Actual source code: relax.h

petsc-master 2019-12-10
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  2: /*
  3:     This is included by sbaij.c to generate unsigned short and regular versions of these two functions
  4: */

  6: /* We cut-and-past below from aij.h to make a "no_function" version of PetscSparseDensePlusDot().
  7:  * This is necessary because the USESHORT case cannot use the inlined functions that may be employed. */

  9: #if defined(PETSC_KERNEL_USE_UNROLL_4)
 10: #define PetscSparseDensePlusDot_no_function(sum,r,xv,xi,nnz) { \
 11:     if (nnz > 0) { \
 12:       PetscInt nnz2=nnz,rem=nnz&0x3; \
 13:       switch (rem) { \
 14:       case 3: sum += *xv++ *r[*xi++]; \
 15:       case 2: sum += *xv++ *r[*xi++]; \
 16:       case 1: sum += *xv++ *r[*xi++]; \
 17:         nnz2      -= rem;} \
 18:       while (nnz2 > 0) { \
 19:         sum +=  xv[0] * r[xi[0]] + xv[1] * r[xi[1]] + \
 20:                 xv[2] * r[xi[2]] + xv[3] * r[xi[3]]; \
 21:         xv += 4; xi += 4; nnz2 -= 4; \
 22:       } \
 23:       xv -= nnz; xi -= nnz; \
 24:     } \
 25:   }

 27: #elif defined(PETSC_KERNEL_USE_UNROLL_2)
 28: #define PetscSparseDensePlusDot_no_function(sum,r,xv,xi,nnz) { \
 29:     PetscInt __i,__i1,__i2; \
 30:     for (__i=0; __i<nnz-1; __i+=2) {__i1 = xi[__i]; __i2=xi[__i+1]; \
 31:                                     sum += (xv[__i]*r[__i1] + xv[__i+1]*r[__i2]);} \
 32:     if (nnz & 0x1) sum += xv[__i] * r[xi[__i]];}

 34: #else
 35: #define PetscSparseDensePlusDot_no_function(sum,r,xv,xi,nnz) { \
 36:     PetscInt __i; \
 37:     for (__i=0; __i<nnz; __i++) sum += xv[__i] * r[xi[__i]];}
 38: #endif


 41: #if defined(USESHORT)
 42: PetscErrorCode MatMult_SeqSBAIJ_1_ushort(Mat A,Vec xx,Vec zz)
 43: #else
 44: PetscErrorCode MatMult_SeqSBAIJ_1(Mat A,Vec xx,Vec zz)
 45: #endif
 46: {
 47:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
 48:   const PetscScalar *x;
 49:   PetscScalar       *z,x1,sum;
 50:   const MatScalar   *v;
 51:   MatScalar         vj;
 52:   PetscErrorCode    ierr;
 53:   PetscInt          mbs=a->mbs,i,j,nz;
 54:   const PetscInt    *ai=a->i;
 55: #if defined(USESHORT)
 56:   const unsigned short *ib=a->jshort;
 57:   unsigned short       ibt;
 58: #else
 59:   const PetscInt *ib=a->j;
 60:   PetscInt       ibt;
 61: #endif
 62:   PetscInt nonzerorow=0,jmin;
 63: #if defined(PETSC_USE_COMPLEX)
 64:   const int aconj = A->hermitian;
 65: #else
 66:   const int aconj = 0;
 67: #endif

 70:   VecSet(zz,0.0);
 71:   VecGetArrayRead(xx,&x);
 72:   VecGetArray(zz,&z);

 74:   v = a->a;
 75:   for (i=0; i<mbs; i++) {
 76:     nz = ai[i+1] - ai[i];          /* length of i_th row of A */
 77:     if (!nz) continue; /* Move to the next row if the current row is empty */
 78:     nonzerorow++;
 79:     sum  = 0.0;
 80:     jmin = 0;
 81:     x1   = x[i];
 82:     if (ib[0] == i) {
 83:       sum = v[0]*x1;                 /* diagonal term */
 84:       jmin++;
 85:     }
 86:     PetscPrefetchBlock(ib+nz,nz,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
 87:     PetscPrefetchBlock(v+nz,nz,0,PETSC_PREFETCH_HINT_NTA);  /* Entries for the next row */
 88:     if (aconj) {
 89:       for (j=jmin; j<nz; j++) {
 90:         ibt     = ib[j];
 91:         vj      = v[j];
 92:         z[ibt] += PetscConj(vj) * x1; /* (strict lower triangular part of A)*x  */
 93:         sum    += vj * x[ibt];        /* (strict upper triangular part of A)*x  */
 94:       }
 95:     } else {
 96:       for (j=jmin; j<nz; j++) {
 97:         ibt     = ib[j];
 98:         vj      = v[j];
 99:         z[ibt] += vj * x1;       /* (strict lower triangular part of A)*x  */
100:         sum    += vj * x[ibt];   /* (strict upper triangular part of A)*x  */
101:       }
102:     }
103:     z[i] += sum;
104:     v    += nz;
105:     ib   += nz;
106:   }

