xref: /petsc/src/mat/impls/baij/seq/dgefa4.c (revision d71ae5a4db6382e7f06317b8d368875286fe9008)

/*
       Inverts 4 by 4 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 4.

*/
#include <petscsys.h>

PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_4(MatScalar *a, PetscReal shift, PetscBool allowzeropivot, PetscBool *zeropivotdetected)
{
  PetscInt   i__2, i__3, kp1, j, k, l, ll, i, ipvt[4], kb, k3;
  PetscInt   k4, j3;
  MatScalar *aa, *ax, *ay, work[16], stmp;
  MatReal    tmp, max;

  PetscFunctionBegin;
  if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE;
  shift = .25 * shift * (1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[5]) + PetscAbsScalar(a[10]) + PetscAbsScalar(a[15]));

  /* Parameter adjustments */
  a -= 5;

  for (k = 1; k <= 3; ++k) {
    kp1 = k + 1;
    k3  = 4 * k;
    k4  = k3 + k;

    /* find l = pivot index */
    i__2 = 5 - 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 {
        /* SHIFT is applied to SINGLE diagonal entry; does this make any sense? */
        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 = 4 - 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 <= 4; ++j) {
      j3   = 4 * j;
      stmp = a[l + j3];
      if (l != k) {
        a[l + j3] = a[k + j3];
        a[k + j3] = stmp;
      }

      i__3 = 4 - k;
      ay   = &a[1 + k + j3];
      for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll];
    }
  }
  ipvt[3] = 4;
  if (a[20] == 0.0) {
    if (PetscLikely(allowzeropivot)) {
      PetscCall(PetscInfo(NULL, "Zero pivot, row 3\n"));
      if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
    } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 3");
  }

  /* Now form the inverse */
  /* compute inverse(u) */
  for (k = 1; k <= 4; ++k) {
    k3    = 4 * 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 (4 < kp1) continue;
    ax = aa;
    for (j = kp1; j <= 4; ++j) {
      j3        = 4 * 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 <= 3; ++kb) {
    k   = 4 - kb;
    k3  = 4 * k;
    kp1 = k + 1;
    aa  = a + k3;
    for (i = kp1; i <= 4; ++i) {
      work[i - 1] = aa[i];
      aa[i]       = 0.0;
    }
    for (j = kp1; j <= 4; ++j) {
      stmp = work[j - 1];
      ax   = &a[4 * 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];
    }
    l = ipvt[k - 1];
    if (l != k) {
      ax    = &a[k3 + 1];
      ay    = &a[4 * 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;
    }
  }
  PetscFunctionReturn(0);
}

#if defined(PETSC_HAVE_SSE)
  #include PETSC_HAVE_SSE

PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_4_SSE(float *a)
{
  /*
     This routine is converted from Intel's Small Matrix Library.
     See: Streaming SIMD Extensions -- Inverse of 4x4 Matrix
     Order Number: 245043-001
     March 1999
     https://www.intel.com/content/www/us/en/homepage.html

     Inverse of a 4x4 matrix via Kramer's Rule:
     bool Invert4x4(SMLXMatrix &);
  */
  PetscFunctionBegin;
  SSE_SCOPE_BEGIN;
  SSE_INLINE_BEGIN_1(a)

  /* ----------------------------------------------- */

  SSE_LOADL_PS(SSE_ARG_1, FLOAT_0, XMM0)
  SSE_LOADH_PS(SSE_ARG_1, FLOAT_4, XMM0)

  SSE_LOADL_PS(SSE_ARG_1, FLOAT_8, XMM5)
  SSE_LOADH_PS(SSE_ARG_1, FLOAT_12, XMM5)

  SSE_COPY_PS(XMM3, XMM0)
  SSE_SHUFFLE(XMM3, XMM5, 0x88)

  SSE_SHUFFLE(XMM5, XMM0, 0xDD)

  SSE_LOADL_PS(SSE_ARG_1, FLOAT_2, XMM0)
  SSE_LOADH_PS(SSE_ARG_1, FLOAT_6, XMM0)

  SSE_LOADL_PS(SSE_ARG_1, FLOAT_10, XMM6)
  SSE_LOADH_PS(SSE_ARG_1, FLOAT_14, XMM6)

  SSE_COPY_PS(XMM4, XMM0)
  SSE_SHUFFLE(XMM4, XMM6, 0x88)

