xref: /petsc/src/mat/impls/baij/seq/baijfact.c (revision 943b08df42612e9951e8b4eeb65ee9d08f045bf3)
1 #ifndef lint
2 static char vcid[] = "$Id: baijfact.c,v 1.14 1996/04/12 23:31:32 balay Exp bsmith $";
3 #endif
4 /*
5     Factorization code for BAIJ format.
6 */
7 
8 #include "baij.h"
9 
10 /*
11     The symbolic factorization code is identical to that for AIJ format,
12   except for very small changes since this is now a SeqBAIJ datastructure.
13   NOT good code reuse.
14 */
15 int MatLUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,Mat *B)
16 {
17   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
18   IS          isicol;
19   int         *r,*ic, ierr, i, n = a->mbs, *ai = a->i, *aj = a->j;
20   int         *ainew,*ajnew, jmax,*fill, *ajtmp, nz, bs = a->bs, bs2=a->bs2;
21   int         *idnew, idx, row,m,fm, nnz, nzi,len, realloc = 0,nzbd,*im;
22 
23   if (a->m != a->n) SETERRQ(1,"MatLUFactorSymbolic_SeqBAIJ:Must be square");
24   if (!isrow) SETERRQ(1,"MatLUFactorSymbolic_SeqBAIJ:Must have row permutation");
25   if (!iscol) SETERRQ(1,"MatLUFactorSymbolic_SeqBAIJ:Must have col. permutation");
26 
27   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
28   ISGetIndices(isrow,&r); ISGetIndices(isicol,&ic);
29 
30   /* get new row pointers */
31   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
32   ainew[0] = 0;
33   /* don't know how many column pointers are needed so estimate */
34   jmax = (int) (f*ai[n] + 1);
35   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
36   /* fill is a linked list of nonzeros in active row */
37   fill = (int *) PetscMalloc( (2*n+1)*sizeof(int)); CHKPTRQ(fill);
38   im = fill + n + 1;
39   /* idnew is location of diagonal in factor */
40   idnew = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(idnew);
41   idnew[0] = 0;
42 
43   for ( i=0; i<n; i++ ) {
44     /* first copy previous fill into linked list */
45     nnz     = nz    = ai[r[i]+1] - ai[r[i]];
46     ajtmp   = aj + ai[r[i]];
47     fill[n] = n;
48     while (nz--) {
49       fm  = n;
50       idx = ic[*ajtmp++];
51       do {
52         m  = fm;
53         fm = fill[m];
54       } while (fm < idx);
55       fill[m]   = idx;
56       fill[idx] = fm;
57     }
58     row = fill[n];
59     while ( row < i ) {
60       ajtmp = ajnew + idnew[row] + 1;
61       nzbd  = 1 + idnew[row] - ainew[row];
62       nz    = im[row] - nzbd;
63       fm    = row;
64       while (nz-- > 0) {
65         idx = *ajtmp++;
66         nzbd++;
67         if (idx == i) im[row] = nzbd;
68         do {
69           m  = fm;
70           fm = fill[m];
71         } while (fm < idx);
72         if (fm != idx) {
73           fill[m]   = idx;
74           fill[idx] = fm;
75           fm        = idx;
76           nnz++;
77         }
78       }
79       row = fill[row];
80     }
81     /* copy new filled row into permanent storage */
82     ainew[i+1] = ainew[i] + nnz;
83     if (ainew[i+1] > jmax+1) {
84       /* allocate a longer ajnew */
85       int maxadd;
86       maxadd = (int) ((f*(ai[n]+1)*(n-i+5))/n);
87       if (maxadd < nnz) maxadd = (n-i)*(nnz+1);
88       jmax += maxadd;
89       ajtmp = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(ajtmp);
90       PetscMemcpy(ajtmp,ajnew,ainew[i]*sizeof(int));
91       PetscFree(ajnew);
92       ajnew = ajtmp;
93       realloc++; /* count how many times we realloc */
94     }
95     ajtmp = ajnew + ainew[i];
96     fm    = fill[n];
97     nzi   = 0;
98     im[i] = nnz;
99     while (nnz--) {
100       if (fm < i) nzi++;
101       *ajtmp++ = fm;
102       fm       = fill[fm];
103     }
104     idnew[i] = ainew[i] + nzi;
105   }
106 
107   PLogInfo(A,
108     "Info:MatLUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
109                              realloc,f,((double)ainew[n])/((double)ai[i]));
110 
111   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
112   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
113 
114   PetscFree(fill);
115 
116   /* put together the new matrix */
117   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,B); CHKERRQ(ierr);
118   PLogObjectParent(*B,isicol);
119   ierr = ISDestroy(isicol); CHKERRQ(ierr);
120   b = (Mat_SeqBAIJ *) (*B)->data;
121   PetscFree(b->imax);
122   b->singlemalloc = 0;
123   len             = ainew[n]*sizeof(Scalar);
124   /* the next line frees the default space generated by the Create() */
125   PetscFree(b->a); PetscFree(b->ilen);
126   b->a          = (Scalar *) PetscMalloc( len*bs2 ); CHKPTRQ(b->a);
127   b->j          = ajnew;
128   b->i          = ainew;
129   b->diag       = idnew;
130   b->ilen       = 0;
131   b->imax       = 0;
132   b->row        = isrow;
133   b->col        = iscol;
134   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
135   CHKPTRQ(b->solve_work);
136   /* In b structure:  Free imax, ilen, old a, old j.
137      Allocate idnew, solve_work, new a, new j */
138   PLogObjectMemory(*B,(ainew[n]-n)*(sizeof(int)+sizeof(Scalar)));
139   b->maxnz = b->nz = ainew[n];
140 
141   return 0;
142 }
143 
144 #include "pinclude/plapack.h"
145 int  Linpack_DGEFA(Scalar *,int, int *);
146 int  Linpack_DGEDI(Scalar *,int, int *,Scalar *);
147 
148 
149 /* ----------------------------------------------------------- */
150 int MatLUFactorNumeric_SeqBAIJ_N(Mat A,Mat *B)
151 {
152   Mat             C = *B;
153   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
154   IS              iscol = b->col, isrow = b->row, isicol;
155   int             *r,*ic, ierr, i, j, n = a->mbs, *ai = b->i, *aj = b->j;
156   int             *ajtmpold, *ajtmp, nz, row, bslog;
157   int             *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs,*v_pivots;
158   register Scalar *pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
159   Scalar          one = 1.0, zero = 0.0, mone = -1.0;
160   register int    *pj;
161 
162   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
163   PLogObjectParent(*B,isicol);
164   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
165   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
166   rtmp  = (Scalar *) PetscMalloc(bs2*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
167 
168   /* generate work space needed by dense LU factorization */
169   v_work     = (Scalar *) PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(Scalar));
170                CHKPTRQ(v_work);
171   multiplier = v_work + bs;
172   v_pivots   = (int *) (multiplier + bs2);
173 
174   /* flops in while loop */
175   bslog = 2*bs*bs2;
176 
177   for ( i=0; i<n; i++ ) {
178     nz    = ai[i+1] - ai[i];
179     ajtmp = aj + ai[i];
180     for  ( j=0; j<nz; j++ ) {
181       PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(Scalar));
182     }
183     /* load in initial (unfactored row) */
184     nz       = a->i[r[i]+1] - a->i[r[i]];
185     ajtmpold = a->j + a->i[r[i]];
186     v        = a->a + bs2*a->i[r[i]];
187     for ( j=0; j<nz; j++ ) {
188       PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(Scalar));
189     }
190     row = *ajtmp++;
191     while (row < i) {
192       pc = rtmp + bs2*row;
193 /*      if (*pc) { */
194         pv = b->a + bs2*diag_offset[row];
195         pj = b->j + diag_offset[row] + 1;
196         BLgemm_("N","N",&bs,&bs,&bs,&one,pc,&bs,pv,&bs,&zero,
197                 multiplier,&bs);
198         PetscMemcpy(pc,multiplier,bs2*sizeof(Scalar));
199         nz = ai[row+1] - diag_offset[row] - 1;
200         pv += bs2;
201         for (j=0; j<nz; j++) {
202           BLgemm_("N","N",&bs,&bs,&bs,&mone,multiplier,&bs,pv+bs2*j,&bs,
203                   &one,rtmp+bs2*pj[j],&bs);
204         }
205         PLogFlops(bslog*(nz+1)-bs);
206 /*      } */
207         row = *ajtmp++;
208     }
209     /* finished row so stick it into b->a */
210     pv = b->a + bs2*ai[i];
211     pj = b->j + ai[i];
212     nz = ai[i+1] - ai[i];
213     for ( j=0; j<nz; j++ ) {
214       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(Scalar));
215     }
216     diag = diag_offset[i] - ai[i];
217     /* invert diagonal block */
218     w = pv + bs2*diag;
219 
220     /* Old version that used LAPACK, make v_work bs2 length for this
221           LAgetrf_(&bs,&bs,w,&bs,v_pivots,&info); CHKERRQ(info);
222           PetscMemzero(v_work,bs2*sizeof(Scalar));
223           for ( j=0; j<bs; j++ ) { v_work[j + bs*j] = 1.0; }
224           LAgetrs_("N",&bs,&bs,w,&bs,v_pivots,v_work,&bs, &info);CHKERRQ(info);
225           PetscMemcpy(w,v_work,bs2*sizeof(Scalar));
226     */
227 
228     ierr = Linpack_DGEFA(w,bs,v_pivots); CHKERRQ(ierr);
229     ierr = Linpack_DGEDI(w,bs,v_pivots,v_work); CHKERRQ(ierr);
230   }
231 
232   PetscFree(rtmp); PetscFree(v_work);
233   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
234   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
235   ierr = ISDestroy(isicol); CHKERRQ(ierr);
236   C->factor = FACTOR_LU;
237   C->assembled = PETSC_TRUE;
238   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
239   return 0;
240 }
241 /* ------------------------------------------------------------*/
242 /*
243       Version for when blocks are 5 by 5
244 */
245 int MatLUFactorNumeric_SeqBAIJ_5(Mat A,Mat *B)
246 {
247   Mat             C = *B;
248   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
249   IS              iscol = b->col, isrow = b->row, isicol;
250   int             *r,*ic, ierr, i, j, n = a->mbs, *ai = b->i, *aj = b->j;
251   int             *ajtmpold, *ajtmp, nz, row, v_pivots[5];
252   int             *diag_offset = b->diag,bs = 5,idx;
253   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
254   Scalar          p1,p2,p3,p4,v_work[5],m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
255   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
256   Scalar          x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
257   Scalar          p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
258   Scalar          m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
259   register int    *pj;
260 
261   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
262   PLogObjectParent(*B,isicol);
263   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
264   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
265   rtmp  = (Scalar *) PetscMalloc(25*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
266 
267   for ( i=0; i<n; i++ ) {
268     nz    = ai[i+1] - ai[i];
269     ajtmp = aj + ai[i];
270     for  ( j=0; j<nz; j++ ) {
271       x = rtmp+25*ajtmp[j];
272       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
273       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
274       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
275     }
276     /* load in initial (unfactored row) */
277     idx      = r[i];
278     nz       = a->i[idx+1] - a->i[idx];
279     ajtmpold = a->j + a->i[idx];
280     v        = a->a + 25*a->i[idx];