108:   VecRestoreArrayRead(xx,&x);
109:   VecRestoreArray(zz,&z);
110:   PetscLogFlops(2.0*(2.0*a->nz - nonzerorow) - nonzerorow);
111:   return(0);
112: }

114: #if defined(USESHORT)
115: PetscErrorCode MatSOR_SeqSBAIJ_ushort(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
116: #else
117: PetscErrorCode MatSOR_SeqSBAIJ(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
118: #endif
119: {
120:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
121:   const MatScalar   *aa=a->a,*v,*v1,*aidiag;
122:   PetscScalar       *x,*t,sum;
123:   const PetscScalar *b;
124:   MatScalar         tmp;
125:   PetscErrorCode    ierr;
126:   PetscInt          m  =a->mbs,bs=A->rmap->bs,j;
127:   const PetscInt    *ai=a->i;
128: #if defined(USESHORT)
129:   const unsigned short *aj=a->jshort,*vj,*vj1;
130: #else
131:   const PetscInt *aj=a->j,*vj,*vj1;
132: #endif
133:   PetscInt nz,nz1,i;

136:   if (fshift == -1.0) fshift = 0.0; /* negative fshift indicates do not error on zero diagonal; this code never errors on zero diagonal */
137:   if (flag & SOR_EISENSTAT) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for Eisenstat");

139:   its = its*lits;
140:   if (its <= 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Relaxation requires global its %D and local its %D both positive",its,lits);

142:   if (bs > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"SSOR for block size > 1 is not yet implemented");

144:   VecGetArray(xx,&x);
145:   VecGetArrayRead(bb,&b);

147:   if (!a->idiagvalid) {
148:     if (!a->idiag) {
149:       PetscMalloc1(m,&a->idiag);
150:     }
151:     for (i=0; i<a->mbs; i++) a->idiag[i] = 1.0/a->a[a->i[i]];
152:     a->idiagvalid = PETSC_TRUE;
153:   }

155:   if (!a->sor_work) {
156:     PetscMalloc1(m,&a->sor_work);
157:   }
158:   t = a->sor_work;

160:   aidiag = a->idiag;

162:   if (flag == SOR_APPLY_UPPER) {
163:     /* apply (U + D/omega) to the vector */
164:     PetscScalar d;
165:     for (i=0; i<m; i++) {
166:       d   = fshift + aa[ai[i]];
167:       nz  = ai[i+1] - ai[i] - 1;
168:       vj  = aj + ai[i] + 1;
169:       v   = aa + ai[i] + 1;
170:       sum = b[i]*d/omega;
171: #ifdef USESHORT
172:       PetscSparseDensePlusDot_no_function(sum,b,v,vj,nz);
173: #else
174:       PetscSparseDensePlusDot(sum,b,v,vj,nz);
175: #endif
176:       x[i] = sum;
177:     }
178:     PetscLogFlops(a->nz);
179:   }

181:   if (flag & SOR_ZERO_INITIAL_GUESS) {
182:     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
183:       PetscArraycpy(t,b,m);

185:       v  = aa + 1;
186:       vj = aj + 1;
187:       for (i=0; i<m; i++) {
188:         nz  = ai[i+1] - ai[i] - 1;
189:         tmp = -(x[i] = omega*t[i]*aidiag[i]);
190:         for (j=0; j<nz; j++) t[vj[j]] += tmp*v[j];
191:         v  += nz + 1;
192:         vj += nz + 1;
193:       }
194:       PetscLogFlops(2*a->nz);
195:     }

