Actual source code: relax.h
petsc-3.10.5 2019-03-28
Report Typos and Errors

      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_Hermitian_ushort(Mat A,Vec xx,Vec zz)
     43: #else
     44: PetscErrorCode MatMult_SeqSBAIJ_1_Hermitian(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;

     65:   VecSet(zz,0.0);
     66:   VecGetArrayRead(xx,&x);
     67:   VecGetArray(zz,&z);

     69:   v = a->a;
     70:   for (i=0; i<mbs; i++) {
     71:     nz = ai[i+1] - ai[i];    /* length of i_th row of A */
     72:     if (!nz) continue; /* Move to the next row if the current row is empty */
     73:     nonzerorow++;
     74:     x1   = x[i];
     75:     sum  = 0.0;
     76:     jmin = 0;
     77:     if (ib[0] == i) {
     78:       sum = v[0]*x1;           /* diagonal term */
     79:       jmin++;
     80:     }
     81:     for (j=jmin; j<nz; j++) {
     82:       ibt     = ib[j];
     83:       vj      = v[j];
     84:       sum    += vj * x[ibt]; /* (strict upper triangular part of A)*x  */
     85:       z[ibt] += PetscConj(v[j]) * x1;    /* (strict lower triangular part of A)*x  */
     86:     }
     87:     z[i] += sum;
     88:     v    +=    nz;
     89:     ib   += nz;
     90:   }

     92:   VecRestoreArrayRead(xx,&x);
     93:   VecRestoreArray(zz,&z);
     94:   PetscLogFlops(2.0*(2.0*a->nz - nonzerorow) - nonzerorow);
     95:   return(0);
     96: }

     98: #if defined(USESHORT)
     99: PetscErrorCode MatMult_SeqSBAIJ_1_ushort(Mat A,Vec xx,Vec zz)
    100: #else
    101: PetscErrorCode MatMult_SeqSBAIJ_1(Mat A,Vec xx,Vec zz)
    102: #endif
    103: {
    104:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
    105:   const PetscScalar *x;
    106:   PetscScalar       *z,x1,sum;
    107:   const MatScalar   *v;
    108:   MatScalar         vj;
    109:   PetscErrorCode    ierr;
    110:   PetscInt          mbs=a->mbs,i,j,nz;
    111:   const PetscInt    *ai=a->i;
    112: #if defined(USESHORT)
    113:   const unsigned short *ib=a->jshort;
    114:   unsigned short       ibt;
    115: #else
    116:   const PetscInt *ib=a->j;
    117:   PetscInt       ibt;
    118: #endif
    119:   PetscInt nonzerorow=0,jmin;

    122:   VecSet(zz,0.0);
    123:   VecGetArrayRead(xx,&x);
    124:   VecGetArray(zz,&z);

    126:   v = a->a;
    127:   for (i=0; i<mbs; i++) {
    128:     nz = ai[i+1] - ai[i];          /* length of i_th row of A */
    129:     if (!nz) continue; /* Move to the next row if the current row is empty */
    130:     nonzerorow++;
    131:     sum  = 0.0;
    132:     jmin = 0;
    133:     x1   = x[i];
    134:     if (ib[0] == i) {
    135:       sum = v[0]*x1;                 /* diagonal term */
    136:       jmin++;
    137:     }
    138:     PetscPrefetchBlock(ib+nz,nz,0,PETSC_PREFETCH_HINT_NTA); /* Indices for the next row (assumes same size as this one) */
    139:     PetscPrefetchBlock(v+nz,nz,0,PETSC_PREFETCH_HINT_NTA);  /* Entries for the next row */
    140:     for (j=jmin; j<nz; j++) {
    141:       ibt     = ib[j];
    142:       vj      = v[j];
    143:       z[ibt] += vj * x1;       /* (strict lower triangular part of A)*x  */
    144:       sum    += vj * x[ibt];   /* (strict upper triangular part of A)*x  */
    145:     }
    146:     z[i] += sum;
    147:     v    += nz;
    148:     ib   += nz;
    149:   }

    151:   VecRestoreArrayRead(xx,&x);
    152:   VecRestoreArray(zz,&z);
    153:   PetscLogFlops(2.0*(2.0*a->nz - nonzerorow) - nonzerorow);
    154:   return(0);
    155: }

