Actual source code: sbaijfact12.c


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

  5: /*
  6:       Version for when blocks are 7 by 7 Using natural ordering
  7: */
  8: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_7_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;
 13:   MatScalar    *ba = b->a, *aa, *ap, *dk, *uik;
 14:   MatScalar    *u, *d, *w, *wp, u0, u1, u2, u3, u4, u5, u6, u7, u8, u9, u10, u11, u12;
 15:   MatScalar     u13, u14, u15, u16, u17, u18, u19, u20, u21, u22, u23, u24, u25, u26, u27;
 16:   MatScalar     u28, u29, u30, u31, u32, u33, u34, u35, u36, u37, u38, u39, u40, u41;
 17:   MatScalar     u42, u43, u44, u45, u46, u47, u48;
 18:   PetscReal     shift = info->shiftamount;
 19:   PetscBool     allowzeropivot, zeropivotdetected;

 21:   PetscFunctionBegin;
 22:   /* initialization */
 23:   allowzeropivot = PetscNot(A->erroriffailure);
 24:   PetscCall(PetscCalloc1(49 * mbs, &w));
 25:   PetscCall(PetscMalloc2(mbs, &il, mbs, &jl));
 26:   il[0] = 0;
 27:   for (i = 0; i < mbs; i++) jl[i] = mbs;

 29:   PetscCall(PetscMalloc2(49, &dk, 49, &uik));
 30:   ai = a->i;
 31:   aj = a->j;
 32:   aa = a->a;

 34:   /* for each row k */
 35:   for (k = 0; k < mbs; k++) {
 36:     /*initialize k-th row with elements nonzero in row k of A */
 37:     jmin = ai[k];
 38:     jmax = ai[k + 1];
 39:     if (jmin < jmax) {
 40:       ap = aa + jmin * 49;
 41:       for (j = jmin; j < jmax; j++) {
 42:         vj = aj[j]; /* block col. index */
 43:         wp = w + vj * 49;
 44:         PetscCall(PetscArraycpy(wp, ap, 49));
 45:         ap += 49;
 46:       }
 47:     }

 49:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
 50:     PetscCall(PetscArraycpy(dk, w + k * 49, 49));
 51:     i = jl[k]; /* first row to be added to k_th row  */

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

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

 59:       /* uik = -inv(Di)*U_bar(i,k) */
 60:       d = ba + i * 49;
 61:       u = ba + ili * 49;

 63:       u0  = u[0];
 64:       u1  = u[1];
 65:       u2  = u[2];
 66:       u3  = u[3];
 67:       u4  = u[4];
 68:       u5  = u[5];
 69:       u6  = u[6];
 70:       u7  = u[7];
 71:       u8  = u[8];
 72:       u9  = u[9];
 73:       u10 = u[10];
 74:       u11 = u[11];
 75:       u12 = u[12];
 76:       u13 = u[13];
 77:       u14 = u[14];
 78:       u15 = u[15];
 79:       u16 = u[16];
 80:       u17 = u[17];
 81:       u18 = u[18];
 82:       u19 = u[19];
 83:       u20 = u[20];
 84:       u21 = u[21];
 85:       u22 = u[22];
 86:       u23 = u[23];
 87:       u24 = u[24];
 88:       u25 = u[25];
 89:       u26 = u[26];
 90:       u27 = u[27];
 91:       u28 = u[28];
 92:       u29 = u[29];
 93:       u30 = u[30];
 94:       u31 = u[31];
 95:       u32 = u[32];
 96:       u33 = u[33];
 97:       u34 = u[34];
 98:       u35 = u[35];
 99:       u36 = u[36];
100:       u37 = u[37];
101:       u38 = u[38];
102:       u39 = u[39];
103:       u40 = u[40];
104:       u41 = u[41];
105:       u42 = u[42];
106:       u43 = u[43];
107:       u44 = u[44];
108:       u45 = u[45];
109:       u46 = u[46];
110:       u47 = u[47];
111:       u48 = u[48];

