Actual source code: sbaijfact8.c


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

  5: /*
  6:       Version for when blocks are 5 by 5 Using natural ordering
  7: */
  8: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat C, Mat A, const MatFactorInfo *info)
  9: {
 10:   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data, *b = (Mat_SeqSBAIJ *)C->data;
 11:   PetscInt      i, j, mbs = a->mbs, *bi = b->i, *bj = b->j;
 12:   PetscInt     *ai, *aj, k, k1, jmin, jmax, *jl, *il, vj, nexti, ili, ipvt[5];
 13:   MatScalar    *ba = b->a, *aa, *ap, *dk, *uik;
 14:   MatScalar    *u, *d, *rtmp, *rtmp_ptr, work[25];
 15:   PetscReal     shift = info->shiftamount;
 16:   PetscBool     allowzeropivot, zeropivotdetected;

 18:   PetscFunctionBegin;
 19:   /* initialization */
 20:   allowzeropivot = PetscNot(A->erroriffailure);
 21:   PetscCall(PetscCalloc1(25 * mbs, &rtmp));
 22:   PetscCall(PetscMalloc2(mbs, &il, mbs, &jl));
 23:   il[0] = 0;
 24:   for (i = 0; i < mbs; i++) jl[i] = mbs;

 26:   PetscCall(PetscMalloc2(25, &dk, 25, &uik));
 27:   ai = a->i;
 28:   aj = a->j;
 29:   aa = a->a;

 31:   /* for each row k */
 32:   for (k = 0; k < mbs; k++) {
 33:     /*initialize k-th row with elements nonzero in row k of A */
 34:     jmin = ai[k];
 35:     jmax = ai[k + 1];
 36:     if (jmin < jmax) {
 37:       ap = aa + jmin * 25;
 38:       for (j = jmin; j < jmax; j++) {
 39:         vj       = aj[j]; /* block col. index */
 40:         rtmp_ptr = rtmp + vj * 25;
 41:         for (i = 0; i < 25; i++) *rtmp_ptr++ = *ap++;
 42:       }
 43:     }

 45:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
 46:     PetscCall(PetscArraycpy(dk, rtmp + k * 25, 25));
 47:     i = jl[k]; /* first row to be added to k_th row  */

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

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

 55:       /* uik = -inv(Di)*U_bar(i,k) */
 56:       d = ba + i * 25;
 57:       u = ba + ili * 25;

 59:       uik[0] = -(d[0] * u[0] + d[5] * u[1] + d[10] * u[2] + d[15] * u[3] + d[20] * u[4]);
 60:       uik[1] = -(d[1] * u[0] + d[6] * u[1] + d[11] * u[2] + d[16] * u[3] + d[21] * u[4]);
 61:       uik[2] = -(d[2] * u[0] + d[7] * u[1] + d[12] * u[2] + d[17] * u[3] + d[22] * u[4]);
 62:       uik[3] = -(d[3] * u[0] + d[8] * u[1] + d[13] * u[2] + d[18] * u[3] + d[23] * u[4]);
 63:       uik[4] = -(d[4] * u[0] + d[9] * u[1] + d[14] * u[2] + d[19] * u[3] + d[24] * u[4]);

 65:       uik[5] = -(d[0] * u[5] + d[5] * u[6] + d[10] * u[7] + d[15] * u[8] + d[20] * u[9]);
 66:       uik[6] = -(d[1] * u[5] + d[6] * u[6] + d[11] * u[7] + d[16] * u[8] + d[21] * u[9]);
 67:       uik[7] = -(d[2] * u[5] + d[7] * u[6] + d[12] * u[7] + d[17] * u[8] + d[22] * u[9]);
 68:       uik[8] = -(d[3] * u[5] + d[8] * u[6] + d[13] * u[7] + d[18] * u[8] + d[23] * u[9]);
 69:       uik[9] = -(d[4] * u[5] + d[9] * u[6] + d[14] * u[7] + d[19] * u[8] + d[24] * u[9]);

