xref: /petsc/src/mat/impls/baij/seq/baijfact.c (revision ab94cc7af4fcd5c63a93b94bdec4707d4e0807cd)
1 #ifndef lint
2 static char vcid[] = "$Id: baijfact.c,v 1.18 1996/04/20 04:20:18 bsmith Exp balay $";
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     ierr = Linpack_DGEFA(w,bs,v_pivots); CHKERRQ(ierr);
220     ierr = Linpack_DGEDI(w,bs,v_pivots,v_work); CHKERRQ(ierr);
221   }
222 
223   PetscFree(rtmp); PetscFree(v_work);
224   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
225   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
226   ierr = ISDestroy(isicol); CHKERRQ(ierr);
227   C->factor = FACTOR_LU;
228   C->assembled = PETSC_TRUE;
229   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
230   return 0;
231 }
232 /* ------------------------------------------------------------*/
233 /*
234       Version for when blocks are 5 by 5
235 */
236 int MatLUFactorNumeric_SeqBAIJ_5(Mat A,Mat *B)
237 {
238   Mat             C = *B;
239   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
240   IS              iscol = b->col, isrow = b->row, isicol;
241   int             *r,*ic, ierr, i, j, n = a->mbs, *ai = b->i, *aj = b->j;
242   int             *ajtmpold, *ajtmp, nz, row, v_pivots[5];
243   int             *diag_offset = b->diag,bs = 5,idx;
244   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
245   Scalar          p1,p2,p3,p4,v_work[5],m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
246   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
247   Scalar          x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
248   Scalar          p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
249   Scalar          m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
250   register int    *pj;
251 
252   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
253   PLogObjectParent(*B,isicol);
254   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
255   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
256   rtmp  = (Scalar *) PetscMalloc(25*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
257 
258   for ( i=0; i<n; i++ ) {
259     nz    = ai[i+1] - ai[i];
260     ajtmp = aj + ai[i];
261     for  ( j=0; j<nz; j++ ) {
262       x = rtmp+25*ajtmp[j];
263       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
264       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
265       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
266     }
267     /* load in initial (unfactored row) */
268     idx      = r[i];
269     nz       = a->i[idx+1] - a->i[idx];
270     ajtmpold = a->j + a->i[idx];
271     v        = a->a + 25*a->i[idx];
272     for ( j=0; j<nz; j++ ) {
273       x    = rtmp+25*ic[ajtmpold[j]];
274       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
275       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
276       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
277       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
278       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
279       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
280       v    += 25;
281     }
282     row = *ajtmp++;
283     while (row < i) {
284       pc = rtmp + 25*row;
285       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
286       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
287       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
288       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
289       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
290       p25 = pc[24];
291       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
292           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
293           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
294           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
295           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
296           p23 != 0.0 || p24 != 0.0) {
297         pv = b->a + 25*diag_offset[row];
298         pj = b->j + diag_offset[row] + 1;
299         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
300         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
301         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
302         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
303         x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
304         x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
305         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
306         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
307         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
308         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
309         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
310 
311         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
312         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
313         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
314         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
315         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
316 
317         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
318         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
319         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
320         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
321         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
322 
323         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
324         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
325         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
326         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
327         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
328 
329         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
330         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
331         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
332         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
333         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
334 
335         nz = ai[row+1] - diag_offset[row] - 1;
336         pv += 25;
337         for (j=0; j<nz; j++) {
338           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
339           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
340           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
341           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
342           x18  = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
343           x22  = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
344           x    = rtmp + 25*pj[j];
345           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
346           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
347           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
348           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
349           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
350 
351           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
352           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
353           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
354           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
355           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
356 
357           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
358           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
359           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
360           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
