Actual source code: dgefa5.c


  2: /*
  3:       Inverts 5 by 5 matrix using gaussian elimination with partial pivoting.

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

  8:        This is a combination of the Linpack routines
  9:     dgefa() and dgedi() specialized for a size of 5.

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

 14: PETSC_EXTERN PetscErrorCode PetscKernel_A_gets_inverse_A_5(MatScalar *a, PetscInt *ipvt, MatScalar *work, PetscReal shift, PetscBool allowzeropivot, PetscBool *zeropivotdetected)
 15: {
 16:   PetscInt   i__2, i__3, kp1, j, k, l, ll, i, kb, k3;
 17:   PetscInt   k4, j3;
 18:   MatScalar *aa, *ax, *ay, stmp;
 19:   MatReal    tmp, max;

 21:   PetscFunctionBegin;
 22:   if (zeropivotdetected) *zeropivotdetected = PETSC_FALSE;
 23:   shift = .25 * shift * (1.e-12 + PetscAbsScalar(a[0]) + PetscAbsScalar(a[6]) + PetscAbsScalar(a[12]) + PetscAbsScalar(a[18]) + PetscAbsScalar(a[24]));

 25:   /* Parameter adjustments */
 26:   a -= 6;

 28:   for (k = 1; k <= 4; ++k) {
 29:     kp1 = k + 1;
 30:     k3  = 5 * k;
 31:     k4  = k3 + k;

 33:     /* find l = pivot index */
 34:     i__2 = 6 - k;
 35:     aa   = &a[k4];
 36:     max  = PetscAbsScalar(aa[0]);
 37:     l    = 1;
 38:     for (ll = 1; ll < i__2; ll++) {
 39:       tmp = PetscAbsScalar(aa[ll]);
 40:       if (tmp > max) {
 41:         max = tmp;
 42:         l   = ll + 1;
 43:       }
 44:     }
 45:     l += k - 1;
 46:     ipvt[k - 1] = l;

 48:     if (a[l + k3] == 0.0) {
 49:       if (shift == 0.0) {
 50:         if (allowzeropivot) {
 51:           PetscCall(PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1));
 52:           *zeropivotdetected = PETSC_TRUE;
 53:         } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1);
 54:       } else {
 55:         /* SHIFT is applied to SINGLE diagonal entry; does this make any sense? */
 56:         a[l + k3] = shift;
 57:       }
 58:     }

 60:     /* interchange if necessary */
 61:     if (l != k) {
 62:       stmp      = a[l + k3];
 63:       a[l + k3] = a[k4];
 64:       a[k4]     = stmp;
 65:     }

 67:     /* compute multipliers */
 68:     stmp = -1. / a[k4];
 69:     i__2 = 5 - k;
 70:     aa   = &a[1 + k4];
 71:     for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;

 73:     /* row elimination with column indexing */
 74:     ax = &a[k4 + 1];
 75:     for (j = kp1; j <= 5; ++j) {
 76:       j3   = 5 * j;
 77:       stmp = a[l + j3];
 78:       if (l != k) {
 79:         a[l + j3] = a[k + j3];
 80:         a[k + j3] = stmp;
 81:       }

 83:       i__3 = 5 - k;
 84:       ay   = &a[1 + k + j3];
 85:       for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll];
 86:     }
 87:   }
 88:   ipvt[4] = 5;
 89:   if (a[30] == 0.0) {
 90:     if (PetscLikely(allowzeropivot)) {
 91:       PetscCall(PetscInfo(NULL, "Zero pivot, row 4\n"));
 92:       *zeropivotdetected = PETSC_TRUE;
 93:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 4");
 94:   }

 96:   /* Now form the inverse */
 97:   /* compute inverse(u) */
 98:   for (k = 1; k <= 5; ++k) {
 99:     k3    = 5 * k;
100:     k4    = k3 + k;
101:     a[k4] = 1.0 / a[k4];
102:     stmp  = -a[k4];
103:     i__2  = k - 1;
104:     aa    = &a[k3 + 1];
105:     for (ll = 0; ll < i__2; ll++) aa[ll] *= stmp;
106:     kp1 = k + 1;
107:     if (5 < kp1) continue;
108:     ax = aa;
109:     for (j = kp1; j <= 5; ++j) {
110:       j3        = 5 * j;
111:       stmp      = a[k + j3];
112:       a[k + j3] = 0.0;
113:       ay        = &a[j3 + 1];
114:       for (ll = 0; ll < k; ll++) ay[ll] += stmp * ax[ll];
115:     }
116:   }

118:   /* form inverse(u)*inverse(l) */
119:   for (kb = 1; kb <= 4; ++kb) {
120:     k   = 5 - kb;
121:     k3  = 5 * k;
122:     kp1 = k + 1;
123:     aa  = a + k3;
124:     for (i = kp1; i <= 5; ++i) {
125:       work[i - 1] = aa[i];
126:       aa[i]       = 0.0;
127:     }
128:     for (j = kp1; j <= 5; ++j) {
129:       stmp = work[j - 1];
130:       ax   = &a[5 * j + 1];
131:       ay   = &a[k3 + 1];
132:       ay[0] += stmp * ax[0];
133:       ay[1] += stmp * ax[1];
134:       ay[2] += stmp * ax[2];
135:       ay[3] += stmp * ax[3];
136:       ay[4] += stmp * ax[4];
137:     }
138:     l = ipvt[k - 1];
139:     if (l != k) {
140:       ax    = &a[k3 + 1];
141:       ay    = &a[5 * l + 1];
142:       stmp  = ax[0];
143:       ax[0] = ay[0];
144:       ay[0] = stmp;
145:       stmp  = ax[1];
146:       ax[1] = ay[1];
147:       ay[1] = stmp;
148:       stmp  = ax[2];
149:       ax[2] = ay[2];
150:       ay[2] = stmp;
151:       stmp  = ax[3];
152:       ax[3] = ay[3];
153:       ay[3] = stmp;
154:       stmp  = ax[4];
155:       ax[4] = ay[4];
156:       ay[4] = stmp;
157:     }
158:   }
159:   PetscFunctionReturn(PETSC_SUCCESS);
160: }