Actual source code: relax.h

      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(2.0*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(2.0*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(2.0*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: }