues_ScaLAPACK,
    1314:        0,
    1315:        0,
    1316:        MatMult_ScaLAPACK,
    1317: /* 4*/ MatMultAdd_ScaLAPACK,
    1318:        MatMultTranspose_ScaLAPACK,
    1319:        MatMultTransposeAdd_ScaLAPACK,
    1320:        MatSolve_ScaLAPACK,
    1321:        MatSolveAdd_ScaLAPACK,
    1322:        0,
    1323: /*10*/ 0,
    1324:        MatLUFactor_ScaLAPACK,
    1325:        MatCholeskyFactor_ScaLAPACK,
    1326:        0,
    1327:        MatTranspose_ScaLAPACK,
    1328: /*15*/ MatGetInfo_ScaLAPACK,
    1329:        0,
    1330:        MatGetDiagonal_ScaLAPACK,
    1331:        MatDiagonalScale_ScaLAPACK,
    1332:        MatNorm_ScaLAPACK,
    1333: /*20*/ MatAssemblyBegin_ScaLAPACK,
    1334:        MatAssemblyEnd_ScaLAPACK,
    1335:        MatSetOption_ScaLAPACK,
    1336:        MatZeroEntries_ScaLAPACK,
    1337: /*24*/ 0,
    1338:        MatLUFactorSymbolic_ScaLAPACK,
    1339:        MatLUFactorNumeric_ScaLAPACK,
    1340:        MatCholeskyFactorSymbolic_ScaLAPACK,
    1341:        MatCholeskyFactorNumeric_ScaLAPACK,
    1342: /*29*/ MatSetUp_ScaLAPACK,
    1343:        0,
    1344:        0,
    1345:        0,
    1346:        0,
    1347: /*34*/ MatDuplicate_ScaLAPACK,
    1348:        0,
    1349:        0,
    1350:        0,
    1351:        0,
    1352: /*39*/ MatAXPY_ScaLAPACK,
    1353:        0,
    1354:        0,
    1355:        0,
    1356:        MatCopy_ScaLAPACK,
    1357: /*44*/ 0,
    1358:        MatScale_ScaLAPACK,
    1359:        MatShift_ScaLAPACK,
    1360:        0,
    1361:        0,
    1362: /*49*/ 0,
    1363:        0,
    1364:        0,
    1365:        0,
    1366:        0,
    1367: /*54*/ 0,
    1368:        0,
    1369:        0,
    1370:        0,
    1371:        0,
    1372: /*59*/ 0,
    1373:        MatDestroy_ScaLAPACK,
    1374:        MatView_ScaLAPACK,
    1375:        0,
    1376:        0,
    1377: /*64*/ 0,
    1378:        0,
    1379:        0,
    1380:        0,
    1381:        0,
    1382: /*69*/ 0,
    1383:        0,
    1384:        MatConvert_ScaLAPACK_Dense,
    1385:        0,
    1386:        0,
    1387: /*74*/ 0,
    1388:        0,
    1389:        0,
    1390:        0,
    1391:        0,
    1392: /*79*/ 0,
    1393:        0,
    1394:        0,
    1395:        0,
    1396:        MatLoad_ScaLAPACK,
    1397: /*84*/ 0,
    1398:        0,
    1399:        0,
    1400:        0,
    1401:        0,
    1402: /*89*/ 0,
    1403:        0,
    1404:        MatMatMultNumeric_ScaLAPACK,
    1405:        0,
    1406:        0,
    1407: /*94*/ 0,
    1408:        0,
    1409:        0,
    1410:        MatMatTransposeMultNumeric_ScaLAPACK,
    1411:        0,
    1412: /*99*/ MatProductSetFromOptions_ScaLAPACK,
    1413:        0,
    1414:        0,
    1415:        MatConjugate_ScaLAPACK,
    1416:        0,
    1417: /*104*/0,
    1418:        0,
    1419:        0,
    1420:        0,
    1421:        0,
    1422: /*109*/MatMatSolve_ScaLAPACK,
    1423:        0,
    1424:        0,
    1425:        0,
    1426:        MatMissingDiagonal_ScaLAPACK,
    1427: /*114*/0,
    1428:        0,
    1429:        0,
    1430:        0,
    1431:        0,
    1432: /*119*/0,
    1433:        MatHermitianTranspose_ScaLAPACK,
    1434:        0,
    1435:        0,
    1436:        0,
    1437: /*124*/0,
    1438:        0,
    1439:        0,
    1440:        0,
    1441:        0,
    1442: /*129*/0,
    1443:        0,
    1444:        0,
    1445:        0,
    1446:        0,
    1447: /*134*/0,
    1448:        0,
    1449:        0,
    1450:        0,
    1451:        0,
    1452:        0,
    1453: /*140*/0,
    1454:        0,
    1455:        0,
    1456:        0,
    1457:        0,
    1458: /*145*/0,
    1459:        0,
    1460:        0
    1461: };

