Date: 2026-03-31T05:46:22+00:00

Actual source code: matscalapack.c

      1: #include <petsc/private/petscscalapack.h>

      3: const char       ScaLAPACKCitation[] = "@BOOK{scalapack-user-guide,\n"
      4:                                        "       AUTHOR = {L. S. Blackford and J. Choi and A. Cleary and E. D'Azevedo and\n"
      5:                                        "                 J. Demmel and I. Dhillon and J. Dongarra and S. Hammarling and\n"
      6:                                        "                 G. Henry and A. Petitet and K. Stanley and D. Walker and R. C. Whaley},\n"
      7:                                        "       TITLE = {Sca{LAPACK} Users' Guide},\n"
      8:                                        "       PUBLISHER = {SIAM},\n"
      9:                                        "       ADDRESS = {Philadelphia, PA},\n"
     10:                                        "       YEAR = 1997\n"
     11:                                        "}\n";
     12: static PetscBool ScaLAPACKCite       = PETSC_FALSE;

     14: #define DEFAULT_BLOCKSIZE 64

     16: /*
     17:     The variable Petsc_ScaLAPACK_keyval is used to indicate an MPI attribute that
     18:   is attached to a communicator, in this case the attribute is a Mat_ScaLAPACK_Grid
     19: */
     20: static PetscMPIInt Petsc_ScaLAPACK_keyval = MPI_KEYVAL_INVALID;

     22: static PetscErrorCode Petsc_ScaLAPACK_keyval_free(void)
     23: {
     24:   PetscFunctionBegin;
     25:   PetscCall(PetscInfo(NULL, "Freeing Petsc_ScaLAPACK_keyval\n"));
     26:   PetscCallMPI(MPI_Comm_free_keyval(&Petsc_ScaLAPACK_keyval));
     27:   PetscFunctionReturn(PETSC_SUCCESS);
     28: }

     30: static PetscErrorCode MatView_ScaLAPACK(Mat A, PetscViewer viewer)
     31: {
     32:   Mat_ScaLAPACK    *a = (Mat_ScaLAPACK *)A->data;
     33:   PetscBool         isascii;
     34:   PetscViewerFormat format;
     35:   Mat               Adense;

     37:   PetscFunctionBegin;
     38:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
     39:   if (isascii) {
     40:     PetscCall(PetscViewerGetFormat(viewer, &format));
     41:     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
     42:       PetscCall(PetscViewerASCIIPrintf(viewer, "block sizes: %d,%d\n", (int)a->mb, (int)a->nb));
     43:       PetscCall(PetscViewerASCIIPrintf(viewer, "grid height=%d, grid width=%d\n", (int)a->grid->nprow, (int)a->grid->npcol));
     44:       PetscCall(PetscViewerASCIIPrintf(viewer, "coordinates of process owning first row and column: (%d,%d)\n", (int)a->rsrc, (int)a->csrc));
     45:       PetscCall(PetscViewerASCIIPrintf(viewer, "dimension of largest local matrix: %d x %d\n", (int)a->locr, (int)a->locc));
     46:       PetscFunctionReturn(PETSC_SUCCESS);
     47:     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
     48:       PetscFunctionReturn(PETSC_SUCCESS);
     49:     }
     50:   }
     51:   /* convert to dense format and call MatView() */
     52:   PetscCall(MatConvert(A, MATDENSE, MAT_INITIAL_MATRIX, &Adense));
     53:   PetscCall(MatView(Adense, viewer));
     54:   PetscCall(MatDestroy(&Adense));
     55:   PetscFunctionReturn(PETSC_SUCCESS);
     56: }

     58: static PetscErrorCode MatGetInfo_ScaLAPACK(Mat A, MatInfoType flag, MatInfo *info)
     59: {
     60:   Mat_ScaLAPACK *a = (Mat_ScaLAPACK *)A->data;
     61:   PetscLogDouble isend[2], irecv[2];

     63:   PetscFunctionBegin;
     64:   info->block_size = 1.0;

     66:   isend[0] = a->lld * a->locc;  /* locally allocated */
     67:   isend[1] = a->locr * a->locc; /* used submatrix */
     68:   if (flag == MAT_LOCAL || flag == MAT_GLOBAL_MAX) {
     69:     info->nz_allocated = isend[0];
     70:     info->nz_used      = isend[1];
     71:   } else if (flag == MAT_GLOBAL_MAX) {
     72:     PetscCallMPI(MPIU_Allreduce(isend, irecv, 2, MPIU_PETSCLOGDOUBLE, MPI_MAX, PetscObjectComm((PetscObject)A)));
     73:     info->nz_allocated = irecv[0];
     74:     info->nz_used      = irecv[1];
     75:   } else if (flag == MAT_GLOBAL_SUM) {
     76:     PetscCallMPI(MPIU_Allreduce(isend, irecv, 2, MPIU_PETSCLOGDOUBLE, MPI_SUM, PetscObjectComm((PetscObject)A)));
     77:     info->nz_allocated = irecv[0];
     78:     info->nz_used      = irecv[1];
     79:   }

     81:   info->nz_unneeded       = 0;
     82:   info->assemblies        = A->num_ass;
     83:   info->mallocs           = 0;
     84:   info->memory            = 0; /* REVIEW ME */
     85:   info->fill_ratio_given  = 0;
     86:   info->fill_ratio_needed = 0;
     87:   info->factor_mallocs    = 0;
     88:   PetscFunctionReturn(PETSC_SUCCESS);
     89: }

     91: static PetscErrorCode MatSetOption_ScaLAPACK(Mat A, MatOption op, PetscBool flg)
     92: {
     93:   Mat_ScaLAPACK *a = (Mat_ScaLAPACK *)A->data;

     95:   PetscFunctionBegin;
     96:   switch (op) {
     97:   case MAT_NEW_NONZERO_LOCATIONS:
     98:   case MAT_NEW_NONZERO_LOCATION_ERR:
     99:   case MAT_NEW_NONZERO_ALLOCATION_ERR:
    100:   case MAT_SYMMETRIC:
    101:   case MAT_SORTED_FULL:
    102:   case MAT_HERMITIAN:
    103:     break;
    104:   case MAT_ROW_ORIENTED:
    105:     a->roworiented = flg;
    106:     break;
    107:   default:
    108:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unsupported option %s", MatOptions[op]);
    109:   }
    110:   PetscFunctionReturn(PETSC_SUCCESS);
    111: }

    113: static PetscErrorCode MatSetValues_ScaLAPACK(Mat A, PetscInt nr, const PetscInt *rows, PetscInt nc, const PetscInt *cols, const PetscScalar *vals, InsertMode imode)
    114: {
    115:   Mat_ScaLAPACK *a = (Mat_ScaLAPACK *)A->data;
    116:   PetscInt       i, j;
    117:   PetscBLASInt   gridx, gcidx, lridx, lcidx, rsrc, csrc;
    118:   PetscBool      roworiented = a->roworiented;

    120:   PetscFunctionBegin;
    121:   PetscCheck(imode == INSERT_VALUES || imode == ADD_VALUES, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "No support for InsertMode %d", (int)imode);
    122:   for (i = 0; i < nr; i++) {
    123:     if (rows[i] < 0) continue;
    124:     PetscCall(PetscBLASIntCast(rows[i] + 1, &gridx));
    125:     for (j = 0; j < nc; j++) {
    126:       if (cols[j] < 0) continue;
    127:       PetscCall(PetscBLASIntCast(cols[j] + 1, &gcidx));
    128:       PetscCallBLAS("SCALAPACKinfog2l", SCALAPACKinfog2l_(&gridx, &gcidx, a->desc, &a->grid->nprow, &a->grid->npcol, &a->grid->myrow, &a->grid->mycol, &lridx, &lcidx, &rsrc, &csrc));
    129:       if (rsrc == a->grid->myrow && csrc == a->grid->mycol) {
    130:         if (roworiented) {
    131:           switch (imode) {
    132:           case INSERT_VALUES:
    133:             a->loc[lridx - 1 + (lcidx - 1) * a->lld] = vals[i * nc + j];
    134:             break;
    135:           default:
    136:             a->loc[lridx - 1 + (lcidx - 1) * a->lld] += vals[i * nc + j];
    137:             break;
    138:           }
    139:         } else {
    140:           switch (imode) {
    141:           case INSERT_VALUES:
    142:             a->loc[lridx - 1 + (lcidx - 1) * a->lld] = vals[i + j * nr];
    143:             break;
    144:           default:
    145:             a->loc[lridx - 1 + (lcidx - 1) * a->lld] += vals[i + j * nr];
    146:             break;
    147:           }
    148:         }
    149:       } else {
    150:         PetscCheck(!A->nooffprocentries, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Setting off process entry even though MatSetOption(,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) was set");
    151:         A->assembled = PETSC_FALSE;
    152:         PetscCall(MatStashValuesRow_Private(&A->stash, rows[i], 1, cols + j, roworiented ? vals + i * nc + j : vals + i + j * nr, (PetscBool)(imode == ADD_VALUES)));
    153:       }
    154:     }
    155:   }
    156:   PetscFunctionReturn(PETSC_SUCCESS);
    157: }

    159: static PetscErrorCode MatMultXXXYYY_ScaLAPACK(Mat A, PetscBool transpose, PetscBool hermitian, PetscScalar beta, const PetscScalar *x, PetscScalar *y)
    160: {
    161:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK *)A->data;
    162:   PetscScalar    *x2d, *y2d, alpha = 1.0;
    163:   const PetscInt *ranges;
    164:   PetscBLASInt    xdesc[9], ydesc[9], x2desc[9], y2desc[9], mb, nb, lszx, lszy, zero = 0, one = 1, xlld, ylld, info;

    166:   PetscFunctionBegin;
    167:   if (transpose) {
    168:     /* create ScaLAPACK descriptors for vectors (1d block distribution) */
    169:     PetscCall(PetscLayoutGetRanges(A->rmap, &ranges));
    170:     PetscCall(PetscBLASIntCast(ranges[1], &mb)); /* x block size */
    171:     PetscCall(PetscBLASIntCast(PetscMax(1, A->rmap->n), &xlld));
    172:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(xdesc, &a->M, &one, &mb, &one, &zero, &zero, &a->grid->ictxcol, &xlld, &info));
    173:     PetscCheckScaLapackInfo("descinit", info);
    174:     PetscCall(PetscLayoutGetRanges(A->cmap, &ranges));
    175:     PetscCall(PetscBLASIntCast(ranges[1], &nb)); /* y block size */
    176:     ylld = 1;
    177:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(ydesc, &one, &a->N, &one, &nb, &zero, &zero, &a->grid->ictxrow, &ylld, &info));
    178:     PetscCheckScaLapackInfo("descinit", info);

    180:     /* allocate 2d vectors */
    181:     lszx = SCALAPACKnumroc_(&a->M, &a->mb, &a->grid->myrow, &a->rsrc, &a->grid->nprow);
    182:     lszy = SCALAPACKnumroc_(&a->N, &a->nb, &a->grid->mycol, &a->csrc, &a->grid->npcol);
    183:     PetscCall(PetscMalloc2(lszx, &x2d, lszy, &y2d));
    184:     PetscCall(PetscBLASIntCast(PetscMax(1, lszx), &xlld));

    186:     /* create ScaLAPACK descriptors for vectors (2d block distribution) */
    187:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(x2desc, &a->M, &one, &a->mb, &one, &zero, &zero, &a->grid->ictxt, &xlld, &info));
    188:     PetscCheckScaLapackInfo("descinit", info);
    189:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(y2desc, &one, &a->N, &one, &a->nb, &zero, &zero, &a->grid->ictxt, &ylld, &info));
    190:     PetscCheckScaLapackInfo("descinit", info);

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

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

    198:     /* call PBLAS subroutine */
    199:     if (hermitian) PetscCallBLAS("PBLASgemv", PBLASgemv_("C", &a->M, &a->N, &alpha, a->loc, &one, &one, a->desc, x2d, &one, &one, x2desc, &one, &beta, y2d, &one, &one, y2desc, &one));
    200:     else PetscCallBLAS("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));

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

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

    207:     /* create ScaLAPACK descriptors for vectors (1d block distribution) */
    208:     PetscCall(PetscLayoutGetRanges(A->cmap, &ranges));
    209:     PetscCall(PetscBLASIntCast(ranges[1], &nb)); /* x block size */
    210:     xlld = 1;
    211:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(xdesc, &one, &a->N, &one, &nb, &zero, &zero, &a->grid->ictxrow, &xlld, &info));
    212:     PetscCheckScaLapackInfo("descinit", info);
    213:     PetscCall(PetscLayoutGetRanges(A->rmap, &ranges));
    214:     PetscCall(PetscBLASIntCast(ranges[1], &mb)); /* y block size */
    215:     PetscCall(PetscBLASIntCast(PetscMax(1, A->rmap->n), &ylld));
    216:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(ydesc, &a->M, &one, &mb, &one, &zero, &zero, &a->grid->ictxcol, &ylld, &info));
    217:     PetscCheckScaLapackInfo("descinit", info);

    219:     /* allocate 2d vectors */
    220:     lszy = SCALAPACKnumroc_(&a->M, &a->mb, &a->grid->myrow, &a->rsrc, &a->grid->nprow);
    221:     lszx = SCALAPACKnumroc_(&a->N, &a->nb, &a->grid->mycol, &a->csrc, &a->grid->npcol);
    222:     PetscCall(PetscMalloc2(lszx, &x2d, lszy, &y2d));
    223:     PetscCall(PetscBLASIntCast(PetscMax(1, lszy), &ylld));

    225:     /* create ScaLAPACK descriptors for vectors (2d block distribution) */
    226:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(x2desc, &one, &a->N, &one, &a->nb, &zero, &zero, &a->grid->ictxt, &xlld, &info));
    227:     PetscCheckScaLapackInfo("descinit", info);
    228:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(y2desc, &a->M, &one, &a->mb, &one, &zero, &zero, &a->grid->ictxt, &ylld, &info));
    229:     PetscCheckScaLapackInfo("descinit", info);