  SSE_SHUFFLE(XMM6, XMM0, 0xDD)

  /* ----------------------------------------------- */

  SSE_COPY_PS(XMM7, XMM4)
  SSE_MULT_PS(XMM7, XMM6)

  SSE_SHUFFLE(XMM7, XMM7, 0xB1)

  SSE_COPY_PS(XMM0, XMM5)
  SSE_MULT_PS(XMM0, XMM7)

  SSE_COPY_PS(XMM2, XMM3)
  SSE_MULT_PS(XMM2, XMM7)

  SSE_SHUFFLE(XMM7, XMM7, 0x4E)

  SSE_COPY_PS(XMM1, XMM5)
  SSE_MULT_PS(XMM1, XMM7)
  SSE_SUB_PS(XMM1, XMM0)

  SSE_MULT_PS(XMM7, XMM3)
  SSE_SUB_PS(XMM7, XMM2)

  SSE_SHUFFLE(XMM7, XMM7, 0x4E)
  SSE_STORE_PS(SSE_ARG_1, FLOAT_4, XMM7)

  /* ----------------------------------------------- */

  SSE_COPY_PS(XMM0, XMM5)
  SSE_MULT_PS(XMM0, XMM4)

  SSE_SHUFFLE(XMM0, XMM0, 0xB1)

  SSE_COPY_PS(XMM2, XMM6)
  SSE_MULT_PS(XMM2, XMM0)
  SSE_ADD_PS(XMM2, XMM1)

  SSE_COPY_PS(XMM7, XMM3)
  SSE_MULT_PS(XMM7, XMM0)

  SSE_SHUFFLE(XMM0, XMM0, 0x4E)

  SSE_COPY_PS(XMM1, XMM6)
  SSE_MULT_PS(XMM1, XMM0)
  SSE_SUB_PS(XMM2, XMM1)

  SSE_MULT_PS(XMM0, XMM3)
  SSE_SUB_PS(XMM0, XMM7)

  SSE_SHUFFLE(XMM0, XMM0, 0x4E)
  SSE_STORE_PS(SSE_ARG_1, FLOAT_12, XMM0)

  /* ----------------------------------------------- */

  SSE_COPY_PS(XMM7, XMM5)
  SSE_SHUFFLE(XMM7, XMM5, 0x4E)
  SSE_MULT_PS(XMM7, XMM6)

  SSE_SHUFFLE(XMM7, XMM7, 0xB1)

  SSE_SHUFFLE(XMM4, XMM4, 0x4E)

  SSE_COPY_PS(XMM0, XMM4)
  SSE_MULT_PS(XMM0, XMM7)
  SSE_ADD_PS(XMM0, XMM2)

  SSE_COPY_PS(XMM2, XMM3)
  SSE_MULT_PS(XMM2, XMM7)

  SSE_SHUFFLE(XMM7, XMM7, 0x4E)

  SSE_COPY_PS(XMM1, XMM4)
  SSE_MULT_PS(XMM1, XMM7)
  SSE_SUB_PS(XMM0, XMM1)
  SSE_STORE_PS(SSE_ARG_1, FLOAT_0, XMM0)

  SSE_MULT_PS(XMM7, XMM3)
  SSE_SUB_PS(XMM7, XMM2)

  SSE_SHUFFLE(XMM7, XMM7, 0x4E)

  /* ----------------------------------------------- */

  SSE_COPY_PS(XMM1, XMM3)
  SSE_MULT_PS(XMM1, XMM5)

  SSE_SHUFFLE(XMM1, XMM1, 0xB1)

  SSE_COPY_PS(XMM0, XMM6)
  SSE_MULT_PS(XMM0, XMM1)
  SSE_ADD_PS(XMM0, XMM7)

  SSE_COPY_PS(XMM2, XMM4)
  SSE_MULT_PS(XMM2, XMM1)
  SSE_SUB_PS_M(XMM2, SSE_ARG_1, FLOAT_12)

  SSE_SHUFFLE(XMM1, XMM1, 0x4E)

  SSE_COPY_PS(XMM7, XMM6)
  SSE_MULT_PS(XMM7, XMM1)
  SSE_SUB_PS(XMM7, XMM0)

