xref: /petsc/src/mat/impls/aij/seq/matrart.c (revision d71ae5a4db6382e7f06317b8d368875286fe9008)

/*
  Defines projective product routines where A is a SeqAIJ matrix
          C = R * A * R^T
*/

#include <../src/mat/impls/aij/seq/aij.h>
#include <../src/mat/utils/freespace.h>
#include <../src/mat/impls/dense/seq/dense.h> /*I "petscmat.h" I*/

PetscErrorCode MatDestroy_SeqAIJ_RARt(void *data)
{
  Mat_RARt *rart = (Mat_RARt *)data;

  PetscFunctionBegin;
  PetscCall(MatTransposeColoringDestroy(&rart->matcoloring));
  PetscCall(MatDestroy(&rart->Rt));
  PetscCall(MatDestroy(&rart->RARt));
  PetscCall(MatDestroy(&rart->ARt));
  PetscCall(PetscFree(rart->work));
  if (rart->destroy) PetscCall((*rart->destroy)(rart->data));
  PetscCall(PetscFree(rart));
  PetscFunctionReturn(0);
}

PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ_colorrart(Mat A, Mat R, PetscReal fill, Mat C)
{
  Mat                  P;
  Mat_RARt            *rart;
  MatColoring          coloring;
  MatTransposeColoring matcoloring;
  ISColoring           iscoloring;
  Mat                  Rt_dense, RARt_dense;

  PetscFunctionBegin;
  MatCheckProduct(C, 4);
  PetscCheck(!C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data not empty");
  /* create symbolic P=Rt */
  PetscCall(MatTransposeSymbolic(R, &P));

  /* get symbolic C=Pt*A*P */
  PetscCall(MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A, P, fill, C));
  PetscCall(MatSetBlockSizes(C, PetscAbs(R->rmap->bs), PetscAbs(R->rmap->bs)));
  C->ops->rartnumeric = MatRARtNumeric_SeqAIJ_SeqAIJ_colorrart;

  /* create a supporting struct */
  PetscCall(PetscNew(&rart));
  C->product->data    = rart;
  C->product->destroy = MatDestroy_SeqAIJ_RARt;

  /* ------ Use coloring ---------- */
  /* inode causes memory problem */
  PetscCall(MatSetOption(C, MAT_USE_INODES, PETSC_FALSE));

  /* Create MatTransposeColoring from symbolic C=R*A*R^T */
  PetscCall(MatColoringCreate(C, &coloring));
  PetscCall(MatColoringSetDistance(coloring, 2));
  PetscCall(MatColoringSetType(coloring, MATCOLORINGSL));
  PetscCall(MatColoringSetFromOptions(coloring));
  PetscCall(MatColoringApply(coloring, &iscoloring));
  PetscCall(MatColoringDestroy(&coloring));
  PetscCall(MatTransposeColoringCreate(C, iscoloring, &matcoloring));

  rart->matcoloring = matcoloring;
  PetscCall(ISColoringDestroy(&iscoloring));

  /* Create Rt_dense */
  PetscCall(MatCreate(PETSC_COMM_SELF, &Rt_dense));
  PetscCall(MatSetSizes(Rt_dense, A->cmap->n, matcoloring->ncolors, A->cmap->n, matcoloring->ncolors));
  PetscCall(MatSetType(Rt_dense, MATSEQDENSE));
  PetscCall(MatSeqDenseSetPreallocation(Rt_dense, NULL));

  Rt_dense->assembled = PETSC_TRUE;
  rart->Rt            = Rt_dense;

  /* Create RARt_dense = R*A*Rt_dense */
  PetscCall(MatCreate(PETSC_COMM_SELF, &RARt_dense));
  PetscCall(MatSetSizes(RARt_dense, C->rmap->n, matcoloring->ncolors, C->rmap->n, matcoloring->ncolors));
  PetscCall(MatSetType(RARt_dense, MATSEQDENSE));
  PetscCall(MatSeqDenseSetPreallocation(RARt_dense, NULL));

  rart->RARt = RARt_dense;

  /* Allocate work array to store columns of A*R^T used in MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqDense() */
  PetscCall(PetscMalloc1(A->rmap->n * 4, &rart->work));

  /* clean up */
  PetscCall(MatDestroy(&P));

#if defined(PETSC_USE_INFO)
  {
    Mat_SeqAIJ *c       = (Mat_SeqAIJ *)C->data;
    PetscReal   density = (PetscReal)(c->nz) / (RARt_dense->rmap->n * RARt_dense->cmap->n);
    PetscCall(PetscInfo(C, "C=R*(A*Rt) via coloring C - use sparse-dense inner products\n"));
    PetscCall(PetscInfo(C, "RARt_den %" PetscInt_FMT " %" PetscInt_FMT "; Rt %" PetscInt_FMT " %" PetscInt_FMT " (RARt->nz %" PetscInt_FMT ")/(m*ncolors)=%g\n", RARt_dense->rmap->n, RARt_dense->cmap->n, R->cmap->n, R->rmap->n, c->nz, (double)density));
  }
#endif
  PetscFunctionReturn(0);
}