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

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

    237:     /* call PBLAS subroutine */
    238:     PetscCallBLAS("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));

    240:     /* redistribute y from a column of a 2d matrix */
    241:     PetscCallBLAS("SCALAPACKgemr2d", SCALAPACKgemr2d_(&a->M, &one, y2d, &one, &one, y2desc, y, &one, &one, ydesc, &a->grid->ictxcol));
    242:   }
    243:   PetscCall(PetscFree2(x2d, y2d));
    244:   PetscFunctionReturn(PETSC_SUCCESS);
    245: }

    247: static PetscErrorCode MatMult_ScaLAPACK(Mat A, Vec x, Vec y)
    248: {
    249:   const PetscScalar *xarray;
    250:   PetscScalar       *yarray;

    252:   PetscFunctionBegin;
    253:   PetscCall(VecGetArrayRead(x, &xarray));
    254:   PetscCall(VecGetArray(y, &yarray));
    255:   PetscCall(MatMultXXXYYY_ScaLAPACK(A, PETSC_FALSE, PETSC_FALSE, 0.0, xarray, yarray));
    256:   PetscCall(VecRestoreArrayRead(x, &xarray));
    257:   PetscCall(VecRestoreArray(y, &yarray));
    258:   PetscFunctionReturn(PETSC_SUCCESS);
    259: }

    261: static PetscErrorCode MatMultTranspose_ScaLAPACK(Mat A, Vec x, Vec y)
    262: {
    263:   const PetscScalar *xarray;
    264:   PetscScalar       *yarray;

    266:   PetscFunctionBegin;
    267:   PetscCall(VecGetArrayRead(x, &xarray));
    268:   PetscCall(VecGetArray(y, &yarray));
    269:   PetscCall(MatMultXXXYYY_ScaLAPACK(A, PETSC_TRUE, PETSC_FALSE, 0.0, xarray, yarray));
    270:   PetscCall(VecRestoreArrayRead(x, &xarray));
    271:   PetscCall(VecRestoreArray(y, &yarray));
    272:   PetscFunctionReturn(PETSC_SUCCESS);
    273: }

    275: static PetscErrorCode MatMultHermitianTranspose_ScaLAPACK(Mat A, Vec x, Vec y)
    276: {
    277:   const PetscScalar *xarray;
    278:   PetscScalar       *yarray;

    280:   PetscFunctionBegin;
    281:   PetscCall(VecGetArrayRead(x, &xarray));
    282:   PetscCall(VecGetArrayWrite(y, &yarray));
    283:   PetscCall(MatMultXXXYYY_ScaLAPACK(A, PETSC_TRUE, PETSC_TRUE, 0.0, xarray, yarray));
    284:   PetscCall(VecRestoreArrayRead(x, &xarray));
    285:   PetscCall(VecRestoreArrayWrite(y, &yarray));
    286:   PetscFunctionReturn(PETSC_SUCCESS);
    287: }

    289: static PetscErrorCode MatMultAdd_ScaLAPACK(Mat A, Vec x, Vec y, Vec z)
    290: {
    291:   const PetscScalar *xarray;
    292:   PetscScalar       *zarray;

    294:   PetscFunctionBegin;
    295:   if (y != z) PetscCall(VecCopy(y, z));
    296:   PetscCall(VecGetArrayRead(x, &xarray));
    297:   PetscCall(VecGetArray(z, &zarray));
    298:   PetscCall(MatMultXXXYYY_ScaLAPACK(A, PETSC_FALSE, PETSC_FALSE, 1.0, xarray, zarray));
    299:   PetscCall(VecRestoreArrayRead(x, &xarray));
    300:   PetscCall(VecRestoreArray(z, &zarray));
    301:   PetscFunctionReturn(PETSC_SUCCESS);
    302: }

    304: static PetscErrorCode MatMultTransposeAdd_ScaLAPACK(Mat A, Vec x, Vec y, Vec z)
    305: {
    306:   const PetscScalar *xarray;
    307:   PetscScalar       *zarray;

    309:   PetscFunctionBegin;
    310:   if (y != z) PetscCall(VecCopy(y, z));
    311:   PetscCall(VecGetArrayRead(x, &xarray));
    312:   PetscCall(VecGetArray(z, &zarray));
    313:   PetscCall(MatMultXXXYYY_ScaLAPACK(A, PETSC_TRUE, PETSC_FALSE, 1.0, xarray, zarray));
    314:   PetscCall(VecRestoreArrayRead(x, &xarray));
    315:   PetscCall(VecRestoreArray(z, &zarray));
    316:   PetscFunctionReturn(PETSC_SUCCESS);
    317: }

    319: static PetscErrorCode MatMultHermitianTransposeAdd_ScaLAPACK(Mat A, Vec x, Vec y, Vec z)
    320: {
    321:   const PetscScalar *xarray;
    322:   PetscScalar       *zarray;

    324:   PetscFunctionBegin;
    325:   if (y != z) PetscCall(VecCopy(y, z));
    326:   PetscCall(VecGetArrayRead(x, &xarray));
    327:   PetscCall(VecGetArray(z, &zarray));
    328:   PetscCall(MatMultXXXYYY_ScaLAPACK(A, PETSC_TRUE, PETSC_TRUE, 1.0, xarray, zarray));
    329:   PetscCall(VecRestoreArrayRead(x, &xarray));
    330:   PetscCall(VecRestoreArray(z, &zarray));
    331:   PetscFunctionReturn(PETSC_SUCCESS);
    332: }

    334: PetscErrorCode MatMatMultNumeric_ScaLAPACK(Mat A, Mat B, Mat C)
    335: {
    336:   Mat_ScaLAPACK *a    = (Mat_ScaLAPACK *)A->data;
    337:   Mat_ScaLAPACK *b    = (Mat_ScaLAPACK *)B->data;
    338:   Mat_ScaLAPACK *c    = (Mat_ScaLAPACK *)C->data;
    339:   PetscScalar    sone = 1.0, zero = 0.0;
    340:   PetscBLASInt   one = 1;

    342:   PetscFunctionBegin;
    343:   PetscCallBLAS("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));
    344:   C->assembled = PETSC_TRUE;
    345:   PetscFunctionReturn(PETSC_SUCCESS);
    346: }

    348: PetscErrorCode MatMatMultSymbolic_ScaLAPACK(Mat A, Mat B, PetscReal fill, Mat C)
    349: {
    350:   PetscFunctionBegin;
    351:   PetscCall(MatSetSizes(C, A->rmap->n, B->cmap->n, PETSC_DECIDE, PETSC_DECIDE));
    352:   PetscCall(MatSetType(C, MATSCALAPACK));
    353:   PetscCall(MatSetUp(C));
    354:   C->ops->matmultnumeric = MatMatMultNumeric_ScaLAPACK;
    355:   PetscFunctionReturn(PETSC_SUCCESS);
    356: }

    358: static PetscErrorCode MatTransposeMatMultNumeric_ScaLAPACK(Mat A, Mat B, Mat C)
    359: {
    360:   Mat_ScaLAPACK *a    = (Mat_ScaLAPACK *)A->data;
    361:   Mat_ScaLAPACK *b    = (Mat_ScaLAPACK *)B->data;
    362:   Mat_ScaLAPACK *c    = (Mat_ScaLAPACK *)C->data;
    363:   PetscScalar    sone = 1.0, zero = 0.0;
    364:   PetscBLASInt   one = 1;

    366:   PetscFunctionBegin;
    367:   PetscCallBLAS("PBLASgemm", PBLASgemm_("T", "N", &a->N, &b->N, &a->M, &sone, a->loc, &one, &one, a->desc, b->loc, &one, &one, b->desc, &zero, c->loc, &one, &one, c->desc));
    368:   C->assembled = PETSC_TRUE;
    369:   PetscFunctionReturn(PETSC_SUCCESS);
    370: }

    372: static PetscErrorCode MatTransposeMatMultSymbolic_ScaLAPACK(Mat A, Mat B, PetscReal fill, Mat C)
    373: {
    374:   PetscFunctionBegin;
    375:   PetscCall(MatSetSizes(C, A->cmap->n, B->cmap->n, PETSC_DECIDE, PETSC_DECIDE));
    376:   PetscCall(MatSetType(C, MATSCALAPACK));
    377:   PetscCall(MatSetUp(C));
    378:   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_ScaLAPACK;
    379:   PetscFunctionReturn(PETSC_SUCCESS);
    380: }

    382: static PetscErrorCode MatMatTransposeMultNumeric_ScaLAPACK(Mat A, Mat B, Mat C)
    383: {
    384:   Mat_ScaLAPACK *a    = (Mat_ScaLAPACK *)A->data;
    385:   Mat_ScaLAPACK *b    = (Mat_ScaLAPACK *)B->data;
    386:   Mat_ScaLAPACK *c    = (Mat_ScaLAPACK *)C->data;
    387:   PetscScalar    sone = 1.0, zero = 0.0;
    388:   PetscBLASInt   one = 1;

    390:   PetscFunctionBegin;
    391:   PetscCallBLAS("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));
    392:   C->assembled = PETSC_TRUE;
    393:   PetscFunctionReturn(PETSC_SUCCESS);
    394: }

    396: static PetscErrorCode MatMatTransposeMultSymbolic_ScaLAPACK(Mat A, Mat B, PetscReal fill, Mat C)
    397: {
    398:   PetscFunctionBegin;
    399:   PetscCall(MatSetSizes(C, A->rmap->n, B->rmap->n, PETSC_DECIDE, PETSC_DECIDE));
    400:   PetscCall(MatSetType(C, MATSCALAPACK));
    401:   PetscCall(MatSetUp(C));
    402:   C->ops->mattransposemultnumeric = MatMatTransposeMultNumeric_ScaLAPACK;
    403:   PetscFunctionReturn(PETSC_SUCCESS);
    404: }

    406: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_ScaLAPACK(Mat C)
    407: {
    408:   Mat_Product *product = C->product;

    410:   PetscFunctionBegin;
    411:   switch (product->type) {
    412:   case MATPRODUCT_AB:
    413:     C->ops->matmultsymbolic = MatMatMultSymbolic_ScaLAPACK;
    414:     C->ops->productsymbolic = MatProductSymbolic_AB;
    415:     break;
    416:   case MATPRODUCT_AtB:
    417:     C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_ScaLAPACK;
    418:     C->ops->productsymbolic          = MatProductSymbolic_AtB;
    419:     break;
    420:   case MATPRODUCT_ABt:
    421:     C->ops->mattransposemultsymbolic = MatMatTransposeMultSymbolic_ScaLAPACK;
    422:     C->ops->productsymbolic          = MatProductSymbolic_ABt;
    423:     break;
    424:   default:
    425:     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_SUP, "MatProduct type %s is not supported for ScaLAPACK and ScaLAPACK matrices", MatProductTypes[product->type]);
    426:   }
    427:   PetscFunctionReturn(PETSC_SUCCESS);
    428: }

    430: static PetscErrorCode MatGetDiagonal_ScaLAPACK(Mat A, Vec D)
    431: {
    432:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK *)A->data;
    433:   PetscScalar    *darray, *d2d, v;
    434:   const PetscInt *ranges;
    435:   PetscBLASInt    j, ddesc[9], d2desc[9], mb, nb, lszd, zero = 0, one = 1, dlld, info;

    437:   PetscFunctionBegin;
    438:   PetscCall(VecGetArray(D, &darray));

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

    442:     /* create ScaLAPACK descriptor for vector (1d block distribution) */
    443:     PetscCall(PetscLayoutGetRanges(A->rmap, &ranges));
    444:     PetscCall(PetscBLASIntCast(ranges[1], &mb)); /* D block size */
    445:     PetscCall(PetscBLASIntCast(PetscMax(1, A->rmap->n), &dlld));
    446:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(ddesc, &a->M, &one, &mb, &one, &zero, &zero, &a->grid->ictxcol, &dlld, &info));
    447:     PetscCheckScaLapackInfo("descinit", info);

    449:     /* allocate 2d vector */
    450:     lszd = SCALAPACKnumroc_(&a->M, &a->mb, &a->grid->myrow, &a->rsrc, &a->grid->nprow);
    451:     PetscCall(PetscCalloc1(lszd, &d2d));
    452:     PetscCall(PetscBLASIntCast(PetscMax(1, lszd), &dlld));

    454:     /* create ScaLAPACK descriptor for vector (2d block distribution) */
    455:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(d2desc, &a->M, &one, &a->mb, &one, &zero, &zero, &a->grid->ictxt, &dlld, &info));
    456:     PetscCheckScaLapackInfo("descinit", info);

    458:     /* collect diagonal */
    459:     for (j = 1; j <= a->M; j++) {
    460:       PetscCallBLAS("SCALAPACKelget", SCALAPACKelget_("R", " ", &v, a->loc, &j, &j, a->desc));
    461:       PetscCallBLAS("SCALAPACKelset", SCALAPACKelset_(d2d, &j, &one, d2desc, &v));
    462:     }

    464:     /* redistribute d from a column of a 2d matrix */
    465:     PetscCallBLAS("SCALAPACKgemr2d", SCALAPACKgemr2d_(&a->M, &one, d2d, &one, &one, d2desc, darray, &one, &one, ddesc, &a->grid->ictxcol));
    466:     PetscCall(PetscFree(d2d));

    468:   } else { /* column version */

    470:     /* create ScaLAPACK descriptor for vector (1d block distribution) */
    471:     PetscCall(PetscLayoutGetRanges(A->cmap, &ranges));
    472:     PetscCall(PetscBLASIntCast(ranges[1], &nb)); /* D block size */
    473:     dlld = 1;
    474:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(ddesc, &one, &a->N, &one, &nb, &zero, &zero, &a->grid->ictxrow, &dlld, &info));
    475:     PetscCheckScaLapackInfo("descinit", info);