361           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
362 
363           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
364           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
365           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
366           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
367           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
368 
369           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
370           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
371           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
372           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
373           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
374 
375           pv   += 25;
376         }
377         PLogFlops(250*nz+225);
378       }
379       row = *ajtmp++;
380     }
381     /* finished row so stick it into b->a */
382     pv = b->a + 25*ai[i];
383     pj = b->j + ai[i];
384     nz = ai[i+1] - ai[i];
385     for ( j=0; j<nz; j++ ) {
386       x     = rtmp+25*pj[j];
387       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
388       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
389       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
390       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
391       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
392       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
393       pv   += 25;
394     }
395     /* invert diagonal block */
396     w = b->a + 25*diag_offset[i];
397     ierr = Linpack_DGEFA(w,bs,v_pivots); CHKERRQ(ierr);
398     ierr = Linpack_DGEDI(w,bs,v_pivots,v_work); CHKERRQ(ierr);
399   }
400 
401   PetscFree(rtmp);
402   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
403   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
404   ierr = ISDestroy(isicol); CHKERRQ(ierr);
405   C->factor = FACTOR_LU;
406   C->assembled = PETSC_TRUE;
407   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
408   return 0;
409 }
410 
411 /* ------------------------------------------------------------*/
412 /*
413       Version for when blocks are 4 by 4
414 */
415 int MatLUFactorNumeric_SeqBAIJ_4(Mat A,Mat *B)
416 {
417   Mat             C = *B;
418   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
419   IS              iscol = b->col, isrow = b->row, isicol;
420   int             *r,*ic, ierr, i, j, n = a->mbs, *ai = b->i, *aj = b->j;
421   int             *ajtmpold, *ajtmp, nz, row, v_pivots[4];
422   int             *diag_offset = b->diag,bs = 4,idx;
423   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
424   Scalar          p1,p2,p3,p4,v_work[4],m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
425   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
426   Scalar          p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
427   Scalar          m13,m14,m15,m16;
428   register int    *pj;
429 
430   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
431   PLogObjectParent(*B,isicol);
432   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
433   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
434   rtmp  = (Scalar *) PetscMalloc(16*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
435 
436   for ( i=0; i<n; i++ ) {
437     nz    = ai[i+1] - ai[i];
438     ajtmp = aj + ai[i];
439     for  ( j=0; j<nz; j++ ) {
440       x = rtmp+16*ajtmp[j];
441       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
442       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
443     }
444     /* load in initial (unfactored row) */
445     idx      = r[i];
446     nz       = a->i[idx+1] - a->i[idx];
447     ajtmpold = a->j + a->i[idx];
448     v        = a->a + 16*a->i[idx];
449     for ( j=0; j<nz; j++ ) {
450       x    = rtmp+16*ic[ajtmpold[j]];
451       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
452       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
453       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
454       x[14] = v[14]; x[15] = v[15];
455       v    += 16;
456     }
457     row = *ajtmp++;
458     while (row < i) {
459       pc = rtmp + 16*row;
460       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
461       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
462       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
463       p15 = pc[14]; p16 = pc[15];
464       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
465           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
466           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
467           || p16 != 0.0) {
468         pv = b->a + 16*diag_offset[row];
469         pj = b->j + diag_offset[row] + 1;
470         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
471         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
472         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
473         x15 = pv[14]; x16 = pv[15];
474         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
475         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
476         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
477         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
478 
479         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
480         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
481         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
482         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
483 
484         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
485         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
486         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
487         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
488 
489         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
490         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
491         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
492         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
493 
494         nz = ai[row+1] - diag_offset[row] - 1;
495         pv += 16;
496         for (j=0; j<nz; j++) {
497           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
498           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
499           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
500           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
501           x    = rtmp + 16*pj[j];
502           x[0] -= m1*x1 + m5*x2  + m9*x3 + m13*x4;
503           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
504           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
505           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
506 
507           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
508           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
509           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
510           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
511 
512           x[8] -= m1*x9  + m5*x10  + m9*x11 + m13*x12;
513           x[9] -= m2*x9  + m6*x10  + m10*x11 + m14*x12;
514           x[10] -= m3*x9 + m7*x10  + m11*x11 + m15*x12;
515           x[11] -= m4*x9 + m8*x10  + m12*x11 + m16*x12;
516 
517           x[12] -= m1*x13 + m5*x14  + m9*x15 + m13*x16;
518           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
519           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
520           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
521 
522           pv   += 16;
523         }
524         PLogFlops(128*nz+112);
525       }
526       row = *ajtmp++;
527     }
