xref: /petsc/src/mat/impls/baij/seq/dgefa2.c (revision 3ba1676111f5c958fe6c2729b46ca4d523958bb3)

/*
     Inverts 2 by 2 matrix using gaussian elimination with partial pivoting.

       Used by the sparse factorization routines in
     src/mat/impls/baij/seq

       This is a combination of the Linpack routines
    dgefa() and dgedi() specialized for a size of 2.

*/
#include <petscsys.h>

PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_2(MatScalar *a, PetscReal shift, PetscBool allowzeropivot, PetscBool *zeropivotdetected)
{
  PetscInt   i__2, i__3, kp1, j, k, l, ll, i, ipvt[2], k3;
  PetscInt   k4, j3;
  MatScalar *aa, *ax, *ay, work[4], stmp;
  MatReal    tmp, max;

  PetscFunctionBegin;
  if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE;
  shift = .25 * shift * (1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[3]));

  /* Parameter adjustments */
  a -= 3;

  k   = 1;
  kp1 = k + 1;
  k3  = 2 * k;
  k4  = k3 + k;

  /* find l = pivot index */
  i__2 = 3 - k;
  aa   = &a[k4];
  max  = PetscAbsScalar(aa[0]);
  l    = 1;
  for (ll = 1; ll < i__2; ll++) {
    tmp = PetscAbsScalar(aa[ll]);
    if (tmp > max) {
      max = tmp;
      l   = ll + 1;
    }
  }
  l += k - 1;
  ipvt[k - 1] = l;

  if (a[l + k3] == 0.0) {
    if (shift == 0.0) {
      if (allowzeropivot) {
        PetscCall(PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1));
        if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
      } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1);
    } else {
      a[l + k3] = shift;
    }
  }

  /* interchange if necessary */
  if (l != k) {
    stmp      = a[l + k3];
    a[l + k3] = a[k4];
    a[k4]     = stmp;
  }

  /* compute multipliers */
  stmp = -1. / a[k4];
  i__2 = 2 - k;
  aa   = &a[1 + k4];
  for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;

  /* row elimination with column indexing */
  ax = &a[k4 + 1];
  for (j = kp1; j <= 2; ++j) {
    j3   = 2 * j;
    stmp = a[l + j3];
    if (l != k) {
      a[l + j3] = a[k + j3];
      a[k + j3] = stmp;
    }

    i__3 = 2 - k;
    ay   = &a[1 + k + j3];
    for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll];
  }

  ipvt[1] = 2;
  if (a[6] == 0.0) {
    if (PetscLikely(allowzeropivot)) {
      PetscCall(PetscInfo(NULL, "Zero pivot, row 1\n"));
      if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
    } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 1");
  }

  /* Now form the inverse */
  /* compute inverse(u) */
  for (k = 1; k <= 2; ++k) {
    k3    = 2 * k;
    k4    = k3 + k;
    a[k4] = 1.0 / a[k4];
    stmp  = -a[k4];
    i__2  = k - 1;
    aa    = &a[k3 + 1];
    for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;
    kp1 = k + 1;
    if (2 < kp1) continue;
    ax = aa;
    for (j = kp1; j <= 2; ++j) {
      j3        = 2 * j;
      stmp      = a[k + j3];
      a[k + j3] = 0.0;
      ay        = &a[j3 + 1];
      for (ll = 0; ll < k; ll++) ay[ll] += stmp * ax[ll];
    }
  }

  /* form inverse(u)*inverse(l) */
  k   = 1;
  k3  = 2 * k;
  kp1 = k + 1;
  aa  = a + k3;
  for (i = kp1; i <= 2; ++i) {
    work[i - 1] = aa[i];
    aa[i]       = 0.0;
  }
  for (j = kp1; j <= 2; ++j) {
    stmp = work[j - 1];
    ax   = &a[2 * j + 1];
    ay   = &a[k3 + 1];
    ay[0] += stmp * ax[0];
    ay[1] += stmp * ax[1];
  }
  l = ipvt[k - 1];
  if (l != k) {
    ax    = &a[k3 + 1];
    ay    = &a[2 * l + 1];
    stmp  = ax[0];
    ax[0] = ay[0];
    ay[0] = stmp;
    stmp  = ax[1];
    ax[1] = ay[1];
    ay[1] = stmp;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* gaussian elimination with partial pivoting */
PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_9(MatScalar *a, PetscReal shift, PetscBool allowzeropivot, PetscBool *zeropivotdetected)
{
  PetscInt   i__2, i__3, kp1, j, k, l, ll, i, ipvt[9], kb, k3;
  PetscInt   k4, j3;
  MatScalar *aa, *ax, *ay, work[81], stmp;
  MatReal    tmp, max;

  PetscFunctionBegin;
  if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE;

  /* Parameter adjustments */
  a -= 10;

  for (k = 1; k <= 8; ++k) {
    kp1 = k + 1;
    k3  = 9 * k;
    k4  = k3 + k;

