xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact4.c (revision e8e8640d1cb9a3a2f50c0c0d7b26e5c4d521e2e4)

#include <../src/mat/impls/sbaij/seq/sbaij.h>
#include <petsc/private/kernels/blockinvert.h>

/*
      Version for when blocks are 3 by 3 Using natural ordering
*/
PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat C, Mat A, const MatFactorInfo *info)
{
  Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data, *b = (Mat_SeqSBAIJ *)C->data;
  PetscInt      i, j, mbs = a->mbs, *bi = b->i, *bj = b->j;
  PetscInt     *ai, *aj, k, k1, jmin, jmax, *jl, *il, vj, nexti, ili;
  MatScalar    *ba = b->a, *aa, *ap, *dk, *uik;
  MatScalar    *u, *diag, *rtmp, *rtmp_ptr;
  PetscReal     shift = info->shiftamount;
  PetscBool     allowzeropivot, zeropivotdetected;

  PetscFunctionBegin;
  /* initialization */
  allowzeropivot = PetscNot(A->erroriffailure);
  PetscCall(PetscCalloc1(9 * mbs, &rtmp));
  PetscCall(PetscMalloc2(mbs, &il, mbs, &jl));
  il[0] = 0;
  for (i = 0; i < mbs; i++) jl[i] = mbs;

  PetscCall(PetscMalloc2(9, &dk, 9, &uik));
  ai = a->i;
  aj = a->j;
  aa = a->a;

  /* for each row k */
  for (k = 0; k < mbs; k++) {
    /*initialize k-th row with elements nonzero in row k of A */
    jmin = ai[k];
    jmax = ai[k + 1];
    if (jmin < jmax) {
      ap = aa + jmin * 9;
      for (j = jmin; j < jmax; j++) {
        vj       = aj[j]; /* block col. index */
        rtmp_ptr = rtmp + vj * 9;
        for (i = 0; i < 9; i++) *rtmp_ptr++ = *ap++;
      }
    }

    /* modify k-th row by adding in those rows i with U(i,k) != 0 */
    PetscCall(PetscArraycpy(dk, rtmp + k * 9, 9));
    i = jl[k]; /* first row to be added to k_th row  */

    while (i < mbs) {
      nexti = jl[i]; /* next row to be added to k_th row */

      /* compute multiplier */
      ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */

      /* uik = -inv(Di)*U_bar(i,k) */
      diag = ba + i * 9;
      u    = ba + ili * 9;

      uik[0] = -(diag[0] * u[0] + diag[3] * u[1] + diag[6] * u[2]);
      uik[1] = -(diag[1] * u[0] + diag[4] * u[1] + diag[7] * u[2]);
      uik[2] = -(diag[2] * u[0] + diag[5] * u[1] + diag[8] * u[2]);

      uik[3] = -(diag[0] * u[3] + diag[3] * u[4] + diag[6] * u[5]);
      uik[4] = -(diag[1] * u[3] + diag[4] * u[4] + diag[7] * u[5]);
      uik[5] = -(diag[2] * u[3] + diag[5] * u[4] + diag[8] * u[5]);

      uik[6] = -(diag[0] * u[6] + diag[3] * u[7] + diag[6] * u[8]);
      uik[7] = -(diag[1] * u[6] + diag[4] * u[7] + diag[7] * u[8]);
      uik[8] = -(diag[2] * u[6] + diag[5] * u[7] + diag[8] * u[8]);

      /* update D(k) += -U(i,k)^T * U_bar(i,k) */
      dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2];
      dk[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2];
      dk[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2];

      dk[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5];
      dk[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5];
      dk[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5];

      dk[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8];
      dk[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8];
      dk[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8];

      PetscCall(PetscLogFlops(27.0 * 4.0));

      /* update -U(i,k) */
      PetscCall(PetscArraycpy(ba + ili * 9, uik, 9));

      /* add multiple of row i to k-th row ... */
      jmin = ili + 1;
      jmax = bi[i + 1];
      if (jmin < jmax) {
        for (j = jmin; j < jmax; j++) {
          /* rtmp += -U(i,k)^T * U_bar(i,j) */
          rtmp_ptr = rtmp + bj[j] * 9;
          u        = ba + j * 9;
          rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2];
          rtmp_ptr[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2];
          rtmp_ptr[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2];

          rtmp_ptr[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5];
          rtmp_ptr[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5];
          rtmp_ptr[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5];

          rtmp_ptr[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8];
          rtmp_ptr[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8];
          rtmp_ptr[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8];
        }
        PetscCall(PetscLogFlops(2.0 * 27.0 * (jmax - jmin)));

        /* ... add i to row list for next nonzero entry */
        il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
        j     = bj[jmin];
        jl[i] = jl[j];
        jl[j] = i; /* update jl */
      }
      i = nexti;
    }

    /* save nonzero entries in k-th row of U ... */

    /* invert diagonal block */
    diag = ba + k * 9;
    PetscCall(PetscArraycpy(diag, dk, 9));
    PetscCall(PetscKernel_A_gets_inverse_A_3(diag, shift, allowzeropivot, &zeropivotdetected));
    if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    jmin = bi[k];
    jmax = bi[k + 1];
    if (jmin < jmax) {
      for (j = jmin; j < jmax; j++) {
        vj       = bj[j]; /* block col. index of U */
        u        = ba + j * 9;
        rtmp_ptr = rtmp + vj * 9;
        for (k1 = 0; k1 < 9; k1++) {
          *u++        = *rtmp_ptr;
          *rtmp_ptr++ = 0.0;
        }
      }

      /* ... add k to row list for first nonzero entry in k-th row */
      il[k] = jmin;
      i     = bj[jmin];
      jl[k] = jl[i];
      jl[i] = k;
    }
  }

  PetscCall(PetscFree(rtmp));
  PetscCall(PetscFree2(il, jl));
  PetscCall(PetscFree2(dk, uik));

  C->ops->solve          = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
  C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
  C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
  C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace;

  C->assembled    = PETSC_TRUE;
  C->preallocated = PETSC_TRUE;

  PetscCall(PetscLogFlops(1.3333 * 27 * b->mbs)); /* from inverting diagonal blocks */
  PetscFunctionReturn(PETSC_SUCCESS);
}