528     /* finished row so stick it into b->a */
529     pv = b->a + 16*ai[i];
530     pj = b->j + ai[i];
531     nz = ai[i+1] - ai[i];
532     for ( j=0; j<nz; j++ ) {
533       x     = rtmp+16*pj[j];
534       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
535       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
536       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
537       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
538       pv   += 16;
539     }
540     /* invert diagonal block */
541     w = b->a + 16*diag_offset[i];
542     ierr = Linpack_DGEFA(w,bs,v_pivots); CHKERRQ(ierr);
543     ierr = Linpack_DGEDI(w,bs,v_pivots,v_work); CHKERRQ(ierr);
544   }
545 
546   PetscFree(rtmp);
547   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
548   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
549   ierr = ISDestroy(isicol); CHKERRQ(ierr);
550   C->factor = FACTOR_LU;
551   C->assembled = PETSC_TRUE;
552   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
553   return 0;
554 }
555 /* ------------------------------------------------------------*/
556 /*
557       Version for when blocks are 3 by 3
558 */
559 int MatLUFactorNumeric_SeqBAIJ_3(Mat A,Mat *B)
560 {
561   Mat             C = *B;
562   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
563   IS              iscol = b->col, isrow = b->row, isicol;
564   int             *r,*ic, ierr, i, j, n = a->mbs, *ai = b->i, *aj = b->j;
565   int             *ajtmpold, *ajtmp, nz, row, v_pivots[3];
566   int             *diag_offset = b->diag,bs = 3,idx;
567   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
568   Scalar          p1,p2,p3,p4,v_work[3],m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
569   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
570   register int    *pj;
571 
572   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
573   PLogObjectParent(*B,isicol);
574   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
575   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
576   rtmp  = (Scalar *) PetscMalloc(9*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
577 
578   for ( i=0; i<n; i++ ) {
579     nz    = ai[i+1] - ai[i];
580     ajtmp = aj + ai[i];
581     for  ( j=0; j<nz; j++ ) {
582       x = rtmp+9*ajtmp[j];
583       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
584     }
585     /* load in initial (unfactored row) */
586     idx      = r[i];
587     nz       = a->i[idx+1] - a->i[idx];
588     ajtmpold = a->j + a->i[idx];
589     v        = a->a + 9*a->i[idx];
590     for ( j=0; j<nz; j++ ) {
591       x    = rtmp+9*ic[ajtmpold[j]];
592       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
593       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
594       v    += 9;
595     }
596     row = *ajtmp++;
597     while (row < i) {
598       pc = rtmp + 9*row;
599       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
600       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
601       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
602           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
603         pv = b->a + 9*diag_offset[row];
604         pj = b->j + diag_offset[row] + 1;
605         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
606         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
607         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
608         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
609         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
610 
611         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
612         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
613         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
614 
615         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
616         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
617         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
618         nz = ai[row+1] - diag_offset[row] - 1;
619         pv += 9;
620         for (j=0; j<nz; j++) {
621           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
622           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
623           x    = rtmp + 9*pj[j];
624           x[0] -= m1*x1 + m4*x2 + m7*x3;
625           x[1] -= m2*x1 + m5*x2 + m8*x3;
626           x[2] -= m3*x1 + m6*x2 + m9*x3;
627 
628           x[3] -= m1*x4 + m4*x5 + m7*x6;
629           x[4] -= m2*x4 + m5*x5 + m8*x6;
630           x[5] -= m3*x4 + m6*x5 + m9*x6;
631 
632           x[6] -= m1*x7 + m4*x8 + m7*x9;
633           x[7] -= m2*x7 + m5*x8 + m8*x9;
634           x[8] -= m3*x7 + m6*x8 + m9*x9;
635           pv   += 9;
636         }
637         PLogFlops(54*nz+36);
638       }
639       row = *ajtmp++;
640     }
641     /* finished row so stick it into b->a */
642     pv = b->a + 9*ai[i];
643     pj = b->j + ai[i];
644     nz = ai[i+1] - ai[i];
645     for ( j=0; j<nz; j++ ) {
646       x     = rtmp+9*pj[j];
647       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
648       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
649       pv   += 9;
650     }
651     /* invert diagonal block */
652     w = b->a + 9*diag_offset[i];
653     ierr = Linpack_DGEFA(w,bs,v_pivots); CHKERRQ(ierr);
654     ierr = Linpack_DGEDI(w,bs,v_pivots,v_work); CHKERRQ(ierr);
655   }
656 
657   PetscFree(rtmp);
658   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
659   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
660   ierr = ISDestroy(isicol); CHKERRQ(ierr);
661   C->factor = FACTOR_LU;
662   C->assembled = PETSC_TRUE;
663   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
664   return 0;
665 }
666 
667 /* ------------------------------------------------------------*/
668 /*
669       Version for when blocks are 2 by 2
670 */
671 int MatLUFactorNumeric_SeqBAIJ_2(Mat A,Mat *B)
672 {
673   Mat             C = *B;
674   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
675   IS              iscol = b->col, isrow = b->row, isicol;
676   int             *r,*ic, ierr, i, j, n = a->mbs, *ai = b->i, *aj = b->j;
677   int             *ajtmpold, *ajtmp, nz, row, v_pivots[2];
678   int             *diag_offset=b->diag,bs = 2,idx;
679   register Scalar *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
680   Scalar          p1,p2,p3,p4,v_work[2];
681   register int    *pj;
682 
683   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
684   PLogObjectParent(*B,isicol);
685   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
686   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
687   rtmp  = (Scalar *) PetscMalloc(4*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
688 
689   for ( i=0; i<n; i++ ) {
690     nz    = ai[i+1] - ai[i];
691     ajtmp = aj + ai[i];
692     for  ( j=0; j<nz; j++ ) {
693       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
694     }
695     /* load in initial (unfactored row) */
696     idx      = r[i];
697     nz       = a->i[idx+1] - a->i[idx];
698     ajtmpold = a->j + a->i[idx];
699     v        = a->a + 4*a->i[idx];
700     for ( j=0; j<nz; j++ ) {
701       x    = rtmp+4*ic[ajtmpold[j]];
702       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
703       v    += 4;
704     }
705     row = *ajtmp++;
706     while (row < i) {
707       pc = rtmp + 4*row;
708       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
709       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
710         pv = b->a + 4*diag_offset[row];
711         pj = b->j + diag_offset[row] + 1;
712         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
713         pc[0] = m1 = p1*x1 + p3*x2;