113:       uik[0] = -(d[0] * u0 + d[7] * u1 + d[14] * u2 + d[21] * u3 + d[28] * u4 + d[35] * u5 + d[42] * u6);
114:       uik[1] = -(d[1] * u0 + d[8] * u1 + d[15] * u2 + d[22] * u3 + d[29] * u4 + d[36] * u5 + d[43] * u6);
115:       uik[2] = -(d[2] * u0 + d[9] * u1 + d[16] * u2 + d[23] * u3 + d[30] * u4 + d[37] * u5 + d[44] * u6);
116:       uik[3] = -(d[3] * u0 + d[10] * u1 + d[17] * u2 + d[24] * u3 + d[31] * u4 + d[38] * u5 + d[45] * u6);
117:       uik[4] = -(d[4] * u0 + d[11] * u1 + d[18] * u2 + d[25] * u3 + d[32] * u4 + d[39] * u5 + d[46] * u6);
118:       uik[5] = -(d[5] * u0 + d[12] * u1 + d[19] * u2 + d[26] * u3 + d[33] * u4 + d[40] * u5 + d[47] * u6);
119:       uik[6] = -(d[6] * u0 + d[13] * u1 + d[20] * u2 + d[27] * u3 + d[34] * u4 + d[41] * u5 + d[48] * u6);

121:       uik[7]  = -(d[0] * u7 + d[7] * u8 + d[14] * u9 + d[21] * u10 + d[28] * u11 + d[35] * u12 + d[42] * u13);
122:       uik[8]  = -(d[1] * u7 + d[8] * u8 + d[15] * u9 + d[22] * u10 + d[29] * u11 + d[36] * u12 + d[43] * u13);
123:       uik[9]  = -(d[2] * u7 + d[9] * u8 + d[16] * u9 + d[23] * u10 + d[30] * u11 + d[37] * u12 + d[44] * u13);
124:       uik[10] = -(d[3] * u7 + d[10] * u8 + d[17] * u9 + d[24] * u10 + d[31] * u11 + d[38] * u12 + d[45] * u13);
125:       uik[11] = -(d[4] * u7 + d[11] * u8 + d[18] * u9 + d[25] * u10 + d[32] * u11 + d[39] * u12 + d[46] * u13);
126:       uik[12] = -(d[5] * u7 + d[12] * u8 + d[19] * u9 + d[26] * u10 + d[33] * u11 + d[40] * u12 + d[47] * u13);
127:       uik[13] = -(d[6] * u7 + d[13] * u8 + d[20] * u9 + d[27] * u10 + d[34] * u11 + d[41] * u12 + d[48] * u13);

129:       uik[14] = -(d[0] * u14 + d[7] * u15 + d[14] * u16 + d[21] * u17 + d[28] * u18 + d[35] * u19 + d[42] * u20);
130:       uik[15] = -(d[1] * u14 + d[8] * u15 + d[15] * u16 + d[22] * u17 + d[29] * u18 + d[36] * u19 + d[43] * u20);
131:       uik[16] = -(d[2] * u14 + d[9] * u15 + d[16] * u16 + d[23] * u17 + d[30] * u18 + d[37] * u19 + d[44] * u20);
132:       uik[17] = -(d[3] * u14 + d[10] * u15 + d[17] * u16 + d[24] * u17 + d[31] * u18 + d[38] * u19 + d[45] * u20);
133:       uik[18] = -(d[4] * u14 + d[11] * u15 + d[18] * u16 + d[25] * u17 + d[32] * u18 + d[39] * u19 + d[46] * u20);
134:       uik[19] = -(d[5] * u14 + d[12] * u15 + d[19] * u16 + d[26] * u17 + d[33] * u18 + d[40] * u19 + d[47] * u20);
135:       uik[20] = -(d[6] * u14 + d[13] * u15 + d[20] * u16 + d[27] * u17 + d[34] * u18 + d[41] * u19 + d[48] * u20);

137:       uik[21] = -(d[0] * u21 + d[7] * u22 + d[14] * u23 + d[21] * u24 + d[28] * u25 + d[35] * u26 + d[42] * u27);
138:       uik[22] = -(d[1] * u21 + d[8] * u22 + d[15] * u23 + d[22] * u24 + d[29] * u25 + d[36] * u26 + d[43] * u27);
139:       uik[23] = -(d[2] * u21 + d[9] * u22 + d[16] * u23 + d[23] * u24 + d[30] * u25 + d[37] * u26 + d[44] * u27);
140:       uik[24] = -(d[3] * u21 + d[10] * u22 + d[17] * u23 + d[24] * u24 + d[31] * u25 + d[38] * u26 + d[45] * u27);
141:       uik[25] = -(d[4] * u21 + d[11] * u22 + d[18] * u23 + d[25] * u24 + d[32] * u25 + d[39] * u26 + d[46] * u27);
142:       uik[26] = -(d[5] * u21 + d[12] * u22 + d[19] * u23 + d[26] * u24 + d[33] * u25 + d[40] * u26 + d[47] * u27);
143:       uik[27] = -(d[6] * u21 + d[13] * u22 + d[20] * u23 + d[27] * u24 + d[34] * u25 + d[41] * u26 + d[48] * u27);

