xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact7.c (revision 2b8d69ca7ea5fe9190df62c1dce3bbd66fce84dd)
1 
2 #include <../src/mat/impls/sbaij/seq/sbaij.h>
3 #include <petsc/private/kernels/blockinvert.h>
4 
5 /* Version for when blocks are 5 by 5  */
6 #undef __FUNCT__
7 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqSBAIJ_5"
8 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat C,Mat A,const MatFactorInfo *info)
9 {
10   Mat_SeqSBAIJ   *a   = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
11   IS             perm = b->row;
12   PetscErrorCode ierr;
13   const PetscInt *ai,*aj,*perm_ptr,mbs=a->mbs,*bi=b->i,*bj=b->j;
14   PetscInt       i,j,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili,ipvt[5];
15   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
16   MatScalar      *u,*d,*rtmp,*rtmp_ptr,work[25];
17   PetscReal      shift = info->shiftamount;
18   PetscBool      allowzeropivot,zeropivotdetected;
19 
20   PetscFunctionBegin;
21   /* initialization */
22   allowzeropivot = PetscNot(A->erroriffailure);
23   ierr = PetscCalloc1(25*mbs,&rtmp);CHKERRQ(ierr);
24   ierr = PetscMalloc2(mbs,&il,mbs,&jl);CHKERRQ(ierr);
25   for (i=0; i<mbs; i++) {
26     jl[i] = mbs; il[0] = 0;
27   }
28   ierr = PetscMalloc2(25,&dk,25,&uik);CHKERRQ(ierr);
29   ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
30 
31   /* check permutation */
32   if (!a->permute) {
33     ai = a->i; aj = a->j; aa = a->a;
34   } else {
35     ai   = a->inew; aj = a->jnew;
36     ierr = PetscMalloc1(25*ai[mbs],&aa);CHKERRQ(ierr);
37     ierr = PetscMemcpy(aa,a->a,25*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
38     ierr = PetscMalloc1(ai[mbs],&a2anew);CHKERRQ(ierr);
39     ierr = PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));CHKERRQ(ierr);
40 
41     for (i=0; i<mbs; i++) {
42       jmin = ai[i]; jmax = ai[i+1];
43       for (j=jmin; j<jmax; j++) {
44         while (a2anew[j] != j) {
45           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
46           for (k1=0; k1<25; k1++) {
47             dk[k1]      = aa[k*25+k1];
48             aa[k*25+k1] = aa[j*25+k1];
49             aa[j*25+k1] = dk[k1];
50           }
51         }
52         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
53         if (i > aj[j]) {
54           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
55           ap = aa + j*25;                     /* ptr to the beginning of j-th block of aa */
56           for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
57           for (k=0; k<5; k++) {               /* j-th block of aa <- dk^T */
58             for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*k1];
59           }
60         }
61       }
62     }
63     ierr = PetscFree(a2anew);CHKERRQ(ierr);
64   }
65 
66   /* for each row k */
67   for (k = 0; k<mbs; k++) {
68 
69     /*initialize k-th row with elements nonzero in row perm(k) of A */
70     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
71     if (jmin < jmax) {
72       ap = aa + jmin*25;
73       for (j = jmin; j < jmax; j++) {
74         vj       = perm_ptr[aj[j]];   /* block col. index */
75         rtmp_ptr = rtmp + vj*25;
76         for (i=0; i<25; i++) *rtmp_ptr++ = *ap++;
77       }
78     }
79 
80     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
81     ierr = PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));CHKERRQ(ierr);
82     i    = jl[k]; /* first row to be added to k_th row  */
83 
84     while (i < mbs) {
85       nexti = jl[i]; /* next row to be added to k_th row */
86 
87       /* compute multiplier */
88       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
89 
90       /* uik = -inv(Di)*U_bar(i,k) */
91       d = ba + i*25;
92       u = ba + ili*25;
93 
94       uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]);
95       uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]);
96       uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]);
97       uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]);
98       uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]);
99 
100       uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]);
101       uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]);
102       uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]);
103       uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]);
104       uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]);
105 
106       uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]);
107       uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]);
108       uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]);
109       uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]);
110       uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]);
111 
112       uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]);
113       uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]);
114       uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]);
115       uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]);
116       uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]);
117 
118       uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]);
119       uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]);
120       uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]);
121       uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]);
122       uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]);
123 
124 
125       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
126       dk[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
127       dk[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
128       dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
129       dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