    1463: static PetscErrorCode MatStashScatterBegin_ScaLAPACK(Mat mat,MatStash *stash,PetscInt *owners)
    1464: {
    1465:   PetscInt           *owner,*startv,*starti,tag1=stash->tag1,tag2=stash->tag2,bs2;
    1466:   PetscInt           size=stash->size,nsends;
    1467:   PetscErrorCode     ierr;
    1468:   PetscInt           count,*sindices,**rindices,i,j,l;
    1469:   PetscScalar        **rvalues,*svalues;
    1470:   MPI_Comm           comm = stash->comm;
    1471:   MPI_Request        *send_waits,*recv_waits,*recv_waits1,*recv_waits2;
    1472:   PetscMPIInt        *sizes,*nlengths,nreceives;
    1473:   PetscInt           *sp_idx,*sp_idy;
    1474:   PetscScalar        *sp_val;
    1475:   PetscMatStashSpace space,space_next;
    1476:   PetscBLASInt       gridx,gcidx,lridx,lcidx,rsrc,csrc;
    1477:   Mat_ScaLAPACK      *a = (Mat_ScaLAPACK*)mat->data;

    1480:   {                             /* make sure all processors are either in INSERTMODE or ADDMODE */
    1481:     InsertMode addv;
    1482:     MPIU_Allreduce((PetscEnum*)&mat->insertmode,(PetscEnum*)&addv,1,MPIU_ENUM,MPI_BOR,PetscObjectComm((PetscObject)mat));
    1483:     if (addv == (ADD_VALUES|INSERT_VALUES)) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Some processors inserted others added");
    1484:     mat->insertmode = addv; /* in case this processor had no cache */
    1485:   }

    1487:   bs2 = stash->bs*stash->bs;

    1489:   /*  first count number of contributors to each processor */
    1490:   PetscCalloc1(size,&nlengths);
    1491:   PetscMalloc1(stash->n+1,&owner);

    1493:   i     = j    = 0;
    1494:   space = stash->space_head;
    1495:   while (space) {
    1496:     space_next = space->next;
    1497:     for (l=0; l<space->local_used; l++) {
    1498:       PetscBLASIntCast(space->idx[l]+1,&gridx);
    1499:       PetscBLASIntCast(space->idy[l]+1,&gcidx);
    1500:       PetscStackCallBLAS("SCALAPACKinfog2l",SCALAPACKinfog2l_(&gridx,&gcidx,a->desc,&a->grid->nprow,&a->grid->npcol,&a->grid->myrow,&a->grid->mycol,&lridx,&lcidx,&rsrc,&csrc));
    1501:       j = Cblacs_pnum(a->grid->ictxt,rsrc,csrc);
    1502:       nlengths[j]++; owner[i] = j;
    1503:       i++;
    1504:     }
    1505:     space = space_next;
    1506:   }

    1508:   /* Now check what procs get messages - and compute nsends. */
    1509:   PetscCalloc1(size,&sizes);
    1510:   for (i=0, nsends=0; i<size; i++) {
    1511:     if (nlengths[i]) {
    1512:       sizes[i] = 1; nsends++;
    1513:     }
    1514:   }

    1516:   {PetscMPIInt *onodes,*olengths;
    1517:    /* Determine the number of messages to expect, their lengths, from from-ids */
    1518:    PetscGatherNumberOfMessages(comm,sizes,nlengths,&nreceives);
    1519:    PetscGatherMessageLengths(comm,nsends,nreceives,nlengths,&onodes,&olengths);
    1520:    /* since clubbing row,col - lengths are multiplied by 2 */
    1521:    for (i=0; i<nreceives; i++) olengths[i] *=2;
    1522:    PetscPostIrecvInt(comm,tag1,nreceives,onodes,olengths,&rindices,&recv_waits1);
    1523:    /* values are size 'bs2' lengths (and remove earlier factor 2 */
    1524:    for (i=0; i<nreceives; i++) olengths[i] = olengths[i]*bs2/2;
    1525:    PetscPostIrecvScalar(comm,tag2,nreceives,onodes,olengths,&rvalues,&recv_waits2);
    1526:    PetscFree(onodes);
    1527:    PetscFree(olengths);}