    /* find l = pivot index */
    i__2 = 10 - k;
    aa   = &a[k4];
    max  = PetscAbsScalar(aa[0]);
    l    = 1;
    for (ll = 1; ll < i__2; ll++) {
      tmp = PetscAbsScalar(aa[ll]);
      if (tmp > max) {
        max = tmp;
        l   = ll + 1;
      }
    }
    l += k - 1;
    ipvt[k - 1] = l;

    if (a[l + k3] == 0.0) {
      if (shift == 0.0) {
        if (allowzeropivot) {
          PetscCall(PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1));
          if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
        } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1);
      } else {
        a[l + k3] = shift;
      }
    }

    /* interchange if necessary */
    if (l != k) {
      stmp      = a[l + k3];
      a[l + k3] = a[k4];
      a[k4]     = stmp;
    }

    /* compute multipliers */
    stmp = -1. / a[k4];
    i__2 = 9 - k;
    aa   = &a[1 + k4];
    for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;

    /* row elimination with column indexing */
    ax = &a[k4 + 1];
    for (j = kp1; j <= 9; ++j) {
      j3   = 9 * j;
      stmp = a[l + j3];
      if (l != k) {
        a[l + j3] = a[k + j3];
        a[k + j3] = stmp;
      }

      i__3 = 9 - k;
      ay   = &a[1 + k + j3];
      for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll];
    }
  }
  ipvt[8] = 9;
  if (a[90] == 0.0) {
    if (PetscLikely(allowzeropivot)) {
      PetscCall(PetscInfo(NULL, "Zero pivot, row 8\n"));
      if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
    } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 8");
  }

  /* Now form the inverse */
  /* compute inverse(u) */
  for (k = 1; k <= 9; ++k) {
    k3    = 9 * k;
    k4    = k3 + k;
    a[k4] = 1.0 / a[k4];
    stmp  = -a[k4];
    i__2  = k - 1;
    aa    = &a[k3 + 1];
    for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;
    kp1 = k + 1;
    if (9 < kp1) continue;
    ax = aa;
    for (j = kp1; j <= 9; ++j) {
      j3        = 9 * j;
      stmp      = a[k + j3];
      a[k + j3] = 0.0;
      ay        = &a[j3 + 1];
      for (ll = 0; ll < k; ll++) ay[ll] += stmp * ax[ll];
    }
  }

  /* form inverse(u)*inverse(l) */
  for (kb = 1; kb <= 8; ++kb) {
    k   = 9 - kb;
    k3  = 9 * k;
    kp1 = k + 1;
    aa  = a + k3;
    for (i = kp1; i <= 9; ++i) {
      work[i - 1] = aa[i];
      aa[i]       = 0.0;
    }
    for (j = kp1; j <= 9; ++j) {
      stmp = work[j - 1];
      ax   = &a[9 * j + 1];
      ay   = &a[k3 + 1];
      ay[0] += stmp * ax[0];
      ay[1] += stmp * ax[1];
      ay[2] += stmp * ax[2];
      ay[3] += stmp * ax[3];
      ay[4] += stmp * ax[4];
      ay[5] += stmp * ax[5];
      ay[6] += stmp * ax[6];
      ay[7] += stmp * ax[7];
      ay[8] += stmp * ax[8];
    }
    l = ipvt[k - 1];
    if (l != k) {
      ax    = &a[k3 + 1];
      ay    = &a[9 * l + 1];
      stmp  = ax[0];
      ax[0] = ay[0];
      ay[0] = stmp;
      stmp  = ax[1];
      ax[1] = ay[1];
      ay[1] = stmp;
      stmp  = ax[2];
      ax[2] = ay[2];
      ay[2] = stmp;
      stmp  = ax[3];
      ax[3] = ay[3];
      ay[3] = stmp;
      stmp  = ax[4];
      ax[4] = ay[4];
      ay[4] = stmp;
      stmp  = ax[5];
      ax[5] = ay[5];
      ay[5] = stmp;
      stmp  = ax[6];
      ax[6] = ay[6];
      ay[6] = stmp;
      stmp  = ax[7];
      ax[7] = ay[7];
      ay[7] = stmp;
      stmp  = ax[8];
      ax[8] = ay[8];
      ay[8] = stmp;
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
      Inverts 15 by 15 matrix using gaussian elimination with partial pivoting.

       Used by the sparse factorization routines in
     src/mat/impls/baij/seq

       This is a combination of the Linpack routines
    dgefa() and dgedi() specialized for a size of 15.