/*
 RAB = R * A * B, R and A in seqaij format, B in dense format;
*/
PetscErrorCode MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqDense(Mat R, Mat A, Mat B, Mat RAB, PetscScalar *work)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *r = (Mat_SeqAIJ *)R->data;
  PetscScalar        r1, r2, r3, r4;
  const PetscScalar *b, *b1, *b2, *b3, *b4;
  MatScalar         *aa, *ra;
  PetscInt           cn = B->cmap->n, bm = B->rmap->n, col, i, j, n, *ai = a->i, *aj, am = A->rmap->n;
  PetscInt           am2 = 2 * am, am3 = 3 * am, bm4 = 4 * bm;
  PetscScalar       *d, *c, *c2, *c3, *c4;
  PetscInt          *rj, rm = R->rmap->n, dm = RAB->rmap->n, dn = RAB->cmap->n;
  PetscInt           rm2 = 2 * rm, rm3 = 3 * rm, colrm;

  PetscFunctionBegin;
  if (!dm || !dn) PetscFunctionReturn(0);
  PetscCheck(bm == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number columns in A %" PetscInt_FMT " not equal rows in B %" PetscInt_FMT, A->cmap->n, bm);
  PetscCheck(am == R->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number columns in R %" PetscInt_FMT " not equal rows in A %" PetscInt_FMT, R->cmap->n, am);
  PetscCheck(R->rmap->n == RAB->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number rows in RAB %" PetscInt_FMT " not equal rows in R %" PetscInt_FMT, RAB->rmap->n, R->rmap->n);
  PetscCheck(B->cmap->n == RAB->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number columns in RAB %" PetscInt_FMT " not equal columns in B %" PetscInt_FMT, RAB->cmap->n, B->cmap->n);

  { /*
     This approach is not as good as original ones (will be removed later), but it reveals that
     AB_den=A*B takes almost all execution time in R*A*B for src/ksp/ksp/tutorials/ex56.c
     */
    PetscBool via_matmatmult = PETSC_FALSE;
    PetscCall(PetscOptionsGetBool(NULL, NULL, "-matrart_via_matmatmult", &via_matmatmult, NULL));
    if (via_matmatmult) {
      Mat AB_den = NULL;
      PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &AB_den));
      PetscCall(MatMatMultSymbolic_SeqAIJ_SeqDense(A, B, 0.0, AB_den));
      PetscCall(MatMatMultNumeric_SeqAIJ_SeqDense(A, B, AB_den));
      PetscCall(MatMatMultNumeric_SeqAIJ_SeqDense(R, AB_den, RAB));
      PetscCall(MatDestroy(&AB_den));
      PetscFunctionReturn(0);
    }
  }

  PetscCall(MatDenseGetArrayRead(B, &b));
  PetscCall(MatDenseGetArray(RAB, &d));
  b1 = b;
  b2 = b1 + bm;
  b3 = b2 + bm;
  b4 = b3 + bm;
  c  = work;
  c2 = c + am;
  c3 = c2 + am;
  c4 = c3 + am;
  for (col = 0; col < cn - 4; col += 4) { /* over columns of C */
    for (i = 0; i < am; i++) {            /* over rows of A in those columns */
      r1 = r2 = r3 = r4 = 0.0;
      n                 = ai[i + 1] - ai[i];
      aj                = a->j + ai[i];
      aa                = a->a + ai[i];
      for (j = 0; j < n; j++) {
        r1 += (*aa) * b1[*aj];
        r2 += (*aa) * b2[*aj];
        r3 += (*aa) * b3[*aj];
        r4 += (*aa++) * b4[*aj++];
      }
      c[i]       = r1;
      c[am + i]  = r2;
      c[am2 + i] = r3;
      c[am3 + i] = r4;
    }
    b1 += bm4;
    b2 += bm4;
    b3 += bm4;
    b4 += bm4;