    1529:   /* do sends:
    1530:       1) starts[i] gives the starting index in svalues for stuff going to
    1531:          the ith processor
    1532:   */
    1533:   PetscMalloc2(bs2*stash->n,&svalues,2*(stash->n+1),&sindices);
    1534:   PetscMalloc1(2*nsends,&send_waits);
    1535:   PetscMalloc2(size,&startv,size,&starti);
    1536:   /* use 2 sends the first with all_a, the next with all_i and all_j */
    1537:   startv[0] = 0; starti[0] = 0;
    1538:   for (i=1; i<size; i++) {
    1539:     startv[i] = startv[i-1] + nlengths[i-1];
    1540:     starti[i] = starti[i-1] + 2*nlengths[i-1];
    1541:   }

    1543:   i     = 0;
    1544:   space = stash->space_head;
    1545:   while (space) {
    1546:     space_next = space->next;
    1547:     sp_idx     = space->idx;
    1548:     sp_idy     = space->idy;
    1549:     sp_val     = space->val;
    1550:     for (l=0; l<space->local_used; l++) {
    1551:       j = owner[i];
    1552:       if (bs2 == 1) {
    1553:         svalues[startv[j]] = sp_val[l];
    1554:       } else {
    1555:         PetscInt    k;
    1556:         PetscScalar *buf1,*buf2;
    1557:         buf1 = svalues+bs2*startv[j];
    1558:         buf2 = space->val + bs2*l;
    1559:         for (k=0; k<bs2; k++) buf1[k] = buf2[k];
    1560:       }
    1561:       sindices[starti[j]]             = sp_idx[l];
    1562:       sindices[starti[j]+nlengths[j]] = sp_idy[l];
    1563:       startv[j]++;
    1564:       starti[j]++;
    1565:       i++;
    1566:     }
    1567:     space = space_next;
    1568:   }
    1569:   startv[0] = 0;
    1570:   for (i=1; i<size; i++) startv[i] = startv[i-1] + nlengths[i-1];

    1572:   for (i=0,count=0; i<size; i++) {
    1573:     if (sizes[i]) {
    1574:       MPI_Isend(sindices+2*startv[i],2*nlengths[i],MPIU_INT,i,tag1,comm,send_waits+count++);
    1575:       MPI_Isend(svalues+bs2*startv[i],bs2*nlengths[i],MPIU_SCALAR,i,tag2,comm,send_waits+count++);
    1576:     }
    1577:   }
    1578: #if defined(PETSC_USE_INFO)
    1579:   PetscInfo1(NULL,"No of messages: %d \n",nsends);
    1580:   for (i=0; i<size; i++) {
    1581:     if (sizes[i]) {
    1582:       PetscInfo2(NULL,"Mesg_to: %d: size: %d bytes\n",i,nlengths[i]*(bs2*sizeof(PetscScalar)+2*sizeof(PetscInt)));
    1583:     }
    1584:   }
    1585: #endif
    1586:   PetscFree(nlengths);
    1587:   PetscFree(owner);
    1588:   PetscFree2(startv,starti);
    1589:   PetscFree(sizes);

    1591:   /* recv_waits need to be contiguous for MatStashScatterGetMesg_Private() */
    1592:   PetscMalloc1(2*nreceives,&recv_waits);

    1594:   for (i=0; i<nreceives; i++) {
    1595:     recv_waits[2*i]   = recv_waits1[i];
    1596:     recv_waits[2*i+1] = recv_waits2[i];
    1597:   }
    1598:   stash->recv_waits = recv_waits;

    1600:   PetscFree(recv_waits1);
    1601:   PetscFree(recv_waits2);

    1603:   stash->svalues         = svalues;
    1604:   stash->sindices        = sindices;
    1605:   stash->rvalues         = rvalues;
    1606:   stash->rindices        = rindices;
    1607:   stash->send_waits      = send_waits;
    1608:   stash->nsends          = nsends;
    1609:   stash->nrecvs          = nreceives;
    1610:   stash->reproduce_count = 0;
    1611:   return(0);
    1612: }

