1 #include <../src/mat/impls/sbaij/seq/sbaij.h> 2 #include <petsc/private/kernels/blockinvert.h> 3 4 /* Version for when blocks are 5 by 5 */ 5 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat C, Mat A, const MatFactorInfo *info) 6 { 7 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data, *b = (Mat_SeqSBAIJ *)C->data; 8 IS perm = b->row; 9 const PetscInt *ai, *aj, *perm_ptr, mbs = a->mbs, *bi = b->i, *bj = b->j; 10 PetscInt i, j, *a2anew, k, k1, jmin, jmax, *jl, *il, vj, nexti, ili, ipvt[5]; 11 MatScalar *ba = b->a, *aa, *ap, *dk, *uik; 12 MatScalar *u, *d, *rtmp, *rtmp_ptr, work[25]; 13 PetscReal shift = info->shiftamount; 14 PetscBool allowzeropivot, zeropivotdetected; 15 16 PetscFunctionBegin; 17 /* initialization */ 18 allowzeropivot = PetscNot(A->erroriffailure); 19 PetscCall(PetscCalloc1(25 * mbs, &rtmp)); 20 PetscCall(PetscMalloc2(mbs, &il, mbs, &jl)); 21 il[0] = 0; 22 for (i = 0; i < mbs; i++) jl[i] = mbs; 23 24 PetscCall(PetscMalloc2(25, &dk, 25, &uik)); 25 PetscCall(ISGetIndices(perm, &perm_ptr)); 26 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 PetscCall(PetscMalloc1(25 * ai[mbs], &aa)); 36 PetscCall(PetscArraycpy(aa, a->a, 25 * ai[mbs])); 37 PetscCall(PetscMalloc1(ai[mbs], &a2anew)); 38 PetscCall(PetscArraycpy(a2anew, a->a2anew, ai[mbs])); 39 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 < 25; k1++) { 49 dk[k1] = aa[k * 25 + k1]; 50 aa[k * 25 + k1] = aa[j * 25 + k1]; 51 aa[j * 25 + k1] = dk[k1]; 52 } 53 } 54 /* transform column-oriented blocks that lie in the lower triangle to row-oriented blocks */ 55 if (i > aj[j]) { 56 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 57 ap = aa + j * 25; /* ptr to the beginning of j-th block of aa */ 58 for (k = 0; k < 25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 59 for (k = 0; k < 5; k++) { /* j-th block of aa <- dk^T */ 60 for (k1 = 0; k1 < 5; k1++) *ap++ = dk[k + 5 * k1]; 61 } 62 } 63 } 64 } 65 PetscCall(PetscFree(a2anew)); 66 } 67 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 * 25; 75 for (j = jmin; j < jmax; j++) { 76 vj = perm_ptr[aj[j]]; /* block col. index */ 77 rtmp_ptr = rtmp + vj * 25; 78 for (i = 0; i < 25; i++) *rtmp_ptr++ = *ap++; 79 } 80 } 81 82 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 83 PetscCall(PetscArraycpy(dk, rtmp + k * 25, 25)); 84 i = jl[k]; /* first row to be added to k_th row */ 85 86 while (i < mbs) { 87 nexti = jl[i]; /* next row to be added to k_th row */ 88 89 /* compute multiplier */ 90 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 91 92 /* uik = -inv(Di)*U_bar(i,k) */ 93 d = ba + i * 25; 94 u = ba + ili * 25; 95 96 uik[0] = -(d[0] * u[0] + d[5] * u[1] + d[10] * u[2] + d[15] * u[3] + d[20] * u[4]); 97 uik[1] = -(d[1] * u[0] + d[6] * u[1] + d[11] * u[2] + d[16] * u[3] + d[21] * u[4]); 98 uik[2] = -(d[2] * u[0] + d[7] * u[1] + d[12] * u[2] + d[17] * u[3] + d[22] * u[4]); 99 uik[3] = -(d[3] * u[0] + d[8] * u[1] + d[13] * u[2] + d[18] * u[3] + d[23] * u[4]); 100 