 71:       uik[10] = -(d[0] * u[10] + d[5] * u[11] + d[10] * u[12] + d[15] * u[13] + d[20] * u[14]);
 72:       uik[11] = -(d[1] * u[10] + d[6] * u[11] + d[11] * u[12] + d[16] * u[13] + d[21] * u[14]);
 73:       uik[12] = -(d[2] * u[10] + d[7] * u[11] + d[12] * u[12] + d[17] * u[13] + d[22] * u[14]);
 74:       uik[13] = -(d[3] * u[10] + d[8] * u[11] + d[13] * u[12] + d[18] * u[13] + d[23] * u[14]);
 75:       uik[14] = -(d[4] * u[10] + d[9] * u[11] + d[14] * u[12] + d[19] * u[13] + d[24] * u[14]);

 77:       uik[15] = -(d[0] * u[15] + d[5] * u[16] + d[10] * u[17] + d[15] * u[18] + d[20] * u[19]);
 78:       uik[16] = -(d[1] * u[15] + d[6] * u[16] + d[11] * u[17] + d[16] * u[18] + d[21] * u[19]);
 79:       uik[17] = -(d[2] * u[15] + d[7] * u[16] + d[12] * u[17] + d[17] * u[18] + d[22] * u[19]);
 80:       uik[18] = -(d[3] * u[15] + d[8] * u[16] + d[13] * u[17] + d[18] * u[18] + d[23] * u[19]);
 81:       uik[19] = -(d[4] * u[15] + d[9] * u[16] + d[14] * u[17] + d[19] * u[18] + d[24] * u[19]);

 83:       uik[20] = -(d[0] * u[20] + d[5] * u[21] + d[10] * u[22] + d[15] * u[23] + d[20] * u[24]);
 84:       uik[21] = -(d[1] * u[20] + d[6] * u[21] + d[11] * u[22] + d[16] * u[23] + d[21] * u[24]);
 85:       uik[22] = -(d[2] * u[20] + d[7] * u[21] + d[12] * u[22] + d[17] * u[23] + d[22] * u[24]);
 86:       uik[23] = -(d[3] * u[20] + d[8] * u[21] + d[13] * u[22] + d[18] * u[23] + d[23] * u[24]);
 87:       uik[24] = -(d[4] * u[20] + d[9] * u[21] + d[14] * u[22] + d[19] * u[23] + d[24] * u[24]);

 89:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
 90:       dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3] + uik[4] * u[4];
 91:       dk[1] += uik[5] * u[0] + uik[6] * u[1] + uik[7] * u[2] + uik[8] * u[3] + uik[9] * u[4];
 92:       dk[2] += uik[10] * u[0] + uik[11] * u[1] + uik[12] * u[2] + uik[13] * u[3] + uik[14] * u[4];
 93:       dk[3] += uik[15] * u[0] + uik[16] * u[1] + uik[17] * u[2] + uik[18] * u[3] + uik[19] * u[4];
 94:       dk[4] += uik[20] * u[0] + uik[21] * u[1] + uik[22] * u[2] + uik[23] * u[3] + uik[24] * u[4];

 96:       dk[5] += uik[0] * u[5] + uik[1] * u[6] + uik[2] * u[7] + uik[3] * u[8] + uik[4] * u[9];
 97:       dk[6] += uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8] + uik[9] * u[9];
 98:       dk[7] += uik[10] * u[5] + uik[11] * u[6] + uik[12] * u[7] + uik[13] * u[8] + uik[14] * u[9];
 99:       dk[8] += uik[15] * u[5] + uik[16] * u[6] + uik[17] * u[7] + uik[18] * u[8] + uik[19] * u[9];
100:       dk[9] += uik[20] * u[5] + uik[21] * u[6] + uik[22] * u[7] + uik[23] * u[8] + uik[24] * u[9];

102:       dk[10] += uik[0] * u[10] + uik[1] * u[11] + uik[2] * u[12] + uik[3] * u[13] + uik[4] * u[14];
103:       dk[11] += uik[5] * u[10] + uik[6] * u[11] + uik[7] * u[12] + uik[8] * u[13] + uik[9] * u[14];
104:       dk[12] += uik[10] * u[10] + uik[11] * u[11] + uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14];
105:       dk[13] += uik[15] * u[10] + uik[16] * u[11] + uik[17] * u[12] + uik[18] * u[13] + uik[19] * u[14];
106:       dk[14] += uik[20] * u[10] + uik[21] * u[11] + uik[22] * u[12] + uik[23] * u[13] + uik[24] * u[14];