    1614: static PetscErrorCode MatScaLAPACKSetBlockSizes_ScaLAPACK(Mat A,PetscInt mb,PetscInt nb)
    1615: {
    1617:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK*)A->data;

    1620:   if (A->preallocated) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Cannot change block sizes after MatSetUp");
    1621:   if (mb<1 && mb!=PETSC_DECIDE) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"mb %D must be at least 1",mb);
    1622:   if (nb<1 && nb!=PETSC_DECIDE) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"nb %D must be at least 1",nb);
    1623:   PetscBLASIntCast((mb==PETSC_DECIDE)?DEFAULT_BLOCKSIZE:mb,&a->mb);
    1624:   PetscBLASIntCast((nb==PETSC_DECIDE)?a->mb:nb,&a->nb);
    1625:   return(0);
    1626: }

    1628: /*@
    1629:    MatScaLAPACKSetBlockSizes - Sets the block sizes to be used for the distibution of
    1630:    the ScaLAPACK matrix

    1632:    Logically Collective on A

    1634:    Input Parameter:
    1635: +  A  - a MATSCALAPACK matrix
    1636: .  mb - the row block size
    1637: -  nb - the column block size

    1639:    Level: intermediate

    1641: .seealso: MatCreateScaLAPACK(), MatScaLAPACKGetBlockSizes()
    1642: @*/
    1643: PetscErrorCode MatScaLAPACKSetBlockSizes(Mat A,PetscInt mb,PetscInt nb)
    1644: {

    1651:   PetscTryMethod(A,"MatScaLAPACKSetBlockSizes_C",(Mat,PetscInt,PetscInt),(A,mb,nb));
    1652:   return(0);
    1653: }

    1655: static PetscErrorCode MatScaLAPACKGetBlockSizes_ScaLAPACK(Mat A,PetscInt *mb,PetscInt *nb)
    1656: {
    1657:   Mat_ScaLAPACK *a = (Mat_ScaLAPACK*)A->data;

    1660:   if (mb) *mb = a->mb;
    1661:   if (nb) *nb = a->nb;
    1662:   return(0);
    1663: }

    1665: /*@
    1666:    MatScaLAPACKGetBlockSizes - Gets the block sizes used in the distibution of
    1667:    the ScaLAPACK matrix

    1669:    Not collective

    1671:    Input Parameter:
    1672: .  A  - a MATSCALAPACK matrix

    1674:    Output Parameters:
    1675: +  mb - the row block size
    1676: -  nb - the column block size

    1678:    Level: intermediate

    1680: .seealso: MatCreateScaLAPACK(), MatScaLAPACKSetBlockSizes()
    1681: @*/
    1682: PetscErrorCode MatScaLAPACKGetBlockSizes(Mat A,PetscInt *mb,PetscInt *nb)
    1683: {

    1688:   PetscUseMethod(A,"MatScaLAPACKGetBlockSizes_C",(Mat,PetscInt*,PetscInt*),(A,mb,nb));
    1689:   return(0);
    1690: }

    1692: PETSC_INTERN PetscErrorCode MatStashScatterGetMesg_Ref(MatStash*,PetscMPIInt*,PetscInt**,PetscInt**,PetscScalar**,PetscInt*);
    1693: PETSC_INTERN PetscErrorCode MatStashScatterEnd_Ref(MatStash*);

    1695: /*MC
    1696:    MATSCALAPACK = "scalapack" - A matrix type for dense matrices using the ScaLAPACK package

    1698:    Use ./configure --download-scalapack to install PETSc to use ScaLAPACK

    1700:    Use -pc_type lu -pc_factor_mat_solver_type scalapack to use this direct solver

    1702:    Options Database Keys:
    1703: +  -mat_type scalapack - sets the matrix type to "scalapack" during a call to MatSetFromOptions()
    1704: .  -mat_scalapack_grid_height - sets Grid Height for 2D cyclic ordering of internal matrix
    1705: -  -mat_scalapack_block_sizes - size of the blocks to use (one or two integers separated by comma)

    1707:    Level: beginner

    1709: .seealso: MATDENSE, MATELEMENTAL
    1710: M*/

    1712: PETSC_EXTERN PetscErrorCode MatCreate_ScaLAPACK(Mat A)
    1713: {
    1714:   Mat_ScaLAPACK      *a;
    1715:   PetscErrorCode     ierr;
    1716:   PetscBool          flg,flg1;
    1717:   Mat_ScaLAPACK_Grid *grid;
    1718:   MPI_Comm           icomm;
    1719:   PetscBLASInt       nprow,npcol,myrow,mycol;
    1720:   PetscInt           optv1,k=2,array[2]={0,0};
    1721:   PetscMPIInt        size;