uik[4] = -(d[4] * u[0] + d[9] * u[1] + d[14] * u[2] + d[19] * u[3] + d[24] * u[4]); 101 102 uik[5] = -(d[0] * u[5] + d[5] * u[6] + d[10] * u[7] + d[15] * u[8] + d[20] * u[9]); 103 uik[6] = -(d[1] * u[5] + d[6] * u[6] + d[11] * u[7] + d[16] * u[8] + d[21] * u[9]); 104 uik[7] = -(d[2] * u[5] + d[7] * u[6] + d[12] * u[7] + d[17] * u[8] + d[22] * u[9]); 105 uik[8] = -(d[3] * u[5] + d[8] * u[6] + d[13] * u[7] + d[18] * u[8] + d[23] * u[9]); 106 uik[9] = -(d[4] * u[5] + d[9] * u[6] + d[14] * u[7] + d[19] * u[8] + d[24] * u[9]); 107 108 uik[10] = -(d[0] * u[10] + d[5] * u[11] + d[10] * u[12] + d[15] * u[13] + d[20] * u[14]); 109 uik[11] = -(d[1] * u[10] + d[6] * u[11] + d[11] * u[12] + d[16] * u[13] + d[21] * u[14]); 110 uik[12] = -(d[2] * u[10] + d[7] * u[11] + d[12] * u[12] + d[17] * u[13] + d[22] * u[14]); 111 uik[13] = -(d[3] * u[10] + d[8] * u[11] + d[13] * u[12] + d[18] * u[13] + d[23] * u[14]); 112 uik[14] = -(d[4] * u[10] + d[9] * u[11] + d[14] * u[12] + d[19] * u[13] + d[24] * u[14]); 113 114 uik[15] = -(d[0] * u[15] + d[5] * u[16] + d[10] * u[17] + d[15] * u[18] + d[20] * u[19]); 115 uik[16] = -(d[1] * u[15] + d[6] * u[16] + d[11] * u[17] + d[16] * u[18] + d[21] * u[19]); 116 uik[17] = -(d[2] * u[15] + d[7] * u[16] + d[12] * u[17] + d[17] * u[18] + d[22] * u[19]); 117 uik[18] = -(d[3] * u[15] + d[8] * u[16] + d[13] * u[17] + d[18] * u[18] + d[23] * u[19]); 118 uik[19] = -(d[4] * u[15] + d[9] * u[16] + d[14] * u[17] + d[19] * u[18] + d[24] * u[19]); 119 120 uik[20] = -(d[0] * u[20] + d[5] * u[21] + d[10] * u[22] + d[15] * u[23] + d[20] * u[24]); 121 uik[21] = -(d[1] * u[20] + d[6] * u[21] + d[11] * u[22] + d[16] * u[23] + d[21] * u[24]); 122 uik[22] = -(d[2] * u[20] + d[7] * u[21] + d[12] * u[22] + d[17] * u[23] + d[22] * u[24]); 123 uik[23] = -(d[3] * u[20] + d[8] * u[21] + d[13] * u[22] + d[18] * u[23] + d[23] * u[24]); 124 uik[24] = -(d[4] * u[20] + d[9] * u[21] + d[14] * u[22] + d[19] * u[23] + d[24] * u[24]); 125 126 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 127 dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3] + uik[4] * u[4]; 128 dk[1] += uik[5] * u[0] + uik[6] * u[1] + uik[7] * u[2] + uik[8] * u[3] + uik[9] * u[4]; 129 dk[2] += uik[10] * u[0] + uik[11] * u[1] + uik[12] * u[2] + uik[13] * u[3] + uik[14] * u[4]; 130 dk[3] += uik[15] * u[0] + uik[16] * u[1] + uik[17] * u[2] + uik[18] * u[3] + uik[19] * u[4]; 131 dk[4] += uik[20] * u[0] + uik[21] * u[1] + uik[22] * u[2] + uik[23] * u[3] + uik[24] * u[4]; 132 133 dk[5] += uik[0] * u[5] + uik[1] * u[6] + uik[2] * u[7] + uik[3] * u[8] + uik[4] * u[9]; 134 dk[6] += uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8] + uik[9] * u[9]; 135 dk[7] += uik[10] * u[5] + uik[11] * u[6] + uik[12] * u[7] + uik[13] * u[8] + uik[14] * u[9]; 136 dk[8] += uik[15] * u[5] + uik[16] * u[6] + uik[17] * u[7] + uik[18] * u[8] + uik[19] * u[9]; 137 dk[9] += uik[20] * u[5] + uik[21] * u[6] + uik[22] * u[7] + uik[23] * u[8] + uik[24] * u[9]; 138 139 dk[10] += uik[0] * u[10] + uik[1] * u[11] + uik[2] * u[12] + uik[3] * u[13] + uik[4] * u[14]; 