    477:     /* allocate 2d vector */
    478:     lszd = SCALAPACKnumroc_(&a->N, &a->nb, &a->grid->mycol, &a->csrc, &a->grid->npcol);
    479:     PetscCall(PetscCalloc1(lszd, &d2d));

    481:     /* create ScaLAPACK descriptor for vector (2d block distribution) */
    482:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(d2desc, &one, &a->N, &one, &a->nb, &zero, &zero, &a->grid->ictxt, &dlld, &info));
    483:     PetscCheckScaLapackInfo("descinit", info);

    485:     /* collect diagonal */
    486:     for (j = 1; j <= a->N; j++) {
    487:       PetscCallBLAS("SCALAPACKelget", SCALAPACKelget_("C", " ", &v, a->loc, &j, &j, a->desc));
    488:       PetscCallBLAS("SCALAPACKelset", SCALAPACKelset_(d2d, &one, &j, d2desc, &v));
    489:     }

    491:     /* redistribute d from a row of a 2d matrix */
    492:     PetscCallBLAS("SCALAPACKgemr2d", SCALAPACKgemr2d_(&one, &a->N, d2d, &one, &one, d2desc, darray, &one, &one, ddesc, &a->grid->ictxrow));
    493:     PetscCall(PetscFree(d2d));
    494:   }

    496:   PetscCall(VecRestoreArray(D, &darray));
    497:   PetscCall(VecAssemblyBegin(D));
    498:   PetscCall(VecAssemblyEnd(D));
    499:   PetscFunctionReturn(PETSC_SUCCESS);
    500: }

    502: static PetscErrorCode MatDiagonalScale_ScaLAPACK(Mat A, Vec L, Vec R)
    503: {
    504:   Mat_ScaLAPACK     *a = (Mat_ScaLAPACK *)A->data;
    505:   const PetscScalar *d;
    506:   const PetscInt    *ranges;
    507:   PetscScalar       *d2d;
    508:   PetscBLASInt       i, j, ddesc[9], d2desc[9], mb, nb, lszd, zero = 0, one = 1, dlld, info;

    510:   PetscFunctionBegin;
    511:   if (R) {
    512:     PetscCall(VecGetArrayRead(R, &d));
    513:     /* create ScaLAPACK descriptor for vector (1d block distribution) */
    514:     PetscCall(PetscLayoutGetRanges(A->cmap, &ranges));
    515:     PetscCall(PetscBLASIntCast(ranges[1], &nb)); /* D block size */
    516:     dlld = 1;
    517:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(ddesc, &one, &a->N, &one, &nb, &zero, &zero, &a->grid->ictxrow, &dlld, &info));
    518:     PetscCheckScaLapackInfo("descinit", info);

    520:     /* allocate 2d vector */
    521:     lszd = SCALAPACKnumroc_(&a->N, &a->nb, &a->grid->mycol, &a->csrc, &a->grid->npcol);
    522:     PetscCall(PetscCalloc1(lszd, &d2d));

    524:     /* create ScaLAPACK descriptor for vector (2d block distribution) */
    525:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(d2desc, &one, &a->N, &one, &a->nb, &zero, &zero, &a->grid->ictxt, &dlld, &info));
    526:     PetscCheckScaLapackInfo("descinit", info);

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

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

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

    539:     PetscCall(PetscFree(d2d));
    540:     PetscCall(VecRestoreArrayRead(R, &d));
    541:   }
    542:   if (L) {
    543:     PetscCall(VecGetArrayRead(L, &d));
    544:     /* create ScaLAPACK descriptor for vector (1d block distribution) */
    545:     PetscCall(PetscLayoutGetRanges(A->rmap, &ranges));
    546:     PetscCall(PetscBLASIntCast(ranges[1], &mb)); /* D block size */
    547:     PetscCall(PetscBLASIntCast(PetscMax(1, A->rmap->n), &dlld));
    548:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(ddesc, &a->M, &one, &mb, &one, &zero, &zero, &a->grid->ictxcol, &dlld, &info));
    549:     PetscCheckScaLapackInfo("descinit", info);

    551:     /* allocate 2d vector */
    552:     lszd = SCALAPACKnumroc_(&a->M, &a->mb, &a->grid->myrow, &a->rsrc, &a->grid->nprow);
    553:     PetscCall(PetscCalloc1(lszd, &d2d));
    554:     PetscCall(PetscBLASIntCast(PetscMax(1, lszd), &dlld));

    556:     /* create ScaLAPACK descriptor for vector (2d block distribution) */
    557:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(d2desc, &a->M, &one, &a->mb, &one, &zero, &zero, &a->grid->ictxt, &dlld, &info));
    558:     PetscCheckScaLapackInfo("descinit", info);

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

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

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

    571:     PetscCall(PetscFree(d2d));
    572:     PetscCall(VecRestoreArrayRead(L, &d));
    573:   }
    574:   PetscFunctionReturn(PETSC_SUCCESS);
    575: }

    577: static PetscErrorCode MatScale_ScaLAPACK(Mat X, PetscScalar a)
    578: {
    579:   Mat_ScaLAPACK *x = (Mat_ScaLAPACK *)X->data;
    580:   PetscBLASInt   n, one = 1;

    582:   PetscFunctionBegin;
    583:   n = x->lld * x->locc;
    584:   PetscCallBLAS("BLASscal", BLASscal_(&n, &a, x->loc, &one));
    585:   PetscFunctionReturn(PETSC_SUCCESS);
    586: }

    588: static PetscErrorCode MatShift_ScaLAPACK(Mat X, PetscScalar alpha)
    589: {
    590:   Mat_ScaLAPACK *x = (Mat_ScaLAPACK *)X->data;
    591:   PetscBLASInt   i, n;
    592:   PetscScalar    v;

    594:   PetscFunctionBegin;
    595:   n = PetscMin(x->M, x->N);
    596:   for (i = 1; i <= n; i++) {
    597:     PetscCallBLAS("SCALAPACKelget", SCALAPACKelget_("-", " ", &v, x->loc, &i, &i, x->desc));
    598:     v += alpha;
    599:     PetscCallBLAS("SCALAPACKelset", SCALAPACKelset_(x->loc, &i, &i, x->desc, &v));
    600:   }
    601:   PetscFunctionReturn(PETSC_SUCCESS);
    602: }

    604: static PetscErrorCode MatAXPY_ScaLAPACK(Mat Y, PetscScalar alpha, Mat X, MatStructure str)
    605: {
    606:   Mat_ScaLAPACK *x    = (Mat_ScaLAPACK *)X->data;
    607:   Mat_ScaLAPACK *y    = (Mat_ScaLAPACK *)Y->data;
    608:   PetscBLASInt   one  = 1;
    609:   PetscScalar    beta = 1.0;

    611:   PetscFunctionBegin;
    612:   MatScaLAPACKCheckDistribution(Y, 1, X, 3);
    613:   PetscCallBLAS("SCALAPACKmatadd", SCALAPACKmatadd_(&x->M, &x->N, &alpha, x->loc, &one, &one, x->desc, &beta, y->loc, &one, &one, y->desc));
    614:   PetscCall(PetscObjectStateIncrease((PetscObject)Y));
    615:   PetscFunctionReturn(PETSC_SUCCESS);
    616: }

    618: static PetscErrorCode MatCopy_ScaLAPACK(Mat A, Mat B, MatStructure str)
    619: {
    620:   Mat_ScaLAPACK *a = (Mat_ScaLAPACK *)A->data;
    621:   Mat_ScaLAPACK *b = (Mat_ScaLAPACK *)B->data;

    623:   PetscFunctionBegin;
    624:   PetscCall(PetscArraycpy(b->loc, a->loc, a->lld * a->locc));
    625:   PetscCall(PetscObjectStateIncrease((PetscObject)B));
    626:   PetscFunctionReturn(PETSC_SUCCESS);
    627: }

    629: static PetscErrorCode MatDuplicate_ScaLAPACK(Mat A, MatDuplicateOption op, Mat *B)
    630: {
    631:   Mat            Bs;
    632:   MPI_Comm       comm;
    633:   Mat_ScaLAPACK *a = (Mat_ScaLAPACK *)A->data, *b;

    635:   PetscFunctionBegin;
    636:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
    637:   PetscCall(MatCreate(comm, &Bs));
    638:   PetscCall(MatSetSizes(Bs, A->rmap->n, A->cmap->n, PETSC_DECIDE, PETSC_DECIDE));
    639:   PetscCall(MatSetType(Bs, MATSCALAPACK));
    640:   b       = (Mat_ScaLAPACK *)Bs->data;
    641:   b->M    = a->M;
    642:   b->N    = a->N;
    643:   b->mb   = a->mb;
    644:   b->nb   = a->nb;
    645:   b->rsrc = a->rsrc;
    646:   b->csrc = a->csrc;
    647:   PetscCall(MatSetUp(Bs));
    648:   *B = Bs;
    649:   if (op == MAT_COPY_VALUES) PetscCall(PetscArraycpy(b->loc, a->loc, a->lld * a->locc));
    650:   Bs->assembled = PETSC_TRUE;
    651:   PetscFunctionReturn(PETSC_SUCCESS);
    652: }

    654: static PetscErrorCode MatTranspose_ScaLAPACK(Mat A, MatReuse reuse, Mat *B)
    655: {
    656:   Mat_ScaLAPACK *a    = (Mat_ScaLAPACK *)A->data, *b;
    657:   Mat            Bs   = *B;
    658:   PetscBLASInt   one  = 1;
    659:   PetscScalar    sone = 1.0, zero = 0.0;
    660: #if defined(PETSC_USE_COMPLEX)
    661:   PetscInt i, j;
    662: #endif

    664:   PetscFunctionBegin;
    665:   if (reuse == MAT_REUSE_MATRIX) PetscCall(MatTransposeCheckNonzeroState_Private(A, *B));
    666:   PetscCheck(reuse == MAT_INITIAL_MATRIX, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Only MAT_INITIAL_MATRIX supported");
    667:   PetscCall(MatCreateScaLAPACK(PetscObjectComm((PetscObject)A), a->nb, a->mb, a->N, a->M, a->csrc, a->rsrc, &Bs));
    668:   *B = Bs;
    669:   b  = (Mat_ScaLAPACK *)Bs->data;
    670:   PetscCallBLAS("PBLAStran", PBLAStran_(&a->N, &a->M, &sone, a->loc, &one, &one, a->desc, &zero, b->loc, &one, &one, b->desc));
    671: #if defined(PETSC_USE_COMPLEX)
    672:   /* undo conjugation */
    673:   for (i = 0; i < b->locr; i++)
    674:     for (j = 0; j < b->locc; j++) b->loc[i + j * b->lld] = PetscConj(b->loc[i + j * b->lld]);
    675: #endif
    676:   Bs->assembled = PETSC_TRUE;
    677:   PetscFunctionReturn(PETSC_SUCCESS);
    678: }

    680: static PetscErrorCode MatConjugate_ScaLAPACK(Mat A)
    681: {
    682:   Mat_ScaLAPACK *a = (Mat_ScaLAPACK *)A->data;
    683:   PetscInt       i, j;

    685:   PetscFunctionBegin;
    686:   for (i = 0; i < a->locr; i++)
    687:     for (j = 0; j < a->locc; j++) a->loc[i + j * a->lld] = PetscConj(a->loc[i + j * a->lld]);
    688:   PetscFunctionReturn(PETSC_SUCCESS);
    689: }

    691: static PetscErrorCode MatHermitianTranspose_ScaLAPACK(Mat A, MatReuse reuse, Mat *B)
    692: {
    693:   Mat_ScaLAPACK *a    = (Mat_ScaLAPACK *)A->data, *b;
    694:   Mat            Bs   = *B;
    695:   PetscBLASInt   one  = 1;
    696:   PetscScalar    sone = 1.0, zero = 0.0;

    698:   PetscFunctionBegin;
    699:   PetscCheck(reuse == MAT_INITIAL_MATRIX, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Only MAT_INITIAL_MATRIX supported");
    700:   PetscCall(MatCreateScaLAPACK(PetscObjectComm((PetscObject)A), a->nb, a->mb, a->N, a->M, a->csrc, a->rsrc, &Bs));
    701:   *B = Bs;
    702:   b  = (Mat_ScaLAPACK *)Bs->data;
    703:   PetscCallBLAS("PBLAStran", PBLAStran_(&a->N, &a->M, &sone, a->loc, &one, &one, a->desc, &zero, b->loc, &one, &one, b->desc));
    704:   Bs->assembled = PETSC_TRUE;
    705:   PetscFunctionReturn(PETSC_SUCCESS);
    706: }

    708: static PetscErrorCode MatSolve_ScaLAPACK(Mat A, Vec B, Vec X)
    709: {
    710:   Mat_ScaLAPACK  *a = (Mat_ScaLAPACK *)A->data;
    711:   PetscScalar    *x, *x2d;
    712:   const PetscInt *ranges;
    713:   PetscBLASInt    xdesc[9], x2desc[9], mb, lszx, zero = 0, one = 1, xlld, nrhs = 1, info;

    715:   PetscFunctionBegin;
    716:   PetscCall(VecCopy(B, X));
    717:   PetscCall(VecGetArray(X, &x));

    719:   /* create ScaLAPACK descriptor for a vector (1d block distribution) */
    720:   PetscCall(PetscLayoutGetRanges(A->rmap, &ranges));
    721:   PetscCall(PetscBLASIntCast(ranges[1], &mb)); /* x block size */
    722:   PetscCall(PetscBLASIntCast(PetscMax(1, A->rmap->n), &xlld));
    723:   PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(xdesc, &a->M, &one, &mb, &one, &zero, &zero, &a->grid->ictxcol, &xlld, &info));
    724:   PetscCheckScaLapackInfo("descinit", info);

