1 /* 2 This is included by sbaij.c to generate unsigned short and regular versions of these two functions 3 */ 4 5 /* We cut-and-past below from aij.h to make a "no_function" version of PetscSparseDensePlusDot(). 6 * This is necessary because the USESHORT case cannot use the inlined functions that may be employed. */ 7 8 #if defined(PETSC_KERNEL_USE_UNROLL_4) 9 #define PetscSparseDensePlusDot_no_function(sum, r, xv, xi, nnz) \ 10 do { \ 11 if (nnz > 0) { \ 12 PetscInt nnz2 = nnz, rem = nnz & 0x3; \ 13 switch (rem) { \ 14 case 3: \ 15 sum += *xv++ * r[*xi++]; \ 16 case 2: \ 17 sum += *xv++ * r[*xi++]; \ 18 case 1: \ 19 sum += *xv++ * r[*xi++]; \ 20 nnz2 -= rem; \ 21 } \ 22 while (nnz2 > 0) { \ 23 sum += xv[0] * r[xi[0]] + xv[1] * r[xi[1]] + xv[2] * r[xi[2]] + xv[3] * r[xi[3]]; \ 24 xv += 4; \ 25 xi += 4; \ 26 nnz2 -= 4; \ 27 } \ 28 xv -= nnz; \ 29 xi -= nnz; \ 30 } \ 31 } while (0) 32 33 #elif defined(PETSC_KERNEL_USE_UNROLL_2) 34 #define PetscSparseDensePlusDot_no_function(sum, r, xv, xi, nnz) \ 35 do { \ 36 PetscInt __i, __i1, __i2; \ 37 for (__i = 0; __i < nnz - 1; __i += 2) { \ 38 __i1 = xi[__i]; \ 39 __i2 = xi[__i + 1]; \ 40 sum += (xv[__i] * r[__i1] + xv[__i + 1] * r[__i2]); \ 41 } \ 42 if (nnz & 0x1) sum += xv[__i] * r[xi[__i]]; \ 43 } while (0) 44 45 #else 46 #define PetscSparseDensePlusDot_no_function(sum, r, xv, xi, nnz) \ 47 do { \ 48 PetscInt __i; \ 49 for (__i = 0; __i < nnz; __i++) sum += xv[__i] * r[xi[__i]]; \ 50 } while (0) 51 #endif 52 53 #if defined(USESHORT) 54 PetscErrorCode MatMult_SeqSBAIJ_1_ushort(Mat A, Vec xx, Vec zz) 55 #else 56 PetscErrorCode MatMult_SeqSBAIJ_1(Mat A, Vec xx, Vec zz) 57 #endif 58 { 59 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data; 60 const PetscScalar *x; 61 PetscScalar *z, x1, sum; 62 const MatScalar *v; 63 MatScalar vj; 64 PetscInt mbs = a->mbs, i, j, nz; 65 const PetscInt *ai = a->i; 66 #if defined(USESHORT) 67 const unsigned short *ib = a->jshort; 68 unsigned short ibt; 69 #else 70 const PetscInt *ib = a->j; 71 PetscInt ibt; 72 #endif 73 PetscInt nonzerorow = 0, jmin; 74 const int aconj = PetscDefined(USE_COMPLEX) && A->hermitian == PETSC_BOOL3_TRUE ? 1 : 0; 75 76 PetscFunctionBegin; 77 PetscCall(VecSet(zz, 0.0)); 78 PetscCall(VecGetArrayRead(xx, &x)); 79 PetscCall(VecGetArray(zz, &z)); 80 81 v = a->a; 82 for (i = 0; i < mbs; i++) { 83 nz = ai[i + 1] - ai[i]; /* length of i_th row of A */ 84 if (!nz) continue; /* Move to the next row if the current row is empty */ 85 nonzerorow++; 86 sum = 0.0; 87 jmin = 0; 88 x1 = x[i]; 89 if (ib[0] == i) { 90 sum = v[0] * x1; /* diagonal term */ 91 jmin++; 92 } 93 PetscPrefetchBlock(ib + nz, nz, 0, PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */ 94 PetscPrefetchBlock(v + nz, nz, 0, PETSC_PREFETCH_HINT_NTA); /* Entries for the next row */ 95 if (aconj) { 96 for (j = jmin; j < nz; j++) { 97 ibt = ib[j]; 98 vj = v[j]; 99 z[ibt] += PetscConj(vj) * x1; /* (strict lower triangular part of A)*x */ 100 sum += vj * x[ibt]; /* (strict upper triangular part of