108:       dk[15] += uik[0] * u[15] + uik[1] * u[16] + uik[2] * u[17] + uik[3] * u[18] + uik[4] * u[19];
109:       dk[16] += uik[5] * u[15] + uik[6] * u[16] + uik[7] * u[17] + uik[8] * u[18] + uik[9] * u[19];
110:       dk[17] += uik[10] * u[15] + uik[11] * u[16] + uik[12] * u[17] + uik[13] * u[18] + uik[14] * u[19];
111:       dk[18] += uik[15] * u[15] + uik[16] * u[16] + uik[17] * u[17] + uik[18] * u[18] + uik[19] * u[19];
112:       dk[19] += uik[20] * u[15] + uik[21] * u[16] + uik[22] * u[17] + uik[23] * u[18] + uik[24] * u[19];

114:       dk[20] += uik[0] * u[20] + uik[1] * u[21] + uik[2] * u[22] + uik[3] * u[23] + uik[4] * u[24];
115:       dk[21] += uik[5] * u[20] + uik[6] * u[21] + uik[7] * u[22] + uik[8] * u[23] + uik[9] * u[24];
116:       dk[22] += uik[10] * u[20] + uik[11] * u[21] + uik[12] * u[22] + uik[13] * u[23] + uik[14] * u[24];
117:       dk[23] += uik[15] * u[20] + uik[16] * u[21] + uik[17] * u[22] + uik[18] * u[23] + uik[19] * u[24];
118:       dk[24] += uik[20] * u[20] + uik[21] * u[21] + uik[22] * u[22] + uik[23] * u[23] + uik[24] * u[24];

120:       PetscCall(PetscLogFlops(125.0 * 4.0));

122:       /* update -U(i,k) */
123:       PetscCall(PetscArraycpy(ba + ili * 25, uik, 25));

125:       /* add multiple of row i to k-th row ... */
126:       jmin = ili + 1;
127:       jmax = bi[i + 1];
128:       if (jmin < jmax) {
129:         for (j = jmin; j < jmax; j++) {
130:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
131:           rtmp_ptr = rtmp + bj[j] * 25;
132:           u        = ba + j * 25;
133:           rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3] + uik[4] * u[4];
134:           rtmp_ptr[1] += uik[5] * u[0] + uik[6] * u[1] + uik[7] * u[2] + uik[8] * u[3] + uik[9] * u[4];
135:           rtmp_ptr[2] += uik[10] * u[0] + uik[11] * u[1] + uik[12] * u[2] + uik[13] * u[3] + uik[14] * u[4];
136:           rtmp_ptr[3] += uik[15] * u[0] + uik[16] * u[1] + uik[17] * u[2] + uik[18] * u[3] + uik[19] * u[4];
137:           rtmp_ptr[4] += uik[20] * u[0] + uik[21] * u[1] + uik[22] * u[2] + uik[23] * u[3] + uik[24] * u[4];

139:           rtmp_ptr[5] += uik[0] * u[5] + uik[1] * u[6] + uik[2] * u[7] + uik[3] * u[8] + uik[4] * u[9];
140:           rtmp_ptr[6] += uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8] + uik[9] * u[9];
141:           rtmp_ptr[7] += uik[10] * u[5] + uik[11] * u[6] + uik[12] * u[7] + uik[13] * u[8] + uik[14] * u[9];
142:           rtmp_ptr[8] += uik[15] * u[5] + uik[16] * u[6] + uik[17] * u[7] + uik[18] * u[8] + uik[19] * u[9];
143:           rtmp_ptr[9] += uik[20] * u[5] + uik[21] * u[6] + uik[22] * u[7] + uik[23] * u[8] + uik[24] * u[9];

