1 2 #include <../src/mat/impls/sbaij/seq/sbaij.h> 3 #include <petsc/private/kernels/blockinvert.h> 4 5 /* Version for when blocks are 5 by 5 */ 6 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5(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 i, j, *a2anew, k, k1, jmin, jmax, *jl, *il, vj, nexti, ili, ipvt[5]; 12 MatScalar *ba = b->a, *aa, *ap, *dk, *uik; 13 MatScalar *u, *d, *rtmp, *rtmp_ptr, work[25]; 14 PetscReal shift = info->shiftamount; 15 PetscBool allowzeropivot, zeropivotdetected; 16 17 PetscFunctionBegin; 18 /* initialization */ 19 allowzeropivot = PetscNot(A->erroriffailure); 20 PetscCall(PetscCalloc1(25 * mbs, &rtmp)); 21 PetscCall(PetscMalloc2(mbs, &il, mbs, &jl)); 22 il[0] = 0; 23 for (i = 0; i < mbs; i++) jl[i] = mbs; 24 25 PetscCall(PetscMalloc2(25, &dk, 25, &uik)); 26 PetscCall(ISGetIndices(perm, &perm_ptr)); 27 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(25 * ai[mbs], &aa)); 37 PetscCall(PetscArraycpy(aa, a->a, 25 * ai[mbs])); 38 PetscCall(PetscMalloc1(ai[mbs], &a2anew)); 39 PetscCall(PetscArraycpy(a2anew, a->a2anew, ai[mbs])); 40 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 < 25; k1++) { 50 dk[k1] = aa[k * 25 + k1]; 51 aa[k * 25 + k1] = aa[j * 25 + k1]; 52 aa[j * 25 + 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 * 25; /* ptr to the beginning of j-th block of aa */ 59 for (k = 0; k < 25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 60 for (k = 0; k < 5; k++) { /* j-th block of aa <- dk^T */ 61 for (k1 = 0; k1 < 5; k1++) *ap++ = dk[k + 5 * k1]; 62 } 63 } 64 } 65 } 66 PetscCall(PetscFree(a2anew)); 67 } 68 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 * 25; 76 for (j = jmin; j < jmax; j++) { 77 vj = perm_ptr[aj[j]]; /* block col. index */ 78 rtmp_ptr = rtmp + vj * 25; 79 for (i = 0; i < 25; i++) *rtmp_ptr++ = *ap++; 80 } 81 } 82 83 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 84 PetscCall(PetscArraycpy(dk, rtmp + k * 25, 25)); 85 i = jl[k]; /* first row to be added to k_th row */ 86 87 while (i < mbs) { 88 nexti = jl[i]; /* next row to be added to k_th row */ 89 90 /* compute multiplier */ 91 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 92 93 /* uik = -inv(Di)*U_bar(i,k) */ 94 d = ba + i * 25; 95 u = ba + ili * 25; 96 97 uik[0] = -(d[0] * u[0] + d[5] * u[1] + d[10] * u[2] + d[15] * u[3] + d[20] * u[4]); 98 uik[1] = -(d[1] * u[0] + d[6] * u[1] + d[11] * u[2] + d[16] * u[3] + d[21] * u[4]); 99 uik[2] = -(d[2] * u[0] + d[7] * u[1] + d[12] * u[2] + d[17] * u[3] + d[22] * u[4]); 100 uik[3] = -(d[3] * u[0] + d[8] * u[1] + d[13] * u[2] + d[18] * u[3] + d[23] * u[4]); 101 uik[4] = -(d[4] * u[0] + d[9] * u[1] + d[14] * u[2] + d[19] * u[3] + d[24] * u[4]); 102 103 uik[5] = -(d[0] * u[5] + d[5] * u[6] + d[10] * u[7] + d[15] * u[8] + d[20] * u[9]); 104 uik[6] = -(d[1] * u[5] + d[6] * u[6] + d[11] * u[7] + d[16] * u[8] + d[21] * u[9]); 105 uik[7] = -(d[2] * u[5] + d[7] * u[6] + d[12] * u[7] + d[17] * u[8] + d[22] * u[9]); 