281     for ( j=0; j<nz; j++ ) {
282       x    = rtmp+25*ic[ajtmpold[j]];
283       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
284       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
285       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
286       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
287       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
288       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
289       v    += 25;
290     }
291     row = *ajtmp++;
292     while (row < i) {
293       pc = rtmp + 25*row;
294       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
295       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
296       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
297       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
298       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
299       p25 = pc[24];
300       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
301           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
302           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
303           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
304           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
305           p23 != 0.0 || p24 != 0.0) {
306         pv = b->a + 25*diag_offset[row];
307         pj = b->j + diag_offset[row] + 1;
308         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
309         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
310         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
311         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
312         x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
313         x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
314         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
315         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
316         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
317         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
318         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
319 
320         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
321         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
322         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
323         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
324         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
325 
326         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
327         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
328         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
329         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
330         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
331 
332         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
333         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
334         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
335         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
336         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
337 
338         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
339         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
340         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
341         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
342         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
343 
344         nz = ai[row+1] - diag_offset[row] - 1;
345         pv += 25;
346         for (j=0; j<nz; j++) {
347           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
348           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
349           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
350           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
351           x18  = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
352           x22  = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
353           x    = rtmp + 25*pj[j];
354           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
355           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
356           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
357           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
358           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
359 
360           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
361           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
362           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
363           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
364           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
365 
366           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
367           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
368           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
369           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
370           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
371 
372           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
373           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
374           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
375           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
376           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
377 
378           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
379           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
380           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
381           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
382           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
383 
384           pv   += 25;
385         }
386         PLogFlops(250*nz+225);
387       }
388       row = *ajtmp++;
389     }
390     /* finished row so stick it into b->a */
391     pv = b->a + 25*ai[i];
392     pj = b->j + ai[i];
393     nz = ai[i+1] - ai[i];
394     for ( j=0; j<nz; j++ ) {
395       x     = rtmp+25*pj[j];
396       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
397       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
398       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
399       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
400       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
401       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
402       pv   += 25;
403     }
404     /* invert diagonal block */
405     w = b->a + 25*diag_offset[i];
406     ierr = Linpack_DGEFA(w,bs,v_pivots); CHKERRQ(ierr);
407     ierr = Linpack_DGEDI(w,bs,v_pivots,v_work); CHKERRQ(ierr);
408   }
409 
410   PetscFree(rtmp);
411   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
412   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
413   ierr = ISDestroy(isicol); CHKERRQ(ierr);
414   C->factor = FACTOR_LU;
415   C->assembled = PETSC_TRUE;
416   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
417   return 0;
418 }
419 
420 /* ------------------------------------------------------------*/
421 /*
422       Version for when blocks are 4 by 4
423 */
424 int MatLUFactorNumeric_SeqBAIJ_4(Mat A,Mat *B)
425 {
426   Mat             C = *B;
427   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
428   IS              iscol = b->col, isrow = b->row, isicol;
429   int             *r,*ic, ierr, i, j, n = a->mbs, *ai = b->i, *aj = b->j;
430   int             *ajtmpold, *ajtmp, nz, row, v_pivots[4];
431   int             *diag_offset = b->diag,bs = 4,idx;
432   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
433   Scalar          p1,p2,p3,p4,v_work[4],m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
434   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
435   Scalar          p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
436   Scalar          m13,m14,m15,m16;
437   register int    *pj;
438 
439   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
440   PLogObjectParent(*B,isicol);
441   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
442   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
443   rtmp  = (Scalar *) PetscMalloc(16*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
444 
445   for ( i=0; i<n; i++ ) {
446     nz    = ai[i+1] - ai[i];
447     ajtmp = aj + ai[i];
448     for  ( j=0; j<nz; j++ ) {
449       x = rtmp+16*ajtmp[j];
450       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
451       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
452     }
453     /* load in initial (unfactored row) */
454     idx      = r[i];
455     nz       = a->i[idx+1] - a->i[idx];
456     ajtmpold = a->j + a->i[idx];
457     v        = a->a + 16*a->i[idx];
458     for ( j=0; j<nz; j++ ) {
459       x    = rtmp+16*ic[ajtmpold[j]];
460       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
461       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
462       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
463       x[14] = v[14]; x[15] = v[15];
464       v    += 16;
465     }
466     row = *ajtmp++;
467     while (row < i) {
468       pc = rtmp + 16*row;
469       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
470       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
471       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
472       p15 = pc[14]; p16 = pc[15];
473       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
474           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
475           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
476           || p16 != 0.0) {
477         pv = b->a + 16*diag_offset[row];
478         pj = b->j + diag_offset[row] + 1;
479         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
480         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
481         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
482         x15 = pv[14]; x16 = pv[15];
483         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
484         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
485         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
486         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
487 
488         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
489         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
490         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
491         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
492 
493         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
494         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
495         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
496         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
497 
498         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
