Actual source code: dgefa5.c

  1: /*
  2:       Inverts 5 by 5 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 5.

 10: */
 11: #include <petscsys.h>
 12: #include <petsc/private/kernels/blockinvert.h>

 14: 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:         PetscCheck(allowzeropivot, PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row %" PetscInt_FMT, k - 1);
 51:         PetscCall(PetscInfo(NULL, "Zero pivot, row %" PetscInt_FMT "\n", k - 1));
 52:         *zeropivotdetected = PETSC_TRUE;
 53:       } else {
 54:         /* SHIFT is applied to SINGLE diagonal entry; does this make any sense? */
 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 = 5 - 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 <= 5; ++j) {
 75:       j3   = 5 * 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 = 5 - k;
 83:       ay   = &a[1 + k + j3];
 84:       for (ll = 0; ll < i__3; ll++) ay[ll] += stmp * ax[ll];
 85:     }
 86:   }
 87:   ipvt[4] = 5;
 88:   if (a[30] == 0.0) {
 89:     PetscCheck(PetscLikely(allowzeropivot), PETSC_COMM_SELF, PETSC_ERR_MAT_LU_ZRPVT, "Zero pivot, row 4");
 90:     PetscCall(PetscInfo(NULL, "Zero pivot, row 4\n"));
 91:     *zeropivotdetected = PETSC_TRUE;
 92:   }

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

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