714         pc[1] = m2 = p2*x1 + p4*x2;
715         pc[2] = m3 = p1*x3 + p3*x4;
716         pc[3] = m4 = p2*x3 + p4*x4;
717         nz = ai[row+1] - diag_offset[row] - 1;
718         pv += 4;
719         for (j=0; j<nz; j++) {
720           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
721           x    = rtmp + 4*pj[j];
722           x[0] -= m1*x1 + m3*x2;
723           x[1] -= m2*x1 + m4*x2;
724           x[2] -= m1*x3 + m3*x4;
725           x[3] -= m2*x3 + m4*x4;
726           pv   += 4;
727         }
728         PLogFlops(16*nz+12);
729       }
730       row = *ajtmp++;
731     }
732     /* finished row so stick it into b->a */
733     pv = b->a + 4*ai[i];
734     pj = b->j + ai[i];
735     nz = ai[i+1] - ai[i];
736     for ( j=0; j<nz; j++ ) {
737       x     = rtmp+4*pj[j];
738       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
739       pv   += 4;
740     }
741     /* invert diagonal block */
742     w = b->a + 4*diag_offset[i];
743     ierr = Linpack_DGEFA(w,bs,v_pivots); CHKERRQ(ierr);
744     ierr = Linpack_DGEDI(w,bs,v_pivots,v_work); CHKERRQ(ierr);
745   }
746 
747   PetscFree(rtmp);
748   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
749   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
750   ierr = ISDestroy(isicol); CHKERRQ(ierr);
751   C->factor = FACTOR_LU;
752   C->assembled = PETSC_TRUE;
753   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
754   return 0;
755 }
756 
757 /* ----------------------------------------------------------- */
758 /*
759      Version for when blocks are 1 by 1.
760 */
761 int MatLUFactorNumeric_SeqBAIJ_1(Mat A,Mat *B)
762 {
763   Mat         C = *B;
764   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b = (Mat_SeqBAIJ *)C->data;
765   IS          iscol = b->col, isrow = b->row, isicol;
766   int         *r,*ic, ierr, i, j, n = a->mbs, *ai = b->i, *aj = b->j;
767   int         *ajtmpold, *ajtmp, nz, row;
768   int         *diag_offset = b->diag,diag;
769   register Scalar *pv,*v,*rtmp,multiplier,*pc;
770   register int    *pj;
771 
772   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
773   PLogObjectParent(*B,isicol);
774   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
775   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
776   rtmp  = (Scalar *) PetscMalloc((n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
777 
778   for ( i=0; i<n; i++ ) {
779     nz    = ai[i+1] - ai[i];
780     ajtmp = aj + ai[i];
781     for  ( j=0; j<nz; j++ ) rtmp[ajtmp[j]] = 0.0;
782 
783     /* load in initial (unfactored row) */
784     nz       = a->i[r[i]+1] - a->i[r[i]];
785     ajtmpold = a->j + a->i[r[i]];
786     v        = a->a + a->i[r[i]];
787     for ( j=0; j<nz; j++ ) rtmp[ic[ajtmpold[j]]] =  v[j];
788 
789     row = *ajtmp++;
790     while (row < i) {
791       pc = rtmp + row;
792       if (*pc != 0.0) {
793         pv         = b->a + diag_offset[row];
794         pj         = b->j + diag_offset[row] + 1;
795         multiplier = *pc * *pv++;
796         *pc        = multiplier;
797         nz         = ai[row+1] - diag_offset[row] - 1;
798         for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
799         PLogFlops(1+2*nz);
800       }
801       row = *ajtmp++;
802     }
803     /* finished row so stick it into b->a */
804     pv = b->a + ai[i];
805     pj = b->j + ai[i];
806     nz = ai[i+1] - ai[i];
807     for ( j=0; j<nz; j++ ) {pv[j] = rtmp[pj[j]];}
808     diag = diag_offset[i] - ai[i];
809     /* check pivot entry for current row */
810     if (pv[diag] == 0.0) {
811       SETERRQ(1,"MatLUFactorNumeric_SeqAIJ:Zero pivot");
812     }
813     pv[diag] = 1.0/pv[diag];
814   }
815 
816   PetscFree(rtmp);
817   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
818   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
819   ierr = ISDestroy(isicol); CHKERRQ(ierr);
820   C->factor    = FACTOR_LU;
821   C->assembled = PETSC_TRUE;
822   PLogFlops(b->n);
823   return 0;
824 }
825 
826 /* ----------------------------------------------------------- */
827 int MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,double f)
828 {
829   Mat_SeqBAIJ *mat = (Mat_SeqBAIJ *) A->data;
830   int         ierr;
831   Mat         C;
832 
833   ierr = MatLUFactorSymbolic_SeqBAIJ(A,row,col,f,&C); CHKERRQ(ierr);
834   ierr = MatLUFactorNumeric(A,&C); CHKERRQ(ierr);
835 
836   /* free all the data structures from mat */
837   PetscFree(mat->a);
838   if (!mat->singlemalloc) {PetscFree(mat->i); PetscFree(mat->j);}
839   if (mat->diag) PetscFree(mat->diag);
840   if (mat->ilen) PetscFree(mat->ilen);
841   if (mat->imax) PetscFree(mat->imax);
842   if (mat->solve_work) PetscFree(mat->solve_work);
843   PetscFree(mat);
844 
845   PetscMemcpy(A,C,sizeof(struct _Mat));
846   PetscHeaderDestroy(C);
847   return 0;
848 }
849 /* ----------------------------------------------------------- */
850 static int MatSolveAdd_SeqBAIJ_Private(Mat A,Vec bb,Vec yy,Vec xx)
851 {
852   Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data;
853   IS          iscol=a->col,isrow=a->row;
854   int         *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
855   int         nz,bs=a->bs,bs2=a->bs2,idx,idt,idc,_One=1,m=a->m;
856   Scalar      *xa,*ba,*aa=a->a,*sum,_DOne=1.0,_DMOne=-1.0;
857   Scalar      _DZero=0.0,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5,*y;
858   register Scalar *x,*b,*lsum,*tmp,*v;
859 
860   if (A->factor != FACTOR_LU) SETERRQ(1,"MatSolveAdd_SeqBAIJ_Private:Not for unfactored matrix");
861 
862   ierr = VecGetArray(bb,&ba); CHKERRQ(ierr); b = ba;
863   ierr = VecGetArray(xx,&xa); CHKERRQ(ierr); x = xa;
864   tmp  = a->solve_work;
865 
866   if (yy==PETSC_NULL) PetscMemzero(x,m*sizeof(Scalar)); /* MatSolve() */
867   else if (xx!=yy){
868     ierr = VecGetArray(yy,&y); CHKERRQ(ierr);
869     PetscMemcpy(x,y,m*sizeof(Scalar));
870     ierr = VecRestoreArray(yy,&y); CHKERRQ(ierr);
871   }
872 
873   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
874   ierr = ISGetIndices(iscol,&c);CHKERRQ(ierr); c = c + (n-1);
875 
876   switch (bs) {
877     case 1:
878       /* forward solve the lower triangular */
879       tmp[0] = b[*r++];
880       for ( i=1; i<n; i++ ) {
881         v     = aa + ai[i];
882         vi    = aj + ai[i];
883         nz    = a->diag[i] - ai[i];
884         sum1  = b[*r++];
885         while (nz--) {
886           sum1 -= (*v++)*tmp[*vi++];
887         }
888         tmp[i] = sum1;
889       }
890       /* backward solve the upper triangular */
891       for ( i=n-1; i>=0; i-- ){
892         v    = aa + a->diag[i] + 1;
893         vi   = aj + a->diag[i] + 1;
894         nz   = ai[i+1] - a->diag[i] - 1;
895         sum1 = tmp[i];
896         while (nz--) {
897           sum1 -= (*v++)*tmp[*vi++];
898         }
899         x[*c--] += tmp[i] = aa[a->diag[i]]*sum1;
900       }
901       break;
902     case 2:
903       /* forward solve the lower triangular */
904       idx    = 2*(*r++);
905       tmp[0] = b[idx]; tmp[1] = b[1+idx];
906       for ( i=1; i<n; i++ ) {
907         v     = aa + 4*ai[i];
908         vi    = aj + ai[i];
909         nz    = a->diag[i] - ai[i];
910         idx   = 2*(*r++);
911         sum1  = b[idx]; sum2 = b[1+idx];
912         while (nz--) {
913           idx   = 2*(*vi++);
914           x1    = tmp[idx]; x2 = tmp[1+idx];
915           sum1 -= v[0]*x1 + v[2]*x2;
916           sum2 -= v[1]*x1 + v[3]*x2;
917           v += 4;
918         }
919         idx = 2*i;
920         tmp[idx] = sum1; tmp[1+idx] = sum2;
921       }
922       /* backward solve the upper triangular */
923       for ( i=n-1; i>=0; i-- ){