499         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
500         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
501         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
502 
503         nz = ai[row+1] - diag_offset[row] - 1;
504         pv += 16;
505         for (j=0; j<nz; j++) {
506           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
507           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
508           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
509           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
510           x    = rtmp + 16*pj[j];
511           x[0] -= m1*x1 + m5*x2  + m9*x3 + m13*x4;
512           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
513           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
514           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
515 
516           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
517           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
518           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
519           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
520 
521           x[8] -= m1*x9  + m5*x10  + m9*x11 + m13*x12;
522           x[9] -= m2*x9  + m6*x10  + m10*x11 + m14*x12;
523           x[10] -= m3*x9 + m7*x10  + m11*x11 + m15*x12;
524           x[11] -= m4*x9 + m8*x10  + m12*x11 + m16*x12;
525 
526           x[12] -= m1*x13 + m5*x14  + m9*x15 + m13*x16;
527           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
528           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
529           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
530 
531           pv   += 16;
532         }
533         PLogFlops(128*nz+112);
534       }
535       row = *ajtmp++;
536     }
537     /* finished row so stick it into b->a */
538     pv = b->a + 16*ai[i];
539     pj = b->j + ai[i];
540     nz = ai[i+1] - ai[i];
541     for ( j=0; j<nz; j++ ) {
542       x     = rtmp+16*pj[j];
543       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
544       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
545       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
546       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
547       pv   += 16;
548     }
549     /* invert diagonal block */
550     w = b->a + 16*diag_offset[i];
551     ierr = Linpack_DGEFA(w,bs,v_pivots); CHKERRQ(ierr);
552     ierr = Linpack_DGEDI(w,bs,v_pivots,v_work); CHKERRQ(ierr);
553   }
554 
555   PetscFree(rtmp);
556   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
557   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
558   ierr = ISDestroy(isicol); CHKERRQ(ierr);
559   C->factor = FACTOR_LU;
560   C->assembled = PETSC_TRUE;
561   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
562   return 0;
563 }
564 /* ------------------------------------------------------------*/
565 /*
566       Version for when blocks are 3 by 3
567 */
568 int MatLUFactorNumeric_SeqBAIJ_3(Mat A,Mat *B)
569 {
570   Mat             C = *B;
571   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
572   IS              iscol = b->col, isrow = b->row, isicol;
573   int             *r,*ic, ierr, i, j, n = a->mbs, *ai = b->i, *aj = b->j;
574   int             *ajtmpold, *ajtmp, nz, row, v_pivots[3];
575   int             *diag_offset = b->diag,bs = 3,idx;
576   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
577   Scalar          p1,p2,p3,p4,v_work[3],m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
578   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
579   register int    *pj;
580 
581   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
582   PLogObjectParent(*B,isicol);
583   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
584   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
585   rtmp  = (Scalar *) PetscMalloc(9*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
586 
587   for ( i=0; i<n; i++ ) {
588     nz    = ai[i+1] - ai[i];
589     ajtmp = aj + ai[i];
590     for  ( j=0; j<nz; j++ ) {
591       x = rtmp+9*ajtmp[j];
592       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
593     }
594     /* load in initial (unfactored row) */
595     idx      = r[i];
596     nz       = a->i[idx+1] - a->i[idx];
597     ajtmpold = a->j + a->i[idx];
598     v        = a->a + 9*a->i[idx];
599     for ( j=0; j<nz; j++ ) {
600       x    = rtmp+9*ic[ajtmpold[j]];
601       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
602       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
603       v    += 9;
604     }
605     row = *ajtmp++;
606     while (row < i) {
607       pc = rtmp + 9*row;
608       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
609       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
610       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
611           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
612         pv = b->a + 9*diag_offset[row];
613         pj = b->j + diag_offset[row] + 1;
614         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
615         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
616         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
617         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
618         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
619 
620         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
621         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
622         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
623 
624         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
625         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
626         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
627         nz = ai[row+1] - diag_offset[row] - 1;
628         pv += 9;
629         for (j=0; j<nz; j++) {
630           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
631           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
632           x    = rtmp + 9*pj[j];
633           x[0] -= m1*x1 + m4*x2 + m7*x3;
634           x[1] -= m2*x1 + m5*x2 + m8*x3;
635           x[2] -= m3*x1 + m6*x2 + m9*x3;
636 
637           x[3] -= m1*x4 + m4*x5 + m7*x6;
638           x[4] -= m2*x4 + m5*x5 + m8*x6;
639           x[5] -= m3*x4 + m6*x5 + m9*x6;
640 
641           x[6] -= m1*x7 + m4*x8 + m7*x9;
642           x[7] -= m2*x7 + m5*x8 + m8*x9;
643           x[8] -= m3*x7 + m6*x8 + m9*x9;
644           pv   += 9;
645         }
646         PLogFlops(54*nz+36);
647       }
648       row = *ajtmp++;
649     }
650     /* finished row so stick it into b->a */
651     pv = b->a + 9*ai[i];
652     pj = b->j + ai[i];
653     nz = ai[i+1] - ai[i];
654     for ( j=0; j<nz; j++ ) {
655       x     = rtmp+9*pj[j];
656       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
657       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
658       pv   += 9;
659     }
660     /* invert diagonal block */
661     w = b->a + 9*diag_offset[i];
662     ierr = Linpack_DGEFA(w,bs,v_pivots); CHKERRQ(ierr);
663     ierr = Linpack_DGEDI(w,bs,v_pivots,v_work); CHKERRQ(ierr);
664   }
665 
666   PetscFree(rtmp);
667   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
668   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
669   ierr = ISDestroy(isicol); CHKERRQ(ierr);
670   C->factor = FACTOR_LU;
671   C->assembled = PETSC_TRUE;
672   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
673   return 0;
674 }
675 
676 /* ------------------------------------------------------------*/
677 /*
678       Version for when blocks are 2 by 2
679 */
680 int MatLUFactorNumeric_SeqBAIJ_2(Mat A,Mat *B)
681 {
682   Mat             C = *B;
683   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
684   IS              iscol = b->col, isrow = b->row, isicol;
685   int             *r,*ic, ierr, i, j, n = a->mbs, *ai = b->i, *aj = b->j;
686   int             *ajtmpold, *ajtmp, nz, row, v_pivots[2];
687   int             *diag_offset=b->diag,bs = 2,idx;
688   register Scalar *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
689   Scalar          p1,p2,p3,p4,v_work[2];
690   register int    *pj;
691 
692   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
693   PLogObjectParent(*B,isicol);
694   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
695   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
696   rtmp  = (Scalar *) PetscMalloc(4*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
697 
698   for ( i=0; i<n; i++ ) {
699     nz    = ai[i+1] - ai[i];
700     ajtmp = aj + ai[i];
701     for  ( j=0; j<nz; j++ ) {
702       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
703     }
704     /* load in initial (unfactored row) */
705     idx      = r[i];
706     nz       = a->i[idx+1] - a->i[idx];
707     ajtmpold = a->j + a->i[idx];
708     v        = a->a + 4*a->i[idx];
709     for ( j=0; j<nz; j++ ) {
710       x    = rtmp+4*ic[ajtmpold[j]];
711       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
712       v    += 4;
713     }
714     row = *ajtmp++;
715     while (row < i) {
716       pc = rtmp + 4*row;
717       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
718       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
719         pv = b->a + 4*diag_offset[row];
720         pj = b->j + diag_offset[row] + 1;
721         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
722         pc[0] = m1 = p1*x1 + p3*x2;
723         pc[1] = m2 = p2*x1 + p4*x2;
724         pc[2] = m3 = p1*x3 + p3*x4;
725         pc[3] = m4 = p2*x3 + p4*x4;
726         nz = ai[row+1] - diag_offset[row] - 1;
727         pv += 4;
728         for (j=0; j<nz; j++) {
729           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
730           x    = rtmp + 4*pj[j];
731           x[0] -= m1*x1 + m3*x2;
732           x[1] -= m2*x1 + m4*x2;
733           x[2] -= m1*x3 + m3*x4;
734           x[3] -= m2*x3 + m4*x4;
735           pv   += 4;
736         }
737         PLogFlops(16*nz+12);
738       }
739       row = *ajtmp++;
740     }
741     /* finished row so stick it into b->a */
742     pv = b->a + 4*ai[i];
743     pj = b->j + ai[i];
744     nz = ai[i+1] - ai[i];
745     for ( j=0; j<nz; j++ ) {
746       x     = rtmp+4*pj[j];
747       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
748       pv   += 4;
749     }
750     /* invert diagonal block */
751     w = b->a + 4*diag_offset[i];
752     ierr = Linpack_DGEFA(w,bs,v_pivots); CHKERRQ(ierr);
753     ierr = Linpack_DGEDI(w,bs,v_pivots,v_work); CHKERRQ(ierr);
754   }
755 
756   PetscFree(rtmp);
757   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
758   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
759   ierr = ISDestroy(isicol); CHKERRQ(ierr);
760   C->factor = FACTOR_LU;
761   C->assembled = PETSC_TRUE;
762   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
763   return 0;