    726:   /* allocate 2d vector */
    727:   lszx = SCALAPACKnumroc_(&a->M, &a->mb, &a->grid->myrow, &a->rsrc, &a->grid->nprow);
    728:   PetscCall(PetscMalloc1(lszx, &x2d));
    729:   PetscCall(PetscBLASIntCast(PetscMax(1, lszx), &xlld));

    731:   /* create ScaLAPACK descriptor for a vector (2d block distribution) */
    732:   PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(x2desc, &a->M, &one, &a->mb, &one, &zero, &zero, &a->grid->ictxt, &xlld, &info));
    733:   PetscCheckScaLapackInfo("descinit", info);

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

    738:   /* call ScaLAPACK subroutine */
    739:   switch (A->factortype) {
    740:   case MAT_FACTOR_LU:
    741:     PetscCallBLAS("SCALAPACKgetrs", SCALAPACKgetrs_("N", &a->M, &nrhs, a->loc, &one, &one, a->desc, a->pivots, x2d, &one, &one, x2desc, &info));
    742:     PetscCheckScaLapackInfo("getrs", info);
    743:     break;
    744:   case MAT_FACTOR_CHOLESKY:
    745:     PetscCallBLAS("SCALAPACKpotrs", SCALAPACKpotrs_("L", &a->M, &nrhs, a->loc, &one, &one, a->desc, x2d, &one, &one, x2desc, &info));
    746:     PetscCheckScaLapackInfo("potrs", info);
    747:     break;
    748:   default:
    749:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unfactored Matrix or Unsupported MatFactorType");
    750:   }

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

    755:   PetscCall(PetscFree(x2d));
    756:   PetscCall(VecRestoreArray(X, &x));
    757:   PetscFunctionReturn(PETSC_SUCCESS);
    758: }

    760: static PetscErrorCode MatSolveAdd_ScaLAPACK(Mat A, Vec B, Vec Y, Vec X)
    761: {
    762:   PetscFunctionBegin;
    763:   PetscCall(MatSolve_ScaLAPACK(A, B, X));
    764:   PetscCall(VecAXPY(X, 1, Y));
    765:   PetscFunctionReturn(PETSC_SUCCESS);
    766: }

    768: static PetscErrorCode MatMatSolve_ScaLAPACK(Mat A, Mat B, Mat X)
    769: {
    770:   Mat_ScaLAPACK *a = (Mat_ScaLAPACK *)A->data, *x;
    771:   PetscBool      flg1, flg2;
    772:   PetscBLASInt   one = 1, info;
    773:   Mat            C;
    774:   MatType        type;

    776:   PetscFunctionBegin;
    777:   PetscCall(PetscObjectTypeCompare((PetscObject)B, MATSCALAPACK, &flg1));
    778:   PetscCall(PetscObjectTypeCompare((PetscObject)X, MATSCALAPACK, &flg2));
    779:   if (flg1 && flg2) MatScaLAPACKCheckDistribution(B, 2, X, 3);
    780:   if (flg2) {
    781:     if (flg1) PetscCall(MatCopy(B, X, SAME_NONZERO_PATTERN));
    782:     else PetscCall(MatConvert(B, MATSCALAPACK, MAT_REUSE_MATRIX, &X));
    783:     C = X;
    784:   } else {
    785:     PetscCall(MatConvert(B, MATSCALAPACK, MAT_INITIAL_MATRIX, &C));
    786:   }
    787:   x = (Mat_ScaLAPACK *)C->data;

    789:   switch (A->factortype) {
    790:   case MAT_FACTOR_LU:
    791:     PetscCallBLAS("SCALAPACKgetrs", SCALAPACKgetrs_("N", &a->M, &x->N, a->loc, &one, &one, a->desc, a->pivots, x->loc, &one, &one, x->desc, &info));
    792:     PetscCheckScaLapackInfo("getrs", info);
    793:     break;
    794:   case MAT_FACTOR_CHOLESKY:
    795:     PetscCallBLAS("SCALAPACKpotrs", SCALAPACKpotrs_("L", &a->M, &x->N, a->loc, &one, &one, a->desc, x->loc, &one, &one, x->desc, &info));
    796:     PetscCheckScaLapackInfo("potrs", info);
    797:     break;
    798:   default:
    799:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unfactored Matrix or Unsupported MatFactorType");
    800:   }
    801:   if (!flg2) {
    802:     PetscCall(MatGetType(X, &type));
    803:     PetscCall(MatConvert(C, type, MAT_REUSE_MATRIX, &X));
    804:     PetscCall(MatDestroy(&C));
    805:   }
    806:   PetscFunctionReturn(PETSC_SUCCESS);
    807: }

    809: static PetscErrorCode MatLUFactor_ScaLAPACK(Mat A, IS row, IS col, const MatFactorInfo *factorinfo)
    810: {
    811:   Mat_ScaLAPACK *a   = (Mat_ScaLAPACK *)A->data;
    812:   PetscBLASInt   one = 1, info;

    814:   PetscFunctionBegin;
    815:   if (!a->pivots) PetscCall(PetscMalloc1(a->locr + a->mb, &a->pivots));
    816:   PetscCallBLAS("SCALAPACKgetrf", SCALAPACKgetrf_(&a->M, &a->N, a->loc, &one, &one, a->desc, a->pivots, &info));
    817:   PetscCheckScaLapackInfo("getrf", info);
    818:   A->factortype = MAT_FACTOR_LU;
    819:   A->assembled  = PETSC_TRUE;

    821:   PetscCall(PetscFree(A->solvertype));
    822:   PetscCall(PetscStrallocpy(MATSOLVERSCALAPACK, &A->solvertype));
    823:   PetscFunctionReturn(PETSC_SUCCESS);
    824: }

    826: static PetscErrorCode MatLUFactorNumeric_ScaLAPACK(Mat F, Mat A, const MatFactorInfo *info)
    827: {
    828:   PetscFunctionBegin;
    829:   PetscCall(MatCopy(A, F, SAME_NONZERO_PATTERN));
    830:   PetscCall(MatLUFactor_ScaLAPACK(F, 0, 0, info));
    831:   PetscFunctionReturn(PETSC_SUCCESS);
    832: }

    834: static PetscErrorCode MatLUFactorSymbolic_ScaLAPACK(Mat F, Mat A, IS r, IS c, const MatFactorInfo *info)
    835: {
    836:   PetscFunctionBegin;
    837:   /* F is created and allocated by MatGetFactor_scalapack_petsc(), skip this routine. */
    838:   PetscFunctionReturn(PETSC_SUCCESS);
    839: }

    841: static PetscErrorCode MatCholeskyFactor_ScaLAPACK(Mat A, IS perm, const MatFactorInfo *factorinfo)
    842: {
    843:   Mat_ScaLAPACK *a   = (Mat_ScaLAPACK *)A->data;
    844:   PetscBLASInt   one = 1, info;

    846:   PetscFunctionBegin;
    847:   PetscCallBLAS("SCALAPACKpotrf", SCALAPACKpotrf_("L", &a->M, a->loc, &one, &one, a->desc, &info));
    848:   PetscCheckScaLapackInfo("potrf", info);
    849:   A->factortype = MAT_FACTOR_CHOLESKY;
    850:   A->assembled  = PETSC_TRUE;

    852:   PetscCall(PetscFree(A->solvertype));
    853:   PetscCall(PetscStrallocpy(MATSOLVERSCALAPACK, &A->solvertype));
    854:   PetscFunctionReturn(PETSC_SUCCESS);
    855: }

    857: static PetscErrorCode MatCholeskyFactorNumeric_ScaLAPACK(Mat F, Mat A, const MatFactorInfo *info)
    858: {
    859:   PetscFunctionBegin;
    860:   PetscCall(MatCopy(A, F, SAME_NONZERO_PATTERN));
    861:   PetscCall(MatCholeskyFactor_ScaLAPACK(F, 0, info));
    862:   PetscFunctionReturn(PETSC_SUCCESS);
    863: }

    865: static PetscErrorCode MatCholeskyFactorSymbolic_ScaLAPACK(Mat F, Mat A, IS perm, const MatFactorInfo *info)
    866: {
    867:   PetscFunctionBegin;
    868:   /* F is created and allocated by MatGetFactor_scalapack_petsc(), skip this routine. */
    869:   PetscFunctionReturn(PETSC_SUCCESS);
    870: }

    872: static PetscErrorCode MatFactorGetSolverType_scalapack_scalapack(Mat A, MatSolverType *type)
    873: {
    874:   PetscFunctionBegin;
    875:   *type = MATSOLVERSCALAPACK;
    876:   PetscFunctionReturn(PETSC_SUCCESS);
    877: }

    879: static PetscErrorCode MatGetFactor_scalapack_scalapack(Mat A, MatFactorType ftype, Mat *F)
    880: {
    881:   Mat            B;
    882:   Mat_ScaLAPACK *a = (Mat_ScaLAPACK *)A->data;

    884:   PetscFunctionBegin;
    885:   /* Create the factorization matrix */
    886:   PetscCall(MatCreateScaLAPACK(PetscObjectComm((PetscObject)A), a->mb, a->nb, a->M, a->N, a->rsrc, a->csrc, &B));
    887:   B->trivialsymbolic = PETSC_TRUE;
    888:   B->factortype      = ftype;
    889:   PetscCall(PetscFree(B->solvertype));
    890:   PetscCall(PetscStrallocpy(MATSOLVERSCALAPACK, &B->solvertype));

    892:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_scalapack_scalapack));
    893:   *F = B;
    894:   PetscFunctionReturn(PETSC_SUCCESS);
    895: }

    897: PETSC_INTERN PetscErrorCode MatSolverTypeRegister_ScaLAPACK(void)
    898: {
    899:   PetscFunctionBegin;
    900:   PetscCall(MatSolverTypeRegister(MATSOLVERSCALAPACK, MATSCALAPACK, MAT_FACTOR_LU, MatGetFactor_scalapack_scalapack));
    901:   PetscCall(MatSolverTypeRegister(MATSOLVERSCALAPACK, MATSCALAPACK, MAT_FACTOR_CHOLESKY, MatGetFactor_scalapack_scalapack));
    902:   PetscFunctionReturn(PETSC_SUCCESS);
    903: }

    905: static PetscErrorCode MatNorm_ScaLAPACK(Mat A, NormType type, PetscReal *nrm)
    906: {
    907:   Mat_ScaLAPACK *a   = (Mat_ScaLAPACK *)A->data;
    908:   PetscBLASInt   one = 1, lwork = 0;
    909:   const char    *ntype;
    910:   PetscScalar   *work = NULL, dummy;

    912:   PetscFunctionBegin;
    913:   switch (type) {
    914:   case NORM_1:
    915:     ntype = "1";
    916:     lwork = PetscMax(a->locr, a->locc);
    917:     break;
    918:   case NORM_FROBENIUS:
    919:     ntype = "F";
    920:     work  = &dummy;
    921:     break;
    922:   case NORM_INFINITY:
    923:     ntype = "I";
    924:     lwork = PetscMax(a->locr, a->locc);
    925:     break;
    926:   default:
    927:     SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Unsupported norm type");
    928:   }
    929:   if (lwork) PetscCall(PetscMalloc1(lwork, &work));
    930:   *nrm = SCALAPACKlange_(ntype, &a->M, &a->N, a->loc, &one, &one, a->desc, work);
    931:   if (lwork) PetscCall(PetscFree(work));
    932:   PetscFunctionReturn(PETSC_SUCCESS);
    933: }

    935: static PetscErrorCode MatZeroEntries_ScaLAPACK(Mat A)
    936: {
    937:   Mat_ScaLAPACK *a = (Mat_ScaLAPACK *)A->data;

    939:   PetscFunctionBegin;
    940:   PetscCall(PetscArrayzero(a->loc, a->lld * a->locc));
    941:   PetscFunctionReturn(PETSC_SUCCESS);
    942: }

    944: static PetscErrorCode MatGetOwnershipIS_ScaLAPACK(Mat A, IS *rows, IS *cols)
    945: {
    946:   Mat_ScaLAPACK *a = (Mat_ScaLAPACK *)A->data;
    947:   PetscInt       i, n, nb, isrc, nproc, iproc, *idx;

    949:   PetscFunctionBegin;
    950:   if (rows) {
    951:     n     = a->locr;
    952:     nb    = a->mb;
    953:     isrc  = a->rsrc;
    954:     nproc = a->grid->nprow;
    955:     iproc = a->grid->myrow;
    956:     PetscCall(PetscMalloc1(n, &idx));
    957:     for (i = 0; i < n; i++) idx[i] = nproc * nb * (i / nb) + i % nb + ((nproc + iproc - isrc) % nproc) * nb;
    958:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, n, idx, PETSC_OWN_POINTER, rows));
    959:   }
    960:   if (cols) {
    961:     n     = a->locc;
    962:     nb    = a->nb;
    963:     isrc  = a->csrc;
    964:     nproc = a->grid->npcol;
    965:     iproc = a->grid->mycol;
    966:     PetscCall(PetscMalloc1(n, &idx));
    967:     for (i = 0; i < n; i++) idx[i] = nproc * nb * (i / nb) + i % nb + ((nproc + iproc - isrc) % nproc) * nb;
    968:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, n, idx, PETSC_OWN_POINTER, cols));
    969:   }
    970:   PetscFunctionReturn(PETSC_SUCCESS);
    971: }

    973: static PetscErrorCode MatConvert_ScaLAPACK_Dense(Mat A, MatType newtype, MatReuse reuse, Mat *B)
    974: {
    975:   Mat_ScaLAPACK     *a = (Mat_ScaLAPACK *)A->data;
    976:   Mat                Bmpi;
    977:   MPI_Comm           comm;
    978:   PetscInt           i, M = A->rmap->N, N = A->cmap->N, m, n, rstart, rend, nz, ldb;
    979:   const PetscInt    *ranges, *branges, *cwork;
    980:   const PetscScalar *vwork;
    981:   PetscBLASInt       bdesc[9], bmb, zero = 0, one = 1, lld, info;
    982:   PetscScalar       *barray;
    983:   PetscBool          differ = PETSC_FALSE;
    984:   PetscMPIInt        size;