924         v    = aa + 4*a->diag[i] + 4;
925         vi   = aj + a->diag[i] + 1;
926         nz   = ai[i+1] - a->diag[i] - 1;
927         idt  = 2*i;
928         sum1 = tmp[idt]; sum2 = tmp[1+idt];
929         while (nz--) {
930           idx   = 2*(*vi++);
931           x1    = tmp[idx]; x2 = tmp[1+idx];
932           sum1 -= v[0]*x1 + v[2]*x2;
933           sum2 -= v[1]*x1 + v[3]*x2;
934           v += 4;
935         }
936         idc = 2*(*c--);
937         v   = aa + 4*a->diag[i];
938         x[idc]   += tmp[idt]   = v[0]*sum1 + v[2]*sum2;
939         x[1+idc] += tmp[1+idt] = v[1]*sum1 + v[3]*sum2;
940       }
941       break;
942     case 3:
943       /* forward solve the lower triangular */
944       idx    = 3*(*r++);
945       tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx];
946       for ( i=1; i<n; i++ ) {
947         v     = aa + 9*ai[i];
948         vi    = aj + ai[i];
949         nz    = a->diag[i] - ai[i];
950         idx   = 3*(*r++);
951         sum1  = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx];
952         while (nz--) {
953           idx   = 3*(*vi++);
954           x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
955           sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
956           sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
957           sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
958           v += 9;
959         }
960         idx = 3*i;
961         tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3;
962       }
963       /* backward solve the upper triangular */
964       for ( i=n-1; i>=0; i-- ){
965         v    = aa + 9*a->diag[i] + 9;
966         vi   = aj + a->diag[i] + 1;
967         nz   = ai[i+1] - a->diag[i] - 1;
968         idt  = 3*i;
969         sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt];
970         while (nz--) {
971           idx   = 3*(*vi++);
972           x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
973           sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
974           sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
975           sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
976           v += 9;
977         }
978         idc = 3*(*c--);
979         v   = aa + 9*a->diag[i];
980         x[idc]   += tmp[idt]   = v[0]*sum1 + v[3]*sum2 + v[6]*sum3;
981         x[1+idc] += tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3;
982         x[2+idc] += tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3;
983       }
984       break;
985     case 4:
986       /* forward solve the lower triangular */
987       idx    = 4*(*r++);
988       tmp[0] = b[idx];   tmp[1] = b[1+idx];
989       tmp[2] = b[2+idx]; tmp[3] = b[3+idx];
990       for ( i=1; i<n; i++ ) {
991         v     = aa + 16*ai[i];
992         vi    = aj + ai[i];
993         nz    = a->diag[i] - ai[i];
994         idx   = 4*(*r++);
995         sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
996         while (nz--) {
997           idx   = 4*(*vi++);
998           x1    = tmp[idx];x2 = tmp[1+idx];x3 = tmp[2+idx];x4 = tmp[3+idx];
999           sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
1000           sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
1001           sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
1002           sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
1003           v += 16;
1004         }
1005         idx = 4*i;
1006         tmp[idx]   = sum1;tmp[1+idx] = sum2;
1007         tmp[2+idx] = sum3;tmp[3+idx] = sum4;
1008       }
1009       /* backward solve the upper triangular */
1010       for ( i=n-1; i>=0; i-- ){
1011         v    = aa + 16*a->diag[i] + 16;
1012         vi   = aj + a->diag[i] + 1;
1013         nz   = ai[i+1] - a->diag[i] - 1;
1014         idt  = 4*i;
1015         sum1 = tmp[idt];  sum2 = tmp[1+idt];
1016         sum3 = tmp[2+idt];sum4 = tmp[3+idt];
1017         while (nz--) {
1018           idx   = 4*(*vi++);
1019           x1    = tmp[idx];   x2 = tmp[1+idx];
1020           x3    = tmp[2+idx]; x4 = tmp[3+idx];
1021           sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
1022           sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
1023           sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
1024           sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
1025           v += 16;
1026         }
1027         idc = 4*(*c--);
1028         v   = aa + 16*a->diag[i];
1029         x[idc]   += tmp[idt]   = v[0]*sum1+v[4]*sum2+v[8]*sum3+v[12]*sum4;
1030         x[1+idc] += tmp[1+idt] = v[1]*sum1+v[5]*sum2+v[9]*sum3+v[13]*sum4;
1031         x[2+idc] += tmp[2+idt] = v[2]*sum1+v[6]*sum2+v[10]*sum3+v[14]*sum4;
1032         x[3+idc] += tmp[3+idt] = v[3]*sum1+v[7]*sum2+v[11]*sum3+v[15]*sum4;
1033       }
1034       break;
1035     case 5:
1036       /* forward solve the lower triangular */
1037       idx    = 5*(*r++);
1038       tmp[0] = b[idx];   tmp[1] = b[1+idx];
1039       tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
1040       for ( i=1; i<n; i++ ) {
1041         v     = aa + 25*ai[i];
1042         vi    = aj + ai[i];
1043         nz    = a->diag[i] - ai[i];
1044         idx   = 5*(*r++);
1045         sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1046         sum5  = b[4+idx];
1047         while (nz--) {
1048           idx   = 5*(*vi++);
1049           x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
1050           x4    = tmp[3+idx];x5 = tmp[4+idx];
1051           sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1052           sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1053           sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1054           sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1055           sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1056           v += 25;
1057         }
1058         idx = 5*i;
1059         tmp[idx]   = sum1;tmp[1+idx] = sum2;
1060         tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
1061       }
1062       /* backward solve the upper triangular */
1063       for ( i=n-1; i>=0; i-- ){
1064         v    = aa + 25*a->diag[i] + 25;
1065         vi   = aj + a->diag[i] + 1;
1066         nz   = ai[i+1] - a->diag[i] - 1;
1067         idt  = 5*i;
1068         sum1 = tmp[idt];  sum2 = tmp[1+idt];
1069         sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
1070         while (nz--) {
1071           idx   = 5*(*vi++);
1072           x1    = tmp[idx];   x2 = tmp[1+idx];
1073           x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
1074           sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1075           sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1076           sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1077           sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1078           sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1079           v += 25;
1080         }
1081         idc = 5*(*c--);
1082         v   = aa + 25*a->diag[i];
1083         x[idc]   += tmp[idt]   = v[0]*sum1+v[5]*sum2+v[10]*sum3+
1084                                  v[15]*sum4+v[20]*sum5;
1085         x[1+idc] += tmp[1+idt] = v[1]*sum1+v[6]*sum2+v[11]*sum3+
1086                                  v[16]*sum4+v[21]*sum5;
1087         x[2+idc] += tmp[2+idt] = v[2]*sum1+v[7]*sum2+v[12]*sum3+
1088                                  v[17]*sum4+v[22]*sum5;
1089         x[3+idc] += tmp[3+idt] = v[3]*sum1+v[8]*sum2+v[13]*sum3+
1090                                  v[18]*sum4+v[23]*sum5;
1091         x[4+idc] += tmp[4+idt] = v[4]*sum1+v[9]*sum2+v[14]*sum3+