    1724:   PetscMemcpy(A->ops,&MatOps_Values,sizeof(struct _MatOps));
    1725:   A->insertmode = NOT_SET_VALUES;

    1727:   MatStashCreate_Private(PetscObjectComm((PetscObject)A),1,&A->stash);
    1728:   A->stash.ScatterBegin   = MatStashScatterBegin_ScaLAPACK;
    1729:   A->stash.ScatterGetMesg = MatStashScatterGetMesg_Ref;
    1730:   A->stash.ScatterEnd     = MatStashScatterEnd_Ref;
    1731:   A->stash.ScatterDestroy = NULL;

    1733:   PetscNewLog(A,&a);
    1734:   A->data = (void*)a;

    1736:   /* Grid needs to be shared between multiple Mats on the same communicator, implement by attribute caching on the MPI_Comm */
    1737:   if (Petsc_ScaLAPACK_keyval == MPI_KEYVAL_INVALID) {
    1738:     MPI_Comm_create_keyval(MPI_COMM_NULL_COPY_FN,MPI_COMM_NULL_DELETE_FN,&Petsc_ScaLAPACK_keyval,(void*)0);
    1739:     PetscRegisterFinalize(Petsc_ScaLAPACK_keyval_free);
    1740:   }
    1741:   PetscCommDuplicate(PetscObjectComm((PetscObject)A),&icomm,NULL);
    1742:   MPI_Comm_get_attr(icomm,Petsc_ScaLAPACK_keyval,(void**)&grid,(int*)&flg);
    1743:   if (!flg) {
    1744:     PetscNewLog(A,&grid);

    1746:     MPI_Comm_size(icomm,&size);
    1747:     grid->nprow = (PetscInt) (PetscSqrtReal((PetscReal)size) + 0.001);

    1749:     PetscOptionsBegin(PetscObjectComm((PetscObject)A),((PetscObject)A)->prefix,"ScaLAPACK Grid Options","Mat");
    1750:     PetscOptionsInt("-mat_scalapack_grid_height","Grid Height","None",grid->nprow,&optv1,&flg1);
    1751:     if (flg1) {
    1752:       if (size % optv1) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_INCOMP,"Grid Height %D must evenly divide CommSize %D",optv1,size);
    1753:       grid->nprow = optv1;
    1754:     }
    1755:     PetscOptionsEnd();

    1757:     if (size % grid->nprow) grid->nprow = 1;  /* cannot use a squarish grid, use a 1d grid */
    1758:     grid->npcol = size/grid->nprow;
    1759:     PetscBLASIntCast(grid->nprow,&nprow);
    1760:     PetscBLASIntCast(grid->npcol,&npcol);
    1761:     grid->ictxt = Csys2blacs_handle(icomm);
    1762:     Cblacs_gridinit(&grid->ictxt,"R",nprow,npcol);
    1763:     Cblacs_gridinfo(grid->ictxt,&nprow,&npcol,&myrow,&mycol);
    1764:     grid->grid_refct = 1;
    1765:     grid->nprow      = nprow;
    1766:     grid->npcol      = npcol;
    1767:     grid->myrow      = myrow;
    1768:     grid->mycol      = mycol;
    1769:     /* auxiliary 1d BLACS contexts for 1xsize and sizex1 grids */
    1770:     grid->ictxrow = Csys2blacs_handle(icomm);
    1771:     Cblacs_gridinit(&grid->ictxrow,"R",1,size);
    1772:     grid->ictxcol = Csys2blacs_handle(icomm);
    1773:     Cblacs_gridinit(&grid->ictxcol,"R",size,1);
    1774:     MPI_Comm_set_attr(icomm,Petsc_ScaLAPACK_keyval,(void*)grid);

    1776:   } else grid->grid_refct++;
    1777:   PetscCommDestroy(&icomm);
    1778:   a->grid = grid;
    1779:   a->mb   = DEFAULT_BLOCKSIZE;
    1780:   a->nb   = DEFAULT_BLOCKSIZE;