145:       uik[28] = -(d[0] * u28 + d[7] * u29 + d[14] * u30 + d[21] * u31 + d[28] * u32 + d[35] * u33 + d[42] * u34);
146:       uik[29] = -(d[1] * u28 + d[8] * u29 + d[15] * u30 + d[22] * u31 + d[29] * u32 + d[36] * u33 + d[43] * u34);
147:       uik[30] = -(d[2] * u28 + d[9] * u29 + d[16] * u30 + d[23] * u31 + d[30] * u32 + d[37] * u33 + d[44] * u34);
148:       uik[31] = -(d[3] * u28 + d[10] * u29 + d[17] * u30 + d[24] * u31 + d[31] * u32 + d[38] * u33 + d[45] * u34);
149:       uik[32] = -(d[4] * u28 + d[11] * u29 + d[18] * u30 + d[25] * u31 + d[32] * u32 + d[39] * u33 + d[46] * u34);
150:       uik[33] = -(d[5] * u28 + d[12] * u29 + d[19] * u30 + d[26] * u31 + d[33] * u32 + d[40] * u33 + d[47] * u34);
151:       uik[34] = -(d[6] * u28 + d[13] * u29 + d[20] * u30 + d[27] * u31 + d[34] * u32 + d[41] * u33 + d[48] * u34);

153:       uik[35] = -(d[0] * u35 + d[7] * u36 + d[14] * u37 + d[21] * u38 + d[28] * u39 + d[35] * u40 + d[42] * u41);
154:       uik[36] = -(d[1] * u35 + d[8] * u36 + d[15] * u37 + d[22] * u38 + d[29] * u39 + d[36] * u40 + d[43] * u41);
155:       uik[37] = -(d[2] * u35 + d[9] * u36 + d[16] * u37 + d[23] * u38 + d[30] * u39 + d[37] * u40 + d[44] * u41);
156:       uik[38] = -(d[3] * u35 + d[10] * u36 + d[17] * u37 + d[24] * u38 + d[31] * u39 + d[38] * u40 + d[45] * u41);
157:       uik[39] = -(d[4] * u35 + d[11] * u36 + d[18] * u37 + d[25] * u38 + d[32] * u39 + d[39] * u40 + d[46] * u41);
158:       uik[40] = -(d[5] * u35 + d[12] * u36 + d[19] * u37 + d[26] * u38 + d[33] * u39 + d[40] * u40 + d[47] * u41);
159:       uik[41] = -(d[6] * u35 + d[13] * u36 + d[20] * u37 + d[27] * u38 + d[34] * u39 + d[41] * u40 + d[48] * u41);

161:       uik[42] = -(d[0] * u42 + d[7] * u43 + d[14] * u44 + d[21] * u45 + d[28] * u46 + d[35] * u47 + d[42] * u48);
162:       uik[43] = -(d[1] * u42 + d[8] * u43 + d[15] * u44 + d[22] * u45 + d[29] * u46 + d[36] * u47 + d[43] * u48);
163:       uik[44] = -(d[2] * u42 + d[9] * u43 + d[16] * u44 + d[23] * u45 + d[30] * u46 + d[37] * u47 + d[44] * u48);
164:       uik[45] = -(d[3] * u42 + d[10] * u43 + d[17] * u44 + d[24] * u45 + d[31] * u46 + d[38] * u47 + d[45] * u48);
165:       uik[46] = -(d[4] * u42 + d[11] * u43 + d[18] * u44 + d[25] * u45 + d[32] * u46 + d[39] * u47 + d[46] * u48);
166:       uik[47] = -(d[5] * u42 + d[12] * u43 + d[19] * u44 + d[26] * u45 + d[33] * u46 + d[40] * u47 + d[47] * u48);
167:       uik[48] = -(d[6] * u42 + d[13] * u43 + d[20] * u44 + d[27] * u45 + d[34] * u46 + d[41] * u47 + d[48] * u48);

169:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
170:       dk[0] += uik[0] * u0 + uik[1] * u1 + uik[2] * u2 + uik[3] * u3 + uik[4] * u4 + uik[5] * u5 + uik[6] * u6;
171:       dk[1] += uik[7] * u0 + uik[8] * u1 + uik[9] * u2 + uik[10] * u3 + uik[11] * u4 + uik[12] * u5 + uik[13] * u6;
172:       dk[2] += uik[14] * u0 + uik[15] * u1 + uik[16] * u2 + uik[17] * u3 + uik[18] * u4 + uik[19] * u5 + uik[20] * u6;
173:       dk[3] += uik[21] * u0 + uik[22] * u1 + uik[23] * u2 + uik[24] * u3 + uik[25] * u4 + uik[26] * u5 + uik[27] * u6;
174:       dk[4] += uik[28] * u0 + uik[29] * u1 + uik[30] * u2 + uik[31] * u3 + uik[32] * u4 + uik[33] * u5 + uik[34] * u6;
175:       dk[5] += uik[35] * u0 + uik[36] * u1 + uik[37] * u2 + uik[38] * u3 + uik[39] * u4 + uik[40] * u5 + uik[41] * u6;
176:       dk[6] += uik[42] * u0 + uik[43] * u1 + uik[44] * u2 + uik[45] * u3 + uik[46] * u4 + uik[47] * u5 + uik[48] * u6;

178:       dk[7] += uik[0] * u7 + uik[1] * u8 + uik[2] * u9 + uik[3] * u10 + uik[4] * u11 + uik[5] * u12 + uik[6] * u13;
179:       dk[8] += uik[7] * u7 + uik[8] * u8 + uik[9] * u9 + uik[10] * u10 + uik[11] * u11 + uik[12] * u12 + uik[13] * u13;
180:       dk[9] += uik[14] * u7 + uik[15] * u8 + uik[16] * u9 + uik[17] * u10 + uik[18] * u11 + uik[19] * u12 + uik[20] * u13;
181:       dk[10] += uik[21] * u7 + uik[22] * u8 + uik[23] * u9 + uik[24] * u10 + uik[25] * u11 + uik[26] * u12 + uik[27] * u13;
182:       dk[11] += uik[28] * u7 + uik[29] * u8 + uik[30] * u9 + uik[31] * u10 + uik[32] * u11 + uik[33] * u12 + uik[34] * u13;
183:       dk[12] += uik[35] * u7 + uik[36] * u8 + uik[37] * u9 + uik[38] * u10 + uik[39] * u11 + uik[40] * u12 + uik[41] * u13;
184:       dk[13] += uik[42] * u7 + uik[43] * u8 + uik[44] * u9 + uik[45] * u10 + uik[46] * u11 + uik[47] * u12 + uik[48] * u13;

186:       dk[14] += uik[0] * u14 + uik[1] * u15 + uik[2] * u16 + uik[3] * u17 + uik[4] * u18 + uik[5] * u19 + uik[6] * u20;
187:       dk[15] += uik[7] * u14 + uik[8] * u15 + uik[9] * u16 + uik[10] * u17 + uik[11] * u18 + uik[12] * u19 + uik[13] * u20;
188:       dk[16] += uik[14] * u14 + uik[15] * u15 + uik[16] * u16 + uik[17] * u17 + uik[18] * u18 + uik[19] * u19 + uik[20] * u20;
189:       dk[17] += uik[21] * u14 + uik[22] * u15 + uik[23] * u16 + uik[24] * u17 + uik[25] * u18 + uik[26] * u19 + uik[27] * u20;
190:       dk[18] += uik[28] * u14 + uik[29] * u15 + uik[30] * u16 + uik[31] * u17 + uik[32] * u18 + uik[33] * u19 + uik[34] * u20;
191:       dk[19] += uik[35] * u14 + uik[36] * u15 + uik[37] * u16 + uik[38] * u17 + uik[39] * u18 + uik[40] * u19 + uik[41] * u20;
192:       dk[20] += uik[42] * u14 + uik[43] * u15 + uik[44] * u16 + uik[45] * u17 + uik[46] * u18 + uik[47] * u19 + uik[48] * u20;

194:       dk[21] += uik[0] * u21 + uik[1] * u22 + uik[2] * u23 + uik[3] * u24 + uik[4] * u25 + uik[5] * u26 + uik[6] * u27;
195:       dk[22] += uik[7] * u21 + uik[8] * u22 + uik[9] * u23 + uik[10] * u24 + uik[11] * u25 + uik[12] * u26 + uik[13] * u27;
196:       dk[23] += uik[14] * u21 + uik[15] * u22 + uik[16] * u23 + uik[17] * u24 + uik[18] * u25 + uik[19] * u26 + uik[20] * u27;
197:       dk[24] += uik[21] * u21 + uik[22] * u22 + uik[23] * u23 + uik[24] * u24 + uik[25] * u25 + uik[26] * u26 + uik[27] * u27;
198:       dk[25] += uik[28] * u21 + uik[29] * u22 + uik[30] * u23 + uik[31] * u24 + uik[32] * u25 + uik[33] * u26 + uik[34] * u27;
199:       dk[26] += uik[35] * u21 + uik[36] * u22 + uik[37] * u23 + uik[38] * u24 + uik[39] * u25 + uik[40] * u26 + uik[41] * u27;
200:       dk[27] += uik[42] * u21 + uik[43] * u22 + uik[44] * u23 + uik[45] * u24 + uik[46] * u25 + uik[47] * u26 + uik[48] * u27;

