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

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

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

 41:     for (i = 0; i < mbs; i++) {
 42:       jmin = ai[i];
 43:       jmax = ai[i + 1];
 44:       for (j = jmin; j < jmax; j++) {
 45:         while (a2anew[j] != j) {
 46:           k         = a2anew[j];
 47:           a2anew[j] = a2anew[k];
 48:           a2anew[k] = k;
 49:           for (k1 = 0; k1 < 9; k1++) {
 50:             dk[k1]         = aa[k * 9 + k1];
 51:             aa[k * 9 + k1] = aa[j * 9 + k1];
 52:             aa[j * 9 + k1] = dk[k1];
 53:           }
 54:         }
 55:         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
 56:         if (i > aj[j]) {
 57:           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
 58:           ap = aa + j * 9;                       /* ptr to the beginning of j-th block of aa */
 59:           for (k = 0; k < 9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
 60:           for (k = 0; k < 3; k++) {              /* j-th block of aa <- dk^T */
 61:             for (k1 = 0; k1 < 3; k1++) *ap++ = dk[k + 3 * k1];
 62:           }
 63:         }
 64:       }
 65:     }
 66:     PetscCall(PetscFree(a2anew));
 67:   }

 69:   /* for each row k */
 70:   for (k = 0; k < mbs; k++) {
 71:     /*initialize k-th row with elements nonzero in row perm(k) of A */
 72:     jmin = ai[perm_ptr[k]];
 73:     jmax = ai[perm_ptr[k] + 1];
 74:     if (jmin < jmax) {
 75:       ap = aa + jmin * 9;
 76:       for (j = jmin; j < jmax; j++) {
 77:         vj       = perm_ptr[aj[j]]; /* block col. index */
 78:         rtmp_ptr = rtmp + vj * 9;
 79:         for (i = 0; i < 9; i++) *rtmp_ptr++ = *ap++;
 80:       }
 81:     }

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

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

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

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

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

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

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

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

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

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

122:       PetscCall(PetscLogFlops(27.0 * 4.0));

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

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

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

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

149:         /* ... add i to row list for next nonzero entry */
150:         il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
151:         j     = bj[jmin];
152:         jl[i] = jl[j];
153:         jl[j] = i; /* update jl */
154:       }
155:       i = nexti;
156:     }

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

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

166:     jmin = bi[k];
167:     jmax = bi[k + 1];
168:     if (jmin < jmax) {
169:       for (j = jmin; j < jmax; j++) {
170:         vj       = bj[j]; /* block col. index of U */
171:         u        = ba + j * 9;
172:         rtmp_ptr = rtmp + vj * 9;
173:         for (k1 = 0; k1 < 9; k1++) {
174:           *u++        = *rtmp_ptr;
175:           *rtmp_ptr++ = 0.0;
176:         }
177:       }

179:       /* ... add k to row list for first nonzero entry in k-th row */
180:       il[k] = jmin;
181:       i     = bj[jmin];
182:       jl[k] = jl[i];
183:       jl[i] = k;
184:     }
185:   }

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

192:   PetscCall(ISRestoreIndices(perm, &perm_ptr));

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

199:   PetscCall(PetscLogFlops(1.3333 * 27 * b->mbs)); /* from inverting diagonal blocks */
200:   PetscFunctionReturn(PETSC_SUCCESS);
201: }