  SSE_MULT_PS(XMM1, XMM4)
  SSE_SUB_PS(XMM2, XMM1)
  SSE_STORE_PS(SSE_ARG_1, FLOAT_12, XMM2)

  /* ----------------------------------------------- */

  SSE_COPY_PS(XMM1, XMM3)
  SSE_MULT_PS(XMM1, XMM6)

  SSE_SHUFFLE(XMM1, XMM1, 0xB1)

  SSE_COPY_PS(XMM2, XMM4)
  SSE_MULT_PS(XMM2, XMM1)
  SSE_LOAD_PS(SSE_ARG_1, FLOAT_4, XMM0)
  SSE_SUB_PS(XMM0, XMM2)

  SSE_COPY_PS(XMM2, XMM5)
  SSE_MULT_PS(XMM2, XMM1)
  SSE_ADD_PS(XMM2, XMM7)

  SSE_SHUFFLE(XMM1, XMM1, 0x4E)

  SSE_COPY_PS(XMM7, XMM4)
  SSE_MULT_PS(XMM7, XMM1)
  SSE_ADD_PS(XMM7, XMM0)

  SSE_MULT_PS(XMM1, XMM5)
  SSE_SUB_PS(XMM2, XMM1)

  /* ----------------------------------------------- */

  SSE_MULT_PS(XMM4, XMM3)

  SSE_SHUFFLE(XMM4, XMM4, 0xB1)

  SSE_COPY_PS(XMM1, XMM6)
  SSE_MULT_PS(XMM1, XMM4)
  SSE_ADD_PS(XMM1, XMM7)

  SSE_COPY_PS(XMM0, XMM5)
  SSE_MULT_PS(XMM0, XMM4)
  SSE_LOAD_PS(SSE_ARG_1, FLOAT_12, XMM7)
  SSE_SUB_PS(XMM7, XMM0)

  SSE_SHUFFLE(XMM4, XMM4, 0x4E)

  SSE_MULT_PS(XMM6, XMM4)
  SSE_SUB_PS(XMM1, XMM6)

  SSE_MULT_PS(XMM5, XMM4)
  SSE_ADD_PS(XMM5, XMM7)

  /* ----------------------------------------------- */

  SSE_LOAD_PS(SSE_ARG_1, FLOAT_0, XMM0)
  SSE_MULT_PS(XMM3, XMM0)

  SSE_COPY_PS(XMM4, XMM3)
  SSE_SHUFFLE(XMM4, XMM3, 0x4E)
  SSE_ADD_PS(XMM4, XMM3)

  SSE_COPY_PS(XMM6, XMM4)
  SSE_SHUFFLE(XMM6, XMM4, 0xB1)
  SSE_ADD_SS(XMM6, XMM4)

  SSE_COPY_PS(XMM3, XMM6)
  SSE_RECIP_SS(XMM3, XMM6)
  SSE_COPY_SS(XMM4, XMM3)
  SSE_ADD_SS(XMM4, XMM3)
  SSE_MULT_SS(XMM3, XMM3)
  SSE_MULT_SS(XMM6, XMM3)
  SSE_SUB_SS(XMM4, XMM6)

  SSE_SHUFFLE(XMM4, XMM4, 0x00)

  SSE_MULT_PS(XMM0, XMM4)
  SSE_STOREL_PS(SSE_ARG_1, FLOAT_0, XMM0)
  SSE_STOREH_PS(SSE_ARG_1, FLOAT_2, XMM0)

  SSE_MULT_PS(XMM1, XMM4)
  SSE_STOREL_PS(SSE_ARG_1, FLOAT_4, XMM1)
  SSE_STOREH_PS(SSE_ARG_1, FLOAT_6, XMM1)

  SSE_MULT_PS(XMM2, XMM4)
  SSE_STOREL_PS(SSE_ARG_1, FLOAT_8, XMM2)
  SSE_STOREH_PS(SSE_ARG_1, FLOAT_10, XMM2)

  SSE_MULT_PS(XMM4, XMM5)
  SSE_STOREL_PS(SSE_ARG_1, FLOAT_12, XMM4)
  SSE_STOREH_PS(SSE_ARG_1, FLOAT_14, XMM4)

  /* ----------------------------------------------- */

  SSE_INLINE_END_1;
  SSE_SCOPE_END;
  PetscFunctionReturn(0);
}

#endif