*/

PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_15(MatScalar *a, PetscInt *ipvt, MatScalar *work, PetscReal shift, PetscBool allowzeropivot, PetscBool *zeropivotdetected)
{
  PetscInt   i__2, i__3, kp1, j, k, l, ll, i, kb, k3;
  PetscInt   k4, j3;
  MatScalar *aa, *ax, *ay, stmp;
  MatReal    tmp, max;

  PetscFunctionBegin;
  if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE;

  /* Parameter adjustments */
  a -= 16;

  for (k = 1; k <= 14; ++k) {
    kp1 = k + 1;
    k3  = 15 * k;
    k4  = k3 + k;

    /* find l = pivot index */
    i__2 = 16 - k;
    aa   = &a[k4];
    max  = PetscAbsScalar(aa[0]);
    l    = 1;
    for (ll = 1; ll < i__2; ll++) {
      tmp = PetscAbsScalar(aa[ll]);
      if (tmp > max) {
        max = tmp;
        l   = ll + 1;
      }
    }
    l += k - 1;
    ipvt[k - 1] = l;

    if (a[l + k3] == 0.0) {
      if (shift == 0.0) {
        if (allowzeropivot) {
          PetscCall(PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1));
          if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
        } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1);
      } else {
        a[l + k3] = shift;
      }
    }

    /* interchange if necessary */
    if (l != k) {
      stmp      = a[l + k3];
      a[l + k3] = a[k4];
      a[k4]     = stmp;
    }

    /* compute multipliers */
    stmp = -1. / a[k4];
    i__2 = 15 - k;
    aa   = &a[1 + k4];
    for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;

    /* row elimination with column indexing */
    ax = &a[k4 + 1];
    for (j = kp1; j <= 15; ++j) {
      j3   = 15 * j;
      stmp = a[l + j3];
      if (l != k) {
        a[l + j3] = a[k + j3];
        a[k + j3] = stmp;
      }

      i__3 = 15 - k;
      ay   = &a[1 + k + j3];
      for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll];
    }
  }
  ipvt[14] = 15;
  if (a[240] == 0.0) {
    if (PetscLikely(allowzeropivot)) {
      PetscCall(PetscInfo(NULL, "Zero pivot, row 14\n"));
      if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
    } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 14");
  }

  /* Now form the inverse */
  /* compute inverse(u) */
  for (k = 1; k <= 15; ++k) {
    k3    = 15 * k;
    k4    = k3 + k;
    a[k4] = 1.0 / a[k4];
    stmp  = -a[k4];
    i__2  = k - 1;
    aa    = &a[k3 + 1];
    for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;
    kp1 = k + 1;
    if (15 < kp1) continue;
    ax = aa;
    for (j = kp1; j <= 15; ++j) {
      j3        = 15 * j;
      stmp      = a[k + j3];
      a[k + j3] = 0.0;
      ay        = &a[j3 + 1];
      for (ll = 0; ll < k; ll++) ay[ll] += stmp * ax[ll];
    }
  }

  /* form inverse(u)*inverse(l) */
  for (kb = 1; kb <= 14; ++kb) {
    k   = 15 - kb;
    k3  = 15 * k;
    kp1 = k + 1;
    aa  = a + k3;
    for (i = kp1; i <= 15; ++i) {
      work[i - 1] = aa[i];
      aa[i]       = 0.0;
    }
    for (j = kp1; j <= 15; ++j) {
      stmp = work[j - 1];
      ax   = &a[15 * j + 1];
      ay   = &a[k3 + 1];
      ay[0] += stmp * ax[0];
      ay[1] += stmp * ax[1];
      ay[2] += stmp * ax[2];
      ay[3] += stmp * ax[3];
      ay[4] += stmp * ax[4];
      ay[5] += stmp * ax[5];
      ay[6] += stmp * ax[6];
      ay[7] += stmp * ax[7];
      ay[8] += stmp * ax[8];
      ay[9] += stmp * ax[9];
      ay[10] += stmp * ax[10];
      ay[11] += stmp * ax[11];
      ay[12] += stmp * ax[12];
      ay[13] += stmp * ax[13];
      ay[14] += stmp * ax[14];
    }
    l = ipvt[k - 1];
    if (l != k) {
      ax     = &a[k3 + 1];
      ay     = &a[15 * l + 1];
      stmp   = ax[0];
      ax[0]  = ay[0];
      ay[0]  = stmp;
      stmp   = ax[1];
      ax[1]  = ay[1];
      ay[1]  = stmp;
      stmp   = ax[2];
      ax[2]  = ay[2];
      ay[2]  = stmp;
      stmp   = ax[3];
      ax[3]  = ay[3];
      ay[3]  = stmp;
      stmp   = ax[4];
      ax[4]  = ay[4];
      ay[4]  = stmp;
      stmp   = ax[5];
      ax[5]  = ay[5];
      ay[5]  = stmp;
      stmp   = ax[6];
      ax[6]  = ay[6];
      ay[6]  = stmp;
      stmp   = ax[7];
      ax[7]  = ay[7];
      ay[7]  = stmp;
      stmp   = ax[8];
      ax[8]  = ay[8];
      ay[8]  = stmp;
      stmp   = ax[9];
      ax[9]  = ay[9];
      ay[9]  = stmp;
      stmp   = ax[10];
      ax[10] = ay[10];
      ay[10] = stmp;
      stmp   = ax[11];
      ax[11] = ay[11];
      ay[11] = stmp;
      stmp   = ax[12];
      ax[12] = ay[12];
      ay[12] = stmp;
      stmp   = ax[13];
      ax[13] = ay[13];
      ay[13] = stmp;
      stmp   = ax[14];
      ax[14] = ay[14];
      ay[14] = stmp;
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}