1 2 #include <../src/mat/impls/sbaij/seq/sbaij.h> 3 #include <petsc/private/kernels/blockinvert.h> 4 5 /* Version for when blocks are 4 by 4 */ 6 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4(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; 12 MatScalar *ba = b->a, *aa, *ap, *dk, *uik; 13 MatScalar *u, *diag, *rtmp, *rtmp_ptr; 14 PetscBool pivotinblocks = b->pivotinblocks; 15 PetscReal shift = info->shiftamount; 16 PetscBool allowzeropivot, zeropivotdetected = PETSC_FALSE; 17 18 PetscFunctionBegin; 19 /* initialization */ 20 allowzeropivot = PetscNot(A->erroriffailure); 21 PetscCall(PetscCalloc1(16 * mbs, &rtmp)); 22 PetscCall(PetscMalloc2(mbs, &il, mbs, &jl)); 23 il[0] = 0; 24 for (i = 0; i < mbs; i++) jl[i] = mbs; 25 26 PetscCall(PetscMalloc2(16, &dk, 16, &uik)); 27 PetscCall(ISGetIndices(perm, &perm_ptr)); 28 29 /* check permutation */ 30 if (!a->permute) { 31 ai = a->i; 32 aj = a->j; 33 aa = a->a; 34 } else { 35 ai = a->inew; 36 aj = a->jnew; 37 PetscCall(PetscMalloc1(16 * ai[mbs], &aa)); 38 PetscCall(PetscArraycpy(aa, a->a, 16 * ai[mbs])); 39 PetscCall(PetscMalloc1(ai[mbs], &a2anew)); 40 PetscCall(PetscArraycpy(a2anew, a->a2anew, ai[mbs])); 41 42 for (i = 0; i < mbs; i++) { 43 jmin = ai[i]; 44 jmax = ai[i + 1]; 45 for (j = jmin; j < jmax; j++) { 46 while (a2anew[j] != j) { 47 k = a2anew[j]; 48 a2anew[j] = a2anew[k]; 49 a2anew[k] = k; 50 for (k1 = 0; k1 < 16; k1++) { 51 dk[k1] = aa[k * 16 + k1]; 52 aa[k * 16 + k1] = aa[j * 16 + k1]; 53 aa[j * 16 + k1] = dk[k1]; 54 } 55 } 56 /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */ 57 if (i > aj[j]) { 58 /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */ 59 ap = aa + j * 16; /* ptr to the beginning of j-th block of aa */ 60 for (k = 0; k < 16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 61 for (k = 0; k < 4; k++) { /* j-th block of aa <- dk^T */ 62 for (k1 = 0; k1 < 4; k1++) *ap++ = dk[k + 4 * k1]; 63 } 64 } 65 } 66 } 67 PetscCall(PetscFree(a2anew)); 68 } 69 70 /* for each row k */ 71 for (k = 0; k < mbs; k++) { 72 /*initialize k-th row with elements nonzero in row perm(k) of A */ 73 jmin = ai[perm_ptr[k]]; 74 jmax = ai[perm_ptr[k] + 1]; 75 if (jmin < jmax) { 76 ap = aa + jmin * 16; 77 for (j = jmin; j < jmax; j++) { 78 vj = perm_ptr[aj[j]]; /* block col. index */ 79 rtmp_ptr = rtmp + vj * 16; 80 for (i = 0; i < 16; i++) *rtmp_ptr++ = *ap++; 81 } 82 } 83 84 /* modify k-th row by adding in those rows i with U(i,k) != 0 */ 85 PetscCall(PetscArraycpy(dk, rtmp + k * 16, 16)); 86 i = jl[k]; /* first row to be added to k_th row */ 87 88 while (i < mbs) { 89 nexti = jl[i]; /* next row to be added to k_th row */ 90 91 /* compute multiplier */ 92 ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */ 93 94 /* uik = -inv(Di)*U_bar(i,k) */ 95 diag = ba + i * 16; 96 u = ba + ili * 16; 97 98 uik[0] = -(diag[0] * u[0] + diag[4] * u[1] + diag[8] * u[2] + diag[12] * u[3]); 99 uik[1] = -(diag[1] * u[0] + diag[5] * u[1] + diag[9] * u[2] + diag[13] * u[3]); 100 