    /* RAB[:,col] = R*C[:,col] */
    colrm = col * rm;
    for (i = 0; i < rm; i++) { /* over rows of R in those columns */
      r1 = r2 = r3 = r4 = 0.0;
      n                 = r->i[i + 1] - r->i[i];
      rj                = r->j + r->i[i];
      ra                = r->a + r->i[i];
      for (j = 0; j < n; j++) {
        r1 += (*ra) * c[*rj];
        r2 += (*ra) * c2[*rj];
        r3 += (*ra) * c3[*rj];
        r4 += (*ra++) * c4[*rj++];
      }
      d[colrm + i]       = r1;
      d[colrm + rm + i]  = r2;
      d[colrm + rm2 + i] = r3;
      d[colrm + rm3 + i] = r4;
    }
  }
  for (; col < cn; col++) {    /* over extra columns of C */
    for (i = 0; i < am; i++) { /* over rows of A in those columns */
      r1 = 0.0;
      n  = a->i[i + 1] - a->i[i];
      aj = a->j + a->i[i];
      aa = a->a + a->i[i];
      for (j = 0; j < n; j++) r1 += (*aa++) * b1[*aj++];
      c[i] = r1;
    }
    b1 += bm;

    for (i = 0; i < rm; i++) { /* over rows of R in those columns */
      r1 = 0.0;
      n  = r->i[i + 1] - r->i[i];
      rj = r->j + r->i[i];
      ra = r->a + r->i[i];
      for (j = 0; j < n; j++) r1 += (*ra++) * c[*rj++];
      d[col * rm + i] = r1;
    }
  }
  PetscCall(PetscLogFlops(cn * 2.0 * (a->nz + r->nz)));

  PetscCall(MatDenseRestoreArrayRead(B, &b));
  PetscCall(MatDenseRestoreArray(RAB, &d));
  PetscCall(MatAssemblyBegin(RAB, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(RAB, MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(0);
}

PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ_colorrart(Mat A, Mat R, Mat C)
{
  Mat_RARt            *rart;
  MatTransposeColoring matcoloring;
  Mat                  Rt, RARt;

  PetscFunctionBegin;
  MatCheckProduct(C, 3);
  PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
  rart = (Mat_RARt *)C->product->data;

  /* Get dense Rt by Apply MatTransposeColoring to R */
  matcoloring = rart->matcoloring;
  Rt          = rart->Rt;
  PetscCall(MatTransColoringApplySpToDen(matcoloring, R, Rt));

  /* Get dense RARt = R*A*Rt -- dominates! */
  RARt = rart->RARt;
  PetscCall(MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqDense(R, A, Rt, RARt, rart->work));

  /* Recover C from C_dense */
  PetscCall(MatTransColoringApplyDenToSp(matcoloring, RARt, C));
  PetscFunctionReturn(0);
}

PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ_matmattransposemult(Mat A, Mat R, PetscReal fill, Mat C)
{
  Mat       ARt;
  Mat_RARt *rart;
  char     *alg;

  PetscFunctionBegin;
  MatCheckProduct(C, 4);
  PetscCheck(!C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data not empty");
  /* create symbolic ARt = A*R^T  */
  PetscCall(MatProductCreate(A, R, NULL, &ARt));
  PetscCall(MatProductSetType(ARt, MATPRODUCT_ABt));
  PetscCall(MatProductSetAlgorithm(ARt, "sorted"));
  PetscCall(MatProductSetFill(ARt, fill));
  PetscCall(MatProductSetFromOptions(ARt));
  PetscCall(MatProductSymbolic(ARt));

  /* compute symbolic C = R*ARt */
  /* set algorithm for C = R*ARt */
  PetscCall(PetscStrallocpy(C->product->alg, &alg));
  PetscCall(MatProductSetAlgorithm(C, "sorted"));
  PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(R, ARt, fill, C));
  /* resume original algorithm for C */
  PetscCall(MatProductSetAlgorithm(C, alg));
  PetscCall(PetscFree(alg));

  C->ops->rartnumeric = MatRARtNumeric_SeqAIJ_SeqAIJ_matmattransposemult;

  PetscCall(PetscNew(&rart));
  rart->ARt           = ARt;
  C->product->data    = rart;
  C->product->destroy = MatDestroy_SeqAIJ_RARt;
  PetscCall(PetscInfo(C, "Use ARt=A*R^T, C=R*ARt via MatMatTransposeMult(). Coloring can be applied to A*R^T.\n"));
  PetscFunctionReturn(0);
}

PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ_matmattransposemult(Mat A, Mat R, Mat C)
{
  Mat_RARt *rart;

  PetscFunctionBegin;
  MatCheckProduct(C, 3);
  PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
  rart = (Mat_RARt *)C->product->data;
  PetscCall(MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A, R, rart->ARt)); /* dominate! */
  PetscCall(MatMatMultNumeric_SeqAIJ_SeqAIJ(R, rart->ARt, C));
  PetscFunctionReturn(0);
}

PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ(Mat A, Mat R, PetscReal fill, Mat C)
{
  Mat       Rt;
  Mat_RARt *rart;