130       dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];
131 
132       dk[5] +=  uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
133       dk[6] +=  uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
134       dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
135       dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
136       dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];
137 
138       dk[10] +=  uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
139       dk[11] +=  uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
140       dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
141       dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
142       dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];
143 
144       dk[15] +=  uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
145       dk[16] +=  uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
146       dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
147       dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
148       dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];
149 
150       dk[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
151       dk[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
152       dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
153       dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
154       dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
155 
156       ierr = PetscLogFlops(125.0*4.0);CHKERRQ(ierr);
157 
158       /* update -U(i,k) */
159       ierr = PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));CHKERRQ(ierr);
160 
161       /* add multiple of row i to k-th row ... */
162       jmin = ili + 1; jmax = bi[i+1];
163       if (jmin < jmax) {
164         for (j=jmin; j<jmax; j++) {
165           /* rtmp += -U(i,k)^T * U_bar(i,j) */
166           rtmp_ptr     = rtmp + bj[j]*25;
167           u            = ba + j*25;
168           rtmp_ptr[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
169           rtmp_ptr[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
170           rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
171           rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
172           rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];
173 
174           rtmp_ptr[5] +=  uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
175           rtmp_ptr[6] +=  uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
176           rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
177           rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
178           rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];
179 
180           rtmp_ptr[10] +=  uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
181           rtmp_ptr[11] +=  uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
182           rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
183           rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
184           rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];
185 
186           rtmp_ptr[15] +=  uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
187           rtmp_ptr[16] +=  uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
188           rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
189           rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
190           rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];
191 
192           rtmp_ptr[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
193           rtmp_ptr[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
194           rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
195           rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
196           rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
197         }
198         ierr = PetscLogFlops(2.0*125.0*(jmax-jmin));CHKERRQ(ierr);
199 
200         /* ... add i to row list for next nonzero entry */
201         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
202         j     = bj[jmin];
203         jl[i] = jl[j]; jl[j] = i; /* update jl */
204       }
205       i = nexti;
206     }
207 
208     /* save nonzero entries in k-th row of U ... */
209 
210     /* invert diagonal block */
211     d    = ba+k*25;
212     ierr = PetscMemcpy(d,dk,25*sizeof(MatScalar));CHKERRQ(ierr);
213     ierr = PetscKernel_A_gets_inverse_A_5(d,ipvt,work,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
214     if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
215 
216     jmin = bi[k]; jmax = bi[k+1];
217     if (jmin < jmax) {
218       for (j=jmin; j<jmax; j++) {
219         vj       = bj[j];      /* block col. index of U */
220         u        = ba + j*25;
221         rtmp_ptr = rtmp + vj*25;
222         for (k1=0; k1<25; k1++) {
223           *u++        = *rtmp_ptr;
224           *rtmp_ptr++ = 0.0;
225         }
226       }
227 
228       /* ... add k to row list for first nonzero entry in k-th row */
229       il[k] = jmin;
230       i     = bj[jmin];
231       jl[k] = jl[i]; jl[i] = k;
232     }
233   }
234 
235   ierr = PetscFree(rtmp);CHKERRQ(ierr);
236   ierr = PetscFree2(il,jl);CHKERRQ(ierr);
237   ierr = PetscFree2(dk,uik);CHKERRQ(ierr);
238   if (a->permute) {
239     ierr = PetscFree(aa);CHKERRQ(ierr);
240   }
241 
242   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
243 
244   C->ops->solve          = MatSolve_SeqSBAIJ_5_inplace;
245   C->ops->solvetranspose = MatSolve_SeqSBAIJ_5_inplace;
246   C->assembled           = PETSC_TRUE;
247   C->preallocated        = PETSC_TRUE;
248 
249   ierr = PetscLogFlops(1.3333*125*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
250   PetscFunctionReturn(0);
251 }
252