202:       dk[28] += uik[0] * u28 + uik[1] * u29 + uik[2] * u30 + uik[3] * u31 + uik[4] * u32 + uik[5] * u33 + uik[6] * u34;
203:       dk[29] += uik[7] * u28 + uik[8] * u29 + uik[9] * u30 + uik[10] * u31 + uik[11] * u32 + uik[12] * u33 + uik[13] * u34;
204:       dk[30] += uik[14] * u28 + uik[15] * u29 + uik[16] * u30 + uik[17] * u31 + uik[18] * u32 + uik[19] * u33 + uik[20] * u34;
205:       dk[31] += uik[21] * u28 + uik[22] * u29 + uik[23] * u30 + uik[24] * u31 + uik[25] * u32 + uik[26] * u33 + uik[27] * u34;
206:       dk[32] += uik[28] * u28 + uik[29] * u29 + uik[30] * u30 + uik[31] * u31 + uik[32] * u32 + uik[33] * u33 + uik[34] * u34;
207:       dk[33] += uik[35] * u28 + uik[36] * u29 + uik[37] * u30 + uik[38] * u31 + uik[39] * u32 + uik[40] * u33 + uik[41] * u34;
208:       dk[34] += uik[42] * u28 + uik[43] * u29 + uik[44] * u30 + uik[45] * u31 + uik[46] * u32 + uik[47] * u33 + uik[48] * u34;

210:       dk[35] += uik[0] * u35 + uik[1] * u36 + uik[2] * u37 + uik[3] * u38 + uik[4] * u39 + uik[5] * u40 + uik[6] * u41;
211:       dk[36] += uik[7] * u35 + uik[8] * u36 + uik[9] * u37 + uik[10] * u38 + uik[11] * u39 + uik[12] * u40 + uik[13] * u41;
212:       dk[37] += uik[14] * u35 + uik[15] * u36 + uik[16] * u37 + uik[17] * u38 + uik[18] * u39 + uik[19] * u40 + uik[20] * u41;
213:       dk[38] += uik[21] * u35 + uik[22] * u36 + uik[23] * u37 + uik[24] * u38 + uik[25] * u39 + uik[26] * u40 + uik[27] * u41;
214:       dk[39] += uik[28] * u35 + uik[29] * u36 + uik[30] * u37 + uik[31] * u38 + uik[32] * u39 + uik[33] * u40 + uik[34] * u41;
215:       dk[40] += uik[35] * u35 + uik[36] * u36 + uik[37] * u37 + uik[38] * u38 + uik[39] * u39 + uik[40] * u40 + uik[41] * u41;
216:       dk[41] += uik[42] * u35 + uik[43] * u36 + uik[44] * u37 + uik[45] * u38 + uik[46] * u39 + uik[47] * u40 + uik[48] * u41;

218:       dk[42] += uik[0] * u42 + uik[1] * u43 + uik[2] * u44 + uik[3] * u45 + uik[4] * u46 + uik[5] * u47 + uik[6] * u48;
219:       dk[43] += uik[7] * u42 + uik[8] * u43 + uik[9] * u44 + uik[10] * u45 + uik[11] * u46 + uik[12] * u47 + uik[13] * u48;
220:       dk[44] += uik[14] * u42 + uik[15] * u43 + uik[16] * u44 + uik[17] * u45 + uik[18] * u46 + uik[19] * u47 + uik[20] * u48;
221:       dk[45] += uik[21] * u42 + uik[22] * u43 + uik[23] * u44 + uik[24] * u45 + uik[25] * u46 + uik[26] * u47 + uik[27] * u48;
222:       dk[46] += uik[28] * u42 + uik[29] * u43 + uik[30] * u44 + uik[31] * u45 + uik[32] * u46 + uik[33] * u47 + uik[34] * u48;
223:       dk[47] += uik[35] * u42 + uik[36] * u43 + uik[37] * u44 + uik[38] * u45 + uik[39] * u46 + uik[40] * u47 + uik[41] * u48;
224:       dk[48] += uik[42] * u42 + uik[43] * u43 + uik[44] * u44 + uik[45] * u45 + uik[46] * u46 + uik[47] * u47 + uik[48] * u48;

226:       PetscCall(PetscLogFlops(343.0 * 4.0));