    1782:   PetscOptionsBegin(PetscObjectComm((PetscObject)A),NULL,"ScaLAPACK Options","Mat");
    1783:   PetscOptionsIntArray("-mat_scalapack_block_sizes","Size of the blocks to use (one or two comma-separated integers)","MatCreateScaLAPACK",array,&k,&flg);
    1784:   if (flg) {
    1785:     a->mb = array[0];
    1786:     a->nb = (k>1)? array[1]: a->mb;
    1787:   }
    1788:   PetscOptionsEnd();

    1790:   PetscObjectComposeFunction((PetscObject)A,"MatGetOwnershipIS_C",MatGetOwnershipIS_ScaLAPACK);
    1791:   PetscObjectComposeFunction((PetscObject)A,"MatScaLAPACKSetBlockSizes_C",MatScaLAPACKSetBlockSizes_ScaLAPACK);
    1792:   PetscObjectComposeFunction((PetscObject)A,"MatScaLAPACKGetBlockSizes_C",MatScaLAPACKGetBlockSizes_ScaLAPACK);
    1793:   PetscObjectChangeTypeName((PetscObject)A,MATSCALAPACK);
    1794:   return(0);
    1795: }

    1797: /*@C
    1798:    MatCreateScaLAPACK - Creates a dense parallel matrix in ScaLAPACK format
    1799:    (2D block cyclic distribution).

    1801:    Collective

    1803:    Input Parameters:
    1804: +  comm - MPI communicator
    1805: .  mb   - row block size (or PETSC_DECIDE to have it set)
    1806: .  nb   - column block size (or PETSC_DECIDE to have it set)
    1807: .  M    - number of global rows
    1808: .  N    - number of global columns
    1809: .  rsrc - coordinate of process that owns the first row of the distributed matrix
    1810: -  csrc - coordinate of process that owns the first column of the distributed matrix

    1812:    Output Parameter:
    1813: .  A - the matrix

    1815:    Options Database Keys:
    1816: .  -mat_scalapack_block_sizes - size of the blocks to use (one or two integers separated by comma)

    1818:    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
    1819:    MatXXXXSetPreallocation() paradigm instead of this routine directly.
    1820:    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]

    1822:    Notes:
    1823:    If PETSC_DECIDE is used for the block sizes, then an appropriate value
    1824:    is chosen.

    1826:    Storage Information:
    1827:    Storate is completely managed by ScaLAPACK, so this requires PETSc to be
    1828:    configured with ScaLAPACK. In particular, PETSc's local sizes lose
    1829:    significance and are thus ignored. The block sizes refer to the values
    1830:    used for the distributed matrix, not the same meaning as in BAIJ.

    1832:    Level: intermediate

    1834: .seealso: MatCreate(), MatCreateDense(), MatSetValues()
    1835: @*/
    1836: PetscErrorCode MatCreateScaLAPACK(MPI_Comm comm,PetscInt mb,PetscInt nb,PetscInt M,PetscInt N,PetscInt rsrc,PetscInt csrc,Mat *A)
    1837: {
    1839:   Mat_ScaLAPACK  *a;
    1840:   PetscInt       m,n;

    1843:   MatCreate(comm,A);
    1844:   MatSetType(*A,MATSCALAPACK);
    1845:   if (M==PETSC_DECIDE || N==PETSC_DECIDE) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Cannot use PETSC_DECIDE for matrix dimensions");
    1846:   /* rows and columns are NOT distributed according to PetscSplitOwnership */
    1847:   m = PETSC_DECIDE;
    1848:   PetscSplitOwnershipEqual(comm,&m,&M);
    1849:   n = PETSC_DECIDE;
    1850:   PetscSplitOwnershipEqual(comm,&n,&N);
    1851:   MatSetSizes(*A,m,n,M,N);
    1852:   a = (Mat_ScaLAPACK*)(*A)->data;
    1853:   PetscBLASIntCast(M,&a->M);
    1854:   PetscBLASIntCast(N,&a->N);
    1855:   PetscBLASIntCast((mb==PETSC_DECIDE)?DEFAULT_BLOCKSIZE:mb,&a->mb);
    1856:   PetscBLASIntCast((nb==PETSC_DECIDE)?a->mb:nb,&a->nb);
    1857:   PetscBLASIntCast(rsrc,&a->rsrc);
    1858:   PetscBLASIntCast(csrc,&a->csrc);
    1859:   MatSetUp(*A);
    1860:   return(0);
    1861: }