Actual source code: sbaijfact6.c

  1: /*$Id: sbaijfact6.c,v 1.3 2001/03/23 23:22:21 balay Exp $*/
  2: #include "sbaij.h"
  3: #include "src/inline/ilu.h"

  5: /* Version for when blocks are 4 by 4  */
  6: int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B)
  7: {
  8:   Mat                C = *B;
  9:   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
 10:   IS                 perm = b->row;
 11:   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
 12:   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
 13:   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
 14:   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;

 17:   /* initialization */
 18:   PetscMalloc(16*mbs*sizeof(MatScalar),&rtmp);
 19:   PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));
 20:   PetscMalloc(2*mbs*sizeof(int),&il);
 21:   jl   = il + mbs;
 22:   for (i=0; i<mbs; i++) {
 23:     jl[i] = mbs; il[0] = 0;
 24:   }
 25:   PetscMalloc(32*sizeof(MatScalar),&dk);
 26:   uik  = dk + 16;
 27:   ISGetIndices(perm,&perm_ptr);

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

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

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

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

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

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

 88:       /* uik = -inv(Di)*U_bar(i,k) */
 89:       diag = ba + i*16;
 90:       u    = ba + ili*16;

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

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

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

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

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

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

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

128:       dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
129:       dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
130:       dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
131:       dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
132: 
133:       /* update -U(i,k) */
134:       PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));

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

148:           rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
149:           rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
150:           rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
151:           rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];

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

158:           rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
159:           rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
160:           rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
161:           rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
162:         }
163: 
164:         /* ... add i to row list for next nonzero entry */
165:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
166:         j     = bj[jmin];
167:         jl[i] = jl[j]; jl[j] = i; /* update jl */
168:       }
169:       i = nexti;
170:     }

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

174:     /* invert diagonal block */
175:     diag = ba+k*16;
176:     PetscMemcpy(diag,dk,16*sizeof(MatScalar));
177:     Kernel_A_gets_inverse_A_4(diag);
178: 
179:     jmin = bi[k]; jmax = bi[k+1];
180:     if (jmin < jmax) {
181:       for (j=jmin; j<jmax; j++){
182:          vj = bj[j];           /* block col. index of U */
183:          u   = ba + j*16;
184:          rtmp_ptr = rtmp + vj*16;
185:          for (k1=0; k1<16; k1++){
186:            *u++        = *rtmp_ptr;
187:            *rtmp_ptr++ = 0.0;
188:          }
189:       }
190: 
191:       /* ... add k to row list for first nonzero entry in k-th row */
192:       il[k] = jmin;
193:       i     = bj[jmin];
194:       jl[k] = jl[i]; jl[i] = k;
195:     }
196:   }

198:   PetscFree(rtmp);
199:   PetscFree(il);
200:   PetscFree(dk);
201:   if (a->permute){
202:     PetscFree(aa);
203:   }

205:   ISRestoreIndices(perm,&perm_ptr);
206:   C->factor    = FACTOR_CHOLESKY;
207:   C->assembled = PETSC_TRUE;
208:   C->preallocated = PETSC_TRUE;
209:   PetscLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
210:   return(0);
211: }