106 uik[8] = -(d[3] * u[5] + d[8] * u[6] + d[13] * u[7] + d[18] * u[8] + d[23] * u[9]); 107 uik[9] = -(d[4] * u[5] + d[9] * u[6] + d[14] * u[7] + d[19] * u[8] + d[24] * u[9]); 108 109 uik[10] = -(d[0] * u[10] + d[5] * u[11] + d[10] * u[12] + d[15] * u[13] + d[20] * u[14]); 110 uik[11] = -(d[1] * u[10] + d[6] * u[11] + d[11] * u[12] + d[16] * u[13] + d[21] * u[14]); 111 uik[12] = -(d[2] * u[10] + d[7] * u[11] + d[12] * u[12] + d[17] * u[13] + d[22] * u[14]); 112 uik[13] = -(d[3] * u[10] + d[8] * u[11] + d[13] * u[12] + d[18] * u[13] + d[23] * u[14]); 113 uik[14] = -(d[4] * u[10] + d[9] * u[11] + d[14] * u[12] + d[19] * u[13] + d[24] * u[14]); 114 115 uik[15] = -(d[0] * u[15] + d[5] * u[16] + d[10] * u[17] + d[15] * u[18] + d[20] * u[19]); 116 uik[16] = -(d[1] * u[15] + d[6] * u[16] + d[11] * u[17] + d[16] * u[18] + d[21] * u[19]); 117 uik[17] = -(d[2] * u[15] + d[7] * u[16] + d[12] * u[17] + d[17] * u[18] + d[22] * u[19]); 118 uik[18] = -(d[3] * u[15] + d[8] * u[16] + d[13] * u[17] + d[18] * u[18] + d[23] * u[19]); 119 uik[19] = -(d[4] * u[15] + d[9] * u[16] + d[14] * u[17] + d[19] * u[18] + d[24] * u[19]); 120 121 uik[20] = -(d[0] * u[20] + d[5] * u[21] + d[10] * u[22] + d[15] * u[23] + d[20] * u[24]); 122 uik[21] = -(d[1] * u[20] + d[6] * u[21] + d[11] * u[22] + d[16] * u[23] + d[21] * u[24]); 123 uik[22] = -(d[2] * u[20] + d[7] * u[21] + d[12] * u[22] + d[17] * u[23] + d[22] * u[24]); 124 uik[23] = -(d[3] * u[20] + d[8] * u[21] + d[13] * u[22] + d[18] * u[23] + d[23] * u[24]); 125 uik[24] = -(d[4] * u[20] + d[9] * u[21] + d[14] * u[22] + d[19] * u[23] + d[24] * u[24]); 126 127 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 128 dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3] + uik[4] * u[4]; 129 dk[1] += uik[5] * u[0] + uik[6] * u[1] + uik[7] * u[2] + uik[8] * u[3] + uik[9] * u[4]; 130 dk[2] += uik[10] * u[0] + uik[11] * u[1] + uik[12] * u[2] + uik[13] * u[3] + uik[14] * u[4]; 131 dk[3] += uik[15] * u[0] + uik[16] * u[1] + uik[17] * u[2] + uik[18] * u[3] + uik[19] * u[4]; 132 dk[4] += uik[20] * u[0] + uik[21] * u[1] + uik[22] * u[2] + uik[23] * u[3] + uik[24] * u[4]; 133 134 dk[5] += uik[0] * u[5] + uik[1] * u[6] + uik[2] * u[7] + uik[3] * u[8] + uik[4] * u[9]; 135 dk[6] += uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8] + uik[9] * u[9]; 136 dk[7] += uik[10] * u[5] + uik[11] * u[6] + uik[12] * u[7] + uik[13] * u[8] + uik[14] * u[9]; 137 dk[8] += uik[15] * u[5] + uik[16] * u[6] + uik[17] * u[7] + uik[18] * u[8] + uik[19] * u[9]; 138 dk[9] += uik[20] * u[5] + uik[21] * u[6] + uik[22] * u[7] + uik[23] * u[8] + uik[24] * u[9]; 139 140 dk[10] += uik[0] * u[10] + uik[1] * u[11] + uik[2] * u[12] + uik[3] * u[13] + uik[4] * u[14]; 141 dk[11] += uik[5] * u[10] + uik[6] * u[11] + uik[7] * u[12] + uik[8] * u[13] + uik[9] * u[14]; 142 dk[12] += uik[10] * u[10] + uik[11] * u[11] + uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14]; 