140 dk[11] += uik[5] * u[10] + uik[6] * u[11] + uik[7] * u[12] + uik[8] * u[13] + uik[9] * u[14]; 141 dk[12] += uik[10] * u[10] + uik[11] * u[11] + uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14]; 142 dk[13] += uik[15] * u[10] + uik[16] * u[11] + uik[17] * u[12] + uik[18] * u[13] + uik[19] * u[14]; 143 dk[14] += uik[20] * u[10] + uik[21] * u[11] + uik[22] * u[12] + uik[23] * u[13] + uik[24] * u[14]; 144 145 dk[15] += uik[0] * u[15] + uik[1] * u[16] + uik[2] * u[17] + uik[3] * u[18] + uik[4] * u[19]; 146 dk[16] += uik[5] * u[15] + uik[6] * u[16] + uik[7] * u[17] + uik[8] * u[18] + uik[9] * u[19]; 147 dk[17] += uik[10] * u[15] + uik[11] * u[16] + uik[12] * u[17] + uik[13] * u[18] + uik[14] * u[19]; 148 dk[18] += uik[15] * u[15] + uik[16] * u[16] + uik[17] * u[17] + uik[18] * u[18] + uik[19] * u[19]; 149 dk[19] += uik[20] * u[15] + uik[21] * u[16] + uik[22] * u[17] + uik[23] * u[18] + uik[24] * u[19]; 150 151 dk[20] += uik[0] * u[20] + uik[1] * u[21] + uik[2] * u[22] + uik[3] * u[23] + uik[4] * u[24]; 152 dk[21] += uik[5] * u[20] + uik[6] * u[21] + uik[7] * u[22] + uik[8] * u[23] + uik[9] * u[24]; 153 dk[22] += uik[10] * u[20] + uik[11] * u[21] + uik[12] * u[22] + uik[13] * u[23] + uik[14] * u[24]; 154 dk[23] += uik[15] * u[20] + uik[16] * u[21] + uik[17] * u[22] + uik[18] * u[23] + uik[19] * u[24]; 155 dk[24] += uik[20] * u[20] + uik[21] * u[21] + uik[22] * u[22] + uik[23] * u[23] + uik[24] * u[24]; 156 157 PetscCall(PetscLogFlops(125.0 * 4.0)); 158 159 /* update -U(i,k) */ 160 PetscCall(PetscArraycpy(ba + ili * 25, uik, 25)); 161 162 /* add multiple of row i to k-th row ... */ 163 jmin = ili + 1; 164 jmax = bi[i + 1]; 165 if (jmin < jmax) { 166 for (j = jmin; j < jmax; j++) { 167 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 168 rtmp_ptr = rtmp + bj[j] * 25; 169 u = ba + j * 25; 170 rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3] + uik[4] * u[4]; 171 rtmp_ptr[1] += uik[5] * u[0] + uik[6] * u[1] + uik[7] * u[2] + uik[8] * u[3] + uik[9] * u[4]; 172 rtmp_ptr[2] += uik[10] * u[0] + uik[11] * u[1] + uik[12] * u[2] + uik[13] * u[3] + uik[14] * u[4]; 173 rtmp_ptr[3] += uik[15] * u[0] + uik[16] * u[1] + uik[17] * u[2] + uik[18] * u[3] + uik[19] * u[4]; 174 rtmp_ptr[4] += uik[20] * u[0] + uik[21] * u[1] + uik[22] * u[2] + uik[23] * u[3] + uik[24] * u[4]; 175 176 rtmp_ptr[5] += uik[0] * u[5] + uik[1] * u[6] + uik[2] * u[7] + uik[3] * u[8] + uik[4] * u[9]; 177 rtmp_ptr[6] += uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8] + uik[9] * u[9]; 178 rtmp_ptr[7] += uik[10] * u[5] + uik[11] * u[6] + uik[12] * u[7] + uik[13] * u[8] + uik[14] * u[9]; 179 rtmp_ptr[8] += uik[15] * u[5] + uik[16] * u[6] + uik[17] * u[7] + uik[18] * u[8] + uik[19] * u[9]; 180 rtmp_ptr[9] += uik[20] * u[5] + uik[21] * u[6] + uik[22] * u[7] + uik[23] * u[8] + uik[24] * u[9]; 181 182 rtmp_ptr[10] += uik[0] * u[10] + uik[1] * u[11] + uik[2] * u[12] + uik[3] * u[13] + uik[4] * u[14]; 183 rtmp_ptr[11] += uik[5] * u[10] + uik[6] * u[11] + uik[7] * u[12] + uik[8] * u[13] + uik[9] * u[14]; 