xref: /petsc/src/mat/impls/baij/seq/dgefa2.c (revision 9566063d113dddea24716c546802770db7481bc0)

/*
     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(0);
}

/* 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(0);
}

/*
      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(0);
}