1 2 #include <../src/mat/impls/sbaij/seq/sbaij.h> 3 #include <petsc/private/kernels/blockinvert.h> 4 5 /* Version for when blocks are 3 by 3 */ 6 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3(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 *a2anew, i, j, 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 PetscReal shift = info->shiftamount; 15 PetscBool allowzeropivot, zeropivotdetected; 16 17 PetscFunctionBegin; 18 /* initialization */ 19 allowzeropivot = PetscNot(A->erroriffailure); 20 PetscCall(PetscCalloc1(9 * 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(9, &dk, 9, &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(9 * ai[mbs], &aa)); 37 PetscCall(PetscArraycpy(aa, a->a, 9 * 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 < 9; k1++) { 50 dk[k1] = aa[k * 9 + k1]; 51 aa[k * 9 + k1] = aa[j * 9 + k1]; 52 aa[j * 9 + 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 * 9; /* ptr to the beginning of j-th block of aa */ 59 for (k = 0; k < 9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 60 for (k = 0; k < 3; k++) { /* j-th block of aa <- dk^T */ 61 for (k1 = 0; k1 < 3; k1++) *ap++ = dk[k + 3 * 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 * 9; 76 for (j = jmin; j < jmax; j++) { 77 vj = perm_ptr[aj[j]]; /* block col. index */ 78 rtmp_ptr = rtmp + vj * 9; 79 for (i = 0; i < 9; 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 * 9, 9)); 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 diag = ba + i * 9; 95 u = ba + ili * 9; 96 97 uik[0] = -(diag[0] * u[0] + diag[3] * u[1] + diag[6] * u[2]); 98 uik[1] = -(diag[1] * u[0] + diag[4] * u[1] + diag[7] * u[2]); 99 uik[2] = -(diag[2] * u[0] + diag[5] * u[1] + diag[8] * u[2]); 100 101 uik[3] = -(diag[0] * u[3] + diag[3] * u[4] + diag[6] * u[5]); 102 uik[4] = -(diag[1] * u[3] + diag[4] * u[4] + diag[7] * u[5]); 103 uik[5] = -(diag[2] * u[3] + diag[5] * u[4] + diag[8] * u[5]); 104 105 uik[6] = -(diag[0] * u[6] + diag[3] * u[7] + diag[6] * u[8]); 106 uik[7] = -(diag[1] * u[6] + diag[4] * u[7] + diag[7] * u[8]); 107 uik[8] = -(diag[2] * u[6] + diag[5] * u[7] + diag[8] * u[8]); 108 109 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 110 dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2]; 111 dk[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2]; 112 dk[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2]; 113 114 dk[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5]; 115 dk[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5]; 116 dk[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5]; 117 118 dk[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8]; 119 dk[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8]; 120 dk[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8]; 121 122 PetscCall(PetscLogFlops(27.0 * 4.0)); 123 124 /* update -U(i,k) */ 125 PetscCall(PetscArraycpy(ba + ili * 9, uik, 9)); 126 127 /* add multiple of row i to k-th row ... */ 128 jmin = ili + 1; 129 jmax = bi[i + 1]; 130 if (jmin < jmax) { 131 for (j = jmin; j < jmax; j++) { 132 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 133 rtmp_ptr = rtmp + bj[j] * 9; 134 u = ba + j * 9; 135 rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2]; 136 rtmp_ptr[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2]; 137 rtmp_ptr[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2]; 138 139 rtmp_ptr[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5]; 140 rtmp_ptr[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5]; 141 rtmp_ptr[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5]; 142 143 rtmp_ptr[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8]; 144 rtmp_ptr[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8]; 145 rtmp_ptr[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8]; 146 } 147 PetscCall(PetscLogFlops(2.0 * 27.0 * (jmax - jmin))); 148 149 /* ... add i to row list for next nonzero entry */ 150 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 151 j = bj[jmin]; 152 jl[i] = jl[j]; 153 jl[j] = i; /* update jl */ 154 } 155 i = nexti; 156 } 157 158 /* save nonzero entries in k-th row of U ... */ 159 160 /* invert diagonal block */ 161 diag = ba + k * 9; 162 PetscCall(PetscArraycpy(diag, dk, 9)); 163 PetscCall(PetscKernel_A_gets_inverse_A_3(diag, shift, allowzeropivot, &zeropivotdetected)); 164 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 165 166 jmin = bi[k]; 167 jmax = bi[k + 1]; 168 if (jmin < jmax) { 169 for (j = jmin; j < jmax; j++) { 170 vj = bj[j]; /* block col. index of U */ 171 u = ba + j * 9; 172 rtmp_ptr = rtmp + vj * 9; 173 for (k1 = 0; k1 < 9; k1++) { 174 *u++ = *rtmp_ptr; 175 *rtmp_ptr++ = 0.0; 176 } 177 } 178 179 /* ... add k to row list for first nonzero entry in k-th row */ 180 il[k] = jmin; 181 i = bj[jmin]; 182 jl[k] = jl[i]; 183 jl[i] = k; 184 } 185 } 186 187 PetscCall(PetscFree(rtmp)); 188 PetscCall(PetscFree2(il, jl)); 189 PetscCall(PetscFree2(dk, uik)); 190 if (a->permute) PetscCall(PetscFree(aa)); 191 192 PetscCall(ISRestoreIndices(perm, &perm_ptr)); 193 194 C->ops->solve = MatSolve_SeqSBAIJ_3_inplace; 195 C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_inplace; 196 C->assembled = PETSC_TRUE; 197 C->preallocated = PETSC_TRUE; 198 199 PetscCall(PetscLogFlops(1.3333 * 27 * b->mbs)); /* from inverting diagonal blocks */ 200 PetscFunctionReturn(PETSC_SUCCESS); 201 } 202