764 }
765 
766 /* ----------------------------------------------------------- */
767 /*
768      Version for when blocks are 1 by 1.
769 */
770 int MatLUFactorNumeric_SeqBAIJ_1(Mat A,Mat *B)
771 {
772   Mat         C = *B;
773   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b = (Mat_SeqBAIJ *)C->data;
774   IS          iscol = b->col, isrow = b->row, isicol;
775   int         *r,*ic, ierr, i, j, n = a->mbs, *ai = b->i, *aj = b->j;
776   int         *ajtmpold, *ajtmp, nz, row;
777   int         *diag_offset = b->diag,diag;
778   register Scalar *pv,*v,*rtmp,multiplier,*pc;
779   register int    *pj;
780 
781   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
782   PLogObjectParent(*B,isicol);
783   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
784   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
785   rtmp  = (Scalar *) PetscMalloc((n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
786 
787   for ( i=0; i<n; i++ ) {
788     nz    = ai[i+1] - ai[i];
789     ajtmp = aj + ai[i];
790     for  ( j=0; j<nz; j++ ) rtmp[ajtmp[j]] = 0.0;
791 
792     /* load in initial (unfactored row) */
793     nz       = a->i[r[i]+1] - a->i[r[i]];
794     ajtmpold = a->j + a->i[r[i]];
795     v        = a->a + a->i[r[i]];
796     for ( j=0; j<nz; j++ ) rtmp[ic[ajtmpold[j]]] =  v[j];
797 
798     row = *ajtmp++;
799     while (row < i) {
800       pc = rtmp + row;
801       if (*pc != 0.0) {
802         pv         = b->a + diag_offset[row];
803         pj         = b->j + diag_offset[row] + 1;
804         multiplier = *pc * *pv++;
805         *pc        = multiplier;
806         nz         = ai[row+1] - diag_offset[row] - 1;
807         for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
808         PLogFlops(1+2*nz);
809       }
810       row = *ajtmp++;
811     }
812     /* finished row so stick it into b->a */
813     pv = b->a + ai[i];
814     pj = b->j + ai[i];
815     nz = ai[i+1] - ai[i];
816     for ( j=0; j<nz; j++ ) {pv[j] = rtmp[pj[j]];}
817     diag = diag_offset[i] - ai[i];
818     /* check pivot entry for current row */
819     if (pv[diag] == 0.0) {
820       SETERRQ(1,"MatLUFactorNumeric_SeqAIJ:Zero pivot");
821     }
822     pv[diag] = 1.0/pv[diag];
823   }
824 
825   PetscFree(rtmp);
826   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
827   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
828   ierr = ISDestroy(isicol); CHKERRQ(ierr);
829   C->factor    = FACTOR_LU;
830   C->assembled = PETSC_TRUE;
831   PLogFlops(b->n);
832   return 0;
833 }
834 
835 /* ----------------------------------------------------------- */
836 int MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,double f)
837 {
838   Mat_SeqBAIJ *mat = (Mat_SeqBAIJ *) A->data;
839   int         ierr;
840   Mat         C;
841 
842   ierr = MatLUFactorSymbolic_SeqBAIJ(A,row,col,f,&C); CHKERRQ(ierr);
843   ierr = MatLUFactorNumeric(A,&C); CHKERRQ(ierr);
844 
845   /* free all the data structures from mat */
846   PetscFree(mat->a);
847   if (!mat->singlemalloc) {PetscFree(mat->i); PetscFree(mat->j);}
848   if (mat->diag) PetscFree(mat->diag);
849   if (mat->ilen) PetscFree(mat->ilen);
850   if (mat->imax) PetscFree(mat->imax);
851   if (mat->solve_work) PetscFree(mat->solve_work);
852   PetscFree(mat);
853 
854   PetscMemcpy(A,C,sizeof(struct _Mat));
855   PetscHeaderDestroy(C);
856   return 0;
857 }
858 /* ----------------------------------------------------------- */
859 static int MatSolveAdd_SeqBAIJ_Private(Mat A,Vec bb,Vec yy,Vec xx)
860 {
861   Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data;
862   IS          iscol=a->col,isrow=a->row;
863   int         *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
864   int         nz,bs=a->bs,bs2=a->bs2,idx,idt,idc,_One=1,m=a->m;
865   Scalar      *xa,*ba,*aa=a->a,*sum,_DOne=1.0,_DMOne=-1.0;
866   Scalar      _DZero=0.0,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5,*y;
867   register Scalar *x,*b,*lsum,*tmp,*v;
868 
869   if (A->factor != FACTOR_LU) SETERRQ(1,"MatSolveAdd_SeqBAIJ_Private:Not for unfactored matrix");
870 
871   ierr = VecGetArray(bb,&ba); CHKERRQ(ierr); b = ba;
872   ierr = VecGetArray(xx,&xa); CHKERRQ(ierr); x = xa;
873   tmp  = a->solve_work;
874 
875   if (yy==PETSC_NULL) PetscMemzero(x,m*sizeof(Scalar)); /* MatSolve() */
876   else if (xx!=yy){
877     ierr = VecGetArray(yy,&y); CHKERRQ(ierr);
878     PetscMemcpy(x,y,m*sizeof(Scalar));
879     ierr = VecRestoreArray(yy,&y); CHKERRQ(ierr);
880   }
881 
882   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
883   ierr = ISGetIndices(iscol,&c);CHKERRQ(ierr); c = c + (n-1);
884 
885   switch (bs) {
886     case 1:
887       /* forward solve the lower triangular */
888       tmp[0] = b[*r++];
889       for ( i=1; i<n; i++ ) {
890         v     = aa + ai[i];
891         vi    = aj + ai[i];
892         nz    = a->diag[i] - ai[i];
893         sum1  = b[*r++];
894         while (nz--) {
895           sum1 -= (*v++)*tmp[*vi++];
896         }
897         tmp[i] = sum1;
898       }
899       /* backward solve the upper triangular */
900       for ( i=n-1; i>=0; i-- ){
901         v    = aa + a->diag[i] + 1;
902         vi   = aj + a->diag[i] + 1;
903         nz   = ai[i+1] - a->diag[i] - 1;
904         sum1 = tmp[i];
905         while (nz--) {
906           sum1 -= (*v++)*tmp[*vi++];
907         }
908         x[*c--] += tmp[i] = aa[a->diag[i]]*sum1;
909       }
910       break;
911     case 2:
912       /* forward solve the lower triangular */
913       idx    = 2*(*r++);
914       tmp[0] = b[idx]; tmp[1] = b[1+idx];
915       for ( i=1; i<n; i++ ) {
916         v     = aa + 4*ai[i];
917         vi    = aj + ai[i];
918         nz    = a->diag[i] - ai[i];
919         idx   = 2*(*r++);
920         sum1  = b[idx]; sum2 = b[1+idx];
921         while (nz--) {
922           idx   = 2*(*vi++);
923           x1    = tmp[idx]; x2 = tmp[1+idx];
924           sum1 -= v[0]*x1 + v[2]*x2;
925           sum2 -= v[1]*x1 + v[3]*x2;
926           v += 4;
927         }
928         idx = 2*i;
929         tmp[idx] = sum1; tmp[1+idx] = sum2;
930       }
931       /* backward solve the upper triangular */
932       for ( i=n-1; i>=0; i-- ){
933         v    = aa + 4*a->diag[i] + 4;
934         vi   = aj + a->diag[i] + 1;
935         nz   = ai[i+1] - a->diag[i] - 1;
936         idt  = 2*i;
937         sum1 = tmp[idt]; sum2 = tmp[1+idt];
938         while (nz--) {
939           idx   = 2*(*vi++);
940           x1    = tmp[idx]; x2 = tmp[1+idx];
941           sum1 -= v[0]*x1 + v[2]*x2;
942           sum2 -= v[1]*x1 + v[3]*x2;
943           v += 4;
944         }
945         idc = 2*(*c--);
946         v   = aa + 4*a->diag[i];
947         x[idc]   += tmp[idt]   = v[0]*sum1 + v[2]*sum2;
948         x[1+idc] += tmp[1+idt] = v[1]*sum1 + v[3]*sum2;
949       }
950       break;
951     case 3:
952       /* forward solve the lower triangular */
953       idx    = 3*(*r++);
954       tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx];
955       for ( i=1; i<n; i++ ) {
956         v     = aa + 9*ai[i];
957         vi    = aj + ai[i];
958         nz    = a->diag[i] - ai[i];
959         idx   = 3*(*r++);
960         sum1  = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx];
961         while (nz--) {
962           idx   = 3*(*vi++);