    986:   PetscFunctionBegin;
    987:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
    988:   PetscCall(PetscLayoutGetRanges(A->rmap, &ranges));

    990:   if (reuse == MAT_REUSE_MATRIX) { /* check if local sizes differ in A and B */
    991:     PetscCallMPI(MPI_Comm_size(comm, &size));
    992:     PetscCall(PetscLayoutGetRanges((*B)->rmap, &branges));
    993:     for (i = 0; i < size; i++)
    994:       if (ranges[i + 1] != branges[i + 1]) {
    995:         differ = PETSC_TRUE;
    996:         break;
    997:       }
    998:   }

    1000:   if (reuse == MAT_REUSE_MATRIX && differ) { /* special case, use auxiliary dense matrix */
    1001:     PetscCall(MatCreate(comm, &Bmpi));
    1002:     m = PETSC_DECIDE;
    1003:     PetscCall(PetscSplitOwnershipEqual(comm, &m, &M));
    1004:     n = PETSC_DECIDE;
    1005:     PetscCall(PetscSplitOwnershipEqual(comm, &n, &N));
    1006:     PetscCall(MatSetSizes(Bmpi, m, n, M, N));
    1007:     PetscCall(MatSetType(Bmpi, MATDENSE));
    1008:     PetscCall(MatSetUp(Bmpi));

    1010:     /* create ScaLAPACK descriptor for B (1d block distribution) */
    1011:     PetscCall(PetscBLASIntCast(ranges[1], &bmb)); /* row block size */
    1012:     PetscCall(MatDenseGetLDA(Bmpi, &ldb));
    1013:     PetscCall(PetscBLASIntCast(PetscMax(ldb, 1), &lld)); /* local leading dimension */
    1014:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(bdesc, &a->M, &a->N, &bmb, &a->N, &zero, &zero, &a->grid->ictxcol, &lld, &info));
    1015:     PetscCheckScaLapackInfo("descinit", info);

    1017:     /* redistribute matrix */
    1018:     PetscCall(MatDenseGetArray(Bmpi, &barray));
    1019:     PetscCallBLAS("SCALAPACKgemr2d", SCALAPACKgemr2d_(&a->M, &a->N, a->loc, &one, &one, a->desc, barray, &one, &one, bdesc, &a->grid->ictxcol));
    1020:     PetscCall(MatDenseRestoreArray(Bmpi, &barray));
    1021:     PetscCall(MatAssemblyBegin(Bmpi, MAT_FINAL_ASSEMBLY));
    1022:     PetscCall(MatAssemblyEnd(Bmpi, MAT_FINAL_ASSEMBLY));

    1024:     /* transfer rows of auxiliary matrix to the final matrix B */
    1025:     PetscCall(MatGetOwnershipRange(Bmpi, &rstart, &rend));
    1026:     for (i = rstart; i < rend; i++) {
    1027:       PetscCall(MatGetRow(Bmpi, i, &nz, &cwork, &vwork));
    1028:       PetscCall(MatSetValues(*B, 1, &i, nz, cwork, vwork, INSERT_VALUES));
    1029:       PetscCall(MatRestoreRow(Bmpi, i, &nz, &cwork, &vwork));
    1030:     }
    1031:     PetscCall(MatAssemblyBegin(*B, MAT_FINAL_ASSEMBLY));
    1032:     PetscCall(MatAssemblyEnd(*B, MAT_FINAL_ASSEMBLY));
    1033:     PetscCall(MatDestroy(&Bmpi));

    1035:   } else { /* normal cases */

    1037:     if (reuse == MAT_REUSE_MATRIX) Bmpi = *B;
    1038:     else {
    1039:       PetscCall(MatCreate(comm, &Bmpi));
    1040:       m = PETSC_DECIDE;
    1041:       PetscCall(PetscSplitOwnershipEqual(comm, &m, &M));
    1042:       n = PETSC_DECIDE;
    1043:       PetscCall(PetscSplitOwnershipEqual(comm, &n, &N));
    1044:       PetscCall(MatSetSizes(Bmpi, m, n, M, N));
    1045:       PetscCall(MatSetType(Bmpi, MATDENSE));
    1046:       PetscCall(MatSetUp(Bmpi));
    1047:     }

    1049:     /* create ScaLAPACK descriptor for B (1d block distribution) */
    1050:     PetscCall(PetscBLASIntCast(ranges[1], &bmb)); /* row block size */
    1051:     PetscCall(MatDenseGetLDA(Bmpi, &ldb));
    1052:     PetscCall(PetscBLASIntCast(PetscMax(ldb, 1), &lld)); /* local leading dimension */
    1053:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(bdesc, &a->M, &a->N, &bmb, &a->N, &zero, &zero, &a->grid->ictxcol, &lld, &info));
    1054:     PetscCheckScaLapackInfo("descinit", info);

    1056:     /* redistribute matrix */
    1057:     PetscCall(MatDenseGetArray(Bmpi, &barray));
    1058:     PetscCallBLAS("SCALAPACKgemr2d", SCALAPACKgemr2d_(&a->M, &a->N, a->loc, &one, &one, a->desc, barray, &one, &one, bdesc, &a->grid->ictxcol));
    1059:     PetscCall(MatDenseRestoreArray(Bmpi, &barray));

    1061:     PetscCall(MatAssemblyBegin(Bmpi, MAT_FINAL_ASSEMBLY));
    1062:     PetscCall(MatAssemblyEnd(Bmpi, MAT_FINAL_ASSEMBLY));
    1063:     if (reuse == MAT_INPLACE_MATRIX) PetscCall(MatHeaderReplace(A, &Bmpi));
    1064:     else *B = Bmpi;
    1065:   }
    1066:   PetscFunctionReturn(PETSC_SUCCESS);
    1067: }

    1069: static inline PetscErrorCode MatScaLAPACKCheckLayout(PetscLayout map, PetscBool *correct)
    1070: {
    1071:   const PetscInt *ranges;
    1072:   PetscMPIInt     size;
    1073:   PetscInt        i, n;

    1075:   PetscFunctionBegin;
    1076:   *correct = PETSC_TRUE;
    1077:   PetscCallMPI(MPI_Comm_size(map->comm, &size));
    1078:   if (size > 1) {
    1079:     PetscCall(PetscLayoutGetRanges(map, &ranges));
    1080:     n = ranges[1] - ranges[0];
    1081:     for (i = 1; i < size; i++)
    1082:       if (ranges[i + 1] - ranges[i] != n) break;
    1083:     *correct = (PetscBool)(i == size || (i == size - 1 && ranges[i + 1] - ranges[i] <= n));
    1084:   }
    1085:   PetscFunctionReturn(PETSC_SUCCESS);
    1086: }

    1088: PETSC_INTERN PetscErrorCode MatConvert_Dense_ScaLAPACK(Mat A, MatType newtype, MatReuse reuse, Mat *B)
    1089: {
    1090:   Mat_ScaLAPACK     *b;
    1091:   Mat                Bmpi;
    1092:   MPI_Comm           comm;
    1093:   PetscInt           M = A->rmap->N, N = A->cmap->N, m, n;
    1094:   const PetscInt    *ranges, *rows, *cols;
    1095:   PetscBLASInt       adesc[9], amb, zero = 0, one = 1, lld, info;
    1096:   const PetscScalar *aarray;
    1097:   IS                 ir, ic;
    1098:   PetscInt           lda;
    1099:   PetscBool          flg;

    1101:   PetscFunctionBegin;
    1102:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));

    1104:   if (reuse == MAT_REUSE_MATRIX) Bmpi = *B;
    1105:   else {
    1106:     PetscCall(MatCreate(comm, &Bmpi));
    1107:     m = PETSC_DECIDE;
    1108:     PetscCall(PetscSplitOwnershipEqual(comm, &m, &M));
    1109:     n = PETSC_DECIDE;
    1110:     PetscCall(PetscSplitOwnershipEqual(comm, &n, &N));
    1111:     PetscCall(MatSetSizes(Bmpi, m, n, M, N));
    1112:     PetscCall(MatSetType(Bmpi, MATSCALAPACK));
    1113:     PetscCall(MatSetUp(Bmpi));
    1114:   }
    1115:   b = (Mat_ScaLAPACK *)Bmpi->data;

    1117:   PetscCall(MatDenseGetLDA(A, &lda));
    1118:   PetscCall(MatDenseGetArrayRead(A, &aarray));
    1119:   PetscCall(MatScaLAPACKCheckLayout(A->rmap, &flg));
    1120:   if (flg) PetscCall(MatScaLAPACKCheckLayout(A->cmap, &flg));
    1121:   if (flg) { /* if the input Mat has a ScaLAPACK-compatible layout, use ScaLAPACK for the redistribution */
    1122:     /* create ScaLAPACK descriptor for A (1d block distribution) */
    1123:     PetscCall(PetscLayoutGetRanges(A->rmap, &ranges));
    1124:     PetscCall(PetscBLASIntCast(ranges[1], &amb));        /* row block size */
    1125:     PetscCall(PetscBLASIntCast(PetscMax(lda, 1), &lld)); /* local leading dimension */
    1126:     PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(adesc, &b->M, &b->N, &amb, &b->N, &zero, &zero, &b->grid->ictxcol, &lld, &info));
    1127:     PetscCheckScaLapackInfo("descinit", info);

    1129:     /* redistribute matrix */
    1130:     PetscCallBLAS("SCALAPACKgemr2d", SCALAPACKgemr2d_(&b->M, &b->N, aarray, &one, &one, adesc, b->loc, &one, &one, b->desc, &b->grid->ictxcol));
    1131:     Bmpi->nooffprocentries = PETSC_TRUE;
    1132:   } else { /* if the input Mat has a ScaLAPACK-incompatible layout, redistribute via MatSetValues() */
    1133:     PetscCheck(lda == A->rmap->n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Leading dimension (%" PetscInt_FMT ") different than local number of rows (%" PetscInt_FMT ")", lda, A->rmap->n);
    1134:     b->roworiented = PETSC_FALSE;
    1135:     PetscCall(MatGetOwnershipIS(A, &ir, &ic));
    1136:     PetscCall(ISGetIndices(ir, &rows));
    1137:     PetscCall(ISGetIndices(ic, &cols));
    1138:     PetscCall(MatSetValues(Bmpi, A->rmap->n, rows, A->cmap->N, cols, aarray, INSERT_VALUES));
    1139:     PetscCall(ISRestoreIndices(ir, &rows));
    1140:     PetscCall(ISRestoreIndices(ic, &cols));
    1141:     PetscCall(ISDestroy(&ic));
    1142:     PetscCall(ISDestroy(&ir));
    1143:   }
    1144:   PetscCall(MatDenseRestoreArrayRead(A, &aarray));
    1145:   PetscCall(MatAssemblyBegin(Bmpi, MAT_FINAL_ASSEMBLY));
    1146:   PetscCall(MatAssemblyEnd(Bmpi, MAT_FINAL_ASSEMBLY));
    1147:   if (reuse == MAT_INPLACE_MATRIX) PetscCall(MatHeaderReplace(A, &Bmpi));
    1148:   else *B = Bmpi;
    1149:   PetscFunctionReturn(PETSC_SUCCESS);
    1150: }

    1152: PETSC_INTERN PetscErrorCode MatConvert_AIJ_ScaLAPACK(Mat A, MatType newtype, MatReuse reuse, Mat *newmat)
    1153: {
    1154:   Mat                mat_scal;
    1155:   PetscInt           M = A->rmap->N, N = A->cmap->N, rstart = A->rmap->rstart, rend = A->rmap->rend, m, n, row, ncols;
    1156:   const PetscInt    *cols;
    1157:   const PetscScalar *vals;

    1159:   PetscFunctionBegin;
    1160:   if (reuse == MAT_REUSE_MATRIX) {
    1161:     mat_scal = *newmat;
    1162:     PetscCall(MatZeroEntries(mat_scal));
    1163:   } else {
    1164:     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &mat_scal));
    1165:     m = PETSC_DECIDE;
    1166:     PetscCall(PetscSplitOwnershipEqual(PetscObjectComm((PetscObject)A), &m, &M));
    1167:     n = PETSC_DECIDE;
    1168:     PetscCall(PetscSplitOwnershipEqual(PetscObjectComm((PetscObject)A), &n, &N));
    1169:     PetscCall(MatSetSizes(mat_scal, m, n, M, N));
    1170:     PetscCall(MatSetType(mat_scal, MATSCALAPACK));
    1171:     PetscCall(MatSetUp(mat_scal));
    1172:   }
    1173:   for (row = rstart; row < rend; row++) {
    1174:     PetscCall(MatGetRow(A, row, &ncols, &cols, &vals));
    1175:     PetscCall(MatSetValues(mat_scal, 1, &row, ncols, cols, vals, INSERT_VALUES));
    1176:     PetscCall(MatRestoreRow(A, row, &ncols, &cols, &vals));
    1177:   }
    1178:   PetscCall(MatAssemblyBegin(mat_scal, MAT_FINAL_ASSEMBLY));
    1179:   PetscCall(MatAssemblyEnd(mat_scal, MAT_FINAL_ASSEMBLY));

    1181:   if (reuse == MAT_INPLACE_MATRIX) PetscCall(MatHeaderReplace(A, &mat_scal));
    1182:   else *newmat = mat_scal;
    1183:   PetscFunctionReturn(PETSC_SUCCESS);
    1184: }

    1186: PETSC_INTERN PetscErrorCode MatConvert_SBAIJ_ScaLAPACK(Mat A, MatType newtype, MatReuse reuse, Mat *newmat)
    1187: {
    1188:   Mat                mat_scal;
    1189:   PetscInt           M = A->rmap->N, N = A->cmap->N, m, n, row, ncols, j, rstart = A->rmap->rstart, rend = A->rmap->rend;
    1190:   const PetscInt    *cols;
    1191:   const PetscScalar *vals;
    1192:   PetscScalar        v;