228:       /* update -U(i,k) */
229:       PetscCall(PetscArraycpy(ba + ili * 49, uik, 49));

231:       /* add multiple of row i to k-th row ... */
232:       jmin = ili + 1;
233:       jmax = bi[i + 1];
234:       if (jmin < jmax) {
235:         for (j = jmin; j < jmax; j++) {
236:           /* w += -U(i,k)^T * U_bar(i,j) */
237:           wp = w + bj[j] * 49;
238:           u  = ba + j * 49;

240:           u0  = u[0];
241:           u1  = u[1];
242:           u2  = u[2];
243:           u3  = u[3];
244:           u4  = u[4];
245:           u5  = u[5];
246:           u6  = u[6];
247:           u7  = u[7];
248:           u8  = u[8];
249:           u9  = u[9];
250:           u10 = u[10];
251:           u11 = u[11];
252:           u12 = u[12];
253:           u13 = u[13];
254:           u14 = u[14];
255:           u15 = u[15];
256:           u16 = u[16];
257:           u17 = u[17];
258:           u18 = u[18];
259:           u19 = u[19];
260:           u20 = u[20];
261:           u21 = u[21];
262:           u22 = u[22];
263:           u23 = u[23];
264:           u24 = u[24];
265:           u25 = u[25];
266:           u26 = u[26];
267:           u27 = u[27];
268:           u28 = u[28];
269:           u29 = u[29];
270:           u30 = u[30];
271:           u31 = u[31];
272:           u32 = u[32];
273:           u33 = u[33];
274:           u34 = u[34];
275:           u35 = u[35];
276:           u36 = u[36];
277:           u37 = u[37];
278:           u38 = u[38];
279:           u39 = u[39];
280:           u40 = u[40];
281:           u41 = u[41];
282:           u42 = u[42];
283:           u43 = u[43];
284:           u44 = u[44];
285:           u45 = u[45];
286:           u46 = u[46];
287:           u47 = u[47];
288:           u48 = u[48];

290:           wp[0] += uik[0] * u0 + uik[1] * u1 + uik[2] * u2 + uik[3] * u3 + uik[4] * u4 + uik[5] * u5 + uik[6] * u6;
291:           wp[1] += uik[7] * u0 + uik[8] * u1 + uik[9] * u2 + uik[10] * u3 + uik[11] * u4 + uik[12] * u5 + uik[13] * u6;
292:           wp[2] += uik[14] * u0 + uik[15] * u1 + uik[16] * u2 + uik[17] * u3 + uik[18] * u4 + uik[19] * u5 + uik[20] * u6;
293:           wp[3] += uik[21] * u0 + uik[22] * u1 + uik[23] * u2 + uik[24] * u3 + uik[25] * u4 + uik[26] * u5 + uik[27] * u6;
294:           wp[4] += uik[28] * u0 + uik[29] * u1 + uik[30] * u2 + uik[31] * u3 + uik[32] * u4 + uik[33] * u5 + uik[34] * u6;
295:           wp[5] += uik[35] * u0 + uik[36] * u1 + uik[37] * u2 + uik[38] * u3 + uik[39] * u4 + uik[40] * u5 + uik[41] * u6;
296:           wp[6] += uik[42] * u0 + uik[43] * u1 + uik[44] * u2 + uik[45] * u3 + uik[46] * u4 + uik[47] * u5 + uik[48] * u6;

298:           wp[7] += uik[0] * u7 + uik[1] * u8 + uik[2] * u9 + uik[3] * u10 + uik[4] * u11 + uik[5] * u12 + uik[6] * u13;
299:           wp[8] += uik[7] * u7 + uik[8] * u8 + uik[9] * u9 + uik[10] * u10 + uik[11] * u11 + uik[12] * u12 + uik[13] * u13;
300:           wp[9] += uik[14] * u7 + uik[15] * u8 + uik[16] * u9 + uik[17] * u10 + uik[18] * u11 + uik[19] * u12 + uik[20] * u13;
301:           wp[10] += uik[21] * u7 + uik[22] * u8 + uik[23] * u9 + uik[24] * u10 + uik[25] * u11 + uik[26] * u12 + uik[27] * u13;
302:           wp[11] += uik[28] * u7 + uik[29] * u8 + uik[30] * u9 + uik[31] * u10 + uik[32] * u11 + uik[33] * u12 + uik[34] * u13;
303:           wp[12] += uik[35] * u7 + uik[36] * u8 + uik[37] * u9 + uik[38] * u10 + uik[39] * u11 + uik[40] * u12 + uik[41] * u13;
304:           wp[13] += uik[42] * u7 + uik[43] * u8 + uik[44] * u9 + uik[45] * u10 + uik[46] * u11 + uik[47] * u12 + uik[48] * u13;