963           x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
964           sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
965           sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
966           sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
967           v += 9;
968         }
969         idx = 3*i;
970         tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3;
971       }
972       /* backward solve the upper triangular */
973       for ( i=n-1; i>=0; i-- ){
974         v    = aa + 9*a->diag[i] + 9;
975         vi   = aj + a->diag[i] + 1;
976         nz   = ai[i+1] - a->diag[i] - 1;
977         idt  = 3*i;
978         sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt];
979         while (nz--) {
980           idx   = 3*(*vi++);
981           x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
982           sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
983           sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
984           sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
985           v += 9;
986         }
987         idc = 3*(*c--);
988         v   = aa + 9*a->diag[i];
989         x[idc]   += tmp[idt]   = v[0]*sum1 + v[3]*sum2 + v[6]*sum3;
990         x[1+idc] += tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3;
991         x[2+idc] += tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3;
992       }
993       break;
994     case 4:
995       /* forward solve the lower triangular */
996       idx    = 4*(*r++);
997       tmp[0] = b[idx];   tmp[1] = b[1+idx];
998       tmp[2] = b[2+idx]; tmp[3] = b[3+idx];
999       for ( i=1; i<n; i++ ) {
1000         v     = aa + 16*ai[i];
1001         vi    = aj + ai[i];
1002         nz    = a->diag[i] - ai[i];
1003         idx   = 4*(*r++);
1004         sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1005         while (nz--) {
1006           idx   = 4*(*vi++);
1007           x1    = tmp[idx];x2 = tmp[1+idx];x3 = tmp[2+idx];x4 = tmp[3+idx];
1008           sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
1009           sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
1010           sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
1011           sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
1012           v += 16;
1013         }
1014         idx = 4*i;
1015         tmp[idx]   = sum1;tmp[1+idx] = sum2;
1016         tmp[2+idx] = sum3;tmp[3+idx] = sum4;
1017       }
1018       /* backward solve the upper triangular */
1019       for ( i=n-1; i>=0; i-- ){
1020         v    = aa + 16*a->diag[i] + 16;
1021         vi   = aj + a->diag[i] + 1;
1022         nz   = ai[i+1] - a->diag[i] - 1;
1023         idt  = 4*i;
1024         sum1 = tmp[idt];  sum2 = tmp[1+idt];
1025         sum3 = tmp[2+idt];sum4 = tmp[3+idt];
1026         while (nz--) {
1027           idx   = 4*(*vi++);
1028           x1    = tmp[idx];   x2 = tmp[1+idx];
1029           x3    = tmp[2+idx]; x4 = tmp[3+idx];
1030           sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
1031           sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
1032           sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
1033           sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
1034           v += 16;
1035         }
1036         idc = 4*(*c--);
1037         v   = aa + 16*a->diag[i];
1038         x[idc]   += tmp[idt]   = v[0]*sum1+v[4]*sum2+v[8]*sum3+v[12]*sum4;
1039         x[1+idc] += tmp[1+idt] = v[1]*sum1+v[5]*sum2+v[9]*sum3+v[13]*sum4;
1040         x[2+idc] += tmp[2+idt] = v[2]*sum1+v[6]*sum2+v[10]*sum3+v[14]*sum4;
1041         x[3+idc] += tmp[3+idt] = v[3]*sum1+v[7]*sum2+v[11]*sum3+v[15]*sum4;
1042       }
1043       break;
1044     case 5:
1045       /* forward solve the lower triangular */
1046       idx    = 5*(*r++);
1047       tmp[0] = b[idx];   tmp[1] = b[1+idx];
1048       tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
1049       for ( i=1; i<n; i++ ) {
1050         v     = aa + 25*ai[i];
1051         vi    = aj + ai[i];
1052         nz    = a->diag[i] - ai[i];
1053         idx   = 5*(*r++);
1054         sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1055         sum5  = b[4+idx];
1056         while (nz--) {
1057           idx   = 5*(*vi++);
1058           x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
1059           x4    = tmp[3+idx];x5 = tmp[4+idx];
1060           sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1061           sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1062           sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1063           sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1064           sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1065           v += 25;
1066         }
1067         idx = 5*i;
1068         tmp[idx]   = sum1;tmp[1+idx] = sum2;
1069         tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
1070       }
1071       /* backward solve the upper triangular */
1072       for ( i=n-1; i>=0; i-- ){
1073         v    = aa + 25*a->diag[i] + 25;
1074         vi   = aj + a->diag[i] + 1;
1075         nz   = ai[i+1] - a->diag[i] - 1;
1076         idt  = 5*i;
1077         sum1 = tmp[idt];  sum2 = tmp[1+idt];
1078         sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
1079         while (nz--) {
1080           idx   = 5*(*vi++);
1081           x1    = tmp[idx];   x2 = tmp[1+idx];
1082           x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
1083           sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1084           sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1085           sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1086           sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1087           sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1088           v += 25;
1089         }
1090         idc = 5*(*c--);
1091         v   = aa + 25*a->diag[i];
1092         x[idc]   += tmp[idt]   = v[0]*sum1+v[5]*sum2+v[10]*sum3+
1093                                  v[15]*sum4+v[20]*sum5;
1094         x[1+idc] += tmp[1+idt] = v[1]*sum1+v[6]*sum2+v[11]*sum3+
1095                                  v[16]*sum4+v[21]*sum5;
1096         x[2+idc] += tmp[2+idt] = v[2]*sum1+v[7]*sum2+v[12]*sum3+
1097                                  v[17]*sum4+v[22]*sum5;
1098         x[3+idc] += tmp[3+idt] = v[3]*sum1+v[8]*sum2+v[13]*sum3+
1099                                  v[18]*sum4+v[23]*sum5;
1100         x[4+idc] += tmp[4+idt] = v[4]*sum1+v[9]*sum2+v[14]*sum3+
1101                                  v[19]*sum4+v[24]*sum5;
1102       }
1103       break;
1104     default: {
1105       /* forward solve the lower triangular */
1106       PetscMemcpy(tmp,b + bs*(*r++), bs*sizeof(Scalar));
1107       for ( i=1; i<n; i++ ) {
1108         v   = aa + bs2*ai[i];
1109         vi  = aj + ai[i];
1110         nz  = a->diag[i] - ai[i];
1111         sum = tmp + bs*i;
1112         PetscMemcpy(sum,b+bs*(*r++),bs*sizeof(Scalar));
1113         while (nz--) {
1114           LAgemv_("N",&bs,&bs,&_DMOne,v,&bs,tmp+bs*(*vi++),&_One,&_DOne,sum,&_One);
1115           v += bs2;
1116         }
1117       }
1118       /* backward solve the upper triangular */
1119       lsum = a->solve_work + a->n;
1120       for ( i=n-1; i>=0; i-- ){
1121         v   = aa + bs2*(a->diag[i] + 1);
