Actual source code: sbaijfact6.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 4 by 4  */
  9: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,MatFactorInfo *info,Mat *B)
 10: {
 11:   Mat            C = *B;
 12:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
 13:   IS             perm = b->row;
 15:   PetscInt       *perm_ptr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
 16:   PetscInt       *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
 17:   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
 18:   MatScalar      *u,*diag,*rtmp,*rtmp_ptr;
 19:   PetscTruth     pivotinblocks = b->pivotinblocks;

 22:   /* initialization */
 23:   PetscMalloc(16*mbs*sizeof(MatScalar),&rtmp);
 24:   PetscMemzero(rtmp,16*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(32*sizeof(MatScalar),&dk);
 31:   uik  = dk + 16;
 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(16*ai[mbs]*sizeof(MatScalar),&aa);
 40:     PetscMemcpy(aa,a->a,16*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<16; k1++){
 50:             dk[k1]       = aa[k*16+k1];
 51:             aa[k*16+k1] = aa[j*16+k1];
 52:             aa[j*16+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*16;                     /* ptr to the beginning of j-th block of aa */
 59:           for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
 60:           for (k=0; k<4; k++){               /* j-th block of aa <- dk^T */
 61:             for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*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*16;
 76:       for (j = jmin; j < jmax; j++){
 77:         vj = perm_ptr[aj[j]];         /* block col. index */
 78:         rtmp_ptr = rtmp + vj*16;
 79:         for (i=0; i<16; 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*16,16*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*16;
 95:       u    = ba + ili*16;

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

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

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

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

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

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

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

133:       dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
134:       dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
135:       dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
136:       dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
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: 
169:         /* ... add i to row list for next nonzero entry */
170:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
171:         j     = bj[jmin];
172:         jl[i] = jl[j]; jl[j] = i; /* update jl */
173:       }
174:       i = nexti;
175:     }

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

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

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

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

208:   PetscFree(rtmp);
209:   PetscFree(il);
210:   PetscFree(dk);
211:   if (a->permute){
212:     PetscFree(aa);
213:   }

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