uik[2] = -(diag[2] * u[0] + diag[6] * u[1] + diag[10] * u[2] + diag[14] * u[3]); 101 uik[3] = -(diag[3] * u[0] + diag[7] * u[1] + diag[11] * u[2] + diag[15] * u[3]); 102 103 uik[4] = -(diag[0] * u[4] + diag[4] * u[5] + diag[8] * u[6] + diag[12] * u[7]); 104 uik[5] = -(diag[1] * u[4] + diag[5] * u[5] + diag[9] * u[6] + diag[13] * u[7]); 105 uik[6] = -(diag[2] * u[4] + diag[6] * u[5] + diag[10] * u[6] + diag[14] * u[7]); 106 uik[7] = -(diag[3] * u[4] + diag[7] * u[5] + diag[11] * u[6] + diag[15] * u[7]); 107 108 uik[8] = -(diag[0] * u[8] + diag[4] * u[9] + diag[8] * u[10] + diag[12] * u[11]); 109 uik[9] = -(diag[1] * u[8] + diag[5] * u[9] + diag[9] * u[10] + diag[13] * u[11]); 110 uik[10] = -(diag[2] * u[8] + diag[6] * u[9] + diag[10] * u[10] + diag[14] * u[11]); 111 uik[11] = -(diag[3] * u[8] + diag[7] * u[9] + diag[11] * u[10] + diag[15] * u[11]); 112 113 uik[12] = -(diag[0] * u[12] + diag[4] * u[13] + diag[8] * u[14] + diag[12] * u[15]); 114 uik[13] = -(diag[1] * u[12] + diag[5] * u[13] + diag[9] * u[14] + diag[13] * u[15]); 115 uik[14] = -(diag[2] * u[12] + diag[6] * u[13] + diag[10] * u[14] + diag[14] * u[15]); 116 uik[15] = -(diag[3] * u[12] + diag[7] * u[13] + diag[11] * u[14] + diag[15] * u[15]); 117 118 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 119 dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3]; 120 dk[1] += uik[4] * u[0] + uik[5] * u[1] + uik[6] * u[2] + uik[7] * u[3]; 121 dk[2] += uik[8] * u[0] + uik[9] * u[1] + uik[10] * u[2] + uik[11] * u[3]; 122 dk[3] += uik[12] * u[0] + uik[13] * u[1] + uik[14] * u[2] + uik[15] * u[3]; 123 124 dk[4] += uik[0] * u[4] + uik[1] * u[5] + uik[2] * u[6] + uik[3] * u[7]; 125 dk[5] += uik[4] * u[4] + uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7]; 126 dk[6] += uik[8] * u[4] + uik[9] * u[5] + uik[10] * u[6] + uik[11] * u[7]; 127 dk[7] += uik[12] * u[4] + uik[13] * u[5] + uik[14] * u[6] + uik[15] * u[7]; 128 129 dk[8] += uik[0] * u[8] + uik[1] * u[9] + uik[2] * u[10] + uik[3] * u[11]; 130 dk[9] += uik[4] * u[8] + uik[5] * u[9] + uik[6] * u[10] + uik[7] * u[11]; 131 dk[10] += uik[8] * u[8] + uik[9] * u[9] + uik[10] * u[10] + uik[11] * u[11]; 132 dk[11] += uik[12] * u[8] + uik[13] * u[9] + uik[14] * u[10] + uik[15] * u[11]; 133 134 dk[12] += uik[0] * u[12] + uik[1] * u[13] + uik[2] * u[14] + uik[3] * u[15]; 135 dk[13] += uik[4] * u[12] + uik[5] * u[13] + uik[6] * u[14] + uik[7] * u[15]; 136 dk[14] += uik[8] * u[12] + uik[9] * u[13] + uik[10] * u[14] + uik[11] * u[15]; 137 dk[15] += uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14] + uik[15] * u[15]; 138 139 PetscCall(PetscLogFlops(64.0 * 4.0)); 140 141 /* update -U(i,k) */ 142 PetscCall(PetscArraycpy(ba + ili * 16, uik, 16)); 143 144 /* add multiple of row i to k-th row ... */ 145 jmin = ili + 1; 146 jmax = bi[i + 1]; 147 if (jmin < jmax) { 148 for (j = jmin; j < jmax; j++) { 149 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 150 rtmp_ptr = rtmp + bj[j] * 16; 151 u = ba + j * 16; 152 rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2] + uik[3] * u[3]; 