143 dk[13] += uik[15] * u[10] + uik[16] * u[11] + uik[17] * u[12] + uik[18] * u[13] + uik[19] * u[14]; 144 dk[14] += uik[20] * u[10] + uik[21] * u[11] + uik[22] * u[12] + uik[23] * u[13] + uik[24] * u[14]; 145 146 dk[15] += uik[0] * u[15] + uik[1] * u[16] + uik[2] * u[17] + uik[3] * u[18] + uik[4] * u[19]; 147 dk[16] += uik[5] * u[15] + uik[6] * u[16] + uik[7] * u[17] + uik[8] * u[18] + uik[9] * u[19]; 148 dk[17] += uik[10] * u[15] + uik[11] * u[16] + uik[12] * u[17] + uik[13] * u[18] + uik[14] * u[19]; 149 dk[18] += uik[15] * u[15] + uik[16] * u[16] + uik[17] * u[17] + uik[18] * u[18] + uik[19] * u[19]; 150 dk[19] += uik[20] * u[15] + uik[21] * u[16] + uik[22] * u[17] + uik[23] * u[18] + uik[24] * u[19]; 151 152 dk[20] += uik[0] * u[20] + uik[1] * u[21] + uik[2] * u[22] + uik[3] * u[23] + uik[4] * u[24]; 153 dk[21] += uik[5] * u[20] + uik[6] * u[21] + uik[7] * u[22] + uik[8] * u[23] + uik[9] * u[24]; 154 dk[22] += uik[10] * u[20] + uik[11] * u[21] + uik[12] * u[22] + uik[13] * u[23] + uik[14] * u[24]; 155 dk[23] += uik[15] * u[20] + uik[16] * u[21] + uik[17] * u[22] + uik[18] * u[23] + uik[19] * u[24]; 156 dk[24] += uik[20] * u[20] + uik[21] * u[21] + uik[22] * u[22] + uik[23] * u[23] + uik[24] * u[24]; 157 158 PetscCall(PetscLogFlops(125.0 * 4.0)); 159 160 /* update -U(i,k) */ 161 PetscCall(PetscArraycpy(ba + ili * 25, uik, 25)); 162 163 /* add multiple of row i to k-th row ... */ 164 jmin = ili + 1; 165 jmax = bi[i + 1]; 166 if (jmin < jmax) { 167 for (j = jmin; j < jmax; j++) { 168 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 169 rtmp_ptr = rtmp + bj[j] * 25; 170 u = ba + j * 25; 171 rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3] + uik[4] * u[4]; 172 rtmp_ptr[1] += uik[5] * u[0] + uik[6] * u[1] + uik[7] * u[2] + uik[8] * u[3] + uik[9] * u[4]; 173 rtmp_ptr[2] += uik[10] * u[0] + uik[11] * u[1] + uik[12] * u[2] + uik[13] * u[3] + uik[14] * u[4]; 174 rtmp_ptr[3] += uik[15] * u[0] + uik[16] * u[1] + uik[17] * u[2] + uik[18] * u[3] + uik[19] * u[4]; 175 rtmp_ptr[4] += uik[20] * u[0] + uik[21] * u[1] + uik[22] * u[2] + uik[23] * u[3] + uik[24] * u[4]; 176 177 rtmp_ptr[5] += uik[0] * u[5] + uik[1] * u[6] + uik[2] * u[7] + uik[3] * u[8] + uik[4] * u[9]; 178 rtmp_ptr[6] += uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8] + uik[9] * u[9]; 179 rtmp_ptr[7] += uik[10] * u[5] + uik[11] * u[6] + uik[12] * u[7] + uik[13] * u[8] + uik[14] * u[9]; 180 rtmp_ptr[8] += uik[15] * u[5] + uik[16] * u[6] + uik[17] * u[7] + uik[18] * u[8] + uik[19] * u[9]; 181 rtmp_ptr[9] += uik[20] * u[5] + uik[21] * u[6] + uik[22] * u[7] + uik[23] * u[8] + uik[24] * u[9]; 182 183 rtmp_ptr[10] += uik[0] * u[10] + uik[1] * u[11] + uik[2] * u[12] + uik[3] * u[13] + uik[4] * u[14]; 184 rtmp_ptr[11] += uik[5] * u[10] + uik[6] * u[11] + uik[7] * u[12] + uik[8] * u[13] + uik[9] * u[14]; 185 rtmp_ptr[12] += uik[10] * u[10] + uik[11] * u[11] + uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14]; 