Actual source code: sbaijfact3.c

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

  5: /* Version for when blocks are 3 by 3  */
  8: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B)
  9: {
 10:   Mat            C = *B;
 11:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
 12:   IS             perm = b->row;
 14:   PetscInt       *perm_ptr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
 15:   PetscInt       *ai,*aj,*a2anew,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;

 20: 
 21:   /* initialization */
 22:   PetscMalloc(9*mbs*sizeof(MatScalar),&rtmp);
 23:   PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));
 24:   PetscMalloc(2*mbs*sizeof(PetscInt),&il);
 25:   jl   = il + mbs;
 26:   for (i=0; i<mbs; i++) {
 27:     jl[i] = mbs; il[0] = 0;
 28:   }
 29:   PetscMalloc(18*sizeof(MatScalar),&dk);
 30:   uik  = dk + 9;
 31:   ISGetIndices(perm,&perm_ptr);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

135:           rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
136:           rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
137:           rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];

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

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

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

178:   PetscFree(rtmp);
179:   PetscFree(il);
180:   PetscFree(dk);
181:   if (a->permute){
182:     PetscFree(aa);
183:   }

185:   ISRestoreIndices(perm,&perm_ptr);
186:   C->factor    = FACTOR_CHOLESKY;
187:   C->assembled = PETSC_TRUE;
188:   C->preallocated = PETSC_TRUE;
189:   PetscLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
190:   return(0);
191: }