    157: #if defined(USESHORT)
    158: PetscErrorCode MatSOR_SeqSBAIJ_ushort(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
    159: #else
    160: PetscErrorCode MatSOR_SeqSBAIJ(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
    161: #endif
    162: {
    163:   Mat_SeqSBAIJ      *a = (Mat_SeqSBAIJ*)A->data;
    164:   const MatScalar   *aa=a->a,*v,*v1,*aidiag;
    165:   PetscScalar       *x,*t,sum;
    166:   const PetscScalar *b;
    167:   MatScalar         tmp;
    168:   PetscErrorCode    ierr;
    169:   PetscInt          m  =a->mbs,bs=A->rmap->bs,j;
    170:   const PetscInt    *ai=a->i;
    171: #if defined(USESHORT)
    172:   const unsigned short *aj=a->jshort,*vj,*vj1;
    173: #else
    174:   const PetscInt *aj=a->j,*vj,*vj1;
    175: #endif
    176:   PetscInt nz,nz1,i;

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

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

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

    187:   VecGetArray(xx,&x);
    188:   VecGetArrayRead(bb,&b);

    190:   if (!a->idiagvalid) {
    191:     if (!a->idiag) {
    192:       PetscMalloc1(m,&a->idiag);
    193:     }
    194:     for (i=0; i<a->mbs; i++) a->idiag[i] = 1.0/a->a[a->i[i]];
    195:     a->idiagvalid = PETSC_TRUE;
    196:   }

    198:   if (!a->sor_work) {
    199:     PetscMalloc1(m,&a->sor_work);
    200:   }
    201:   t = a->sor_work;

    203:   aidiag = a->idiag;

    205:   if (flag == SOR_APPLY_UPPER) {
    206:     /* apply (U + D/omega) to the vector */
    207:     PetscScalar d;
    208:     for (i=0; i<m; i++) {
    209:       d   = fshift + aa[ai[i]];
    210:       nz  = ai[i+1] - ai[i] - 1;
    211:       vj  = aj + ai[i] + 1;
    212:       v   = aa + ai[i] + 1;
    213:       sum = b[i]*d/omega;
    214: #ifdef USESHORT
    215:       PetscSparseDensePlusDot_no_function(sum,b,v,vj,nz);
    216: #else
    217:       PetscSparseDensePlusDot(sum,b,v,vj,nz);
    218: #endif
    219:       x[i] = sum;
    220:     }
    221:     PetscLogFlops(a->nz);
    222:   }

    224:   if (flag & SOR_ZERO_INITIAL_GUESS) {
    225:     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
    226:       PetscMemcpy(t,b,m*sizeof(PetscScalar));

    228:       v  = aa + 1;
    229:       vj = aj + 1;
    230:       for (i=0; i<m; i++) {
    231:         nz  = ai[i+1] - ai[i] - 1;
    232:         tmp = -(x[i] = omega*t[i]*aidiag[i]);
    233:         for (j=0; j<nz; j++) t[vj[j]] += tmp*v[j];
    234:         v  += nz + 1;
    235:         vj += nz + 1;
    236:       }
    237:       PetscLogFlops(2*a->nz);
    238:     }