197:     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
198:       int nz2;
199:       if (!(flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP)) {
200: #if defined(PETSC_USE_BACKWARD_LOOP)
201:         v  = aa + ai[m] - 1;
202:         vj = aj + ai[m] - 1;
203:         for (i=m-1; i>=0; i--) {
204:           sum = b[i];
205:           nz  = ai[i+1] - ai[i] - 1;
206:           {PetscInt __i;for (__i=0; __i<nz; __i++) sum -= v[-__i] * x[vj[-__i]];}
207: #else
208:         v  = aa + ai[m-1] + 1;
209:         vj = aj + ai[m-1] + 1;
210:         nz = 0;
211:         for (i=m-1; i>=0; i--) {
212:           sum = b[i];
213:           nz2 = ai[i] - ai[PetscMax(i-1,0)] - 1; /* avoid referencing ai[-1], nonsense nz2 is okay on last iteration */
214:           PETSC_Prefetch(v-nz2-1,0,PETSC_PREFETCH_HINT_NTA);
215:           PETSC_Prefetch(vj-nz2-1,0,PETSC_PREFETCH_HINT_NTA);
216:           PetscSparseDenseMinusDot(sum,x,v,vj,nz);
217:           nz = nz2;
218: #endif
219:           x[i] = omega*sum*aidiag[i];
220:           v   -= nz + 1;
221:           vj  -= nz + 1;
222:         }
223:         PetscLogFlops(2*a->nz);
224:       } else {
225:         v  = aa + ai[m-1] + 1;
226:         vj = aj + ai[m-1] + 1;
227:         nz = 0;
228:         for (i=m-1; i>=0; i--) {
229:           sum = t[i];
230:           nz2 = ai[i] - ai[PetscMax(i-1,0)] - 1; /* avoid referencing ai[-1], nonsense nz2 is okay on last iteration */
231:           PETSC_Prefetch(v-nz2-1,0,PETSC_PREFETCH_HINT_NTA);
232:           PETSC_Prefetch(vj-nz2-1,0,PETSC_PREFETCH_HINT_NTA);
233:           PetscSparseDenseMinusDot(sum,x,v,vj,nz);
234:           x[i] = (1-omega)*x[i] + omega*sum*aidiag[i];
235:           nz   = nz2;
236:           v   -= nz + 1;
237:           vj  -= nz + 1;
238:         }
239:         PetscLogFlops(2*a->nz);
240:       }
241:     }
242:     its--;
243:   }

245:   while (its--) {
246:     /*
247:        forward sweep:
248:        for i=0,...,m-1:
249:          sum[i] = (b[i] - U(i,:)x)/d[i];
250:          x[i]   = (1-omega)x[i] + omega*sum[i];
251:          b      = b - x[i]*U^T(i,:);

253:     */
254:     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
255:       PetscArraycpy(t,b,m);

257:       for (i=0; i<m; i++) {
258:         v    = aa + ai[i] + 1; v1=v;
259:         vj   = aj + ai[i] + 1; vj1=vj;
260:         nz   = ai[i+1] - ai[i] - 1; nz1=nz;
261:         sum  = t[i];
262:         while (nz1--) sum -= (*v1++)*x[*vj1++];
263:         x[i] = (1-omega)*x[i] + omega*sum*aidiag[i];
264:         while (nz--) t[*vj++] -= x[i]*(*v++);
265:       }
266:       PetscLogFlops(4.0*a->nz);
267:     }

269:     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
270:       /*
271:        backward sweep:
272:        b = b - x[i]*U^T(i,:), i=0,...,n-2
273:        for i=m-1,...,0:
274:          sum[i] = (b[i] - U(i,:)x)/d[i];
275:          x[i]   = (1-omega)x[i] + omega*sum[i];
276:       */
277:       /* if there was a forward sweep done above then I thing the next two for loops are not needed */
278:       PetscArraycpy(t,b,m);

280:       for (i=0; i<m-1; i++) {  /* update rhs */
281:         v    = aa + ai[i] + 1;
282:         vj   = aj + ai[i] + 1;
283:         nz   = ai[i+1] - ai[i] - 1;
284:         while (nz--) t[*vj++] -= x[i]*(*v++);
285:       }
286:       PetscLogFlops(2.0*(a->nz - m));
287:       for (i=m-1; i>=0; i--) {
288:         v    = aa + ai[i] + 1;
289:         vj   = aj + ai[i] + 1;
290:         nz   = ai[i+1] - ai[i] - 1;
291:         sum  = t[i];
292:         while (nz--) sum -= x[*vj++]*(*v++);
293:         x[i] =   (1-omega)*x[i] + omega*sum*aidiag[i];
294:       }
295:       PetscLogFlops(2.0*(a->nz + m));
296:     }
297:   }

299:   VecRestoreArray(xx,&x);
300:   VecRestoreArrayRead(bb,&b);
301:   return(0);
302: }