    1194:   PetscFunctionBegin;
    1195:   if (reuse == MAT_REUSE_MATRIX) {
    1196:     mat_scal = *newmat;
    1197:     PetscCall(MatZeroEntries(mat_scal));
    1198:   } else {
    1199:     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &mat_scal));
    1200:     m = PETSC_DECIDE;
    1201:     PetscCall(PetscSplitOwnershipEqual(PetscObjectComm((PetscObject)A), &m, &M));
    1202:     n = PETSC_DECIDE;
    1203:     PetscCall(PetscSplitOwnershipEqual(PetscObjectComm((PetscObject)A), &n, &N));
    1204:     PetscCall(MatSetSizes(mat_scal, m, n, M, N));
    1205:     PetscCall(MatSetType(mat_scal, MATSCALAPACK));
    1206:     PetscCall(MatSetUp(mat_scal));
    1207:   }
    1208:   PetscCall(MatGetRowUpperTriangular(A));
    1209:   for (row = rstart; row < rend; row++) {
    1210:     PetscCall(MatGetRow(A, row, &ncols, &cols, &vals));
    1211:     PetscCall(MatSetValues(mat_scal, 1, &row, ncols, cols, vals, ADD_VALUES));
    1212:     for (j = 0; j < ncols; j++) { /* lower triangular part */
    1213:       if (cols[j] == row) continue;
    1214:       v = A->hermitian == PETSC_BOOL3_TRUE ? PetscConj(vals[j]) : vals[j];
    1215:       PetscCall(MatSetValues(mat_scal, 1, &cols[j], 1, &row, &v, ADD_VALUES));
    1216:     }
    1217:     PetscCall(MatRestoreRow(A, row, &ncols, &cols, &vals));
    1218:   }
    1219:   PetscCall(MatRestoreRowUpperTriangular(A));
    1220:   PetscCall(MatAssemblyBegin(mat_scal, MAT_FINAL_ASSEMBLY));
    1221:   PetscCall(MatAssemblyEnd(mat_scal, MAT_FINAL_ASSEMBLY));

    1223:   if (reuse == MAT_INPLACE_MATRIX) PetscCall(MatHeaderReplace(A, &mat_scal));
    1224:   else *newmat = mat_scal;
    1225:   PetscFunctionReturn(PETSC_SUCCESS);
    1226: }

    1228: static PetscErrorCode MatScaLAPACKSetPreallocation(Mat A)
    1229: {
    1230:   Mat_ScaLAPACK *a  = (Mat_ScaLAPACK *)A->data;
    1231:   PetscInt       sz = 0;

    1233:   PetscFunctionBegin;
    1234:   PetscCall(PetscLayoutSetUp(A->rmap));
    1235:   PetscCall(PetscLayoutSetUp(A->cmap));
    1236:   if (!a->lld) a->lld = a->locr;

    1238:   PetscCall(PetscFree(a->loc));
    1239:   PetscCall(PetscIntMultError(a->lld, a->locc, &sz));
    1240:   PetscCall(PetscCalloc1(sz, &a->loc));

    1242:   A->preallocated = PETSC_TRUE;
    1243:   PetscFunctionReturn(PETSC_SUCCESS);
    1244: }

    1246: static PetscErrorCode MatDestroy_ScaLAPACK(Mat A)
    1247: {
    1248:   Mat_ScaLAPACK      *a = (Mat_ScaLAPACK *)A->data;
    1249:   Mat_ScaLAPACK_Grid *grid;
    1250:   PetscMPIInt         iflg;
    1251:   MPI_Comm            icomm;

    1253:   PetscFunctionBegin;
    1254:   PetscCall(MatStashDestroy_Private(&A->stash));
    1255:   PetscCall(PetscFree(a->loc));
    1256:   PetscCall(PetscFree(a->pivots));
    1257:   PetscCall(PetscCommDuplicate(PetscObjectComm((PetscObject)A), &icomm, NULL));
    1258:   PetscCallMPI(MPI_Comm_get_attr(icomm, Petsc_ScaLAPACK_keyval, (void **)&grid, &iflg));
    1259:   if (--grid->grid_refct == 0) {
    1260:     Cblacs_gridexit(grid->ictxt);
    1261:     Cblacs_gridexit(grid->ictxrow);
    1262:     Cblacs_gridexit(grid->ictxcol);
    1263:     PetscCall(PetscFree(grid));
    1264:     PetscCallMPI(MPI_Comm_delete_attr(icomm, Petsc_ScaLAPACK_keyval));
    1265:   }
    1266:   PetscCall(PetscCommDestroy(&icomm));
    1267:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatGetOwnershipIS_C", NULL));
    1268:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatFactorGetSolverType_C", NULL));
    1269:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatScaLAPACKSetBlockSizes_C", NULL));
    1270:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatScaLAPACKGetBlockSizes_C", NULL));
    1271:   PetscCall(PetscFree(A->data));
    1272:   PetscFunctionReturn(PETSC_SUCCESS);
    1273: }

    1275: static PetscErrorCode MatSetUp_ScaLAPACK(Mat A)
    1276: {
    1277:   Mat_ScaLAPACK *a    = (Mat_ScaLAPACK *)A->data;
    1278:   PetscBLASInt   info = 0;
    1279:   PetscBool      flg;

    1281:   PetscFunctionBegin;
    1282:   PetscCall(PetscLayoutSetUp(A->rmap));
    1283:   PetscCall(PetscLayoutSetUp(A->cmap));

    1285:   /* check that the layout is as enforced by MatCreateScaLAPACK() */
    1286:   PetscCall(MatScaLAPACKCheckLayout(A->rmap, &flg));
    1287:   PetscCheck(flg, A->rmap->comm, PETSC_ERR_SUP, "MATSCALAPACK must have equal local row sizes in all processes (except possibly the last one), consider using MatCreateScaLAPACK");
    1288:   PetscCall(MatScaLAPACKCheckLayout(A->cmap, &flg));
    1289:   PetscCheck(flg, A->cmap->comm, PETSC_ERR_SUP, "MATSCALAPACK must have equal local column sizes in all processes (except possibly the last one), consider using MatCreateScaLAPACK");

    1291:   /* compute local sizes */
    1292:   PetscCall(PetscBLASIntCast(A->rmap->N, &a->M));
    1293:   PetscCall(PetscBLASIntCast(A->cmap->N, &a->N));
    1294:   a->locr = SCALAPACKnumroc_(&a->M, &a->mb, &a->grid->myrow, &a->rsrc, &a->grid->nprow);
    1295:   a->locc = SCALAPACKnumroc_(&a->N, &a->nb, &a->grid->mycol, &a->csrc, &a->grid->npcol);
    1296:   a->lld  = PetscMax(1, a->locr);

    1298:   /* allocate local array */
    1299:   PetscCall(MatScaLAPACKSetPreallocation(A));

    1301:   /* set up ScaLAPACK descriptor */
    1302:   PetscCallBLAS("SCALAPACKdescinit", SCALAPACKdescinit_(a->desc, &a->M, &a->N, &a->mb, &a->nb, &a->rsrc, &a->csrc, &a->grid->ictxt, &a->lld, &info));
    1303:   PetscCheckScaLapackInfo("descinit", info);
    1304:   PetscFunctionReturn(PETSC_SUCCESS);
    1305: }

    1307: static PetscErrorCode MatAssemblyBegin_ScaLAPACK(Mat A, MatAssemblyType type)
    1308: {
    1309:   PetscInt nstash, reallocs;

    1311:   PetscFunctionBegin;
    1312:   if (A->nooffprocentries) PetscFunctionReturn(PETSC_SUCCESS);
    1313:   PetscCall(MatStashScatterBegin_Private(A, &A->stash, NULL));
    1314:   PetscCall(MatStashGetInfo_Private(&A->stash, &nstash, &reallocs));
    1315:   PetscCall(PetscInfo(A, "Stash has %" PetscInt_FMT " entries, uses %" PetscInt_FMT " mallocs.\n", nstash, reallocs));
    1316:   PetscFunctionReturn(PETSC_SUCCESS);
    1317: }

    1319: static PetscErrorCode MatAssemblyEnd_ScaLAPACK(Mat A, MatAssemblyType type)
    1320: {
    1321:   Mat_ScaLAPACK *a = (Mat_ScaLAPACK *)A->data;
    1322:   PetscMPIInt    n;
    1323:   PetscInt       i, flg, *row, *col;
    1324:   PetscScalar   *val;
    1325:   PetscBLASInt   gridx, gcidx, lridx, lcidx, rsrc, csrc;

    1327:   PetscFunctionBegin;
    1328:   if (A->nooffprocentries) PetscFunctionReturn(PETSC_SUCCESS);
    1329:   while (1) {
    1330:     PetscCall(MatStashScatterGetMesg_Private(&A->stash, &n, &row, &col, &val, &flg));
    1331:     if (!flg) break;
    1332:     for (i = 0; i < n; i++) {
    1333:       PetscCall(PetscBLASIntCast(row[i] + 1, &gridx));
    1334:       PetscCall(PetscBLASIntCast(col[i] + 1, &gcidx));
    1335:       PetscCallBLAS("SCALAPACKinfog2l", SCALAPACKinfog2l_(&gridx, &gcidx, a->desc, &a->grid->nprow, &a->grid->npcol, &a->grid->myrow, &a->grid->mycol, &lridx, &lcidx, &rsrc, &csrc));
    1336:       PetscCheck(rsrc == a->grid->myrow && csrc == a->grid->mycol, PetscObjectComm((PetscObject)A), PETSC_ERR_LIB, "Something went wrong, received value does not belong to this process");
    1337:       switch (A->insertmode) {
    1338:       case INSERT_VALUES:
    1339:         a->loc[lridx - 1 + (lcidx - 1) * a->lld] = val[i];
    1340:         break;
    1341:       case ADD_VALUES:
    1342:         a->loc[lridx - 1 + (lcidx - 1) * a->lld] += val[i];
    1343:         break;
    1344:       default:
    1345:         SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "No support for InsertMode %d", (int)A->insertmode);
    1346:       }
    1347:     }
    1348:   }
    1349:   PetscCall(MatStashScatterEnd_Private(&A->stash));
    1350:   PetscFunctionReturn(PETSC_SUCCESS);
    1351: }

    1353: static PetscErrorCode MatLoad_ScaLAPACK(Mat newMat, PetscViewer viewer)
    1354: {
    1355:   Mat      Adense, As;
    1356:   MPI_Comm comm;

    1358:   PetscFunctionBegin;
    1359:   PetscCall(PetscObjectGetComm((PetscObject)newMat, &comm));
    1360:   PetscCall(MatCreate(comm, &Adense));
    1361:   PetscCall(MatSetType(Adense, MATDENSE));
    1362:   PetscCall(MatLoad(Adense, viewer));
    1363:   PetscCall(MatConvert(Adense, MATSCALAPACK, MAT_INITIAL_MATRIX, &As));
    1364:   PetscCall(MatDestroy(&Adense));
    1365:   PetscCall(MatHeaderReplace(newMat, &As));
    1366:   PetscFunctionReturn(PETSC_SUCCESS);
    1367: }

