Actual source code: sbaijfact6.c

  1: #define PETSCMAT_DLL

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

  6: /* Version for when blocks are 4 by 4  */
  9: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4(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       i,j,*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;
 18:   PetscTruth     pivotinblocks = b->pivotinblocks;
 19:   PetscReal      shift = info->shiftamount;

 22:   /* initialization */
 23:   PetscMalloc(16*mbs*sizeof(MatScalar),&rtmp);
 24:   PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));
 25:   PetscMalloc2(mbs,PetscInt,&il,mbs,PetscInt,&jl);
 26:   for (i=0; i<mbs; i++) {
 27:     jl[i] = mbs; il[0] = 0;
 28:   }
 29:   PetscMalloc2(16,MatScalar,&dk,16,MatScalar,&uik);
 30:   ISGetIndices(perm,&perm_ptr);

 32:   /* check permutation */
 33:   if (!a->permute){
 34:     ai = a->i; aj = a->j; aa = a->a;
 35:   } else {
 36:     ai   = a->inew; aj = a->jnew;
 37:     PetscMalloc(16*ai[mbs]*sizeof(MatScalar),&aa);
 38:     PetscMemcpy(aa,a->a,16*ai[mbs]*sizeof(MatScalar));
 39:     PetscMalloc(ai[mbs]*sizeof(PetscInt),&a2anew);
 40:     PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));

 42:     for (i=0; i<mbs; i++){
 43:       jmin = ai[i]; jmax = ai[i+1];
 44:       for (j=jmin; j<jmax; j++){
 45:         while (a2anew[j] != j){
 46:           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
 47:           for (k1=0; k1<16; k1++){
 48:             dk[k1]       = aa[k*16+k1];
 49:             aa[k*16+k1] = aa[j*16+k1];
 50:             aa[j*16+k1] = dk[k1];
 51:           }
 52:         }
 53:         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
 54:         if (i > aj[j]){
 55:           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
 56:           ap = aa + j*16;                     /* ptr to the beginning of j-th block of aa */
 57:           for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
 58:           for (k=0; k<4; k++){               /* j-th block of aa <- dk^T */
 59:             for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*k1];
 60:           }
 61:         }
 62:       }
 63:     }
 64:     PetscFree(a2anew);
 65:   }
 66: 
 67:   /* for each row k */
 68:   for (k = 0; k<mbs; k++){

 70:     /*initialize k-th row with elements nonzero in row perm(k) of A */
 71:     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
 72:     if (jmin < jmax) {
 73:       ap = aa + jmin*16;
 74:       for (j = jmin; j < jmax; j++){
 75:         vj = perm_ptr[aj[j]];         /* block col. index */
 76:         rtmp_ptr = rtmp + vj*16;
 77:         for (i=0; i<16; i++) *rtmp_ptr++ = *ap++;
 78:       }
 79:     }

 81:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
 82:     PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));
 83:     i = jl[k]; /* first row to be added to k_th row  */

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

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

 91:       /* uik = -inv(Di)*U_bar(i,k) */
 92:       diag = ba + i*16;
 93:       u    = ba + ili*16;

 95:       uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]);
 96:       uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]);
 97:       uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]);
 98:       uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]);

100:       uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]);
101:       uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]);
102:       uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]);
103:       uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]);

105:       uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]);
106:       uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]);
107:       uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]);
108:       uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]);

110:       uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]);
111:       uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]);
112:       uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]);
113:       uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]);

115:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
116:       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
117:       dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
118:       dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
119:       dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];

121:       dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
122:       dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
123:       dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
124:       dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];

126:       dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
127:       dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
128:       dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
129:       dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];

131:       dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
132:       dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
133:       dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
134:       dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];

136:       PetscLogFlops(64.0*4.0);
137: 
138:       /* update -U(i,k) */
139:       PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));

141:       /* add multiple of row i to k-th row ... */
142:       jmin = ili + 1; jmax = bi[i+1];
143:       if (jmin < jmax){
144:         for (j=jmin; j<jmax; j++) {
145:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
146:           rtmp_ptr = rtmp + bj[j]*16;
147:           u = ba + j*16;
148:           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
149:           rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
150:           rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
151:           rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];

153:           rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
154:           rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
155:           rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
156:           rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];

158:           rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
159:           rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
160:           rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
161:           rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];

163:           rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
164:           rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
165:           rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
166:           rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
167:         }
168:         PetscLogFlops(2.0*64.0*(jmax-jmin));
169: 
170:         /* ... add i to row list for next nonzero entry */
171:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
172:         j     = bj[jmin];
173:         jl[i] = jl[j]; jl[j] = i; /* update jl */
174:       }
175:       i = nexti;
176:     }

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

180:     /* invert diagonal block */
181:     diag = ba+k*16;
182:     PetscMemcpy(diag,dk,16*sizeof(MatScalar));

184:     if (pivotinblocks) {
185:       Kernel_A_gets_inverse_A_4(diag,shift);
186:     } else {
187:       Kernel_A_gets_inverse_A_4_nopivot(diag);
188:     }

190:     jmin = bi[k]; jmax = bi[k+1];
191:     if (jmin < jmax) {
192:       for (j=jmin; j<jmax; j++){
193:          vj = bj[j];           /* block col. index of U */
194:          u   = ba + j*16;
195:          rtmp_ptr = rtmp + vj*16;
196:          for (k1=0; k1<16; k1++){
197:            *u++        = *rtmp_ptr;
198:            *rtmp_ptr++ = 0.0;
199:          }
200:       }
201: 
202:       /* ... add k to row list for first nonzero entry in k-th row */
203:       il[k] = jmin;
204:       i     = bj[jmin];
205:       jl[k] = jl[i]; jl[i] = k;
206:     }
207:   }

209:   PetscFree(rtmp);
210:   PetscFree2(il,jl);
211:   PetscFree2(dk,uik);
212:   if (a->permute){
213:     PetscFree(aa);
214:   }

216:   ISRestoreIndices(perm,&perm_ptr);
217:   C->ops->solve          = MatSolve_SeqSBAIJ_4_inplace;
218:   C->ops->solvetranspose = MatSolve_SeqSBAIJ_4_inplace;
219:   C->assembled = PETSC_TRUE;
220:   C->preallocated = PETSC_TRUE;
221:   PetscLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
222:   return(0);
223: }