Actual source code: sbaijfact5.c

  1: /*$Id: sbaijfact5.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 4 by 4 Using natural ordering
  7: */
  8: int MatCholeskyFactorNumeric_SeqSBAIJ_4_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;
 16:   PetscTruth         pivotinblocks = b->pivotinblocks;

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

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

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

 36:     /*initialize k-th row with elements nonzero in row k of A */
 37:     jmin = ai[k]; jmax = ai[k+1];
 38:     if (jmin < jmax) {
 39:       ap = aa + jmin*16;
 40:       for (j = jmin; j < jmax; j++){
 41:         vj = aj[j];         /* block col. index */
 42:         rtmp_ptr = rtmp + vj*16;
 43:         for (i=0; i<16; i++) *rtmp_ptr++ = *ap++;
 44:       }
 45:     }

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

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

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

 57:       /* uik = -inv(Di)*U_bar(i,k) */
 58:       diag = ba + i*16;
 59:       u    = ba + ili*16;

 61:       uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]);
 62:       uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]);
 63:       uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]);
 64:       uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]);

 66:       uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]);
 67:       uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]);
 68:       uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]);
 69:       uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]);

 71:       uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]);
 72:       uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]);
 73:       uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]);
 74:       uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]);

 76:       uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]);
 77:       uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]);
 78:       uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]);
 79:       uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]);

 81:       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
 82:       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
 83:       dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
 84:       dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
 85:       dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];

 87:       dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
 88:       dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
 89:       dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
 90:       dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];

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

 97:       dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
 98:       dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
 99:       dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
100:       dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
101: 
102:       /* update -U(i,k) */
103:       PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));

105:       /* add multiple of row i to k-th row ... */
106:       jmin = ili + 1; jmax = bi[i+1];
107:       if (jmin < jmax){
108:         for (j=jmin; j<jmax; j++) {
109:           /* rtmp += -U(i,k)^T * U_bar(i,j) */
110:           rtmp_ptr = rtmp + bj[j]*16;
111:           u = ba + j*16;
112:           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
113:           rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
114:           rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
115:           rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];

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

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

127:           rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
128:           rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
129:           rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
130:           rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
131:         }
132: 
133:         /* ... add i to row list for next nonzero entry */
134:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
135:         j     = bj[jmin];
136:         jl[i] = jl[j]; jl[j] = i; /* update jl */
137:       }
138:       i = nexti;
139:     }

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

143:     /* invert diagonal block */
144:     diag = ba+k*16;
145:     PetscMemcpy(diag,dk,16*sizeof(MatScalar));
146:     if (pivotinblocks) {
147:       Kernel_A_gets_inverse_A_4(diag);
148:     } else {
149:       Kernel_A_gets_inverse_A_4_nopivot(diag);
150:     }
151: 
152:     jmin = bi[k]; jmax = bi[k+1];
153:     if (jmin < jmax) {
154:       for (j=jmin; j<jmax; j++){
155:          vj = bj[j];           /* block col. index of U */
156:          u   = ba + j*16;
157:          rtmp_ptr = rtmp + vj*16;
158:          for (k1=0; k1<16; k1++){
159:            *u++        = *rtmp_ptr;
160:            *rtmp_ptr++ = 0.0;
161:          }
162:       }
163: 
164:       /* ... add k to row list for first nonzero entry in k-th row */
165:       il[k] = jmin;
166:       i     = bj[jmin];
167:       jl[k] = jl[i]; jl[i] = k;
168:     }
169:   }

171:   PetscFree(rtmp);
172:   PetscFree(il);
173:   PetscFree(dk);
174: 
175:   C->factor    = FACTOR_CHOLESKY;
176:   C->assembled = PETSC_TRUE;
177:   C->preallocated = PETSC_TRUE;
178:   PetscLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
179:   return(0);
180: }