xref: /petsc/src/mat/impls/sbaij/seq/relax.h (revision 174dc0c8cee294b82b85e4dd3b331b29396264fc)
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 #if defined(PETSC_USE_COMPLEX)
75   const int aconj = A->hermitian == PETSC_BOOL3_TRUE;
76 #else
77   const int aconj = 0;
78 #endif
79 
80   PetscFunctionBegin;
81   PetscCall(VecSet(zz, 0.0));
82   PetscCall(VecGetArrayRead(xx, &x));
83   PetscCall(VecGetArray(zz, &z));
84 
85   v = a->a;
86   for (i = 0; i < mbs; i++) {
87     nz = ai[i + 1] - ai[i]; /* length of i_th row of A */
88     if (!nz) continue;      /* Move to the next row if the current row is empty */
89     nonzerorow++;
90     sum  = 0.0;
91     jmin = 0;
92     x1   = x[i];
93     if (ib[0] == i) {
94       sum = v[0] * x1; /* diagonal term */
95       jmin++;
96     }
97     PetscPrefetchBlock(ib + nz, nz, 0, PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
98     PetscPrefetchBlock(v + nz, nz, 0, PETSC_PREFETCH_HINT_NTA);  /* Entries for the next row */
99     if (aconj) {
100       for (j = jmin; j < nz; j++) {
101         ibt = ib[j];
102         vj  = v[j];
103         z[ibt] += PetscConj(vj) * x1; /* (strict lower triangular part of A)*x  */
104         sum += vj * x[ibt];           /* (strict upper triangular part of A)*x  */
105       }
106     } else {
107       for (j = jmin; j < nz; j++) {
108         ibt = ib[j];
109         vj  = v[j];
110         z[ibt] += vj * x1;  /* (strict lower triangular part of A)*x  */
111         sum += vj * x[ibt]; /* (strict upper triangular part of A)*x  */
112       }
113     }
114     z[i] += sum;
115     v += nz;
116     ib += nz;
117   }
118 
119   PetscCall(VecRestoreArrayRead(xx, &x));
120   PetscCall(VecRestoreArray(zz, &z));
121   PetscCall(PetscLogFlops(2.0 * (2.0 * a->nz - nonzerorow) - nonzerorow));
122   PetscFunctionReturn(PETSC_SUCCESS);
123 }
124 
125 #if defined(USESHORT)
126 PetscErrorCode MatSOR_SeqSBAIJ_ushort(Mat A, Vec bb, PetscReal omega, MatSORType flag, PetscReal fshift, PetscInt its, PetscInt lits, Vec xx)
127 #else
128 PetscErrorCode MatSOR_SeqSBAIJ(Mat A, Vec bb, PetscReal omega, MatSORType flag, PetscReal fshift, PetscInt its, PetscInt lits, Vec xx)
129 #endif
130 {
131   Mat_SeqSBAIJ      *a  = (Mat_SeqSBAIJ *)A->data;
132   const MatScalar   *aa = a->a, *v, *v1, *aidiag;
133   PetscScalar       *x, *t, sum;
134   const PetscScalar *b;
135   MatScalar          tmp;
136   PetscInt           m = a->mbs, bs = A->rmap->bs, j;
137   const PetscInt    *ai = a->i;
138 #if defined(USESHORT)
139   const unsigned short *aj = a->jshort, *vj, *vj1;
140 #else
141   const PetscInt *aj = a->j, *vj, *vj1;
142 #endif
143   PetscInt nz, nz1, i;
144 
145   PetscFunctionBegin;
146   if (fshift == -1.0) fshift = 0.0; /* negative fshift indicates do not error on zero diagonal; this code never errors on zero diagonal */
147   PetscCheck(!(flag & SOR_EISENSTAT), PETSC_COMM_SELF, PETSC_ERR_SUP, "No support yet for Eisenstat");
148 
149   its = its * lits;
150   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);
151 
152   PetscCheck(bs <= 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "SSOR for block size > 1 is not yet implemented");
153 
154   PetscCall(VecGetArray(xx, &x));
155   PetscCall(VecGetArrayRead(bb, &b));
156 
157   if (!a->idiagvalid) {
158     if (!a->idiag) PetscCall(PetscMalloc1(m, &a->idiag));
159     for (i = 0; i < a->mbs; i++) a->idiag[i] = 1.0 / a->a[a->i[i]];
160     a->idiagvalid = PETSC_TRUE;
161   }
162 
163   if (!a->sor_work) PetscCall(PetscMalloc1(m, &a->sor_work));
164   t = a->sor_work;
165 
166   aidiag = a->idiag;
167 
168   if (flag == SOR_APPLY_UPPER) {
169     /* apply (U + D/omega) to the vector */
170     PetscScalar d;
171     for (i = 0; i < m; i++) {
172       d   = fshift + aa[ai[i]];
173       nz  = ai[i + 1] - ai[i] - 1;
174       vj  = aj + ai[i] + 1;
175       v   = aa + ai[i] + 1;
176       sum = b[i] * d / omega;
177 #ifdef USESHORT
178       PetscSparseDensePlusDot_no_function(sum, b, v, vj, nz);
179 #else
180       PetscSparseDensePlusDot(sum, b, v, vj, nz);
181 #endif
182       x[i] = sum;