    240:     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
    241:       int nz2;
    242:       if (!(flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP)) {
    243: #if defined(PETSC_USE_BACKWARD_LOOP)
    244:         v  = aa + ai[m] - 1;
    245:         vj = aj + ai[m] - 1;
    246:         for (i=m-1; i>=0; i--) {
    247:           sum = b[i];
    248:           nz  = ai[i+1] - ai[i] - 1;
    249:           {PetscInt __i;for (__i=0; __i<nz; __i++) sum -= v[-__i] * x[vj[-__i]];}
    250: #else
    251:         v  = aa + ai[m-1] + 1;
    252:         vj = aj + ai[m-1] + 1;
    253:         nz = 0;
    254:         for (i=m-1; i>=0; i--) {
    255:           sum = b[i];
    256:           nz2 = ai[i] - ai[PetscMax(i-1,0)] - 1; /* avoid referencing ai[-1], nonsense nz2 is okay on last iteration */
    257:           PETSC_Prefetch(v-nz2-1,0,PETSC_PREFETCH_HINT_NTA);
    258:           PETSC_Prefetch(vj-nz2-1,0,PETSC_PREFETCH_HINT_NTA);
    259:           PetscSparseDenseMinusDot(sum,x,v,vj,nz);
    260:           nz = nz2;
    261: #endif
    262:           x[i] = omega*sum*aidiag[i];
    263:           v   -= nz + 1;
    264:           vj  -= nz + 1;
    265:         }
    266:         PetscLogFlops(2*a->nz);
    267:       } else {
    268:         v  = aa + ai[m-1] + 1;
    269:         vj = aj + ai[m-1] + 1;
    270:         nz = 0;
    271:         for (i=m-1; i>=0; i--) {
    272:           sum = t[i];
    273:           nz2 = ai[i] - ai[PetscMax(i-1,0)] - 1; /* avoid referencing ai[-1], nonsense nz2 is okay on last iteration */
    274:           PETSC_Prefetch(v-nz2-1,0,PETSC_PREFETCH_HINT_NTA);
    275:           PETSC_Prefetch(vj-nz2-1,0,PETSC_PREFETCH_HINT_NTA);
    276:           PetscSparseDenseMinusDot(sum,x,v,vj,nz);
    277:           x[i] = (1-omega)*x[i] + omega*sum*aidiag[i];
    278:           nz   = nz2;
    279:           v   -= nz + 1;
    280:           vj  -= nz + 1;
    281:         }
    282:         PetscLogFlops(2*a->nz);
    283:       }
    284:     }
    285:     its--;
    286:   }

    288:   while (its--) {
    289:     /*
    290:        forward sweep:
    291:        for i=0,...,m-1:
    292:          sum[i] = (b[i] - U(i,:)x)/d[i];
    293:          x[i]   = (1-omega)x[i] + omega*sum[i];
    294:          b      = b - x[i]*U^T(i,:);

    296:     */
    297:     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {
    298:       PetscMemcpy(t,b,m*sizeof(PetscScalar));

    300:       for (i=0; i<m; i++) {
    301:         v    = aa + ai[i] + 1; v1=v;
    302:         vj   = aj + ai[i] + 1; vj1=vj;
    303:         nz   = ai[i+1] - ai[i] - 1; nz1=nz;
    304:         sum  = t[i];
    305:         while (nz1--) sum -= (*v1++)*x[*vj1++];
    306:         x[i] = (1-omega)*x[i] + omega*sum*aidiag[i];
    307:         while (nz--) t[*vj++] -= x[i]*(*v++);
    308:       }
    309:       PetscLogFlops(4.0*a->nz);
    310:     }

    312:     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {
    313:       /*
    314:        backward sweep:
    315:        b = b - x[i]*U^T(i,:), i=0,...,n-2
    316:        for i=m-1,...,0:
    317:          sum[i] = (b[i] - U(i,:)x)/d[i];
    318:          x[i]   = (1-omega)x[i] + omega*sum[i];
    319:       */
    320:       /* if there was a forward sweep done above then I thing the next two for loops are not needed */
    321:       PetscMemcpy(t,b,m*sizeof(PetscScalar));

    323:       for (i=0; i<m-1; i++) {  /* update rhs */
    324:         v    = aa + ai[i] + 1;
    325:         vj   = aj + ai[i] + 1;
    326:         nz   = ai[i+1] - ai[i] - 1;
    327:         while (nz--) t[*vj++] -= x[i]*(*v++);
    328:       }
    329:       PetscLogFlops(2.0*(a->nz - m));
    330:       for (i=m-1; i>=0; i--) {
    331:         v    = aa + ai[i] + 1;
    332:         vj   = aj + ai[i] + 1;
    333:         nz   = ai[i+1] - ai[i] - 1;
    334:         sum  = t[i];
    335:         while (nz--) sum -= x[*vj++]*(*v++);
    336:         x[i] =   (1-omega)*x[i] + omega*sum*aidiag[i];
    337:       }
    338:       PetscLogFlops(2.0*(a->nz + m));
    339:     }
    340:   }

    342:   VecRestoreArray(xx,&x);
    343:   VecRestoreArrayRead(bb,&b);
    344:   return(0);
    345: }