Actual source code: sbaijfact5.c

 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: */
 10: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,Mat *B)
 11: {
 12:   Mat            C = *B;
 13:   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
 15:   PetscInt       i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
 16:   PetscInt       *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
 17:   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
 18:   MatScalar      *u,*diag,*rtmp,*rtmp_ptr;
 19:   PetscTruth     pivotinblocks = b->pivotinblocks;

 22: 
 23:   /* initialization */
 24:   PetscMalloc(16*mbs*sizeof(MatScalar),&rtmp);
 25:   PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));
 26:   PetscMalloc(2*mbs*sizeof(PetscInt),&il);
 27:   jl   = il + mbs;
 28:   for (i=0; i<mbs; i++) {
 29:     jl[i] = mbs; il[0] = 0;
 30:   }
 31:   PetscMalloc(32*sizeof(MatScalar),&dk);
 32:   uik  = dk + 16;

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

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

 39:     /*initialize k-th row with elements nonzero in row k of A */
 40:     jmin = ai[k]; jmax = ai[k+1];
 41:     if (jmin < jmax) {
 42:       ap = aa + jmin*16;
 43:       for (j = jmin; j < jmax; j++){
 44:         vj = aj[j];         /* block col. index */
 45:         rtmp_ptr = rtmp + vj*16;
 46:         for (i=0; i<16; i++) *rtmp_ptr++ = *ap++;
 47:       }
 48:     }

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

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

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

 60:       /* uik = -inv(Di)*U_bar(i,k) */
 61:       diag = ba + i*16;
 62:       u    = ba + ili*16;

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

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

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

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

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

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

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

100:       dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
101:       dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
102:       dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
103:       dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
104: 
105:       /* update -U(i,k) */
106:       PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));

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

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

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

130:           rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
131:           rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
132:           rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
133:           rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
134:         }
135: 
136:         /* ... add i to row list for next nonzero entry */
137:         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
138:         j     = bj[jmin];
139:         jl[i] = jl[j]; jl[j] = i; /* update jl */
140:       }
141:       i = nexti;
142:     }

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

146:     /* invert diagonal block */
147:     diag = ba+k*16;
148:     PetscMemcpy(diag,dk,16*sizeof(MatScalar));
149:     if (pivotinblocks) {
150:       Kernel_A_gets_inverse_A_4(diag);
151:     } else {
152:       Kernel_A_gets_inverse_A_4_nopivot(diag);
153:     }
154: 
155:     jmin = bi[k]; jmax = bi[k+1];
156:     if (jmin < jmax) {
157:       for (j=jmin; j<jmax; j++){
158:          vj = bj[j];           /* block col. index of U */
159:          u   = ba + j*16;
160:          rtmp_ptr = rtmp + vj*16;
161:          for (k1=0; k1<16; k1++){
162:            *u++        = *rtmp_ptr;
163:            *rtmp_ptr++ = 0.0;
164:          }
165:       }
166: 
167:       /* ... add k to row list for first nonzero entry in k-th row */
168:       il[k] = jmin;
169:       i     = bj[jmin];
170:       jl[k] = jl[i]; jl[i] = k;
171:     }
172:   }

174:   PetscFree(rtmp);
175:   PetscFree(il);
176:   PetscFree(dk);
177: 
178:   C->factor    = FACTOR_CHOLESKY;
179:   C->assembled = PETSC_TRUE;
180:   C->preallocated = PETSC_TRUE;
181:   PetscLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
182:   return(0);
183: }