    1369: static struct _MatOps MatOps_Values = {MatSetValues_ScaLAPACK,
    1370:                                        NULL,
    1371:                                        NULL,
    1372:                                        MatMult_ScaLAPACK,
    1373:                                        /* 4*/ MatMultAdd_ScaLAPACK,
    1374:                                        MatMultTranspose_ScaLAPACK,
    1375:                                        MatMultTransposeAdd_ScaLAPACK,
    1376:                                        MatSolve_ScaLAPACK,
    1377:                                        MatSolveAdd_ScaLAPACK,
    1378:                                        NULL,
    1379:                                        /*10*/ NULL,
    1380:                                        MatLUFactor_ScaLAPACK,
    1381:                                        MatCholeskyFactor_ScaLAPACK,
    1382:                                        NULL,
    1383:                                        MatTranspose_ScaLAPACK,
    1384:                                        /*15*/ MatGetInfo_ScaLAPACK,
    1385:                                        NULL,
    1386:                                        MatGetDiagonal_ScaLAPACK,
    1387:                                        MatDiagonalScale_ScaLAPACK,
    1388:                                        MatNorm_ScaLAPACK,
    1389:                                        /*20*/ MatAssemblyBegin_ScaLAPACK,
    1390:                                        MatAssemblyEnd_ScaLAPACK,
    1391:                                        MatSetOption_ScaLAPACK,
    1392:                                        MatZeroEntries_ScaLAPACK,
    1393:                                        /*24*/ NULL,
    1394:                                        MatLUFactorSymbolic_ScaLAPACK,
    1395:                                        MatLUFactorNumeric_ScaLAPACK,
    1396:                                        MatCholeskyFactorSymbolic_ScaLAPACK,
    1397:                                        MatCholeskyFactorNumeric_ScaLAPACK,
    1398:                                        /*29*/ MatSetUp_ScaLAPACK,
    1399:                                        NULL,
    1400:                                        NULL,
    1401:                                        NULL,
    1402:                                        NULL,
    1403:                                        /*34*/ MatDuplicate_ScaLAPACK,
    1404:                                        NULL,
    1405:                                        NULL,
    1406:                                        NULL,
    1407:                                        NULL,
    1408:                                        /*39*/ MatAXPY_ScaLAPACK,
    1409:                                        NULL,
    1410:                                        NULL,
    1411:                                        NULL,
    1412:                                        MatCopy_ScaLAPACK,
    1413:                                        /*44*/ NULL,
    1414:                                        MatScale_ScaLAPACK,
    1415:                                        MatShift_ScaLAPACK,
    1416:                                        NULL,
    1417:                                        NULL,
    1418:                                        /*49*/ NULL,
    1419:                                        NULL,
    1420:                                        NULL,
    1421:                                        NULL,
    1422:                                        NULL,
    1423:                                        /*54*/ NULL,
    1424:                                        NULL,
    1425:                                        NULL,
    1426:                                        NULL,
    1427:                                        NULL,
    1428:                                        /*59*/ NULL,
    1429:                                        MatDestroy_ScaLAPACK,
    1430:                                        MatView_ScaLAPACK,
    1431:                                        NULL,
    1432:                                        NULL,
    1433:                                        /*64*/ NULL,
    1434:                                        NULL,
    1435:                                        NULL,
    1436:                                        NULL,
    1437:                                        NULL,
    1438:                                        /*69*/ NULL,
    1439:                                        MatConvert_ScaLAPACK_Dense,
    1440:                                        NULL,
    1441:                                        NULL,
    1442:                                        NULL,
    1443:                                        /*74*/ NULL,
    1444:                                        NULL,
    1445:                                        NULL,
    1446:                                        NULL,
    1447:                                        MatLoad_ScaLAPACK,
    1448:                                        /*79*/ NULL,
    1449:                                        NULL,
    1450:                                        NULL,
    1451:                                        NULL,
    1452:                                        NULL,
    1453:                                        /*84*/ NULL,
    1454:                                        MatMatMultNumeric_ScaLAPACK,
    1455:                                        NULL,
    1456:                                        NULL,
    1457:                                        MatMatTransposeMultNumeric_ScaLAPACK,
    1458:                                        /*89*/ NULL,
    1459:                                        MatProductSetFromOptions_ScaLAPACK,
    1460:                                        NULL,
    1461:                                        NULL,
    1462:                                        MatConjugate_ScaLAPACK,
    1463:                                        /*94*/ NULL,
    1464:                                        NULL,
    1465:                                        NULL,
    1466:                                        NULL,
    1467:                                        NULL,
    1468:                                        /*99*/ NULL,
    1469:                                        MatMatSolve_ScaLAPACK,
    1470:                                        NULL,
    1471:                                        NULL,
    1472:                                        NULL,
    1473:                                        /*104*/ NULL,
    1474:                                        NULL,
    1475:                                        NULL,
    1476:                                        NULL,
    1477:                                        NULL,
    1478:                                        /*109*/ NULL,
    1479:                                        MatHermitianTranspose_ScaLAPACK,
    1480:                                        MatMultHermitianTranspose_ScaLAPACK,
    1481:                                        MatMultHermitianTransposeAdd_ScaLAPACK,
    1482:                                        NULL,
    1483:                                        /*114*/ NULL,
    1484:                                        NULL,
    1485:                                        NULL,
    1486:                                        NULL,
    1487:                                        NULL,
    1488:                                        /*119*/ NULL,
    1489:                                        NULL,
    1490:                                        MatTransposeMatMultNumeric_ScaLAPACK,
    1491:                                        NULL,
    1492:                                        /*124*/ NULL,
    1493:                                        NULL,
    1494:                                        NULL,
    1495:                                        NULL,
    1496:                                        NULL,
    1497:                                        /*129*/ NULL,
    1498:                                        NULL,
    1499:                                        NULL,
    1500:                                        NULL,
    1501:                                        NULL,
    1502:                                        /*134*/ NULL,
    1503:                                        NULL,
    1504:                                        NULL,
    1505:                                        NULL,
    1506:                                        NULL,
    1507:                                        NULL,
    1508:                                        /*140*/ NULL,
    1509:                                        NULL,
    1510:                                        NULL,
    1511:                                        NULL,
    1512:                                        NULL,
    1513:                                        /*144*/ MatADot_Default,
    1514:                                        MatANorm_Default,
    1515:                                        NULL,
    1516:                                        NULL};

    1518: static PetscErrorCode MatStashScatterBegin_ScaLAPACK(Mat mat, MatStash *stash, PetscInt *owners)
    1519: {
    1520:   PetscInt          *owner, *startv, *starti, bs2;
    1521:   PetscInt           size = stash->size, nsends;
    1522:   PetscInt          *sindices, **rindices, j, l;
    1523:   PetscScalar      **rvalues, *svalues;
    1524:   MPI_Comm           comm = stash->comm;
    1525:   MPI_Request       *send_waits, *recv_waits, *recv_waits1, *recv_waits2;
    1526:   PetscMPIInt        tag1 = stash->tag1, tag2 = stash->tag2, *sizes, *nlengths, nreceives, insends, ii;
    1527:   PetscInt          *sp_idx, *sp_idy;
    1528:   PetscScalar       *sp_val;
    1529:   PetscMatStashSpace space, space_next;
    1530:   PetscBLASInt       gridx, gcidx, lridx, lcidx, rsrc, csrc;
    1531:   Mat_ScaLAPACK     *a = (Mat_ScaLAPACK *)mat->data;

    1533:   PetscFunctionBegin;
    1534:   { /* make sure all processors are either in INSERTMODE or ADDMODE */
    1535:     InsertMode addv;
    1536:     PetscCallMPI(MPIU_Allreduce((PetscEnum *)&mat->insertmode, (PetscEnum *)&addv, 1, MPIU_ENUM, MPI_BOR, PetscObjectComm((PetscObject)mat)));
    1537:     PetscCheck(addv != (ADD_VALUES | INSERT_VALUES), PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Some processors inserted others added");
    1538:     mat->insertmode = addv; /* in case this processor had no cache */
    1539:   }

    1541:   bs2 = stash->bs * stash->bs;

    1543:   /*  first count number of contributors to each processor */
    1544:   PetscCall(PetscCalloc1(size, &nlengths));
    1545:   PetscCall(PetscMalloc1(stash->n + 1, &owner));

    1547:   ii = j = 0;
    1548:   space  = stash->space_head;
    1549:   while (space) {
    1550:     space_next = space->next;
    1551:     for (l = 0; l < space->local_used; l++) {
    1552:       PetscCall(PetscBLASIntCast(space->idx[l] + 1, &gridx));
    1553:       PetscCall(PetscBLASIntCast(space->idy[l] + 1, &gcidx));
    1554:       PetscCallBLAS("SCALAPACKinfog2l", SCALAPACKinfog2l_(&gridx, &gcidx, a->desc, &a->grid->nprow, &a->grid->npcol, &a->grid->myrow, &a->grid->mycol, &lridx, &lcidx, &rsrc, &csrc));
    1555:       j = Cblacs_pnum(a->grid->ictxt, rsrc, csrc);
    1556:       nlengths[j]++;
    1557:       owner[ii] = j;
    1558:       ii++;
    1559:     }
    1560:     space = space_next;
    1561:   }

    1563:   /* Now check what procs get messages - and compute nsends. */
    1564:   PetscCall(PetscCalloc1(size, &sizes));
    1565:   nsends = 0;
    1566:   for (PetscMPIInt i = 0; i < size; i++) {
    1567:     if (nlengths[i]) {
    1568:       sizes[i] = 1;
    1569:       nsends++;
    1570:     }
    1571:   }

    1573:   {
    1574:     PetscMPIInt *onodes, *olengths;

    1576:     /* Determine the number of messages to expect, their lengths, from from-ids */
    1577:     PetscCall(PetscGatherNumberOfMessages(comm, sizes, nlengths, &nreceives));
    1578:     PetscCall(PetscMPIIntCast(nsends, &insends));
    1579:     PetscCall(PetscGatherMessageLengths(comm, insends, nreceives, nlengths, &onodes, &olengths));
    1580:     /* since clubbing row,col - lengths are multiplied by 2 */
    1581:     for (PetscMPIInt i = 0; i < nreceives; i++) olengths[i] *= 2;
    1582:     PetscCall(PetscPostIrecvInt(comm, tag1, nreceives, onodes, olengths, &rindices, &recv_waits1));
    1583:     /* values are size 'bs2' lengths (and remove earlier factor 2 */
    1584:     for (PetscMPIInt i = 0; i < nreceives; i++) olengths[i] = (PetscMPIInt)(olengths[i] * bs2 / 2);
    1585:     PetscCall(PetscPostIrecvScalar(comm, tag2, nreceives, onodes, olengths, &rvalues, &recv_waits2));
    1586:     PetscCall(PetscFree(onodes));
    1587:     PetscCall(PetscFree(olengths));
    1588:   }

    1590:   /* do sends:
    1591:       1) starts[i] gives the starting index in svalues for stuff going to
    1592:          the ith processor
    1593:   */
    1594:   PetscCall(PetscMalloc2(bs2 * stash->n, &svalues, 2 * (stash->n + 1), &sindices));
    1595:   PetscCall(PetscMalloc1(2 * nsends, &send_waits));
    1596:   PetscCall(PetscMalloc2(size, &startv, size, &starti));
    1597:   /* use 2 sends the first with all_a, the next with all_i and all_j */
    1598:   startv[0] = 0;
    1599:   starti[0] = 0;
    1600:   for (PetscMPIInt i = 1; i < size; i++) {
    1601:     startv[i] = startv[i - 1] + nlengths[i - 1];
    1602:     starti[i] = starti[i - 1] + 2 * nlengths[i - 1];
    1603:   }

    1605:   ii    = 0;
    1606:   space = stash->space_head;
    1607:   while (space) {
    1608:     space_next = space->next;
    1609:     sp_idx     = space->idx;
    1610:     sp_idy     = space->idy;
    1611:     sp_val     = space->val;
    1612:     for (l = 0; l < space->local_used; l++) {
    1613:       j = owner[ii];
    1614:       if (bs2 == 1) {
    1615:         svalues[startv[j]] = sp_val[l];
    1616:       } else {
    1617:         PetscInt     k;
    1618:         PetscScalar *buf1, *buf2;
    1619:         buf1 = svalues + bs2 * startv[j];
    1620:         buf2 = space->val + bs2 * l;
    1621:         for (k = 0; k < bs2; k++) buf1[k] = buf2[k];
    1622:       }
    1623:       sindices[starti[j]]               = sp_idx[l];
    1624:       sindices[starti[j] + nlengths[j]] = sp_idy[l];
    1625:       startv[j]++;
    1626:       starti[j]++;
    1627:       ii++;
    1628:     }
    1629:     space = space_next;
    1630:   }
    1631:   startv[0] = 0;
    1632:   for (PetscMPIInt i = 1; i < size; i++) startv[i] = startv[i - 1] + nlengths[i - 1];

    1634:   for (PetscMPIInt i = 0, count = 0; i < size; i++) {
    1635:     if (sizes[i]) {
    1636:       PetscCallMPI(MPIU_Isend(sindices + 2 * startv[i], 2 * nlengths[i], MPIU_INT, i, tag1, comm, send_waits + count++));
    1637:       PetscCallMPI(MPIU_Isend(svalues + bs2 * startv[i], bs2 * nlengths[i], MPIU_SCALAR, i, tag2, comm, send_waits + count++));
    1638:     }
    1639:   }
    1640: #if defined(PETSC_USE_INFO)
    1641:   PetscCall(PetscInfo(NULL, "No of messages: %" PetscInt_FMT "\n", nsends));
    1642:   for (PetscMPIInt i = 0; i < size; i++) {
    1643:     if (sizes[i]) PetscCall(PetscInfo(NULL, "Mesg_to: %d: size: %zu bytes\n", i, (size_t)(nlengths[i] * (bs2 * sizeof(PetscScalar) + 2 * sizeof(PetscInt)))));
    1644:   }
    1645: #endif
    1646:   PetscCall(PetscFree(nlengths));
    1647:   PetscCall(PetscFree(owner));
    1648:   PetscCall(PetscFree2(startv, starti));
    1649:   PetscCall(PetscFree(sizes));

    1651:   /* recv_waits need to be contiguous for MatStashScatterGetMesg_Private() */
    1652:   PetscCall(PetscMalloc1(2 * nreceives, &recv_waits));

    1654:   for (PetscMPIInt i = 0; i < nreceives; i++) {
    1655:     recv_waits[2 * i]     = recv_waits1[i];
    1656:     recv_waits[2 * i + 1] = recv_waits2[i];
    1657:   }
    1658:   stash->recv_waits = recv_waits;

    1660:   PetscCall(PetscFree(recv_waits1));
    1661:   PetscCall(PetscFree(recv_waits2));

    1663:   stash->svalues         = svalues;
    1664:   stash->sindices        = sindices;
    1665:   stash->rvalues         = rvalues;
    1666:   stash->rindices        = rindices;
    1667:   stash->send_waits      = send_waits;
    1668:   stash->nsends          = (PetscMPIInt)nsends;
    1669:   stash->nrecvs          = nreceives;
    1670:   stash->reproduce_count = 0;
    1671:   PetscFunctionReturn(PETSC_SUCCESS);
    1672: }

    1674: static PetscErrorCode MatScaLAPACKSetBlockSizes_ScaLAPACK(Mat A, PetscInt mb, PetscInt nb)
    1675: {
    1676:   Mat_ScaLAPACK *a = (Mat_ScaLAPACK *)A->data;

    1678:   PetscFunctionBegin;
    1679:   PetscCheck(!A->preallocated, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Cannot change block sizes after MatSetUp");
    1680:   PetscCheck(mb >= 1 || mb == PETSC_DECIDE, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "mb %" PetscInt_FMT " must be at least 1", mb);
    1681:   PetscCheck(nb >= 1 || nb == PETSC_DECIDE, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "nb %" PetscInt_FMT " must be at least 1", nb);
    1682:   PetscCall(PetscBLASIntCast((mb == PETSC_DECIDE) ? DEFAULT_BLOCKSIZE : mb, &a->mb));
    1683:   PetscCall(PetscBLASIntCast((nb == PETSC_DECIDE) ? a->mb : nb, &a->nb));
    1684:   PetscFunctionReturn(PETSC_SUCCESS);
    1685: }

    1687: /*@
    1688:   MatScaLAPACKSetBlockSizes - Sets the block sizes to be used for the distribution of
    1689:   the `MATSCALAPACK` matrix

