Actual source code: sbaijfact7.c

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

  5: /* Version for when blocks are 5 by 5  */
  8: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5(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,*d,*rtmp,*rtmp_ptr;

 20:   /* initialization */
 21:   PetscMalloc(25*mbs*sizeof(MatScalar),&rtmp);
 22:   PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));
 23:   PetscMalloc(2*mbs*sizeof(PetscInt),&il);
 24:   jl = il + mbs;
 25:   for (i=0; i<mbs; i++) {
 26:     jl[i] = mbs; il[0] = 0;
 27:   }
 28:   PetscMalloc(50*sizeof(MatScalar),&dk);
 29:   uik  = dk + 25;
 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(25*ai[mbs]*sizeof(MatScalar),&aa);
 38:     PetscMemcpy(aa,a->a,25*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<25; k1++){
 48:             dk[k1]       = aa[k*25+k1];
 49:             aa[k*25+k1] = aa[j*25+k1];
 50:             aa[j*25+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*25;                     /* ptr to the beginning of j-th block of aa */
 57:           for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
 58:           for (k=0; k<5; k++){               /* j-th block of aa <- dk^T */
 59:             for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*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*25;
 74:       for (j = jmin; j < jmax; j++){
 75:         vj = perm_ptr[aj[j]];         /* block col. index */
 76:         rtmp_ptr = rtmp + vj*25;
 77:         for (i=0; i<25; 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*25,25*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:       d = ba + i*25;
 93:       u    = ba + ili*25;

 95:       uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]);
 96:       uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]);
 97:       uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]);
 98:       uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]);
 99:       uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]);

101:       uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]);
102:       uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]);
103:       uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]);
104:       uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]);
105:       uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]);

107:       uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]);
108:       uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]);
109:       uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]);
110:       uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]);
111:       uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]);

113:       uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]);
114:       uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]);
115:       uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]);
116:       uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]);
117:       uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]);

119:       uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]);
120:       uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]);
121:       uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]);
122:       uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]);
123:       uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]);


126:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
127:       dk[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
128:       dk[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
129:       dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
130:       dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
131:       dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];

133:       dk[5] +=  uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
134:       dk[6] +=  uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
135:       dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
136:       dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
137:       dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];

139:       dk[10] +=  uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
140:       dk[11] +=  uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
141:       dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
142:       dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
143:       dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];

145:       dk[15] +=  uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
146:       dk[16] +=  uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
147:       dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
148:       dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
149:       dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];

151:       dk[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
152:       dk[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
153:       dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
154:       dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
155:       dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];

157:       /* update -U(i,k) */
158:       PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));

160:       /* add multiple of row i to k-th row ... */
161:       jmin = ili + 1; jmax = bi[i+1];
162:       if (jmin < jmax){
163:         for (j=jmin; j<jmax; j++) {
164:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
165:           rtmp_ptr = rtmp + bj[j]*25;
166:           u = ba + j*25;
167:           rtmp_ptr[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
168:           rtmp_ptr[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
169:           rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
170:           rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
171:           rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];

173:           rtmp_ptr[5] +=  uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
174:           rtmp_ptr[6] +=  uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
175:           rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
176:           rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
177:           rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];

179:           rtmp_ptr[10] +=  uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
180:           rtmp_ptr[11] +=  uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
181:           rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
182:           rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
183:           rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];

185:           rtmp_ptr[15] +=  uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
186:           rtmp_ptr[16] +=  uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
187:           rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
188:           rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
189:           rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];

191:           rtmp_ptr[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
192:           rtmp_ptr[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
193:           rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
194:           rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
195:           rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
196:         }
197: 
198:         /* ... add i to row list for next nonzero entry */
199:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
200:         j     = bj[jmin];
201:         jl[i] = jl[j]; jl[j] = i; /* update jl */
202:       }
203:       i = nexti;
204:     }

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

208:     /* invert diagonal block */
209:     d = ba+k*25;
210:     PetscMemcpy(d,dk,25*sizeof(MatScalar));
211:     Kernel_A_gets_inverse_A_5(d);
212: 
213:     jmin = bi[k]; jmax = bi[k+1];
214:     if (jmin < jmax) {
215:       for (j=jmin; j<jmax; j++){
216:          vj = bj[j];           /* block col. index of U */
217:          u   = ba + j*25;
218:          rtmp_ptr = rtmp + vj*25;
219:          for (k1=0; k1<25; k1++){
220:            *u++        = *rtmp_ptr;
221:            *rtmp_ptr++ = 0.0;
222:          }
223:       }
224: 
225:       /* ... add k to row list for first nonzero entry in k-th row */
226:       il[k] = jmin;
227:       i     = bj[jmin];
228:       jl[k] = jl[i]; jl[i] = k;
229:     }
230:   }

232:   PetscFree(rtmp);
233:   PetscFree(il);
234:   PetscFree(dk);
235:   if (a->permute){
236:     PetscFree(aa);
237:   }

239:   ISRestoreIndices(perm,&perm_ptr);
240:   C->factor    = FACTOR_CHOLESKY;
241:   C->assembled = PETSC_TRUE;
242:   C->preallocated = PETSC_TRUE;
243:   PetscLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
244:   return(0);
245: }