A)*x */ 101 } 102 } else { 103 for (j = jmin; j < nz; j++) { 104 ibt = ib[j]; 105 vj = v[j]; 106 z[ibt] += vj * x1; /* (strict lower triangular part of A)*x */ 107 sum += vj * x[ibt]; /* (strict upper triangular part of A)*x */ 108 } 109 } 110 z[i] += sum; 111 v += nz; 112 ib += nz; 113 } 114 115 PetscCall(VecRestoreArrayRead(xx, &x)); 116 PetscCall(VecRestoreArray(zz, &z)); 117 PetscCall(PetscLogFlops(2.0 * (2.0 * a->nz - nonzerorow) - nonzerorow)); 118 PetscFunctionReturn(PETSC_SUCCESS); 119 } 120 121 #if defined(USESHORT) 122 PetscErrorCode MatSOR_SeqSBAIJ_ushort(Mat A, Vec bb, PetscReal omega, MatSORType flag, PetscReal fshift, PetscInt its, PetscInt lits, Vec xx) 123 #else 124 PetscErrorCode MatSOR_SeqSBAIJ(Mat A, Vec bb, PetscReal omega, MatSORType flag, PetscReal fshift, PetscInt its, PetscInt lits, Vec xx) 125 #endif 126 { 127 Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ *)A->data; 128 const MatScalar *aa = a->a, *v, *v1, *aidiag; 129 PetscScalar *x, *t, sum; 130 const PetscScalar *b; 131 MatScalar tmp; 132 PetscInt m = a->mbs, bs = A->rmap->bs, j; 133 const PetscInt *ai = a->i; 134 #if defined(USESHORT) 135 const unsigned short *aj = a->jshort, *vj, *vj1; 136 #else 137 const PetscInt *aj = a->j, *vj, *vj1; 138 #endif 139 PetscInt nz, nz1, i; 140 141 PetscFunctionBegin; 142 if (fshift == -1.0) fshift = 0.0; /* negative fshift indicates do not error on zero diagonal; this code never errors on zero diagonal */ 143 PetscCheck(!(flag & SOR_EISENSTAT), PETSC_COMM_SELF, PETSC_ERR_SUP, "No support yet for Eisenstat"); 144 145 its = its * lits; 146 PetscCheck(its > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Relaxation requires global its %" PetscInt_FMT " and local its %" PetscInt_FMT " both positive", its, lits); 147 148 PetscCheck(bs <= 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "SSOR for block size > 1 is not yet implemented"); 149 150 PetscCall(VecGetArray(xx, &x)); 151 PetscCall(VecGetArrayRead(bb, &b)); 152 153 if (!a->idiagvalid) { 154 if (!a->idiag) PetscCall(PetscMalloc1(m, &a->idiag)); 155 for (i = 0; i < a->mbs; i++) a->idiag[i] = 1.0 / a->a[a->i[i]]; 156 a->idiagvalid = PETSC_TRUE; 157 } 158 159 if (!a->sor_work) PetscCall(PetscMalloc1(m, &a->sor_work)); 160 t = a->sor_work; 161 162 aidiag = a->idiag; 163 164 if (flag == SOR_APPLY_UPPER) { 165 /* apply (U + D/omega) to the vector */ 166 PetscScalar d; 167 for (i = 0; i < m; i++) { 168 d = fshift + aa[ai[i]]; 169 nz = ai[i + 1] - ai[i] - 1; 170 vj = aj + ai[i] + 1; 171 v = aa + ai[i] + 1; 172 sum = b[i] * d / omega; 173 #ifdef USESHORT 174 PetscSparseDensePlusDot_no_function(sum, b, v, vj, nz); 175 #else 176 PetscSparseDensePlusDot(sum, b, v, vj, nz); 177 #endif 178 x[i] = sum; 179 } 180 PetscCall(PetscLogFlops(a->nz)); 181 } 182 183 if (flag & SOR_ZERO_INITIAL_GUESS) { 184 if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) { 185 PetscCall(PetscArraycpy(t, b, m)); 186 187 v = aa + 1; 188 vj = aj + 1; 189 for (i = 0; i < m; i++) { 190 nz = ai[i + 1] - ai[i] - 1; 191 tmp = -(x[i] = omega * t[i] * aidiag[i]); 192 for (j = 0; j < nz; j++) t[vj[j]] += tmp * v[j]; 193 v += nz + 1; 194 vj += nz + 1; 195 } 196 PetscCall(PetscLogFlops(2.0 * a->nz)); 197 } 198 199 if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) { 200 PetscInt nz2; 201 if (!(flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP)) { 202 v = aa + ai[m] - 1; 203 vj = aj + ai[m] - 1; 204 for (i = m - 1; i >= 0; i--) { 205 sum = b[i]; 206 nz = ai[i + 1] - ai[i] - 1; 207 { 208 PetscInt __i; 209 for (__i = 0; __i < nz; __i++) sum -= v[-__i] * x[vj[-__i]]; 210 } 211 x[i] = omega * sum * aidiag[i]; 212 v -= nz + 1; 213 vj -= nz + 1; 214 } 215 PetscCall(PetscLogFlops(2.0 * a->nz)); 216 } else { 217 v = aa + ai[m - 1] + 1; 218 vj = aj + ai[m - 1] + 1; 219 nz = 0; 220 for (i = m - 1; i >= 0; i--) { 221 sum = t[i]; 222 nz2 = ai[i] - ai[PetscMax(i - 1, 0)] - 1; /* avoid referencing ai[-1], nonsense nz2 is okay on last iteration */ 223 PETSC_Prefetch(v - nz2 - 1, 0, PETSC_PREFETCH_HINT_NTA); 224 PETSC_Prefetch(vj - nz2 - 1, 0, PETSC_PREFETCH_HINT_NTA); 225 PetscSparseDenseMinusDot(sum, x, v, vj, nz); 226 x[i] = (1 - omega) * x[i] + omega * sum * aidiag[i]; 227 nz = nz2; 228 v -= nz + 1; 229 vj -= nz + 1; 230 } 231 PetscCall(PetscLogFlops(2.0 * a->nz)); 232 } 233 } 234 its--; 235 } 236 237 while (its--) { 238 /* 239 forward sweep: 240 for i=0,...,m-1: 241 sum[i] = (b[i] - U(i,:)x)/d[i]; 242 x[i] = (1-omega)x[i] + omega*sum[i]; 243 b = b - x[i]*U^T(i,:); 244 245 */ 246 if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) { 247 PetscCall(PetscArraycpy(t, b, m)); 248 249 for (i = 0; i < m; i++) { 250 v = aa + ai[i] + 1; 251 v1 = v; 252 vj = aj + ai[i] + 1; 253 vj1 = vj; 254 nz = ai[i + 1] - ai[i] - 1; 255 nz1 = nz; 256 sum = t[i]; 257 while (nz1--) sum -= (*v1++) * x[*vj1++]; 258 x[i] = (1 - omega) * x[i] + omega * sum * aidiag[i]; 259 while (nz--) t[*vj++] -= x[i] * (*v++); 260 } 261 PetscCall(PetscLogFlops(4.0 * a->nz)); 262 } 263 264 if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) { 265 /* 266 backward sweep: 267 b = b - x[i]*U^T(i,:), i=0,...,n-2 268 for i=m-1,...,0: 269 sum[i] = (b[i] - U(i,:)x)/d[i]; 270 x[i] = (1-omega)x[i] + omega*sum[i]; 271 */ 272 /* if there was a forward sweep done above then I thing the next two for loops are not needed */ 273 PetscCall(PetscArraycpy(t, b, m)); 274 275 for (i = 0; i < m - 1; i++) { /* update rhs */ 276 v = aa + ai[i] + 1; 277 vj = aj + ai[i] + 1; 278 nz = ai[i + 1] - ai[i] - 1; 279 while (nz--) t[*vj++] -= x[i] * (*v++); 280 } 281 PetscCall(PetscLogFlops(2.0 * (a->nz - m))); 282 for (i = m - 1; i >= 0; i--) { 283 v = aa + ai[i] + 1; 284 vj = aj + ai[i] + 1; 285 nz = ai[i + 1] - ai[i] - 1; 286 sum = t[i]; 287 while (nz--) sum -= x[*vj++] * (*v++); 288 x[i] = (1 - omega) * x[i] + omega * sum * aidiag[i]; 289 } 290 PetscCall(PetscLogFlops(2.0 * (a->nz + m))); 291 } 292 } 293 294 PetscCall(VecRestoreArray(xx, &x)); 295 PetscCall(VecRestoreArrayRead(bb, &b)); 296 PetscFunctionReturn(PETSC_SUCCESS); 297 } 298