153 rtmp_ptr[1] += uik[4] * u[0] + uik[5] * u[1] + uik[6] * u[2] + uik[7] * u[3]; 154 rtmp_ptr[2] += uik[8] * u[0] + uik[9] * u[1] + uik[10] * u[2] + uik[11] * u[3]; 155 rtmp_ptr[3] += uik[12] * u[0] + uik[13] * u[1] + uik[14] * u[2] + uik[15] * u[3]; 156 157 rtmp_ptr[4] += uik[0] * u[4] + uik[1] * u[5] + uik[2] * u[6] + uik[3] * u[7]; 158 rtmp_ptr[5] += uik[4] * u[4] + uik[5] * u[5] + uik[6] * u[6] + uik[7] * u[7]; 159 rtmp_ptr[6] += uik[8] * u[4] + uik[9] * u[5] + uik[10] * u[6] + uik[11] * u[7]; 160 rtmp_ptr[7] += uik[12] * u[4] + uik[13] * u[5] + uik[14] * u[6] + uik[15] * u[7]; 161 162 rtmp_ptr[8] += uik[0] * u[8] + uik[1] * u[9] + uik[2] * u[10] + uik[3] * u[11]; 163 rtmp_ptr[9] += uik[4] * u[8] + uik[5] * u[9] + uik[6] * u[10] + uik[7] * u[11]; 164 rtmp_ptr[10] += uik[8] * u[8] + uik[9] * u[9] + uik[10] * u[10] + uik[11] * u[11]; 165 rtmp_ptr[11] += uik[12] * u[8] + uik[13] * u[9] + uik[14] * u[10] + uik[15] * u[11]; 166 167 rtmp_ptr[12] += uik[0] * u[12] + uik[1] * u[13] + uik[2] * u[14] + uik[3] * u[15]; 168 rtmp_ptr[13] += uik[4] * u[12] + uik[5] * u[13] + uik[6] * u[14] + uik[7] * u[15]; 169 rtmp_ptr[14] += uik[8] * u[12] + uik[9] * u[13] + uik[10] * u[14] + uik[11] * u[15]; 170 rtmp_ptr[15] += uik[12] * u[12] + uik[13] * u[13] + uik[14] * u[14] + uik[15] * u[15]; 171 } 172 PetscCall(PetscLogFlops(2.0 * 64.0 * (jmax - jmin))); 173 174 /* ... add i to row list for next nonzero entry */ 175 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 176 j = bj[jmin]; 177 jl[i] = jl[j]; 178 jl[j] = i; /* update jl */ 179 } 180 i = nexti; 181 } 182 183 /* save nonzero entries in k-th row of U ... */ 184 185 /* invert diagonal block */ 186 diag = ba + k * 16; 187 PetscCall(PetscArraycpy(diag, dk, 16)); 188 189 if (pivotinblocks) { 190 PetscCall(PetscKernel_A_gets_inverse_A_4(diag, shift, allowzeropivot, &zeropivotdetected)); 191 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 192 } else { 193 PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(diag)); 194 } 195 196 jmin = bi[k]; 197 jmax = bi[k + 1]; 198 if (jmin < jmax) { 199 for (j = jmin; j < jmax; j++) { 200 vj = bj[j]; /* block col. index of U */ 201 u = ba + j * 16; 202 rtmp_ptr = rtmp + vj * 16; 203 for (k1 = 0; k1 < 16; k1++) { 204 *u++ = *rtmp_ptr; 205 *rtmp_ptr++ = 0.0; 206 } 207 } 208 209 /* ... add k to row list for first nonzero entry in k-th row */ 210 il[k] = jmin; 211 i = bj[jmin]; 212 jl[k] = jl[i]; 213 jl[i] = k; 214 } 215 } 216 217 PetscCall(PetscFree(rtmp)); 218 PetscCall(PetscFree2(il, jl)); 219 PetscCall(PetscFree2(dk, uik)); 220 if (a->permute) PetscCall(PetscFree(aa)); 221 222 PetscCall(ISRestoreIndices(perm, &perm_ptr)); 223 224 C->ops->solve = MatSolve_SeqSBAIJ_4_inplace; 225 C->ops->solvetranspose = MatSolve_SeqSBAIJ_4_inplace; 226 C->assembled = PETSC_TRUE; 227 C->preallocated = PETSC_TRUE; 228 229 PetscCall(PetscLogFlops(1.3333 * 64 * b->mbs)); /* from inverting diagonal blocks */ 230 PetscFunctionReturn(PETSC_SUCCESS); 231 } 232