1092                                  v[19]*sum4+v[24]*sum5;
1093       }
1094       break;
1095     default: {
1096       /* forward solve the lower triangular */
1097       PetscMemcpy(tmp,b + bs*(*r++), bs*sizeof(Scalar));
1098       for ( i=1; i<n; i++ ) {
1099         v   = aa + bs2*ai[i];
1100         vi  = aj + ai[i];
1101         nz  = a->diag[i] - ai[i];
1102         sum = tmp + bs*i;
1103         PetscMemcpy(sum,b+bs*(*r++),bs*sizeof(Scalar));
1104         while (nz--) {
1105           LAgemv_("N",&bs,&bs,&_DMOne,v,&bs,tmp+bs*(*vi++),&_One,&_DOne,sum,&_One);
1106           v += bs2;
1107         }
1108       }
1109       /* backward solve the upper triangular */
1110       lsum = a->solve_work + a->n;
1111       for ( i=n-1; i>=0; i-- ){
1112         v   = aa + bs2*(a->diag[i] + 1);
1113         vi  = aj + a->diag[i] + 1;
1114         nz  = ai[i+1] - a->diag[i] - 1;
1115         PetscMemcpy(lsum,tmp+i*bs,bs*sizeof(Scalar));
1116         while (nz--) {
1117           LAgemv_("N",&bs,&bs,&_DMOne,v,&bs,tmp+bs*(*vi++),&_One,&_DOne,lsum,&_One);
1118           v += bs2;
1119         }
1120         LAgemv_("N",&bs,&bs,&_DOne,aa+bs2*a->diag[i],&bs,lsum,&_One,&_DZero,
1121                 tmp+i*bs,&_One);
1122         PetscMemcpy(x + bs*(*c--),tmp+i*bs,bs*sizeof(Scalar));
1123       }
1124     }
1125   }
1126 
1127   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1128   ierr = ISRestoreIndices(iscol,&c); CHKERRQ(ierr);
1129   return 0;
1130 }
1131 
1132 /* ----------------------------------------------------------------*/
1133 
1134 int MatSolve_SeqBAIJ(Mat A,Vec bb, Vec xx)
1135 {
1136   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data;
1137   int         ierr;
1138 
1139   ierr = MatSolveAdd_SeqBAIJ_Private(A,bb,PETSC_NULL,xx); CHKERRQ(ierr);
1140   PLogFlops(2*(a->bs2)*(a->nz) - a->n);
1141   return 0;
1142 }
1143 
1144 /* ----------------------------------------------------------------*/
1145 
1146 int MatSolveAdd_SeqBAIJ(Mat A,Vec bb,Vec yy,Vec xx)
1147 {
1148   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data;
1149   int         ierr;
1150 
1151   ierr = MatSolveAdd_SeqBAIJ_Private(A,bb,yy,xx); CHKERRQ(ierr);
1152   PLogFlops(2*(a->bs2)*(a->nz));
1153   return 0;
1154 }
1155 /* ----------------------------------------------------------- */
1156 static int MatSolveTransAdd_SeqBAIJ_Private(Mat A,Vec bb,Vec yy,Vec xx)
1157 {
1158   Mat_SeqBAIJ *a=(Mat_SeqBAIJ *)A->data;
1159   IS          iscol=a->col,isrow=a->row;
1160   int         *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
1161   int         nz,bs=a->bs,bs2=a->bs2,idx,idt,idc,_One=1,m=a->m;
1162   Scalar      *xa,*ba,*aa=a->a,*sum,_DOne=1.0,_DMOne=-1.0;
1163   Scalar      _DZero=0.0,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5,*y;
1164   register Scalar *x,*b,*lsum,*tmp,*v;
1165 
1166   if (A->factor != FACTOR_LU) SETERRQ(1,"MatSolveAdd_SeqBAIJ_Private:Not for unfactored matrix");
1167 
1168   ierr = VecGetArray(bb,&ba); CHKERRQ(ierr); b = ba;
1169   ierr = VecGetArray(xx,&xa); CHKERRQ(ierr); x = xa;
1170   tmp  = a->solve_work;
1171 
1172   if (yy==PETSC_NULL) PetscMemzero(x,m*sizeof(Scalar)); /* MatSolve() */
1173   else if (xx!=yy){
1174     ierr = VecGetArray(yy,&y); CHKERRQ(ierr);
1175     PetscMemcpy(x,y,m*sizeof(Scalar));
1176     ierr = VecRestoreArray(yy,&y); CHKERRQ(ierr);
1177   }
1178 
1179   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1180   ierr = ISGetIndices(iscol,&c);CHKERRQ(ierr); c = c + (n-1);
1181 
1182   switch (bs) {
1183     case 1:
1184       /* forward solve the lower triangular */
1185       tmp[0] = b[*r++];
1186       for ( i=1; i<n; i++ ) {
1187         v     = aa + ai[i];
1188         vi    = aj + ai[i];
1189         nz    = a->diag[i] - ai[i];
1190         sum1  = b[*r++];
1191         while (nz--) {
1192           sum1 -= (*v++)*tmp[*vi++];
1193         }
1194         tmp[i] = sum1;
1195       }
1196       /* backward solve the upper triangular */
1197       for ( i=n-1; i>=0; i-- ){
1198         v    = aa + a->diag[i] + 1;
1199         vi   = aj + a->diag[i] + 1;
1200         nz   = ai[i+1] - a->diag[i] - 1;
1201         sum1 = tmp[i];
1202         while (nz--) {
1203           sum1 -= (*v++)*tmp[*vi++];
1204         }
1205         x[*c--] += tmp[i] = aa[a->diag[i]]*sum1;
1206       }
1207       break;
1208     case 2:
1209       /* forward solve the lower triangular */
1210       idx    = 2*(*r++);
1211       tmp[0] = b[idx]; tmp[1] = b[1+idx];
1212       for ( i=1; i<n; i++ ) {
1213         v     = aa + 4*ai[i];
1214         vi    = aj + ai[i];
1215         nz    = a->diag[i] - ai[i];
1216         idx   = 2*(*r++);
1217         sum1  = b[idx]; sum2 = b[1+idx];
1218         while (nz--) {
1219           idx   = 2*(*vi++);
1220           x1    = tmp[idx]; x2 = tmp[1+idx];
1221           sum1 -= v[0]*x1 + v[2]*x2;
1222           sum2 -= v[1]*x1 + v[3]*x2;
1223           v += 4;
1224         }
1225         idx = 2*i;
1226         tmp[idx] = sum1; tmp[1+idx] = sum2;
1227       }
1228       /* backward solve the upper triangular */
1229       for ( i=n-1; i>=0; i-- ){
1230         v    = aa + 4*a->diag[i] + 4;
1231         vi   = aj + a->diag[i] + 1;
1232         nz   = ai[i+1] - a->diag[i] - 1;
1233         idt  = 2*i;
1234         sum1 = tmp[idt]; sum2 = tmp[1+idt];
1235         while (nz--) {
1236           idx   = 2*(*vi++);
1237           x1    = tmp[idx]; x2 = tmp[1+idx];
1238           sum1 -= v[0]*x1 + v[2]*x2;
1239           sum2 -= v[1]*x1 + v[3]*x2;
1240           v += 4;
1241         }
1242         idc = 2*(*c--);
1243         v   = aa + 4*a->diag[i];
1244         x[idc]   += tmp[idt]   = v[0]*sum1 + v[2]*sum2;
1245         x[1+idc] += tmp[1+idt] = v[1]*sum1 + v[3]*sum2;
1246       }
1247       break;
1248     case 3:
1249       /* forward solve the lower triangular */
1250       idx    = 3*(*r++);
1251       tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx];
1252       for ( i=1; i<n; i++ ) {
1253         v     = aa + 9*ai[i];
1254         vi    = aj + ai[i];
1255         nz    = a->diag[i] - ai[i];
1256         idx   = 3*(*r++);
1257         sum1  = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx];
1258         while (nz--) {
1259           idx   = 3*(*vi++);
1260           x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1261           sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1262           sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1263           sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1264           v += 9;
1265         }
1266         idx = 3*i;
1267         tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3;
1268       }
1269       /* backward solve the upper triangular */
1270       for ( i=n-1; i>=0; i-- ){
1271         v    = aa + 9*a->diag[i] + 9;
1272         vi   = aj + a->diag[i] + 1;
1273         nz   = ai[i+1] - a->diag[i] - 1;
1274         idt  = 3*i;
1275         sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt];
1276         while (nz--) {
1277           idx   = 3*(*vi++);
1278           x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1279           sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1280           sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1281           sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1282           v += 9;
1283         }
1284         idc = 3*(*c--);
1285         v   = aa + 9*a->diag[i];
1286         x[idc]   += tmp[idt]   = v[0]*sum1 + v[3]*sum2 + v[6]*sum3;
1287         x[1+idc] += tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3;
1288         x[2+idc] += tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3;