306:           wp[14] += uik[0] * u14 + uik[1] * u15 + uik[2] * u16 + uik[3] * u17 + uik[4] * u18 + uik[5] * u19 + uik[6] * u20;
307:           wp[15] += uik[7] * u14 + uik[8] * u15 + uik[9] * u16 + uik[10] * u17 + uik[11] * u18 + uik[12] * u19 + uik[13] * u20;
308:           wp[16] += uik[14] * u14 + uik[15] * u15 + uik[16] * u16 + uik[17] * u17 + uik[18] * u18 + uik[19] * u19 + uik[20] * u20;
309:           wp[17] += uik[21] * u14 + uik[22] * u15 + uik[23] * u16 + uik[24] * u17 + uik[25] * u18 + uik[26] * u19 + uik[27] * u20;
310:           wp[18] += uik[28] * u14 + uik[29] * u15 + uik[30] * u16 + uik[31] * u17 + uik[32] * u18 + uik[33] * u19 + uik[34] * u20;
311:           wp[19] += uik[35] * u14 + uik[36] * u15 + uik[37] * u16 + uik[38] * u17 + uik[39] * u18 + uik[40] * u19 + uik[41] * u20;
312:           wp[20] += uik[42] * u14 + uik[43] * u15 + uik[44] * u16 + uik[45] * u17 + uik[46] * u18 + uik[47] * u19 + uik[48] * u20;

314:           wp[21] += uik[0] * u21 + uik[1] * u22 + uik[2] * u23 + uik[3] * u24 + uik[4] * u25 + uik[5] * u26 + uik[6] * u27;
315:           wp[22] += uik[7] * u21 + uik[8] * u22 + uik[9] * u23 + uik[10] * u24 + uik[11] * u25 + uik[12] * u26 + uik[13] * u27;
316:           wp[23] += uik[14] * u21 + uik[15] * u22 + uik[16] * u23 + uik[17] * u24 + uik[18] * u25 + uik[19] * u26 + uik[20] * u27;
317:           wp[24] += uik[21] * u21 + uik[22] * u22 + uik[23] * u23 + uik[24] * u24 + uik[25] * u25 + uik[26] * u26 + uik[27] * u27;
318:           wp[25] += uik[28] * u21 + uik[29] * u22 + uik[30] * u23 + uik[31] * u24 + uik[32] * u25 + uik[33] * u26 + uik[34] * u27;
319:           wp[26] += uik[35] * u21 + uik[36] * u22 + uik[37] * u23 + uik[38] * u24 + uik[39] * u25 + uik[40] * u26 + uik[41] * u27;
320:           wp[27] += uik[42] * u21 + uik[43] * u22 + uik[44] * u23 + uik[45] * u24 + uik[46] * u25 + uik[47] * u26 + uik[48] * u27;

322:           wp[28] += uik[0] * u28 + uik[1] * u29 + uik[2] * u30 + uik[3] * u31 + uik[4] * u32 + uik[5] * u33 + uik[6] * u34;
323:           wp[29] += uik[7] * u28 + uik[8] * u29 + uik[9] * u30 + uik[10] * u31 + uik[11] * u32 + uik[12] * u33 + uik[13] * u34;
324:           wp[30] += uik[14] * u28 + uik[15] * u29 + uik[16] * u30 + uik[17] * u31 + uik[18] * u32 + uik[19] * u33 + uik[20] * u34;
325:           wp[31] += uik[21] * u28 + uik[22] * u29 + uik[23] * u30 + uik[24] * u31 + uik[25] * u32 + uik[26] * u33 + uik[27] * u34;
326:           wp[32] += uik[28] * u28 + uik[29] * u29 + uik[30] * u30 + uik[31] * u31 + uik[32] * u32 + uik[33] * u33 + uik[34] * u34;
327:           wp[33] += uik[35] * u28 + uik[36] * u29 + uik[37] * u30 + uik[38] * u31 + uik[39] * u32 + uik[40] * u33 + uik[41] * u34;
328:           wp[34] += uik[42] * u28 + uik[43] * u29 + uik[44] * u30 + uik[45] * u31 + uik[46] * u32 + uik[47] * u33 + uik[48] * u34;