    1691:   Logically Collective

    1693:   Input Parameters:
    1694: + A  - a `MATSCALAPACK` matrix
    1695: . mb - the row block size
    1696: - nb - the column block size

    1698:   Level: intermediate

    1700:   Note:
    1701:   This block size has a different meaning from the block size associated with `MatSetBlockSize()` used for sparse matrices

    1703: .seealso: [](ch_matrices), `Mat`, `MATSCALAPACK`, `MatCreateScaLAPACK()`, `MatScaLAPACKGetBlockSizes()`
    1704: @*/
    1705: PetscErrorCode MatScaLAPACKSetBlockSizes(Mat A, PetscInt mb, PetscInt nb)
    1706: {
    1707:   PetscFunctionBegin;
    1711:   PetscTryMethod(A, "MatScaLAPACKSetBlockSizes_C", (Mat, PetscInt, PetscInt), (A, mb, nb));
    1712:   PetscFunctionReturn(PETSC_SUCCESS);
    1713: }

    1715: static PetscErrorCode MatScaLAPACKGetBlockSizes_ScaLAPACK(Mat A, PetscInt *mb, PetscInt *nb)
    1716: {
    1717:   Mat_ScaLAPACK *a = (Mat_ScaLAPACK *)A->data;

    1719:   PetscFunctionBegin;
    1720:   if (mb) *mb = a->mb;
    1721:   if (nb) *nb = a->nb;
    1722:   PetscFunctionReturn(PETSC_SUCCESS);
    1723: }

    1725: /*@
    1726:   MatScaLAPACKGetBlockSizes - Gets the block sizes used in the distribution of
    1727:   the `MATSCALAPACK` matrix

    1729:   Not Collective

    1731:   Input Parameter:
    1732: . A - a `MATSCALAPACK` matrix

    1734:   Output Parameters:
    1735: + mb - the row block size
    1736: - nb - the column block size

    1738:   Level: intermediate

    1740:   Note:
    1741:   This block size has a different meaning from the block size associated with `MatSetBlockSize()` used for sparse matrices

    1743: .seealso: [](ch_matrices), `Mat`, `MATSCALAPACK`, `MatCreateScaLAPACK()`, `MatScaLAPACKSetBlockSizes()`
    1744: @*/
    1745: PetscErrorCode MatScaLAPACKGetBlockSizes(Mat A, PetscInt *mb, PetscInt *nb)
    1746: {
    1747:   PetscFunctionBegin;
    1749:   PetscUseMethod(A, "MatScaLAPACKGetBlockSizes_C", (Mat, PetscInt *, PetscInt *), (A, mb, nb));
    1750:   PetscFunctionReturn(PETSC_SUCCESS);
    1751: }

    1753: PETSC_INTERN PetscErrorCode MatStashScatterGetMesg_Ref(MatStash *, PetscMPIInt *, PetscInt **, PetscInt **, PetscScalar **, PetscInt *);
    1754: PETSC_INTERN PetscErrorCode MatStashScatterEnd_Ref(MatStash *);

    1756: /*MC
    1757:    MATSCALAPACK = "scalapack" - A matrix type for dense matrices using the ScaLAPACK package

    1759:    Use `./configure --download-scalapack` to install PETSc to use ScaLAPACK

    1761:    Options Database Keys:
    1762: +  -mat_type scalapack                  - sets the matrix type to `MATSCALAPACK`
    1763: .  -pc_factor_mat_solver_type scalapack - to use this direct solver with the option `-pc_type lu`
    1764: .  -mat_scalapack_grid_height           - sets Grid Height for 2D cyclic ordering of internal matrix
    1765: -  -mat_scalapack_block_sizes           - size of the blocks to use (one or two integers separated by comma)

    1767:    Level: intermediate

    1769:   Note:
    1770:    Note unlike most matrix formats, this format does not store all the matrix entries for a contiguous
    1771:    range of rows on an MPI rank. Use `MatGetOwnershipIS()` to determine what values are stored on
    1772:    the given rank.

    1774: .seealso: [](ch_matrices), `Mat`, `MATSCALAPACK`, `MATDENSE`, `MATELEMENTAL`, `MatGetOwnershipIS()`, `MatCreateScaLAPACK()`
    1775: M*/

    1777: PETSC_EXTERN PetscErrorCode MatCreate_ScaLAPACK(Mat A)
    1778: {
    1779:   Mat_ScaLAPACK      *a;
    1780:   PetscBool           flg;
    1781:   PetscMPIInt         iflg;
    1782:   Mat_ScaLAPACK_Grid *grid;
    1783:   MPI_Comm            icomm;
    1784:   PetscBLASInt        nprow, npcol, myrow, mycol;
    1785:   PetscInt            optv1, k = 2, array[2] = {0, 0};
    1786:   PetscMPIInt         size;

    1788:   PetscFunctionBegin;
    1789:   A->ops[0]     = MatOps_Values;
    1790:   A->insertmode = NOT_SET_VALUES;

    1792:   PetscCall(MatStashCreate_Private(PetscObjectComm((PetscObject)A), 1, &A->stash));
    1793:   A->stash.ScatterBegin   = MatStashScatterBegin_ScaLAPACK;
    1794:   A->stash.ScatterGetMesg = MatStashScatterGetMesg_Ref;
    1795:   A->stash.ScatterEnd     = MatStashScatterEnd_Ref;
    1796:   A->stash.ScatterDestroy = NULL;

    1798:   PetscCall(PetscNew(&a));
    1799:   A->data = (void *)a;

    1801:   /* Grid needs to be shared between multiple Mats on the same communicator, implement by attribute caching on the MPI_Comm */
    1802:   if (Petsc_ScaLAPACK_keyval == MPI_KEYVAL_INVALID) {
    1803:     PetscCallMPI(MPI_Comm_create_keyval(MPI_COMM_NULL_COPY_FN, MPI_COMM_NULL_DELETE_FN, &Petsc_ScaLAPACK_keyval, NULL));
    1804:     PetscCall(PetscRegisterFinalize(Petsc_ScaLAPACK_keyval_free));
    1805:     PetscCall(PetscCitationsRegister(ScaLAPACKCitation, &ScaLAPACKCite));
    1806:   }
    1807:   PetscCall(PetscCommDuplicate(PetscObjectComm((PetscObject)A), &icomm, NULL));
    1808:   PetscCallMPI(MPI_Comm_get_attr(icomm, Petsc_ScaLAPACK_keyval, (void **)&grid, &iflg));
    1809:   if (!iflg) {
    1810:     PetscCall(PetscNew(&grid));

    1812:     PetscCallMPI(MPI_Comm_size(icomm, &size));
    1813:     PetscCall(PetscBLASIntCast(PetscSqrtReal((PetscReal)size) + 0.001, &grid->nprow));

    1815:     PetscOptionsBegin(PetscObjectComm((PetscObject)A), ((PetscObject)A)->prefix, "ScaLAPACK Grid Options", "Mat");
    1816:     PetscCall(PetscOptionsInt("-mat_scalapack_grid_height", "Grid Height", "None", grid->nprow, &optv1, &flg));
    1817:     if (flg) {
    1818:       PetscCheck(size % optv1 == 0, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_INCOMP, "Grid Height %" PetscInt_FMT " must evenly divide CommSize %d", optv1, size);
    1819:       PetscCall(PetscBLASIntCast(optv1, &grid->nprow));
    1820:     }
    1821:     PetscOptionsEnd();

    1823:     if (size % grid->nprow) grid->nprow = 1; /* cannot use a squarish grid, use a 1d grid */
    1824:     grid->npcol = size / grid->nprow;
    1825:     PetscCall(PetscBLASIntCast(grid->nprow, &nprow));
    1826:     PetscCall(PetscBLASIntCast(grid->npcol, &npcol));
    1827:     grid->ictxt = Csys2blacs_handle(icomm);
    1828:     Cblacs_gridinit(&grid->ictxt, "R", nprow, npcol);
    1829:     Cblacs_gridinfo(grid->ictxt, &nprow, &npcol, &myrow, &mycol);
    1830:     grid->grid_refct = 1;
    1831:     grid->nprow      = nprow;
    1832:     grid->npcol      = npcol;
    1833:     grid->myrow      = myrow;
    1834:     grid->mycol      = mycol;
    1835:     /* auxiliary 1d BLACS contexts for 1xsize and sizex1 grids */
    1836:     grid->ictxrow = Csys2blacs_handle(icomm);
    1837:     Cblacs_gridinit(&grid->ictxrow, "R", 1, size);
    1838:     grid->ictxcol = Csys2blacs_handle(icomm);
    1839:     Cblacs_gridinit(&grid->ictxcol, "R", size, 1);
    1840:     PetscCallMPI(MPI_Comm_set_attr(icomm, Petsc_ScaLAPACK_keyval, (void *)grid));

    1842:   } else grid->grid_refct++;
    1843:   PetscCall(PetscCommDestroy(&icomm));
    1844:   a->grid = grid;
    1845:   a->mb   = DEFAULT_BLOCKSIZE;
    1846:   a->nb   = DEFAULT_BLOCKSIZE;

    1848:   PetscOptionsBegin(PetscObjectComm((PetscObject)A), NULL, "ScaLAPACK Options", "Mat");
    1849:   PetscCall(PetscOptionsIntArray("-mat_scalapack_block_sizes", "Size of the blocks to use (one or two comma-separated integers)", "MatCreateScaLAPACK", array, &k, &flg));
    1850:   if (flg) {
    1851:     a->mb = (PetscMPIInt)array[0];
    1852:     a->nb = (k > 1) ? (PetscMPIInt)array[1] : a->mb;
    1853:   }
    1854:   PetscOptionsEnd();

    1856:   a->roworiented = PETSC_TRUE;
    1857:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatGetOwnershipIS_C", MatGetOwnershipIS_ScaLAPACK));
    1858:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatScaLAPACKSetBlockSizes_C", MatScaLAPACKSetBlockSizes_ScaLAPACK));
    1859:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatScaLAPACKGetBlockSizes_C", MatScaLAPACKGetBlockSizes_ScaLAPACK));
    1860:   PetscCall(PetscObjectChangeTypeName((PetscObject)A, MATSCALAPACK));
    1861:   PetscFunctionReturn(PETSC_SUCCESS);
    1862: }

    1864: /*@C
    1865:   MatCreateScaLAPACK - Creates a dense parallel matrix in ScaLAPACK format
    1866:   (2D block cyclic distribution) for a `MATSCALAPACK` matrix

    1868:   Collective

    1870:   Input Parameters:
    1871: + comm - MPI communicator
    1872: . mb   - row block size (or `PETSC_DECIDE` to have it set)
    1873: . nb   - column block size (or `PETSC_DECIDE` to have it set)
    1874: . M    - number of global rows
    1875: . N    - number of global columns
    1876: . rsrc - coordinate of process that owns the first row of the distributed matrix
    1877: - csrc - coordinate of process that owns the first column of the distributed matrix

    1879:   Output Parameter:
    1880: . A - the matrix

    1882:   Options Database Key:
    1883: . -mat_scalapack_block_sizes - size of the blocks to use (one or two integers separated by comma)

    1885:   Level: intermediate

    1887:   Notes:
    1888:   If `PETSC_DECIDE` is used for the block sizes, then an appropriate value is chosen

    1890:   It is recommended that one use the `MatCreate()`, `MatSetType()` and/or `MatSetFromOptions()`,
    1891:   MatXXXXSetPreallocation() paradigm instead of this routine directly.
    1892:   [MatXXXXSetPreallocation() is, for example, `MatSeqAIJSetPreallocation()`]

    1894:   Storage is completely managed by ScaLAPACK, so this requires PETSc to be
    1895:   configured with ScaLAPACK. In particular, PETSc's local sizes lose
    1896:   significance and are thus ignored. The block sizes refer to the values
    1897:   used for the distributed matrix, not the same meaning as in `MATBAIJ`.

    1899: .seealso: [](ch_matrices), `Mat`, `MATSCALAPACK`, `MATDENSE`, `MATELEMENTAL`, `MatCreate()`, `MatCreateDense()`, `MatSetValues()`
    1900: @*/
    1901: PetscErrorCode MatCreateScaLAPACK(MPI_Comm comm, PetscInt mb, PetscInt nb, PetscInt M, PetscInt N, PetscInt rsrc, PetscInt csrc, Mat *A)
    1902: {
    1903:   Mat_ScaLAPACK *a;
    1904:   PetscInt       m, n;

    1906:   PetscFunctionBegin;
    1907:   PetscCall(MatCreate(comm, A));
    1908:   PetscCall(MatSetType(*A, MATSCALAPACK));
    1909:   PetscCheck(M != PETSC_DECIDE && N != PETSC_DECIDE, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot use PETSC_DECIDE for matrix dimensions");
    1910:   /* rows and columns are NOT distributed according to PetscSplitOwnership */
    1911:   m = PETSC_DECIDE;
    1912:   PetscCall(PetscSplitOwnershipEqual(comm, &m, &M));
    1913:   n = PETSC_DECIDE;
    1914:   PetscCall(PetscSplitOwnershipEqual(comm, &n, &N));
    1915:   PetscCall(MatSetSizes(*A, m, n, M, N));
    1916:   a = (Mat_ScaLAPACK *)(*A)->data;
    1917:   PetscCall(PetscBLASIntCast(M, &a->M));
    1918:   PetscCall(PetscBLASIntCast(N, &a->N));
    1919:   PetscCall(PetscBLASIntCast((mb == PETSC_DECIDE) ? DEFAULT_BLOCKSIZE : mb, &a->mb));
    1920:   PetscCall(PetscBLASIntCast((nb == PETSC_DECIDE) ? a->mb : nb, &a->nb));
    1921:   PetscCall(PetscBLASIntCast(rsrc, &a->rsrc));
    1922:   PetscCall(PetscBLASIntCast(csrc, &a->csrc));
    1923:   PetscCall(MatSetUp(*A));
    1924:   PetscFunctionReturn(PETSC_SUCCESS);
    1925: }