Actual source code: sbaijfact4.c

  1: /*$Id: sbaijfact4.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: /*
  6:       Version for when blocks are 3 by 3 Using natural ordering
  7: */
  8: int MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,Mat *B)
  9: {
 10:   Mat                C = *B;
 11:   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
 12:   int                ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
 13:   int                *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
 14:   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
 15:   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;

 18: 
 19:   /* initialization */
 20:   PetscMalloc(9*mbs*sizeof(MatScalar),&rtmp);
 21:   PetscMemzero(rtmp,9*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(18*sizeof(MatScalar),&dk);
 28:   uik  = dk + 9;

 30:   ai   = a->i; aj = a->j; aa = a->a;

 32:   /* for each row k */
 33:   for (k = 0; k<mbs; k++){

 35:     /*initialize k-th row with elements nonzero in row k of A */
 36:     jmin = ai[k]; jmax = ai[k+1];
 37:     if (jmin < jmax) {
 38:       ap = aa + jmin*9;
 39:       for (j = jmin; j < jmax; j++){
 40:         vj = aj[j];         /* block col. index */
 41:         rtmp_ptr = rtmp + vj*9;
 42:         for (i=0; i<9; i++) *rtmp_ptr++ = *ap++;
 43:       }
 44:     }

 46:     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
 47:     PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));
 48:     i = jl[k]; /* first row to be added to k_th row  */

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

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

 56:       /* uik = -inv(Di)*U_bar(i,k) */
 57:       diag = ba + i*9;
 58:       u    = ba + ili*9;

 60:       uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
 61:       uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
 62:       uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);

 64:       uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
 65:       uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
 66:       uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);

 68:       uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
 69:       uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
 70:       uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);

 72:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
 73:       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
 74:       dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
 75:       dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];

 77:       dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
 78:       dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
 79:       dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];

 81:       dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
 82:       dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
 83:       dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];

 85:       /* update -U(i,k) */
 86:       PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));

 88:       /* add multiple of row i to k-th row ... */
 89:       jmin = ili + 1; jmax = bi[i+1];
 90:       if (jmin < jmax){
 91:         for (j=jmin; j<jmax; j++) {
 92:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
 93:           rtmp_ptr = rtmp + bj[j]*9;
 94:           u = ba + j*9;
 95:           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
 96:           rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
 97:           rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];

 99:           rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
100:           rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
101:           rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];

103:           rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
104:           rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
105:           rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
106:         }
107: 
108:         /* ... add i to row list for next nonzero entry */
109:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
110:         j     = bj[jmin];
111:         jl[i] = jl[j]; jl[j] = i; /* update jl */
112:       }
113:       i = nexti;
114:     }

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

118:     /* invert diagonal block */
119:     diag = ba+k*9;
120:     PetscMemcpy(diag,dk,9*sizeof(MatScalar));
121:     Kernel_A_gets_inverse_A_3(diag);
122: 
123:     jmin = bi[k]; jmax = bi[k+1];
124:     if (jmin < jmax) {
125:       for (j=jmin; j<jmax; j++){
126:          vj = bj[j];           /* block col. index of U */
127:          u   = ba + j*9;
128:          rtmp_ptr = rtmp + vj*9;
129:          for (k1=0; k1<9; k1++){
130:            *u++        = *rtmp_ptr;
131:            *rtmp_ptr++ = 0.0;
132:          }
133:       }
134: 
135:       /* ... add k to row list for first nonzero entry in k-th row */
136:       il[k] = jmin;
137:       i     = bj[jmin];
138:       jl[k] = jl[i]; jl[i] = k;
139:     }
140:   }

142:   PetscFree(rtmp);
143:   PetscFree(il);
144:   PetscFree(dk);

146:   C->factor    = FACTOR_CHOLESKY;
147:   C->assembled = PETSC_TRUE;
148:   C->preallocated = PETSC_TRUE;
149:   PetscLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
150:   return(0);
151: }