1 #include <../src/mat/impls/sbaij/seq/sbaij.h> 2 #include <petsc/private/kernels/blockinvert.h> 3 4 /* Version for when blocks are 3 by 3 */ 5 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3(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 *a2anew, i, j, k, k1, jmin, jmax, *jl, *il, vj, nexti, ili; 11 MatScalar *ba = b->a, *aa, *ap, *dk, *uik; 12 MatScalar *u, *diag, *rtmp, *rtmp_ptr; 13 PetscReal shift = info->shiftamount; 14 PetscBool allowzeropivot, zeropivotdetected; 15 16 PetscFunctionBegin; 17 /* initialization */ 18 allowzeropivot = PetscNot(A->erroriffailure); 19 PetscCall(PetscCalloc1(9 * 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(9, &dk, 9, &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(9 * ai[mbs], &aa)); 36 PetscCall(PetscArraycpy(aa, a->a, 9 * 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 < 9; k1++) { 49 dk[k1] = aa[k * 9 + k1]; 50 aa[k * 9 + k1] = aa[j * 9 + k1]; 51 aa[j * 9 + 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 * 9; /* ptr to the beginning of j-th block of aa */ 58 for (k = 0; k < 9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */ 59 for (k = 0; k < 3; k++) { /* j-th block of aa <- dk^T */ 60 for (k1 = 0; k1 < 3; k1++) *ap++ = dk[k + 3 * 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 * 9; 75 for (j = jmin; j < jmax; j++) { 76 vj = perm_ptr[aj[j]]; /* block col. index */ 77 rtmp_ptr = rtmp + vj * 9; 78 for (i = 0; i < 9; 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 * 9, 9)); 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 diag = ba + i * 9; 94 u = ba + ili * 9; 95 96 uik[0] = -(diag[0] * u[0] + diag[3] * u[1] + diag[6] * u[2]); 97 uik[1] = -(diag[1] * u[0] + diag[4] * u[1] + diag[7] * u[2]); 98 uik[2] = -(diag[2] * u[0] + diag[5] * u[1] + diag[8] * u[2]); 99 100 uik[3] = -(diag[0] * u[3] + diag[3] * u[4] + diag[6] * u[5]); 101 uik[4] = -(diag[1] * u[3] + diag[4] * u[4] + diag[7] * u[5]); 102 uik[5] = -(diag[2] * u[3] + diag[5] * u[4] + diag[8] * u[5]); 103 104 uik[6] = -(diag[0] * u[6] + diag[3] * u[7] + diag[6] * u[8]); 105 uik[7] = -(diag[1] * u[6] + diag[4] * u[7] + diag[7] * u[8]); 106 uik[8] = -(diag[2] * u[6] + diag[5] * u[7] + diag[8] * u[8]); 107 108 /* update D(k) += -U(i,k)^T * U_bar(i,k) */ 109 dk[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2]; 110 dk[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2]; 111 dk[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2]; 112 113 dk[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5]; 114 dk[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5]; 115 dk[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5]; 116 117 dk[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8]; 118 dk[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8]; 119 dk[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8]; 120 121 PetscCall(PetscLogFlops(27.0 * 4.0)); 122 123 /* update -U(i,k) */ 124 PetscCall(PetscArraycpy(ba + ili * 9, uik, 9)); 125 126 /* add multiple of row i to k-th row ... */ 127 jmin = ili + 1; 128 jmax = bi[i + 1]; 129 if (jmin < jmax) { 130 for (j = jmin; j < jmax; j++) { 131 /* rtmp += -U(i,k)^T * U_bar(i,j) */ 132 rtmp_ptr = rtmp + bj[j] * 9; 133 u = ba + j * 9; 134 rtmp_ptr[0] += uik[0] * u[0] + uik[1] * u[1] + uik[2] * u[2]; 135 rtmp_ptr[1] += uik[3] * u[0] + uik[4] * u[1] + uik[5] * u[2]; 136 rtmp_ptr[2] += uik[6] * u[0] + uik[7] * u[1] + uik[8] * u[2]; 137 138 rtmp_ptr[3] += uik[0] * u[3] + uik[1] * u[4] + uik[2] * u[5]; 139 rtmp_ptr[4] += uik[3] * u[3] + uik[4] * u[4] + uik[5] * u[5]; 140 rtmp_ptr[5] += uik[6] * u[3] + uik[7] * u[4] + uik[8] * u[5]; 141 142 rtmp_ptr[6] += uik[0] * u[6] + uik[1] * u[7] + uik[2] * u[8]; 143 rtmp_ptr[7] += uik[3] * u[6] + uik[4] * u[7] + uik[5] * u[8]; 144 rtmp_ptr[8] += uik[6] * u[6] + uik[7] * u[7] + uik[8] * u[8]; 145 } 146 PetscCall(PetscLogFlops(2.0 * 27.0 * (jmax - jmin))); 147 148 /* ... add i to row list for next nonzero entry */ 149 il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */ 150 j = bj[jmin]; 151 jl[i] = jl[j]; 152 jl[j] = i; /* update jl */ 153 } 154 i = nexti; 155 } 156 157 /* save nonzero entries in k-th row of U ... */ 158 159 /* invert diagonal block */ 160 diag = ba + k * 9; 161 PetscCall(PetscArraycpy(diag, dk, 9)); 162 PetscCall(PetscKernel_A_gets_inverse_A_3(diag, shift, allowzeropivot, &zeropivotdetected)); 163 if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT; 164 165 jmin = bi[k]; 166 jmax = bi[k + 1]; 167 if (jmin < jmax) { 168 for (j = jmin; j < jmax; j++) { 169 vj = bj[j]; /* block col. index of U */ 170 u = ba + j * 9; 171 rtmp_ptr = rtmp + vj * 9; 172 for (k1 = 0; k1 < 9; k1++) { 173 *u++ = *rtmp_ptr; 174 *rtmp_ptr++ = 0.0; 175 } 176 } 177 178 /* ... add k to row list for first nonzero entry in k-th row */ 179 il[k] = jmin; 180 i = bj[jmin]; 181 jl[k] = jl[i]; 182 jl[i] = k; 183 } 184 } 185 186 PetscCall(PetscFree(rtmp)); 187 PetscCall(PetscFree2(il, jl)); 188 PetscCall(PetscFree2(dk, uik)); 189 if (a->permute) PetscCall(PetscFree(aa)); 190 191 PetscCall(ISRestoreIndices(perm, &perm_ptr)); 192 193 C->ops->solve = MatSolve_SeqSBAIJ_3_inplace; 194 C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_inplace; 195 C->assembled = PETSC_TRUE; 196 C->preallocated = PETSC_TRUE; 197 198 PetscCall(PetscLogFlops(1.3333 * 27 * b->mbs)); /* from inverting diagonal blocks */ 199 PetscFunctionReturn(PETSC_SUCCESS); 200 } 201