145:           rtmp_ptr[10] += uik[0] * u[10] + uik[1] * u[11] + uik[2] * u[12] + uik[3] * u[13] + uik[4] * u[14];
146:           rtmp_ptr[11] += uik[5] * u[10] + uik[6] * u[11] + uik[7] * u[12] + uik[8] * u[13] + uik[9] * u[14];
147:           rtmp_ptr[12] += uik[10] * u[10] + uik[11] * u[11] + uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14];
148:           rtmp_ptr[13] += uik[15] * u[10] + uik[16] * u[11] + uik[17] * u[12] + uik[18] * u[13] + uik[19] * u[14];
149:           rtmp_ptr[14] += uik[20] * u[10] + uik[21] * u[11] + uik[22] * u[12] + uik[23] * u[13] + uik[24] * u[14];

151:           rtmp_ptr[15] += uik[0] * u[15] + uik[1] * u[16] + uik[2] * u[17] + uik[3] * u[18] + uik[4] * u[19];
152:           rtmp_ptr[16] += uik[5] * u[15] + uik[6] * u[16] + uik[7] * u[17] + uik[8] * u[18] + uik[9] * u[19];
153:           rtmp_ptr[17] += uik[10] * u[15] + uik[11] * u[16] + uik[12] * u[17] + uik[13] * u[18] + uik[14] * u[19];
154:           rtmp_ptr[18] += uik[15] * u[15] + uik[16] * u[16] + uik[17] * u[17] + uik[18] * u[18] + uik[19] * u[19];
155:           rtmp_ptr[19] += uik[20] * u[15] + uik[21] * u[16] + uik[22] * u[17] + uik[23] * u[18] + uik[24] * u[19];

157:           rtmp_ptr[20] += uik[0] * u[20] + uik[1] * u[21] + uik[2] * u[22] + uik[3] * u[23] + uik[4] * u[24];
158:           rtmp_ptr[21] += uik[5] * u[20] + uik[6] * u[21] + uik[7] * u[22] + uik[8] * u[23] + uik[9] * u[24];
159:           rtmp_ptr[22] += uik[10] * u[20] + uik[11] * u[21] + uik[12] * u[22] + uik[13] * u[23] + uik[14] * u[24];
160:           rtmp_ptr[23] += uik[15] * u[20] + uik[16] * u[21] + uik[17] * u[22] + uik[18] * u[23] + uik[19] * u[24];
161:           rtmp_ptr[24] += uik[20] * u[20] + uik[21] * u[21] + uik[22] * u[22] + uik[23] * u[23] + uik[24] * u[24];
162:         }
163:         PetscCall(PetscLogFlops(2.0 * 125.0 * (jmax - jmin)));

165:         /* ... add i to row list for next nonzero entry */
166:         il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
167:         j     = bj[jmin];
168:         jl[i] = jl[j];
169:         jl[j] = i; /* update jl */
170:       }
171:       i = nexti;
172:     }

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

176:     /* invert diagonal block */
177:     d = ba + k * 25;
178:     PetscCall(PetscArraycpy(d, dk, 25));
179:     PetscCall(PetscKernel_A_gets_inverse_A_5(d, ipvt, work, shift, allowzeropivot, &zeropivotdetected));
180:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

182:     jmin = bi[k];
183:     jmax = bi[k + 1];
184:     if (jmin < jmax) {
185:       for (j = jmin; j < jmax; j++) {
186:         vj       = bj[j]; /* block col. index of U */
187:         u        = ba + j * 25;
188:         rtmp_ptr = rtmp + vj * 25;
189:         for (k1 = 0; k1 < 25; k1++) {
190:           *u++        = *rtmp_ptr;
191:           *rtmp_ptr++ = 0.0;
192:         }
193:       }

195:       /* ... add k to row list for first nonzero entry in k-th row */
196:       il[k] = jmin;
197:       i     = bj[jmin];
198:       jl[k] = jl[i];
199:       jl[i] = k;
200:     }
201:   }

203:   PetscCall(PetscFree(rtmp));
204:   PetscCall(PetscFree2(il, jl));
205:   PetscCall(PetscFree2(dk, uik));

207:   C->ops->solve          = MatSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
208:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
209:   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
210:   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
211:   C->assembled           = PETSC_TRUE;
212:   C->preallocated        = PETSC_TRUE;

214:   PetscCall(PetscLogFlops(1.3333 * 125 * b->mbs)); /* from inverting diagonal blocks */
215:   PetscFunctionReturn(PETSC_SUCCESS);
216: }