xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact5.c (revision 5ed2d596fd9914de76abbaed56c65f4792ae57ae)
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"
4 
5 /*
6       Version for when blocks are 4 by 4 Using natural ordering
7 */
8 #undef __FUNCT__
9 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering"
10 int 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;
14   int                ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
15   int                *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
16   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
17   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;
18   PetscTruth         pivotinblocks = b->pivotinblocks;
19 
20   PetscFunctionBegin;
21 
22   /* initialization */
23   ierr = PetscMalloc(16*mbs*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
24   ierr = PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));CHKERRQ(ierr);
25   ierr = PetscMalloc(2*mbs*sizeof(int),&il);CHKERRQ(ierr);
26   jl   = il + mbs;
27   for (i=0; i<mbs; i++) {
28     jl[i] = mbs; il[0] = 0;
29   }
30   ierr = PetscMalloc(32*sizeof(MatScalar),&dk);CHKERRQ(ierr);
31   uik  = dk + 16;
32 
33   ai = a->i; aj = a->j; aa = a->a;
34 
35   /* for each row k */
36   for (k = 0; k<mbs; k++){
37 
38     /*initialize k-th row with elements nonzero in row k of A */
39     jmin = ai[k]; jmax = ai[k+1];
40     if (jmin < jmax) {
41       ap = aa + jmin*16;
42       for (j = jmin; j < jmax; j++){
43         vj = aj[j];         /* block col. index */
44         rtmp_ptr = rtmp + vj*16;
45         for (i=0; i<16; i++) *rtmp_ptr++ = *ap++;
46       }
47     }
48 
49     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
50     ierr = PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));CHKERRQ(ierr);
51     i = jl[k]; /* first row to be added to k_th row  */
52 
53     while (i < mbs){
54       nexti = jl[i]; /* next row to be added to k_th row */
55 
56       /* compute multiplier */
57       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
58 
59       /* uik = -inv(Di)*U_bar(i,k) */
60       diag = ba + i*16;
61       u    = ba + ili*16;
62 
63       uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]);
64       uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]);
65       uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]);
66       uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]);
67 
68       uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]);
69       uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]);
70       uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]);
71       uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]);
72 
73       uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]);
74       uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]);
75       uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]);
76       uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]);
77 
78       uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]);
79       uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]);
80       uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]);
81       uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]);
82 
83       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
84       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
85       dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
86       dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
87       dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
88 
89       dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
90       dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
91       dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
92       dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
93 
94       dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
95       dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
96       dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
97       dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
98 
99       dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
100       dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
101       dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
102       dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
103 
104       /* update -U(i,k) */
105       ierr = PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));CHKERRQ(ierr);
106 
107       /* add multiple of row i to k-th row ... */
108       jmin = ili + 1; jmax = bi[i+1];
109       if (jmin < jmax){
110         for (j=jmin; j<jmax; j++) {
111           /* rtmp += -U(i,k)^T * U_bar(i,j) */
112           rtmp_ptr = rtmp + bj[j]*16;
113           u = ba + j*16;
114           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
115           rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
116           rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
117           rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
118 
119           rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
120           rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
121           rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
122           rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
123 
124           rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
125           rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
126           rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
127           rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
128 
129           rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
130           rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
131           rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
132           rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
133         }
134 
135         /* ... add i to row list for next nonzero entry */
136         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
137         j     = bj[jmin];
138         jl[i] = jl[j]; jl[j] = i; /* update jl */
139       }
140       i = nexti;
141     }
142 
143     /* save nonzero entries in k-th row of U ... */
144 
145     /* invert diagonal block */
146     diag = ba+k*16;
147     ierr = PetscMemcpy(diag,dk,16*sizeof(MatScalar));CHKERRQ(ierr);
148     if (pivotinblocks) {
149       ierr = Kernel_A_gets_inverse_A_4(diag);CHKERRQ(ierr);
150     } else {
151       ierr = Kernel_A_gets_inverse_A_4_nopivot(diag);CHKERRQ(ierr);
152     }
153 
154     jmin = bi[k]; jmax = bi[k+1];
155     if (jmin < jmax) {
156       for (j=jmin; j<jmax; j++){
157          vj = bj[j];           /* block col. index of U */
158          u   = ba + j*16;
159          rtmp_ptr = rtmp + vj*16;
160          for (k1=0; k1<16; k1++){
161            *u++        = *rtmp_ptr;
162            *rtmp_ptr++ = 0.0;
163          }
164       }
165 
166       /* ... add k to row list for first nonzero entry in k-th row */
167       il[k] = jmin;
168       i     = bj[jmin];
169       jl[k] = jl[i]; jl[i] = k;
170     }
171   }
172 
173   ierr = PetscFree(rtmp);CHKERRQ(ierr);
174   ierr = PetscFree(il);CHKERRQ(ierr);
175   ierr = PetscFree(dk);CHKERRQ(ierr);
176 
177   C->factor    = FACTOR_CHOLESKY;
178   C->assembled = PETSC_TRUE;
179   C->preallocated = PETSC_TRUE;
180   PetscLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
181   PetscFunctionReturn(0);
182 }
183