Actual source code: sbaijfact3.c

  1: #define PETSCMAT_DLL

 3:  #include ../src/mat/impls/sbaij/seq/sbaij.h
 4:  #include ../src/inline/ilu.h

  6: /* Version for when blocks are 3 by 3  */
  9: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat C,Mat A,const MatFactorInfo *info)
 10: {
 11:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
 12:   IS             perm = b->row;
 14:   const PetscInt *ai,*aj,*perm_ptr,mbs=a->mbs,*bi=b->i,*bj=b->j;
 15:   PetscInt       *a2anew,i,j,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
 16:   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
 17:   MatScalar      *u,*diag,*rtmp,*rtmp_ptr;
 18:   PetscReal      shift = info->shiftinblocks;

 21: 
 22:   /* initialization */
 23:   PetscMalloc(9*mbs*sizeof(MatScalar),&rtmp);
 24:   PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));
 25:   PetscMalloc(2*mbs*sizeof(PetscInt),&il);
 26:   jl   = il + mbs;
 27:   for (i=0; i<mbs; i++) {
 28:     jl[i] = mbs; il[0] = 0;
 29:   }
 30:   PetscMalloc(18*sizeof(MatScalar),&dk);
 31:   uik  = dk + 9;
 32:   ISGetIndices(perm,&perm_ptr);

 34:   /* check permutation */
 35:   if (!a->permute){
 36:     ai = a->i; aj = a->j; aa = a->a;
 37:   } else {
 38:     ai   = a->inew; aj = a->jnew;
 39:     PetscMalloc(9*ai[mbs]*sizeof(MatScalar),&aa);
 40:     PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));
 41:     PetscMalloc(ai[mbs]*sizeof(PetscInt),&a2anew);
 42:     PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));

 44:     for (i=0; i<mbs; i++){
 45:       jmin = ai[i]; jmax = ai[i+1];
 46:       for (j=jmin; j<jmax; j++){
 47:         while (a2anew[j] != j){
 48:           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
 49:           for (k1=0; k1<9; k1++){
 50:             dk[k1]       = aa[k*9+k1];
 51:             aa[k*9+k1] = aa[j*9+k1];
 52:             aa[j*9+k1] = dk[k1];
 53:           }
 54:         }
 55:         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
 56:         if (i > aj[j]){
 57:           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
 58:           ap = aa + j*9;                     /* ptr to the beginning of j-th block of aa */
 59:           for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
 60:           for (k=0; k<3; k++){               /* j-th block of aa <- dk^T */
 61:             for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1];
 62:           }
 63:         }
 64:       }
 65:     }
 66:     PetscFree(a2anew);
 67:   }
 68: 
 69:   /* for each row k */
 70:   for (k = 0; k<mbs; k++){

 72:     /*initialize k-th row with elements nonzero in row perm(k) of A */
 73:     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
 74:     if (jmin < jmax) {
 75:       ap = aa + jmin*9;
 76:       for (j = jmin; j < jmax; j++){
 77:         vj = perm_ptr[aj[j]];         /* block col. index */
 78:         rtmp_ptr = rtmp + vj*9;
 79:         for (i=0; i<9; i++) *rtmp_ptr++ = *ap++;
 80:       }
 81:     }

 83:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
 84:     PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));
 85:     i = jl[k]; /* first row to be added to k_th row  */

 87:     while (i < mbs){
 88:       nexti = jl[i]; /* next row to be added to k_th row */

 90:       /* compute multiplier */
 91:       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */

 93:       /* uik = -inv(Di)*U_bar(i,k) */
 94:       diag = ba + i*9;
 95:       u    = ba + ili*9;

 97:       uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
 98:       uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
 99:       uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);

101:       uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
102:       uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
103:       uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);

105:       uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
106:       uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
107:       uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);

109:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
110:       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
111:       dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
112:       dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];

114:       dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
115:       dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
116:       dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];

118:       dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
119:       dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
120:       dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];

122:       PetscLogFlops(27*4);

124:       /* update -U(i,k) */
125:       PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));

127:       /* add multiple of row i to k-th row ... */
128:       jmin = ili + 1; jmax = bi[i+1];
129:       if (jmin < jmax){
130:         for (j=jmin; j<jmax; j++) {
131:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
132:           rtmp_ptr = rtmp + bj[j]*9;
133:           u = ba + j*9;
134:           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
135:           rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
136:           rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];

138:           rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
139:           rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
140:           rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];

142:           rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
143:           rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
144:           rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
145:         }
146:         PetscLogFlops(2*27*(jmax-jmin));
147: 
148:         /* ... add i to row list for next nonzero entry */
149:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
150:         j     = bj[jmin];
151:         jl[i] = jl[j]; jl[j] = i; /* update jl */
152:       }
153:       i = nexti;
154:     }

156:     /* save nonzero entries in k-th row of U ... */

158:     /* invert diagonal block */
159:     diag = ba+k*9;
160:     PetscMemcpy(diag,dk,9*sizeof(MatScalar));
161:     Kernel_A_gets_inverse_A_3(diag,shift);
162: 
163:     jmin = bi[k]; jmax = bi[k+1];
164:     if (jmin < jmax) {
165:       for (j=jmin; j<jmax; j++){
166:          vj = bj[j];           /* block col. index of U */
167:          u   = ba + j*9;
168:          rtmp_ptr = rtmp + vj*9;
169:          for (k1=0; k1<9; k1++){
170:            *u++        = *rtmp_ptr;
171:            *rtmp_ptr++ = 0.0;
172:          }
173:       }
174: 
175:       /* ... add k to row list for first nonzero entry in k-th row */
176:       il[k] = jmin;
177:       i     = bj[jmin];
178:       jl[k] = jl[i]; jl[i] = k;
179:     }
180:   }

182:   PetscFree(rtmp);
183:   PetscFree(il);
184:   PetscFree(dk);
185:   if (a->permute){
186:     PetscFree(aa);
187:   }

189:   ISRestoreIndices(perm,&perm_ptr);
190:   C->ops->solve          = MatSolve_SeqSBAIJ_3;
191:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_3;
192:   C->assembled = PETSC_TRUE;
193:   C->preallocated = PETSC_TRUE;
194:   PetscLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
195:   return(0);
196: }