  PetscFunctionBegin;
  MatCheckProduct(C, 4);
  PetscCheck(!C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data not empty");
  PetscCall(MatTranspose(R, MAT_INITIAL_MATRIX, &Rt));
  PetscCall(MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ(R, A, Rt, fill, C));

  PetscCall(PetscNew(&rart));
  rart->data          = C->product->data;
  rart->destroy       = C->product->destroy;
  rart->Rt            = Rt;
  C->product->data    = rart;
  C->product->destroy = MatDestroy_SeqAIJ_RARt;
  C->ops->rartnumeric = MatRARtNumeric_SeqAIJ_SeqAIJ;
  PetscCall(PetscInfo(C, "Use Rt=R^T and C=R*A*Rt via MatMatMatMult() to avoid sparse inner products\n"));
  PetscFunctionReturn(0);
}

PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ(Mat A, Mat R, Mat C)
{
  Mat_RARt *rart;

  PetscFunctionBegin;
  MatCheckProduct(C, 3);
  PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
  rart = (Mat_RARt *)C->product->data;
  PetscCall(MatTranspose(R, MAT_REUSE_MATRIX, &rart->Rt));
  /* MatMatMatMultSymbolic used a different data */
  C->product->data = rart->data;
  PetscCall(MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ(R, A, rart->Rt, C));
  C->product->data = rart;
  PetscFunctionReturn(0);
}

PetscErrorCode MatRARt_SeqAIJ_SeqAIJ(Mat A, Mat R, MatReuse scall, PetscReal fill, Mat *C)
{
  const char *algTypes[3] = {"matmatmatmult", "matmattransposemult", "coloring_rart"};
  PetscInt    alg         = 0; /* set default algorithm */

  PetscFunctionBegin;
  if (scall == MAT_INITIAL_MATRIX) {
    PetscOptionsBegin(PetscObjectComm((PetscObject)A), ((PetscObject)A)->prefix, "MatRARt", "Mat");
    PetscCall(PetscOptionsEList("-matrart_via", "Algorithmic approach", "MatRARt", algTypes, 3, algTypes[0], &alg, NULL));
    PetscOptionsEnd();

    PetscCall(PetscLogEventBegin(MAT_RARtSymbolic, A, R, 0, 0));
    PetscCall(MatCreate(PETSC_COMM_SELF, C));
    switch (alg) {
    case 1:
      /* via matmattransposemult: ARt=A*R^T, C=R*ARt - matrix coloring can be applied to A*R^T */
      PetscCall(MatRARtSymbolic_SeqAIJ_SeqAIJ_matmattransposemult(A, R, fill, *C));
      break;
    case 2:
      /* via coloring_rart: apply coloring C = R*A*R^T                          */
      PetscCall(MatRARtSymbolic_SeqAIJ_SeqAIJ_colorrart(A, R, fill, *C));
      break;
    default:
      /* via matmatmatmult: Rt=R^T, C=R*A*Rt - avoid inefficient sparse inner products */
      PetscCall(MatRARtSymbolic_SeqAIJ_SeqAIJ(A, R, fill, *C));
      break;
    }
    PetscCall(PetscLogEventEnd(MAT_RARtSymbolic, A, R, 0, 0));
  }

  PetscCall(PetscLogEventBegin(MAT_RARtNumeric, A, R, 0, 0));
  PetscCall(((*C)->ops->rartnumeric)(A, R, *C));
  PetscCall(PetscLogEventEnd(MAT_RARtNumeric, A, R, 0, 0));
  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------- */
PetscErrorCode MatProductSymbolic_RARt_SeqAIJ_SeqAIJ(Mat C)
{
  Mat_Product        *product = C->product;
  Mat                 A = product->A, R = product->B;
  MatProductAlgorithm alg  = product->alg;
  PetscReal           fill = product->fill;
  PetscBool           flg;

  PetscFunctionBegin;
  PetscCall(PetscStrcmp(alg, "r*a*rt", &flg));
  if (flg) {
    PetscCall(MatRARtSymbolic_SeqAIJ_SeqAIJ(A, R, fill, C));
    goto next;
  }

  PetscCall(PetscStrcmp(alg, "r*art", &flg));
  if (flg) {
    PetscCall(MatRARtSymbolic_SeqAIJ_SeqAIJ_matmattransposemult(A, R, fill, C));
    goto next;
  }

  PetscCall(PetscStrcmp(alg, "coloring_rart", &flg));
  if (flg) {
    PetscCall(MatRARtSymbolic_SeqAIJ_SeqAIJ_colorrart(A, R, fill, C));
    goto next;
  }

  SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatProductAlgorithm is not supported");

next:
  C->ops->productnumeric = MatProductNumeric_RARt;
  PetscFunctionReturn(0);
}