183     }
184     PetscCall(PetscLogFlops(a->nz));
185   }
186 
187   if (flag & SOR_ZERO_INITIAL_GUESS) {
188     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
189       PetscCall(PetscArraycpy(t, b, m));
190 
191       v  = aa + 1;
192       vj = aj + 1;
193       for (i = 0; i < m; i++) {
194         nz  = ai[i + 1] - ai[i] - 1;
195         tmp = -(x[i] = omega * t[i] * aidiag[i]);
196         for (j = 0; j < nz; j++) t[vj[j]] += tmp * v[j];
197         v += nz + 1;
198         vj += nz + 1;
199       }
200       PetscCall(PetscLogFlops(2.0 * a->nz));
201     }
202 
203     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
204       PetscInt nz2;
205       if (!(flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP)) {
206         v  = aa + ai[m] - 1;
207         vj = aj + ai[m] - 1;
208         for (i = m - 1; i >= 0; i--) {
209           sum = b[i];
210           nz  = ai[i + 1] - ai[i] - 1;
211           {
212             PetscInt __i;
213             for (__i = 0; __i < nz; __i++) sum -= v[-__i] * x[vj[-__i]];
214           }
215           x[i] = omega * sum * aidiag[i];
216           v -= nz + 1;
217           vj -= nz + 1;
218         }
219         PetscCall(PetscLogFlops(2.0 * a->nz));
220       } else {
221         v  = aa + ai[m - 1] + 1;
222         vj = aj + ai[m - 1] + 1;
223         nz = 0;
224         for (i = m - 1; i >= 0; i--) {
225           sum = t[i];
226           nz2 = ai[i] - ai[PetscMax(i - 1, 0)] - 1; /* avoid referencing ai[-1], nonsense nz2 is okay on last iteration */
227           PETSC_Prefetch(v - nz2 - 1, 0, PETSC_PREFETCH_HINT_NTA);
228           PETSC_Prefetch(vj - nz2 - 1, 0, PETSC_PREFETCH_HINT_NTA);
229           PetscSparseDenseMinusDot(sum, x, v, vj, nz);
230           x[i] = (1 - omega) * x[i] + omega * sum * aidiag[i];
231           nz   = nz2;
232           v -= nz + 1;
233           vj -= nz + 1;
234         }
235         PetscCall(PetscLogFlops(2.0 * a->nz));
236       }
237     }
238     its--;
239   }
240 
241   while (its--) {
242     /*
243        forward sweep:
244        for i=0,...,m-1:
245          sum[i] = (b[i] - U(i,:)x)/d[i];
246          x[i]   = (1-omega)x[i] + omega*sum[i];
247          b      = b - x[i]*U^T(i,:);
248 
249     */
250     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
251       PetscCall(PetscArraycpy(t, b, m));
252 
253       for (i = 0; i < m; i++) {
254         v   = aa + ai[i] + 1;
255         v1  = v;
256         vj  = aj + ai[i] + 1;
257         vj1 = vj;
258         nz  = ai[i + 1] - ai[i] - 1;
259         nz1 = nz;
260         sum = t[i];
261         while (nz1--) sum -= (*v1++) * x[*vj1++];
262         x[i] = (1 - omega) * x[i] + omega * sum * aidiag[i];
263         while (nz--) t[*vj++] -= x[i] * (*v++);
264       }
265       PetscCall(PetscLogFlops(4.0 * a->nz));
266     }
267 
268     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
269       /*
270        backward sweep:
271        b = b - x[i]*U^T(i,:), i=0,...,n-2
272        for i=m-1,...,0:
273          sum[i] = (b[i] - U(i,:)x)/d[i];
274          x[i]   = (1-omega)x[i] + omega*sum[i];
275       */
276       /* if there was a forward sweep done above then I thing the next two for loops are not needed */
277       PetscCall(PetscArraycpy(t, b, m));
278 
279       for (i = 0; i < m - 1; i++) { /* update rhs */
280         v  = aa + ai[i] + 1;
281         vj = aj + ai[i] + 1;
282         nz = ai[i + 1] - ai[i] - 1;
283         while (nz--) t[*vj++] -= x[i] * (*v++);
284       }
285       PetscCall(PetscLogFlops(2.0 * (a->nz - m)));
286       for (i = m - 1; i >= 0; i--) {
287         v   = aa + ai[i] + 1;
288         vj  = aj + ai[i] + 1;
289         nz  = ai[i + 1] - ai[i] - 1;
290         sum = t[i];
291         while (nz--) sum -= x[*vj++] * (*v++);
292         x[i] = (1 - omega) * x[i] + omega * sum * aidiag[i];
293       }
294       PetscCall(PetscLogFlops(2.0 * (a->nz + m)));
295     }
296   }
297 
298   PetscCall(VecRestoreArray(xx, &x));
299   PetscCall(VecRestoreArrayRead(bb, &b));
300   PetscFunctionReturn(PETSC_SUCCESS);
301 }
302