330:           wp[35] += uik[0] * u35 + uik[1] * u36 + uik[2] * u37 + uik[3] * u38 + uik[4] * u39 + uik[5] * u40 + uik[6] * u41;
331:           wp[36] += uik[7] * u35 + uik[8] * u36 + uik[9] * u37 + uik[10] * u38 + uik[11] * u39 + uik[12] * u40 + uik[13] * u41;
332:           wp[37] += uik[14] * u35 + uik[15] * u36 + uik[16] * u37 + uik[17] * u38 + uik[18] * u39 + uik[19] * u40 + uik[20] * u41;
333:           wp[38] += uik[21] * u35 + uik[22] * u36 + uik[23] * u37 + uik[24] * u38 + uik[25] * u39 + uik[26] * u40 + uik[27] * u41;
334:           wp[39] += uik[28] * u35 + uik[29] * u36 + uik[30] * u37 + uik[31] * u38 + uik[32] * u39 + uik[33] * u40 + uik[34] * u41;
335:           wp[40] += uik[35] * u35 + uik[36] * u36 + uik[37] * u37 + uik[38] * u38 + uik[39] * u39 + uik[40] * u40 + uik[41] * u41;
336:           wp[41] += uik[42] * u35 + uik[43] * u36 + uik[44] * u37 + uik[45] * u38 + uik[46] * u39 + uik[47] * u40 + uik[48] * u41;

338:           wp[42] += uik[0] * u42 + uik[1] * u43 + uik[2] * u44 + uik[3] * u45 + uik[4] * u46 + uik[5] * u47 + uik[6] * u48;
339:           wp[43] += uik[7] * u42 + uik[8] * u43 + uik[9] * u44 + uik[10] * u45 + uik[11] * u46 + uik[12] * u47 + uik[13] * u48;
340:           wp[44] += uik[14] * u42 + uik[15] * u43 + uik[16] * u44 + uik[17] * u45 + uik[18] * u46 + uik[19] * u47 + uik[20] * u48;
341:           wp[45] += uik[21] * u42 + uik[22] * u43 + uik[23] * u44 + uik[24] * u45 + uik[25] * u46 + uik[26] * u47 + uik[27] * u48;
342:           wp[46] += uik[28] * u42 + uik[29] * u43 + uik[30] * u44 + uik[31] * u45 + uik[32] * u46 + uik[33] * u47 + uik[34] * u48;
343:           wp[47] += uik[35] * u42 + uik[36] * u43 + uik[37] * u44 + uik[38] * u45 + uik[39] * u46 + uik[40] * u47 + uik[41] * u48;
344:           wp[48] += uik[42] * u42 + uik[43] * u43 + uik[44] * u44 + uik[45] * u45 + uik[46] * u46 + uik[47] * u47 + uik[48] * u48;
345:         }
346:         PetscCall(PetscLogFlops(2.0 * 343.0 * (jmax - jmin)));

348:         /* ... add i to row list for next nonzero entry */
349:         il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
350:         j     = bj[jmin];
351:         jl[i] = jl[j];
352:         jl[j] = i; /* update jl */
353:       }
354:       i = nexti;
355:     }

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

359:     /* invert diagonal block */
360:     d = ba + k * 49;
361:     PetscCall(PetscArraycpy(d, dk, 49));
362:     PetscCall(PetscKernel_A_gets_inverse_A_7(d, shift, allowzeropivot, &zeropivotdetected));
363:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

365:     jmin = bi[k];
366:     jmax = bi[k + 1];
367:     if (jmin < jmax) {
368:       for (j = jmin; j < jmax; j++) {
369:         vj = bj[j]; /* block col. index of U */
370:         u  = ba + j * 49;
371:         wp = w + vj * 49;
372:         for (k1 = 0; k1 < 49; k1++) {
373:           *u++  = *wp;
374:           *wp++ = 0.0;
375:         }
376:       }

378:       /* ... add k to row list for first nonzero entry in k-th row */
379:       il[k] = jmin;
380:       i     = bj[jmin];
381:       jl[k] = jl[i];
382:       jl[i] = k;
383:     }
384:   }

386:   PetscCall(PetscFree(w));
387:   PetscCall(PetscFree2(il, jl));
388:   PetscCall(PetscFree2(dk, uik));

390:   C->ops->solve          = MatSolve_SeqSBAIJ_7_NaturalOrdering_inplace;
391:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_7_NaturalOrdering_inplace;
392:   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_7_NaturalOrdering_inplace;
393:   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_7_NaturalOrdering_inplace;
394:   C->assembled           = PETSC_TRUE;
395:   C->preallocated        = PETSC_TRUE;

397:   PetscCall(PetscLogFlops(1.3333 * 343 * b->mbs)); /* from inverting diagonal blocks */
398:   PetscFunctionReturn(PETSC_SUCCESS);
399: }