184 rtmp_ptr[12] += uik[10] * u[10] + uik[11] * u[11] + uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14]; 185 rtmp_ptr[13] += uik[15] * u[10] + uik[16] * u[11] + uik[17] * u[12] + uik[18] * u[13] + uik[19] * u[14]; 186 rtmp_ptr[14] += uik[20] * u[10] + uik[21] * u[11] + uik[22] * u[12] + uik[23] * u[13] + uik[24] * u[14]; 187 188 rtmp_ptr[15] += uik[0] * u[15] + uik[1] * u[16] + uik[2] * u[17] + uik[3] * u[18] + uik[4] * u[19]; 189 rtmp_ptr[16] += uik[5] * u[15] + uik[6] * u[16] + uik[7] * u[17] + uik[8] * u[18] + uik[9] * u[19]; 190 rtmp_ptr[17] += uik[10] * u[15] + uik[11] * u[16] + uik[12] * u[17] + uik[13] * u[18] + uik[14] * u[19]; 191 rtmp_ptr[18] += uik[15] * u[15] + uik[16] * u[16] + uik[17] * u[17] + uik[18] * u[18] + uik[19] * u[19]; 192 rtmp_ptr[19] += uik[20] * u[15] + uik[21] * u[16] + uik[22] * u[17] + uik[23] * u[18] + uik[24] * u[19]; 193 194 rtmp_ptr[20] += uik[0] * u[20] + uik[1] * u[21] + uik[2] * u[22] + uik[3] * u[23] + uik[4] * u[24]; 195 rtmp_ptr[21] += uik[5] * u[20] + uik[6] * u[21] + uik[7] * u[22] + uik[8] * u[23] + uik[9] * u[24]; 196 rtmp_ptr[22] += uik[10] * u[20] + uik[11] * u[21] + uik[12] * u[22] + uik[13] * u[23] + uik[14] * u[24]; 197 rtmp_ptr[23] += uik[15] * u[20] + uik[16] * u[21] + uik[17] * u[22] + uik[18] * u[23] + uik[19] * u[24]; 198 rtmp_ptr[24] += uik[20] * u[20] + uik[21] * u[21] + uik[22] * u[22] + uik[23] * u[23] + uik[24] * u[24]; 199 } 200 PetscCall(PetscLogFlops(2.0 * 125.0 * (jmax - jmin))); 201 202 /* ... add i to row list for next nonzero entry */ 203 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 204 j = bj[jmin]; 205 jl[i] = jl[j]; 206 jl[j] = i; /* update jl */ 207 } 208 i = nexti; 209 } 210 211 /* save nonzero entries in k-th row of U ... */ 212 213 /* invert diagonal block */ 214 d = ba + k * 25; 215 PetscCall(PetscArraycpy(d, dk, 25)); 216 PetscCall(PetscKernel_A_gets_inverse_A_5(d, ipvt, work, shift, allowzeropivot, &zeropivotdetected)); 217 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 218 219 jmin = bi[k]; 220 jmax = bi[k + 1]; 221 if (jmin < jmax) { 222 for (j = jmin; j < jmax; j++) { 223 vj = bj[j]; /* block col. index of U */ 224 u = ba + j * 25; 225 rtmp_ptr = rtmp + vj * 25; 226 for (k1 = 0; k1 < 25; k1++) { 227 *u++ = *rtmp_ptr; 228 *rtmp_ptr++ = 0.0; 229 } 230 } 231 232 /* ... add k to row list for first nonzero entry in k-th row */ 233 il[k] = jmin; 234 i = bj[jmin]; 235 jl[k] = jl[i]; 236 jl[i] = k; 237 } 238 } 239 240 PetscCall(PetscFree(rtmp)); 241 PetscCall(PetscFree2(il, jl)); 242 PetscCall(PetscFree2(dk, uik)); 243 if (a->permute) PetscCall(PetscFree(aa)); 244 245 PetscCall(ISRestoreIndices(perm, &perm_ptr)); 246 247 C->ops->solve = MatSolve_SeqSBAIJ_5_inplace; 248 C->ops->solvetranspose = MatSolve_SeqSBAIJ_5_inplace; 249 C->assembled = PETSC_TRUE; 250 C->preallocated = PETSC_TRUE; 251 252 PetscCall(PetscLogFlops(1.3333 * 125 * b->mbs)); /* from inverting diagonal blocks */ 253 PetscFunctionReturn(PETSC_SUCCESS); 254 } 255