Actual source code: sbaijfact3.c


  2: #include <../src/mat/impls/sbaij/seq/sbaij.h>
  3: #include <petsc/private/kernels/blockinvert.h>

  5: /* Version for when blocks are 3 by 3  */
  6: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat C, Mat A, const MatFactorInfo *info)
  7: {
  8:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ *)A->data, *b = (Mat_SeqSBAIJ *)C->data;
  9:   IS              perm = b->row;
 10:   const PetscInt *ai, *aj, *perm_ptr, mbs = a->mbs, *bi = b->i, *bj = b->j;
 11:   PetscInt       *a2anew, i, j, k, k1, jmin, jmax, *jl, *il, vj, nexti, ili;
 12:   MatScalar      *ba = b->a, *aa, *ap, *dk, *uik;
 13:   MatScalar      *u, *diag, *rtmp, *rtmp_ptr;
 14:   PetscReal       shift = info->shiftamount;
 15:   PetscBool       allowzeropivot, zeropivotdetected;

 17:   /* initialization */
 18:   allowzeropivot = PetscNot(A->erroriffailure);
 19:   PetscCalloc1(9 * mbs, &rtmp);
 20:   PetscMalloc2(mbs, &il, mbs, &jl);
 21:   il[0] = 0;
 22:   for (i = 0; i < mbs; i++) jl[i] = mbs;

 24:   PetscMalloc2(9, &dk, 9, &uik);
 25:   ISGetIndices(perm, &perm_ptr);

 27:   /* check permutation */
 28:   if (!a->permute) {
 29:     ai = a->i;
 30:     aj = a->j;
 31:     aa = a->a;
 32:   } else {
 33:     ai = a->inew;
 34:     aj = a->jnew;
 35:     PetscMalloc1(9 * ai[mbs], &aa);
 36:     PetscArraycpy(aa, a->a, 9 * ai[mbs]);
 37:     PetscMalloc1(ai[mbs], &a2anew);
 38:     PetscArraycpy(a2anew, a->a2anew, ai[mbs]);

 40:     for (i = 0; i < mbs; i++) {
 41:       jmin = ai[i];
 42:       jmax = ai[i + 1];
 43:       for (j = jmin; j < jmax; j++) {
 44:         while (a2anew[j] != j) {
 45:           k         = a2anew[j];
 46:           a2anew[j] = a2anew[k];
 47:           a2anew[k] = k;
 48:           for (k1 = 0; k1 < 9; k1++) {
 49:             dk[k1]         = aa[k * 9 + k1];
 50:             aa[k * 9 + k1] = aa[j * 9 + k1];
 51:             aa[j * 9 + k1] = dk[k1];
 52:           }
 53:         }
 54:         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
 55:         if (i > aj[j]) {
 56:           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
 57:           ap = aa + j * 9;                       /* ptr to the beginning of j-th block of aa */
 58:           for (k = 0; k < 9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
 59:           for (k = 0; k < 3; k++) {              /* j-th block of aa <- dk^T */
 60:             for (k1 = 0; k1 < 3; k1++) *ap++ = dk[k + 3 * k1];
 61:           }
 62:         }
 63:       }
 64:     }
 65:     PetscFree(a2anew);
 66:   }

 68:   /* for each row k */
 69:   for (k = 0; k < mbs; k++) {
 70:     /*initialize k-th row with elements nonzero in row perm(k) of A */
 71:     jmin = ai[perm_ptr[k]];
 72:     jmax = ai[perm_ptr[k] + 1];
 73:     if (jmin < jmax) {
 74:       ap = aa + jmin * 9;
 75:       for (j = jmin; j < jmax; j++) {
 76:         vj       = perm_ptr[aj[j]]; /* block col. index */
 77:         rtmp_ptr = rtmp + vj * 9;
 78:         for (i = 0; i < 9; i++) *rtmp_ptr++ = *ap++;
 79:       }
 80:     }

 82:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
 83:     PetscArraycpy(dk, rtmp + k * 9, 9);
 84:     i = jl[k]; /* first row to be added to k_th row  */

 86:     while (i < mbs) {
 87:       nexti = jl[i]; /* next row to be added to k_th row */

 89:       /* compute multiplier */
 90:       ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */

 92:       /* uik = -inv(Di)*U_bar(i,k) */
 93:       diag = ba + i * 9;
 94:       u    = ba + ili * 9;

 96:       uik[0] = -(diag[0] * u[0] + diag[3] * u[1] + diag[6] * u[2]);
 97:       uik[1] = -(diag[1] * u[0] + diag[4] * u[1] + diag[7] * u[2]);
 98:       uik[2] = -(diag[2] * u[0] + diag[5] * u[1] + diag[8] * u[2]);

100:       uik[3] = -(diag[0] * u[3] + diag[3] * u[4] + diag[6] * u[5]);
101:       uik[4] = -(diag[1] * u[3] + diag[4] * u[4] + diag[7] * u[5]);
102:       uik[5] = -(diag[2] * u[3] + diag[5] * u[4] + diag[8] * u[5]);

104:       uik[6] = -(diag[0] * u[6] + diag[3] * u[7] + diag[6] * u[8]);
105:       uik[7] = -(diag[1] * u[6] + diag[4] * u[7] + diag[7] * u[8]);
106:       uik[8] = -(diag[2] * u[6] + diag[5] * u[7] + diag[8] * u[8]);

108:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
109:       dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2];
110:       dk[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2];
111:       dk[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2];

113:       dk[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5];
114:       dk[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5];
115:       dk[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5];

117:       dk[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8];
118:       dk[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8];
119:       dk[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8];

121:       PetscLogFlops(27.0 * 4.0);

123:       /* update -U(i,k) */
124:       PetscArraycpy(ba + ili * 9, uik, 9);

126:       /* add multiple of row i to k-th row ... */
127:       jmin = ili + 1;
128:       jmax = bi[i + 1];
129:       if (jmin < jmax) {
130:         for (j = jmin; j < jmax; j++) {
131:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
132:           rtmp_ptr = rtmp + bj[j] * 9;
133:           u        = ba + j * 9;
134:           rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2];
135:           rtmp_ptr[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2];
136:           rtmp_ptr[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2];

138:           rtmp_ptr[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5];
139:           rtmp_ptr[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5];
140:           rtmp_ptr[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5];

142:           rtmp_ptr[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8];
143:           rtmp_ptr[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8];
144:           rtmp_ptr[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8];
145:         }
146:         PetscLogFlops(2.0 * 27.0 * (jmax - jmin));

148:         /* ... add i to row list for next nonzero entry */
149:         il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
150:         j     = bj[jmin];
151:         jl[i] = jl[j];
152:         jl[j] = i; /* update jl */
153:       }
154:       i = nexti;
155:     }

157:     /* save nonzero entries in k-th row of U ... */

159:     /* invert diagonal block */
160:     diag = ba + k * 9;
161:     PetscArraycpy(diag, dk, 9);
162:     PetscKernel_A_gets_inverse_A_3(diag, shift, allowzeropivot, &zeropivotdetected);
163:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

165:     jmin = bi[k];
166:     jmax = bi[k + 1];
167:     if (jmin < jmax) {
168:       for (j = jmin; j < jmax; j++) {
169:         vj       = bj[j]; /* block col. index of U */
170:         u        = ba + j * 9;
171:         rtmp_ptr = rtmp + vj * 9;
172:         for (k1 = 0; k1 < 9; k1++) {
173:           *u++        = *rtmp_ptr;
174:           *rtmp_ptr++ = 0.0;
175:         }
176:       }

178:       /* ... add k to row list for first nonzero entry in k-th row */
179:       il[k] = jmin;
180:       i     = bj[jmin];
181:       jl[k] = jl[i];
182:       jl[i] = k;
183:     }
184:   }

186:   PetscFree(rtmp);
187:   PetscFree2(il, jl);
188:   PetscFree2(dk, uik);
189:   if (a->permute) PetscFree(aa);

191:   ISRestoreIndices(perm, &perm_ptr);

193:   C->ops->solve          = MatSolve_SeqSBAIJ_3_inplace;
194:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_inplace;
195:   C->assembled           = PETSC_TRUE;
196:   C->preallocated        = PETSC_TRUE;

198:   PetscLogFlops(1.3333 * 27 * b->mbs); /* from inverting diagonal blocks */
199:   return 0;
200: }