Actual source code: sbaijfact7.c

  1: /*$Id: sbaijfact7.c,v 1.4 2001/06/21 21:17:00 bsmith Exp $*/
 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: int 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;
 13:   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
 14:   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
 15:   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
 16:   MatScalar          *u,*d,*rtmp,*rtmp_ptr;

 19:   /* initialization */
 20:   PetscMalloc(25*mbs*sizeof(MatScalar),&rtmp);
 21:   PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));
 22:   PetscMalloc(2*mbs*sizeof(int),&il);
 23:   jl = il + mbs;
 24:   for (i=0; i<mbs; i++) {
 25:     jl[i] = mbs; il[0] = 0;
 26:   }
 27:   PetscMalloc(50*sizeof(MatScalar),&dk);
 28:   uik  = dk + 25;
 29:   ISGetIndices(perm,&perm_ptr);

 31:   /* check permutation */
 32:   if (!a->permute){
 33:     ai = a->i; aj = a->j; aa = a->a;
 34:   } else {
 35:     ai = a->inew; aj = a->jnew;
 36:     PetscMalloc(25*ai[mbs]*sizeof(MatScalar),&aa);
 37:     PetscMemcpy(aa,a->a,25*ai[mbs]*sizeof(MatScalar));
 38:     PetscMalloc(ai[mbs]*sizeof(int),&a2anew);
 39:     PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));

 41:     for (i=0; i<mbs; i++){
 42:       jmin = ai[i]; jmax = ai[i+1];
 43:       for (j=jmin; j<jmax; j++){
 44:         while (a2anew[j] != j){
 45:           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
 46:           for (k1=0; k1<25; k1++){
 47:             dk[k1]       = aa[k*25+k1];
 48:             aa[k*25+k1] = aa[j*25+k1];
 49:             aa[j*25+k1] = dk[k1];
 50:           }
 51:         }
 52:         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
 53:         if (i > aj[j]){
 54:           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
 55:           ap = aa + j*25;                     /* ptr to the beginning of j-th block of aa */
 56:           for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
 57:           for (k=0; k<5; k++){               /* j-th block of aa <- dk^T */
 58:             for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*k1];
 59:           }
 60:         }
 61:       }
 62:     }
 63:     PetscFree(a2anew);
 64:   }
 65: 
 66:   /* for each row k */
 67:   for (k = 0; k<mbs; k++){

 69:     /*initialize k-th row with elements nonzero in row perm(k) of A */
 70:     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
 71:     if (jmin < jmax) {
 72:       ap = aa + jmin*25;
 73:       for (j = jmin; j < jmax; j++){
 74:         vj = perm_ptr[aj[j]];         /* block col. index */
 75:         rtmp_ptr = rtmp + vj*25;
 76:         for (i=0; i<25; i++) *rtmp_ptr++ = *ap++;
 77:       }
 78:     }

 80:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
 81:     PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));
 82:     i = jl[k]; /* first row to be added to k_th row  */

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

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

 90:       /* uik = -inv(Di)*U_bar(i,k) */
 91:       d = ba + i*25;
 92:       u    = ba + ili*25;

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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