1: /*
  2:      Inverts 3 by 3 matrix using gaussian elimination with partial pivoting.

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

  7:        This is a combination of the Linpack routines
  8:     dgefa() and dgedi() specialized for a size of 3.

 10: */
 11: #include <petscsys.h>

 13: PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_3(MatScalar *a, PetscReal shift, PetscBool allowzeropivot, PetscBool *zeropivotdetected)
 14: {
 15:   PetscInt   i__2, i__3, kp1, j, k, l, ll, i, ipvt[3], kb, k3;
 16:   PetscInt   k4, j3;
 17:   MatScalar *aa, *ax, *ay, work[9], stmp;
 18:   MatReal    tmp, max;

 20:   PetscFunctionBegin;
 21:   if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE;
 22:   shift = .333 * shift * (1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[4]) + PetscAbsScalar(a[8]));

 24:   /* Parameter adjustments */
 25:   a -= 4;

 27:   for (k = 1; k <= 2; ++k) {
 28:     kp1 = k + 1;
 29:     k3  = 3 * k;
 30:     k4  = k3 + k;

 32:     /* find l = pivot index */
 33:     i__2 = 4 - k;
 34:     aa   = &a[k4];
 35:     max  = PetscAbsScalar(aa[0]);
 36:     l    = 1;
 37:     for (ll = 1; ll < i__2; ll++) {
 38:       tmp = PetscAbsScalar(aa[ll]);
 39:       if (tmp > max) {
 40:         max = tmp;
 41:         l   = ll + 1;
 42:       }
 43:     }
 44:     l += k - 1;
 45:     ipvt[k - 1] = l;

 47:     if (a[l + k3] == 0.0) {
 48:       if (shift == 0.0) {
 49:         if (allowzeropivot) {
 50:           PetscCall(PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1));
 51:           if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
 52:         } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1);
 53:       } else {
 54:         /* Shift is applied to single diagonal entry */
 55:         a[l + k3] = shift;
 56:       }
 57:     }

 59:     /* interchange if necessary */
 60:     if (l != k) {
 61:       stmp      = a[l + k3];
 62:       a[l + k3] = a[k4];
 63:       a[k4]     = stmp;
 64:     }

 66:     /* compute multipliers */
 67:     stmp = -1. / a[k4];
 68:     i__2 = 3 - k;
 69:     aa   = &a[1 + k4];
 70:     for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;

 72:     /* row elimination with column indexing */
 73:     ax = &a[k4 + 1];
 74:     for (j = kp1; j <= 3; ++j) {
 75:       j3   = 3 * j;
 76:       stmp = a[l + j3];
 77:       if (l != k) {
 78:         a[l + j3] = a[k + j3];
 79:         a[k + j3] = stmp;
 80:       }

 82:       i__3 = 3 - k;
 83:       ay   = &a[1 + k + j3];
 84:       for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll];
 85:     }
 86:   }
 87:   ipvt[2] = 3;
 88:   if (a[12] == 0.0) {
 89:     if (PetscLikely(allowzeropivot)) {
 90:       PetscCall(PetscInfo(NULL, "Zero pivot, row 2\n"));
 91:       if (zeropivotdetected) *zeropivotdetected = PETSC_TRUE;
 92:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 2");
 93:   }

 95:   /* Now form the inverse */
 96:   /* compute inverse(u) */
 97:   for (k = 1; k <= 3; ++k) {
 98:     k3    = 3 * k;
 99:     k4    = k3 + k;
100:     a[k4] = 1.0 / a[k4];
101:     stmp  = -a[k4];
102:     i__2  = k - 1;
103:     aa    = &a[k3 + 1];
104:     for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;
105:     kp1 = k + 1;
106:     if (3 < kp1) continue;
107:     ax = aa;
108:     for (j = kp1; j <= 3; ++j) {
109:       j3        = 3 * j;
110:       stmp      = a[k + j3];
111:       a[k + j3] = 0.0;
112:       ay        = &a[j3 + 1];
113:       for (ll = 0; ll < k; ll++) ay[ll] += stmp * ax[ll];
114:     }
115:   }

117:   /* form inverse(u)*inverse(l) */
118:   for (kb = 1; kb <= 2; ++kb) {
119:     k   = 3 - kb;
120:     k3  = 3 * k;
121:     kp1 = k + 1;
122:     aa  = a + k3;
123:     for (i = kp1; i <= 3; ++i) {
124:       work[i - 1] = aa[i];
125:       aa[i]       = 0.0;
126:     }
127:     for (j = kp1; j <= 3; ++j) {
128:       stmp = work[j - 1];
129:       ax   = &a[3 * j + 1];
130:       ay   = &a[k3 + 1];
131:       ay[0] += stmp * ax[0];
132:       ay[1] += stmp * ax[1];
133:       ay[2] += stmp * ax[2];
134:     }
135:     l = ipvt[k - 1];
136:     if (l != k) {
137:       ax    = &a[k3 + 1];
138:       ay    = &a[3 * l + 1];
139:       stmp  = ax[0];
140:       ax[0] = ay[0];
141:       ay[0] = stmp;
142:       stmp  = ax[1];
143:       ax[1] = ay[1];
144:       ay[1] = stmp;
145:       stmp  = ax[2];
146:       ax[2] = ay[2];
147:       ay[2] = stmp;
148:     }
149:   }
150:   PetscFunctionReturn(PETSC_SUCCESS);
151: }