1122         vi  = aj + a->diag[i] + 1;
1123         nz  = ai[i+1] - a->diag[i] - 1;
1124         PetscMemcpy(lsum,tmp+i*bs,bs*sizeof(Scalar));
1125         while (nz--) {
1126           LAgemv_("N",&bs,&bs,&_DMOne,v,&bs,tmp+bs*(*vi++),&_One,&_DOne,lsum,&_One);
1127           v += bs2;
1128         }
1129         LAgemv_("N",&bs,&bs,&_DOne,aa+bs2*a->diag[i],&bs,lsum,&_One,&_DZero,
1130                 tmp+i*bs,&_One);
1131         PetscMemcpy(x + bs*(*c--),tmp+i*bs,bs*sizeof(Scalar));
1132       }
1133     }
1134   }
1135 
1136   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1137   ierr = ISRestoreIndices(iscol,&c); CHKERRQ(ierr);
1138   return 0;
1139 }
1140 
1141 /* ----------------------------------------------------------------*/
1142 
1143 int MatSolve_SeqBAIJ(Mat A,Vec bb, Vec xx)
1144 {
1145   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data;
1146   int         ierr,bs2=a->bs2;
1147 
1148   ierr = MatSolveAdd_SeqBAIJ_Private(A,bb,PETSC_NULL,xx); CHKERRQ(ierr);
1149   PLogFlops(2*bs2*(a->nz) - a->n);
1150   return 0;
1151 }
1152 
1153 /* ----------------------------------------------------------------*/
1154 
1155 int MatSolveAdd_SeqBAIJ(Mat A,Vec bb,Vec yy,Vec xx)
1156 {
1157   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data;
1158   int         ierr,bs2=a->bs2;
1159 
1160   ierr = MatSolveAdd_SeqBAIJ_Private(A,bb,yy,xx); CHKERRQ(ierr);
1161   PLogFlops(2*bs2*(a->nz));
1162   return 0;
1163 }
1164 /* ----------------------------------------------------------- */
1165 static int MatSolveTransAdd_SeqBAIJ_Private(Mat A,Vec bb,Vec yy,Vec xx)
1166 {
1167   Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data;
1168   IS          iscol=a->col,isrow=a->row;
1169   int         *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
1170   int         nz,bs=a->bs,bs2=a->bs2,idx,idt,idc,_One=1,N=a->n;
1171   Scalar      *xa,*ba,*aa=a->a,*sum,_DOne=1.0,_DMOne=-1.0;
1172   Scalar      _DZero=0.0,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5,*y;
1173   register Scalar *x,*b,*lsum,*tmp,*v;
1174 
1175   if (A->factor != FACTOR_LU) SETERRQ(1,"MatSolveTransAdd_SeqBAIJ_Private:Not for unfactored matrix");
1176 
1177   ierr = VecGetArray(bb,&ba); CHKERRQ(ierr); b = ba;
1178   ierr = VecGetArray(xx,&xa); CHKERRQ(ierr); x = xa;
1179   tmp  = a->solve_work;
1180 
1181   if (yy==PETSC_NULL) PetscMemzero(x,N*sizeof(Scalar)); /* VecZero()???  MatSolve() */
1182   else if (xx!=yy){ /* VecCopy() ??? */
1183     ierr = VecGetArray(yy,&y); CHKERRQ(ierr);
1184     PetscMemcpy(x,y,N*sizeof(Scalar));
1185     ierr = VecRestoreArray(yy,&y); CHKERRQ(ierr);
1186   }
1187 
1188   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1189   ierr = ISGetIndices(iscol,&c);CHKERRQ(ierr); c = c + (n-1);
1190 
1191   switch (bs) {
1192     case 1:
1193       /* forward solve the lower triangular */
1194       tmp[0] = b[*r++];
1195       for ( i=1; i<n; i++ ) {
1196         v     = aa + ai[i];
1197         vi    = aj + ai[i];
1198         nz    = a->diag[i] - ai[i];
1199         sum1  = b[*r++];
1200         while (nz--) {
1201           sum1 -= (*v++)*tmp[*vi++];
1202         }
1203         tmp[i] = sum1;
1204       }
1205       /* backward solve the upper triangular */
1206       for ( i=n-1; i>=0; i-- ){
1207         v    = aa + a->diag[i] + 1;
1208         vi   = aj + a->diag[i] + 1;
1209         nz   = ai[i+1] - a->diag[i] - 1;
1210         sum1 = tmp[i];
1211         while (nz--) {
1212           sum1 -= (*v++)*tmp[*vi++];
1213         }
1214         x[*c--] += tmp[i] = aa[a->diag[i]]*sum1;
1215       }
1216       break;
1217     case 2:
1218       /* forward solve the lower triangular */
1219       idx    = 2*(*r++);
1220       tmp[0] = b[idx]; tmp[1] = b[1+idx];
1221       for ( i=1; i<n; i++ ) {
1222         v     = aa + 4*ai[i];
1223         vi    = aj + ai[i];
1224         nz    = a->diag[i] - ai[i];
1225         idx   = 2*(*r++);
1226         sum1  = b[idx]; sum2 = b[1+idx];
1227         while (nz--) {
1228           idx   = 2*(*vi++);
1229           x1    = tmp[idx]; x2 = tmp[1+idx];
1230           sum1 -= v[0]*x1 + v[2]*x2;
1231           sum2 -= v[1]*x1 + v[3]*x2;
1232           v += 4;
1233         }
1234         idx = 2*i;
1235         tmp[idx] = sum1; tmp[1+idx] = sum2;
1236       }
1237       /* backward solve the upper triangular */
1238       for ( i=n-1; i>=0; i-- ){
1239         v    = aa + 4*a->diag[i] + 4;
1240         vi   = aj + a->diag[i] + 1;
1241         nz   = ai[i+1] - a->diag[i] - 1;
1242         idt  = 2*i;
1243         sum1 = tmp[idt]; sum2 = tmp[1+idt];
1244         while (nz--) {
1245           idx   = 2*(*vi++);
1246           x1    = tmp[idx]; x2 = tmp[1+idx];
1247           sum1 -= v[0]*x1 + v[2]*x2;
1248           sum2 -= v[1]*x1 + v[3]*x2;
1249           v += 4;
1250         }
1251         idc = 2*(*c--);
1252         v   = aa + 4*a->diag[i];
1253         x[idc]   += tmp[idt]   = v[0]*sum1 + v[2]*sum2;
1254         x[1+idc] += tmp[1+idt] = v[1]*sum1 + v[3]*sum2;
1255       }
1256       break;
1257     case 3:
1258       /* forward solve the lower triangular */
1259       idx    = 3*(*r++);
1260       tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx];
1261       for ( i=1; i<n; i++ ) {
1262         v     = aa + 9*ai[i];
1263         vi    = aj + ai[i];
1264         nz    = a->diag[i] - ai[i];
1265         idx   = 3*(*r++);
1266         sum1  = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx];
1267         while (nz--) {
1268           idx   = 3*(*vi++);
1269           x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1270           sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1271           sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1272           sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1273           v += 9;
1274         }
1275         idx = 3*i;
1276         tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3;
1277       }
1278       /* backward solve the upper triangular */
1279       for ( i=n-1; i>=0; i-- ){
1280         v    = aa + 9*a->diag[i] + 9;
1281         vi   = aj + a->diag[i] + 1;
1282         nz   = ai[i+1] - a->diag[i] - 1;
1283         idt  = 3*i;
1284         sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt];
1285         while (nz--) {
1286           idx   = 3*(*vi++);
1287           x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1288           sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1289           sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1290           sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1291           v += 9;
1292         }
1293         idc = 3*(*c--);
1294         v   = aa + 9*a->diag[i];
1295         x[idc]   += tmp[idt]   = v[0]*sum1 + v[3]*sum2 + v[6]*sum3;
1296         x[1+idc] += tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3;
1297         x[2+idc] += tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3;
1298       }
1299       break;
1300     case 4:
1301       /* forward solve the lower triangular */
1302       idx    = 4*(*r++);
1303       tmp[0] = b[idx];   tmp[1] = b[1+idx];
1304       tmp[2] = b[2+idx]; tmp[3] = b[3+idx];
1305       for ( i=1; i<n; i++ ) {
1306         v     = aa + 16*ai[i];
1307         vi    = aj + ai[i];