1289       }
1290       break;
1291     case 4:
1292       /* forward solve the lower triangular */
1293       idx    = 4*(*r++);
1294       tmp[0] = b[idx];   tmp[1] = b[1+idx];
1295       tmp[2] = b[2+idx]; tmp[3] = b[3+idx];
1296       for ( i=1; i<n; i++ ) {
1297         v     = aa + 16*ai[i];
1298         vi    = aj + ai[i];
1299         nz    = a->diag[i] - ai[i];
1300         idx   = 4*(*r++);
1301         sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1302         while (nz--) {
1303           idx   = 4*(*vi++);
1304           x1    = tmp[idx];x2 = tmp[1+idx];x3 = tmp[2+idx];x4 = tmp[3+idx];
1305           sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
1306           sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
1307           sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
1308           sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
1309           v += 16;
1310         }
1311         idx = 4*i;
1312         tmp[idx]   = sum1;tmp[1+idx] = sum2;
1313         tmp[2+idx] = sum3;tmp[3+idx] = sum4;
1314       }
1315       /* backward solve the upper triangular */
1316       for ( i=n-1; i>=0; i-- ){
1317         v    = aa + 16*a->diag[i] + 16;
1318         vi   = aj + a->diag[i] + 1;
1319         nz   = ai[i+1] - a->diag[i] - 1;
1320         idt  = 4*i;
1321         sum1 = tmp[idt];  sum2 = tmp[1+idt];
1322         sum3 = tmp[2+idt];sum4 = tmp[3+idt];
1323         while (nz--) {
1324           idx   = 4*(*vi++);
1325           x1    = tmp[idx];   x2 = tmp[1+idx];
1326           x3    = tmp[2+idx]; x4 = tmp[3+idx];
1327           sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
1328           sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
1329           sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
1330           sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
1331           v += 16;
1332         }
1333         idc = 4*(*c--);
1334         v   = aa + 16*a->diag[i];
1335         x[idc]   += tmp[idt]   = v[0]*sum1+v[4]*sum2+v[8]*sum3+v[12]*sum4;
1336         x[1+idc] += tmp[1+idt] = v[1]*sum1+v[5]*sum2+v[9]*sum3+v[13]*sum4;
1337         x[2+idc] += tmp[2+idt] = v[2]*sum1+v[6]*sum2+v[10]*sum3+v[14]*sum4;
1338         x[3+idc] += tmp[3+idt] = v[3]*sum1+v[7]*sum2+v[11]*sum3+v[15]*sum4;
1339       }
1340       break;
1341     case 5:
1342       /* forward solve the lower triangular */
1343       idx    = 5*(*r++);
1344       tmp[0] = b[idx];   tmp[1] = b[1+idx];
1345       tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
1346       for ( i=1; i<n; i++ ) {
1347         v     = aa + 25*ai[i];
1348         vi    = aj + ai[i];
1349         nz    = a->diag[i] - ai[i];
1350         idx   = 5*(*r++);
1351         sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1352         sum5  = b[4+idx];
1353         while (nz--) {
1354           idx   = 5*(*vi++);
1355           x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
1356           x4    = tmp[3+idx];x5 = tmp[4+idx];
1357           sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1358           sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1359           sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1360           sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1361           sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1362           v += 25;
1363         }
1364         idx = 5*i;
1365         tmp[idx]   = sum1;tmp[1+idx] = sum2;
1366         tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
1367       }
1368       /* backward solve the upper triangular */
1369       for ( i=n-1; i>=0; i-- ){
1370         v    = aa + 25*a->diag[i] + 25;
1371         vi   = aj + a->diag[i] + 1;
1372         nz   = ai[i+1] - a->diag[i] - 1;
1373         idt  = 5*i;
1374         sum1 = tmp[idt];  sum2 = tmp[1+idt];
1375         sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
1376         while (nz--) {
1377           idx   = 5*(*vi++);
1378           x1    = tmp[idx];   x2 = tmp[1+idx];
1379           x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
1380           sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1381           sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1382           sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1383           sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1384           sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1385           v += 25;
1386         }
1387         idc = 5*(*c--);
1388         v   = aa + 25*a->diag[i];
1389         x[idc]   += tmp[idt]   = v[0]*sum1+v[5]*sum2+v[10]*sum3+
1390                                  v[15]*sum4+v[20]*sum5;
1391         x[1+idc] += tmp[1+idt] = v[1]*sum1+v[6]*sum2+v[11]*sum3+
1392                                  v[16]*sum4+v[21]*sum5;
1393         x[2+idc] += tmp[2+idt] = v[2]*sum1+v[7]*sum2+v[12]*sum3+
1394                                  v[17]*sum4+v[22]*sum5;
1395         x[3+idc] += tmp[3+idt] = v[3]*sum1+v[8]*sum2+v[13]*sum3+
1396                                  v[18]*sum4+v[23]*sum5;
1397         x[4+idc] += tmp[4+idt] = v[4]*sum1+v[9]*sum2+v[14]*sum3+
1398                                  v[19]*sum4+v[24]*sum5;
1399       }
1400       break;
1401     default: {
1402       /* forward solve the lower triangular */
1403       PetscMemcpy(tmp,b + bs*(*r++), bs*sizeof(Scalar));
1404       for ( i=1; i<n; i++ ) {
1405         v   = aa + bs2*ai[i];
1406         vi  = aj + ai[i];
1407         nz  = a->diag[i] - ai[i];
1408         sum = tmp + bs*i;
1409         PetscMemcpy(sum,b+bs*(*r++),bs*sizeof(Scalar));
1410         while (nz--) {
1411           LAgemv_("N",&bs,&bs,&_DMOne,v,&bs,tmp+bs*(*vi++),&_One,&_DOne,sum,&_One);
1412           v += bs2;
1413         }
1414       }
1415       /* backward solve the upper triangular */
1416       lsum = a->solve_work + a->n;
1417       for ( i=n-1; i>=0; i-- ){
1418         v   = aa + bs2*(a->diag[i] + 1);
1419         vi  = aj + a->diag[i] + 1;
1420         nz  = ai[i+1] - a->diag[i] - 1;
1421         PetscMemcpy(lsum,tmp+i*bs,bs*sizeof(Scalar));
1422         while (nz--) {
1423           LAgemv_("N",&bs,&bs,&_DMOne,v,&bs,tmp+bs*(*vi++),&_One,&_DOne,lsum,&_One);
1424           v += bs2;
1425         }
1426         LAgemv_("N",&bs,&bs,&_DOne,aa+bs2*a->diag[i],&bs,lsum,&_One,&_DZero,
1427                 tmp+i*bs,&_One);
1428         PetscMemcpy(x + bs*(*c--),tmp+i*bs,bs*sizeof(Scalar));
1429       }
1430     }
1431   }
1432 
1433   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1434   ierr = ISRestoreIndices(iscol,&c); CHKERRQ(ierr);
1435   return 0;
1436 }
1437 
1438 /* ----------------------------------------------------------------*/
1439 
1440 int MatSolveTrans_SeqBAIJ(Mat A,Vec bb, Vec xx)
1441 {
1442   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data;
1443   int         ierr;
1444 
1445   ierr = MatSolveAdd_SeqBAIJ_Private(A,bb,PETSC_NULL,xx); CHKERRQ(ierr);
1446   PLogFlops(2*(a->bs2)*(a->nz) - a->n);
1447   return 0;
1448 }
1449 
1450 /* ----------------------------------------------------------------*/
1451 
1452 int MatSolveTransAdd_SeqBAIJ(Mat A,Vec bb,Vec yy,Vec xx)
1453 {
1454   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data;
1455   int         ierr;
1456 
1457   ierr = MatSolveAdd_SeqBAIJ_Private(A,bb,yy,xx); CHKERRQ(ierr);
1458   PLogFlops(2*(a->bs2)*(a->nz));
1459   return 0;
1460 }
1461 
1462 /* ----------------------------------------------------------------*/
1463 /*
1464      This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
1465    except that the data structure of Mat_SeqAIJ is slightly different.