186 rtmp_ptr[13] += uik[15] * u[10] + uik[16] * u[11] + uik[17] * u[12] + uik[18] * u[13] + uik[19] * u[14]; 187 rtmp_ptr[14] += uik[20] * u[10] + uik[21] * u[11] + uik[22] * u[12] + uik[23] * u[13] + uik[24] * u[14]; 188 189 rtmp_ptr[15] += uik[0] * u[15] + uik[1] * u[16] + uik[2] * u[17] + uik[3] * u[18] + uik[4] * u[19]; 190 rtmp_ptr[16] += uik[5] * u[15] + uik[6] * u[16] + uik[7] * u[17] + uik[8] * u[18] + uik[9] * u[19]; 191 rtmp_ptr[17] += uik[10] * u[15] + uik[11] * u[16] + uik[12] * u[17] + uik[13] * u[18] + uik[14] * u[19]; 192 rtmp_ptr[18] += uik[15] * u[15] + uik[16] * u[16] + uik[17] * u[17] + uik[18] * u[18] + uik[19] * u[19]; 193 rtmp_ptr[19] += uik[20] * u[15] + uik[21] * u[16] + uik[22] * u[17] + uik[23] * u[18] + uik[24] * u[19]; 194 195 rtmp_ptr[20] += uik[0] * u[20] + uik[1] * u[21] + uik[2] * u[22] + uik[3] * u[23] + uik[4] * u[24]; 196 rtmp_ptr[21] += uik[5] * u[20] + uik[6] * u[21] + uik[7] * u[22] + uik[8] * u[23] + uik[9] * u[24]; 197 rtmp_ptr[22] += uik[10] * u[20] + uik[11] * u[21] + uik[12] * u[22] + uik[13] * u[23] + uik[14] * u[24]; 198 rtmp_ptr[23] += uik[15] * u[20] + uik[16] * u[21] + uik[17] * u[22] + uik[18] * u[23] + uik[19] * u[24]; 199 rtmp_ptr[24] += uik[20] * u[20] + uik[21] * u[21] + uik[22] * u[22] + uik[23] * u[23] + uik[24] * u[24]; 200 } 201 PetscCall(PetscLogFlops(2.0 * 125.0 * (jmax - jmin))); 202 203 /* ... add i to row list for next nonzero entry */ 204 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 205 j = bj[jmin]; 206 jl[i] = jl[j]; 207 jl[j] = i; /* update jl */ 208 } 209 i = nexti; 210 } 211 212 /* save nonzero entries in k-th row of U ... */ 213 214 /* invert diagonal block */ 215 d = ba + k * 25; 216 PetscCall(PetscArraycpy(d, dk, 25)); 217 PetscCall(PetscKernel_A_gets_inverse_A_5(d, ipvt, work, shift, allowzeropivot, &zeropivotdetected)); 218 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 219 220 jmin = bi[k]; 221 jmax = bi[k + 1]; 222 if (jmin < jmax) { 223 for (j = jmin; j < jmax; j++) { 224 vj = bj[j]; /* block col. index of U */ 225 u = ba + j * 25; 226 rtmp_ptr = rtmp + vj * 25; 227 for (k1 = 0; k1 < 25; k1++) { 228 *u++ = *rtmp_ptr; 229 *rtmp_ptr++ = 0.0; 230 } 231 } 232 233 /* ... add k to row list for first nonzero entry in k-th row */ 234 il[k] = jmin; 235 i = bj[jmin]; 236 jl[k] = jl[i]; 237 jl[i] = k; 238 } 239 } 240 241 PetscCall(PetscFree(rtmp)); 242 PetscCall(PetscFree2(il, jl)); 243 PetscCall(PetscFree2(dk, uik)); 244 if (a->permute) PetscCall(PetscFree(aa)); 245 246 PetscCall(ISRestoreIndices(perm, &perm_ptr)); 247 248 C->ops->solve = MatSolve_SeqSBAIJ_5_inplace; 249 C->ops->solvetranspose = MatSolve_SeqSBAIJ_5_inplace; 250 C->assembled = PETSC_TRUE; 251 C->preallocated = PETSC_TRUE; 252 253 PetscCall(PetscLogFlops(1.3333 * 125 * b->mbs)); /* from inverting diagonal blocks */ 254 PetscFunctionReturn(PETSC_SUCCESS); 255 } 256