1308         nz    = a->diag[i] - ai[i];
1309         idx   = 4*(*r++);
1310         sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1311         while (nz--) {
1312           idx   = 4*(*vi++);
1313           x1    = tmp[idx];x2 = tmp[1+idx];x3 = tmp[2+idx];x4 = tmp[3+idx];
1314           sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
1315           sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
1316           sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
1317           sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
1318           v += 16;
1319         }
1320         idx = 4*i;
1321         tmp[idx]   = sum1;tmp[1+idx] = sum2;
1322         tmp[2+idx] = sum3;tmp[3+idx] = sum4;
1323       }
1324       /* backward solve the upper triangular */
1325       for ( i=n-1; i>=0; i-- ){
1326         v    = aa + 16*a->diag[i] + 16;
1327         vi   = aj + a->diag[i] + 1;
1328         nz   = ai[i+1] - a->diag[i] - 1;
1329         idt  = 4*i;
1330         sum1 = tmp[idt];  sum2 = tmp[1+idt];
1331         sum3 = tmp[2+idt];sum4 = tmp[3+idt];
1332         while (nz--) {
1333           idx   = 4*(*vi++);
1334           x1    = tmp[idx];   x2 = tmp[1+idx];
1335           x3    = tmp[2+idx]; x4 = tmp[3+idx];
1336           sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
1337           sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
1338           sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
1339           sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
1340           v += 16;
1341         }
1342         idc = 4*(*c--);
1343         v   = aa + 16*a->diag[i];
1344         x[idc]   += tmp[idt]   = v[0]*sum1+v[4]*sum2+v[8]*sum3+v[12]*sum4;
1345         x[1+idc] += tmp[1+idt] = v[1]*sum1+v[5]*sum2+v[9]*sum3+v[13]*sum4;
1346         x[2+idc] += tmp[2+idt] = v[2]*sum1+v[6]*sum2+v[10]*sum3+v[14]*sum4;
1347         x[3+idc] += tmp[3+idt] = v[3]*sum1+v[7]*sum2+v[11]*sum3+v[15]*sum4;
1348       }
1349       break;
1350     case 5:
1351       /* forward solve the lower triangular */
1352       idx    = 5*(*r++);
1353       tmp[0] = b[idx];   tmp[1] = b[1+idx];
1354       tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
1355       for ( i=1; i<n; i++ ) {
1356         v     = aa + 25*ai[i];
1357         vi    = aj + ai[i];
1358         nz    = a->diag[i] - ai[i];
1359         idx   = 5*(*r++);
1360         sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1361         sum5  = b[4+idx];
1362         while (nz--) {
1363           idx   = 5*(*vi++);
1364           x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
1365           x4    = tmp[3+idx];x5 = tmp[4+idx];
1366           sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1367           sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1368           sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1369           sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1370           sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1371           v += 25;
1372         }
1373         idx = 5*i;
1374         tmp[idx]   = sum1;tmp[1+idx] = sum2;
1375         tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
1376       }
1377       /* backward solve the upper triangular */
1378       for ( i=n-1; i>=0; i-- ){
1379         v    = aa + 25*a->diag[i] + 25;
1380         vi   = aj + a->diag[i] + 1;
1381         nz   = ai[i+1] - a->diag[i] - 1;
1382         idt  = 5*i;
1383         sum1 = tmp[idt];  sum2 = tmp[1+idt];
1384         sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
1385         while (nz--) {
1386           idx   = 5*(*vi++);
1387           x1    = tmp[idx];   x2 = tmp[1+idx];
1388           x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
1389           sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1390           sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1391           sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1392           sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1393           sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1394           v += 25;
1395         }
1396         idc = 5*(*c--);
1397         v   = aa + 25*a->diag[i];
1398         x[idc]   += tmp[idt]   = v[0]*sum1+v[5]*sum2+v[10]*sum3+
1399                                  v[15]*sum4+v[20]*sum5;
1400         x[1+idc] += tmp[1+idt] = v[1]*sum1+v[6]*sum2+v[11]*sum3+
1401                                  v[16]*sum4+v[21]*sum5;
1402         x[2+idc] += tmp[2+idt] = v[2]*sum1+v[7]*sum2+v[12]*sum3+
1403                                  v[17]*sum4+v[22]*sum5;
1404         x[3+idc] += tmp[3+idt] = v[3]*sum1+v[8]*sum2+v[13]*sum3+
1405                                  v[18]*sum4+v[23]*sum5;
1406         x[4+idc] += tmp[4+idt] = v[4]*sum1+v[9]*sum2+v[14]*sum3+
1407                                  v[19]*sum4+v[24]*sum5;
1408       }
1409       break;
1410     default: {
1411       /* forward solve the lower triangular */
1412       PetscMemcpy(tmp,b + bs*(*r++), bs*sizeof(Scalar));
1413       for ( i=1; i<n; i++ ) {
1414         v   = aa + bs2*ai[i];
1415         vi  = aj + ai[i];
1416         nz  = a->diag[i] - ai[i];
1417         sum = tmp + bs*i;
1418         PetscMemcpy(sum,b+bs*(*r++),bs*sizeof(Scalar));
1419         while (nz--) {
1420           LAgemv_("N",&bs,&bs,&_DMOne,v,&bs,tmp+bs*(*vi++),&_One,&_DOne,sum,&_One);
1421           v += bs2;
1422         }
1423       }
1424       /* backward solve the upper triangular */
1425       lsum = a->solve_work + a->n;
1426       for ( i=n-1; i>=0; i-- ){
1427         v   = aa + bs2*(a->diag[i] + 1);
1428         vi  = aj + a->diag[i] + 1;
1429         nz  = ai[i+1] - a->diag[i] - 1;
1430         PetscMemcpy(lsum,tmp+i*bs,bs*sizeof(Scalar));
1431         while (nz--) {
1432           LAgemv_("N",&bs,&bs,&_DMOne,v,&bs,tmp+bs*(*vi++),&_One,&_DOne,lsum,&_One);
1433           v += bs2;
1434         }
1435         LAgemv_("N",&bs,&bs,&_DOne,aa+bs2*a->diag[i],&bs,lsum,&_One,&_DZero,
1436                 tmp+i*bs,&_One);
1437         PetscMemcpy(x + bs*(*c--),tmp+i*bs,bs*sizeof(Scalar));
1438       }
1439     }
1440   }
1441 
1442   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1443   ierr = ISRestoreIndices(iscol,&c); CHKERRQ(ierr);
1444   return 0;
1445 }
1446 
1447 /* ----------------------------------------------------------------*/
1448 
1449 int MatSolveTrans_SeqBAIJ(Mat A,Vec bb, Vec xx)
1450 {
1451   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data;
1452   int         ierr,bs2=a->bs2;
1453 
1454   ierr = MatSolveTransAdd_SeqBAIJ_Private(A,bb,PETSC_NULL,xx); CHKERRQ(ierr);
1455   PLogFlops(2*bs2*(a->nz) - a->n);
1456   return 0;
1457 }
1458 
1459 /* ----------------------------------------------------------------*/
1460 
1461 int MatSolveTransAdd_SeqBAIJ(Mat A,Vec bb,Vec yy,Vec xx)
1462 {
1463   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data;
1464   int         ierr,bs2=a->bs2;
1465 
1466   ierr = MatSolveTransAdd_SeqBAIJ_Private(A,bb,yy,xx); CHKERRQ(ierr);
1467   PLogFlops(2*bs2*(a->nz));
1468   return 0;
1469 }
1470 
1471 /* ----------------------------------------------------------------*/
1472 /*
1473      This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
1474    except that the data structure of Mat_SeqAIJ is slightly different.