1466    Not a good example of code reuse.
1467    */
1468 int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,int levels,
1469                                  Mat *fact)
1470 {
1471   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
1472   IS          isicol;
1473   int         *r,*ic, ierr, prow, n = a->mbs, *ai = a->i, *aj = a->j;
1474   int         *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev;
1475   int         *dloc, idx, row,m,fm, nzf, nzi,len,  realloc = 0;
1476   int         incrlev,nnz,i,bs = a->bs,bs2 = a->bs2;
1477   PetscTruth  col_identity, row_identity;
1478 
1479   if (a->m != a->n) SETERRQ(1,"MatILUFactorSymbolic_SeqBAIJ:Matrix must be square");
1480   if (!isrow) SETERRQ(1,"MatILUFactorSymbolic_SeqBAIJ:Must have row permutation");
1481   if (!iscol) SETERRQ(1,"MatILUFactorSymbolic_SeqBAIJ:Must have column permutation");
1482 
1483   /* special case that simply copies fill pattern */
1484   ISIdentity(isrow,&row_identity); ISIdentity(iscol,&col_identity);
1485   if (levels == 0 && row_identity && col_identity) {
1486     ierr = MatConvertSameType_SeqBAIJ(A,fact,DO_NOT_COPY_VALUES); CHKERRQ(ierr);
1487     (*fact)->factor = FACTOR_LU;
1488     b               = (Mat_SeqBAIJ *) (*fact)->data;
1489     if (!b->diag) {
1490       ierr = MatMarkDiag_SeqBAIJ(*fact); CHKERRQ(ierr);
1491     }
1492     b->row        = isrow;
1493     b->col        = iscol;
1494     b->solve_work = (Scalar *) PetscMalloc((b->m+1+b->bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
1495     return 0;
1496   }
1497 
1498   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
1499   ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr);
1500   ierr = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
1501 
1502   /* get new row pointers */
1503   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
1504   ainew[0] = 0;
1505   /* don't know how many column pointers are needed so estimate */
1506   jmax = (int) (f*ai[n] + 1);
1507   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
1508   /* ajfill is level of fill for each fill entry */
1509   ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajfill);
1510   /* fill is a linked list of nonzeros in active row */
1511   fill = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(fill);
1512   /* im is level for each filled value */
1513   im = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(im);
1514   /* dloc is location of diagonal in factor */
1515   dloc = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(dloc);
1516   dloc[0]  = 0;
1517   for ( prow=0; prow<n; prow++ ) {
1518     /* first copy previous fill into linked list */
1519     nzf     = nz  = ai[r[prow]+1] - ai[r[prow]];
1520     xi      = aj + ai[r[prow]];
1521     fill[n] = n;
1522     while (nz--) {
1523       fm  = n;
1524       idx = ic[*xi++];
1525       do {
1526         m  = fm;
1527         fm = fill[m];
1528       } while (fm < idx);
1529       fill[m]   = idx;
1530       fill[idx] = fm;
1531       im[idx]   = 0;
1532     }
1533     nzi = 0;
1534     row = fill[n];
1535     while ( row < prow ) {
1536       incrlev = im[row] + 1;
1537       nz      = dloc[row];
1538       xi      = ajnew  + ainew[row] + nz;
1539       flev    = ajfill + ainew[row] + nz + 1;
1540       nnz     = ainew[row+1] - ainew[row] - nz - 1;
1541       if (*xi++ != row) {
1542         SETERRQ(1,"MatILUFactorSymbolic_SeqBAIJ:zero pivot");
1543       }
1544       fm      = row;
1545       while (nnz-- > 0) {
1546         idx = *xi++;
1547         if (*flev + incrlev > levels) {
1548           flev++;
1549           continue;
1550         }
1551         do {
1552           m  = fm;
1553           fm = fill[m];
1554         } while (fm < idx);
1555         if (fm != idx) {
1556           im[idx]   = *flev + incrlev;
1557           fill[m]   = idx;
1558           fill[idx] = fm;
1559           fm        = idx;
1560           nzf++;
1561         }
1562         else {
1563           if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
1564         }
1565         flev++;
1566       }
1567       row = fill[row];
1568       nzi++;
1569     }
1570     /* copy new filled row into permanent storage */
1571     ainew[prow+1] = ainew[prow] + nzf;
1572     if (ainew[prow+1] > jmax) {
1573       /* allocate a longer ajnew */
1574       int maxadd;
1575       maxadd = (int) (((f*ai[n]+1)*(n-prow+5))/n);
1576       if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
1577       jmax += maxadd;
1578       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1579       PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int));
1580       PetscFree(ajnew);
1581       ajnew = xi;
1582       /* allocate a longer ajfill */
1583       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1584       PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int));
1585       PetscFree(ajfill);
1586       ajfill = xi;
1587       realloc++;
1588     }
1589     xi          = ajnew + ainew[prow];
1590     flev        = ajfill + ainew[prow];
1591     dloc[prow]  = nzi;
1592     fm          = fill[n];
1593     while (nzf--) {
1594       *xi++   = fm;
1595       *flev++ = im[fm];
1596       fm      = fill[fm];
1597     }
1598   }
1599   PetscFree(ajfill);
1600   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1601   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
1602   ierr = ISDestroy(isicol); CHKERRQ(ierr);
1603   PetscFree(fill); PetscFree(im);
1604 
1605   PLogInfo(A,
1606     "Info:MatILUFactorSymbolic_SeqBAIJ:Realloc %d Fill ratio:given %g needed %g\n",
1607                              realloc,f,((double)ainew[n])/((double)ai[prow]));
1608 
1609   /* put together the new matrix */
1610   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr);
1611   b = (Mat_SeqBAIJ *) (*fact)->data;
1612   PetscFree(b->imax);
1613   b->singlemalloc = 0;
1614   len = bs2*ainew[n]*sizeof(Scalar);
1615   /* the next line frees the default space generated by the Create() */
1616   PetscFree(b->a); PetscFree(b->ilen);
1617   b->a          = (Scalar *) PetscMalloc( len ); CHKPTRQ(b->a);
1618   b->j          = ajnew;
1619   b->i          = ainew;
1620   for ( i=0; i<n; i++ ) dloc[i] += ainew[i];
1621   b->diag       = dloc;
1622   b->ilen       = 0;
1623   b->imax       = 0;
1624   b->row        = isrow;
1625   b->col        = iscol;
1626   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
1627   CHKPTRQ(b->solve_work);
1628   /* In b structure:  Free imax, ilen, old a, old j.
1629      Allocate dloc, solve_work, new a, new j */
1630   PLogObjectMemory(*fact,(ainew[n]-n)*(sizeof(int))+bs2*ainew[n]*sizeof(Scalar));
1631   b->maxnz          = b->nz = ainew[n];
1632   (*fact)->factor   = FACTOR_LU;
1633   return 0;
1634 }
1635 
1636 
1637 
1638 
1639