1475    Not a good example of code reuse.
1476    */
1477 int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,int levels,
1478                                  Mat *fact)
1479 {
1480   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
1481   IS          isicol;
1482   int         *r,*ic, ierr, prow, n = a->mbs, *ai = a->i, *aj = a->j;
1483   int         *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev;
1484   int         *dloc, idx, row,m,fm, nzf, nzi,len,  realloc = 0;
1485   int         incrlev,nnz,i,bs = a->bs,bs2 = a->bs2;
1486   PetscTruth  col_identity, row_identity;
1487 
1488   if (a->m != a->n) SETERRQ(1,"MatILUFactorSymbolic_SeqBAIJ:Matrix must be square");
1489   if (!isrow) SETERRQ(1,"MatILUFactorSymbolic_SeqBAIJ:Must have row permutation");
1490   if (!iscol) SETERRQ(1,"MatILUFactorSymbolic_SeqBAIJ:Must have column permutation");
1491 
1492   /* special case that simply copies fill pattern */
1493   ISIdentity(isrow,&row_identity); ISIdentity(iscol,&col_identity);
1494   if (levels == 0 && row_identity && col_identity) {
1495     ierr = MatConvertSameType_SeqBAIJ(A,fact,DO_NOT_COPY_VALUES); CHKERRQ(ierr);
1496     (*fact)->factor = FACTOR_LU;
1497     b               = (Mat_SeqBAIJ *) (*fact)->data;
1498     if (!b->diag) {
1499       ierr = MatMarkDiag_SeqBAIJ(*fact); CHKERRQ(ierr);
1500     }
1501     b->row        = isrow;
1502     b->col        = iscol;
1503     b->solve_work = (Scalar *) PetscMalloc((b->m+1+b->bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
1504     return 0;
1505   }
1506 
1507   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
1508   ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr);
1509   ierr = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
1510 
1511   /* get new row pointers */
1512   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
1513   ainew[0] = 0;
1514   /* don't know how many column pointers are needed so estimate */
1515   jmax = (int) (f*ai[n] + 1);
1516   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
1517   /* ajfill is level of fill for each fill entry */
1518   ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajfill);
1519   /* fill is a linked list of nonzeros in active row */
1520   fill = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(fill);
1521   /* im is level for each filled value */
1522   im = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(im);
1523   /* dloc is location of diagonal in factor */
1524   dloc = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(dloc);
1525   dloc[0]  = 0;
1526   for ( prow=0; prow<n; prow++ ) {
1527     /* first copy previous fill into linked list */
1528     nzf     = nz  = ai[r[prow]+1] - ai[r[prow]];
1529     xi      = aj + ai[r[prow]];
1530     fill[n] = n;
1531     while (nz--) {
1532       fm  = n;
1533       idx = ic[*xi++];
1534       do {
1535         m  = fm;
1536         fm = fill[m];
1537       } while (fm < idx);
1538       fill[m]   = idx;
1539       fill[idx] = fm;
1540       im[idx]   = 0;
1541     }
1542     nzi = 0;
1543     row = fill[n];
1544     while ( row < prow ) {
1545       incrlev = im[row] + 1;
1546       nz      = dloc[row];
1547       xi      = ajnew  + ainew[row] + nz;
1548       flev    = ajfill + ainew[row] + nz + 1;
1549       nnz     = ainew[row+1] - ainew[row] - nz - 1;
1550       if (*xi++ != row) {
1551         SETERRQ(1,"MatILUFactorSymbolic_SeqBAIJ:zero pivot");
1552       }
1553       fm      = row;
1554       while (nnz-- > 0) {
1555         idx = *xi++;
1556         if (*flev + incrlev > levels) {
1557           flev++;
1558           continue;
1559         }
1560         do {
1561           m  = fm;
1562           fm = fill[m];
1563         } while (fm < idx);
1564         if (fm != idx) {
1565           im[idx]   = *flev + incrlev;
1566           fill[m]   = idx;
1567           fill[idx] = fm;
1568           fm        = idx;
1569           nzf++;
1570         }
1571         else {
1572           if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
1573         }
1574         flev++;
1575       }
1576       row = fill[row];
1577       nzi++;
1578     }
1579     /* copy new filled row into permanent storage */
1580     ainew[prow+1] = ainew[prow] + nzf;
1581     if (ainew[prow+1] > jmax) {
1582       /* allocate a longer ajnew */
1583       int maxadd;
1584       maxadd = (int) (((f*ai[n]+1)*(n-prow+5))/n);
1585       if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
1586       jmax += maxadd;
1587       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1588       PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int));
1589       PetscFree(ajnew);
1590       ajnew = xi;
1591       /* allocate a longer ajfill */
1592       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1593       PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int));
1594       PetscFree(ajfill);
1595       ajfill = xi;
1596       realloc++;
1597     }
1598     xi          = ajnew + ainew[prow];
1599     flev        = ajfill + ainew[prow];
1600     dloc[prow]  = nzi;
1601     fm          = fill[n];
1602     while (nzf--) {
1603       *xi++   = fm;
1604       *flev++ = im[fm];
1605       fm      = fill[fm];
1606     }
1607   }
1608   PetscFree(ajfill);
1609   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1610   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
1611   ierr = ISDestroy(isicol); CHKERRQ(ierr);
1612   PetscFree(fill); PetscFree(im);
1613 
1614   PLogInfo(A,
1615     "Info:MatILUFactorSymbolic_SeqBAIJ:Realloc %d Fill ratio:given %g needed %g\n",
1616                              realloc,f,((double)ainew[n])/((double)ai[prow]));
1617 
1618   /* put together the new matrix */
1619   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr);
1620   b = (Mat_SeqBAIJ *) (*fact)->data;
1621   PetscFree(b->imax);
1622   b->singlemalloc = 0;
1623   len = bs2*ainew[n]*sizeof(Scalar);
1624   /* the next line frees the default space generated by the Create() */
1625   PetscFree(b->a); PetscFree(b->ilen);
1626   b->a          = (Scalar *) PetscMalloc( len ); CHKPTRQ(b->a);
1627   b->j          = ajnew;
1628   b->i          = ainew;
1629   for ( i=0; i<n; i++ ) dloc[i] += ainew[i];
1630   b->diag       = dloc;
1631   b->ilen       = 0;
1632   b->imax       = 0;
1633   b->row        = isrow;
1634   b->col        = iscol;
1635   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
1636   CHKPTRQ(b->solve_work);
1637   /* In b structure:  Free imax, ilen, old a, old j.
1638      Allocate dloc, solve_work, new a, new j */
1639   PLogObjectMemory(*fact,(ainew[n]-n)*(sizeof(int))+bs2*ainew[n]*sizeof(Scalar));
1640   b->maxnz          = b->nz = ainew[n];
1641   (*fact)->factor   = FACTOR_LU;
1642   return 0;
1643 }
1644 
1645 
1646 
1647 
1648