xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact8.c (revision 2b8d69ca7ea5fe9190df62c1dce3bbd66fce84dd)
1 
2 #include <../src/mat/impls/sbaij/seq/sbaij.h>
3 #include <petsc/private/kernels/blockinvert.h>
4 
5 /*
6       Version for when blocks are 5 by 5 Using natural ordering
7 */
8 #undef __FUNCT__
9 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering"
10 PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
11 {
12   Mat_SeqSBAIJ   *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
13   PetscErrorCode ierr;
14   PetscInt       i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
15   PetscInt       *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili,ipvt[5];
16   MatScalar      *ba = b->a,*aa,*ap,*dk,*uik;
17   MatScalar      *u,*d,*rtmp,*rtmp_ptr,work[25];
18   PetscReal      shift = info->shiftamount;
19   PetscBool      allowzeropivot,zeropivotdetected;
20 
21   PetscFunctionBegin;
22   /* initialization */
23   allowzeropivot = PetscNot(A->erroriffailure);
24   ierr = PetscCalloc1(25*mbs,&rtmp);CHKERRQ(ierr);
25   ierr = PetscMalloc2(mbs,&il,mbs,&jl);CHKERRQ(ierr);
26   for (i=0; i<mbs; i++) {
27     jl[i] = mbs; il[0] = 0;
28   }
29   ierr = PetscMalloc2(25,&dk,25,&uik);CHKERRQ(ierr);
30   ai   = a->i; aj = a->j; aa = a->a;
31 
32   /* for each row k */
33   for (k = 0; k<mbs; k++) {
34 
35     /*initialize k-th row with elements nonzero in row k of A */
36     jmin = ai[k]; jmax = ai[k+1];
37     if (jmin < jmax) {
38       ap = aa + jmin*25;
39       for (j = jmin; j < jmax; j++) {
40         vj       = aj[j];   /* block col. index */
41         rtmp_ptr = rtmp + vj*25;
42         for (i=0; i<25; i++) *rtmp_ptr++ = *ap++;
43       }
44     }
45 
46     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
47     ierr = PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));CHKERRQ(ierr);
48     i    = jl[k]; /* first row to be added to k_th row  */
49 
50     while (i < mbs) {
51       nexti = jl[i]; /* next row to be added to k_th row */
52 
53       /* compute multiplier */
54       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
55 
56       /* uik = -inv(Di)*U_bar(i,k) */
57       d = ba + i*25;
58       u = ba + ili*25;
59 
60       uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]);
61       uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]);
62       uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]);
63       uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]);
64       uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]);
65 
66       uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]);
67       uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]);
68       uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]);
69       uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]);
70       uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]);
71 
72       uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]);
73       uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]);
74       uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]);
75       uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]);
76       uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]);
77 
78       uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]);
79       uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]);
80       uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]);
81       uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]);
82       uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]);
83 
84       uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]);
85       uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]);
86       uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]);
87       uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]);
88       uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]);
89 
90 
91       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
92       dk[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
93       dk[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
94       dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
95       dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
96       dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];
97 
98       dk[5] +=  uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
99       dk[6] +=  uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
100       dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
101       dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
102       dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];
103 
104       dk[10] +=  uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
105       dk[11] +=  uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
106       dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
107       dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
108       dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];
109 
110       dk[15] +=  uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
111       dk[16] +=  uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
112       dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
113       dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
114       dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];
115 
116       dk[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
117       dk[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
118       dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
119       dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
120       dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
121 
122       ierr = PetscLogFlops(125.0*4.0);CHKERRQ(ierr);
123 
124       /* update -U(i,k) */
125       ierr = PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));CHKERRQ(ierr);
126 
127       /* add multiple of row i to k-th row ... */
128       jmin = ili + 1; jmax = bi[i+1];
129       if (jmin < jmax) {
130         for (j=jmin; j<jmax; j++) {
131           /* rtmp += -U(i,k)^T * U_bar(i,j) */
132           rtmp_ptr     = rtmp + bj[j]*25;
133           u            = ba + j*25;
134           rtmp_ptr[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
135           rtmp_ptr[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
136           rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
137           rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
138           rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];
139 
140           rtmp_ptr[5] +=  uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
141           rtmp_ptr[6] +=  uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
142           rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
143           rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
144           rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];
145 
146           rtmp_ptr[10] +=  uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
147           rtmp_ptr[11] +=  uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
148           rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
149           rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
150           rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];
151 
152           rtmp_ptr[15] +=  uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
153           rtmp_ptr[16] +=  uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
154           rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
155           rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
156           rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];
157 
158           rtmp_ptr[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
159           rtmp_ptr[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
160           rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
161           rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
162           rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
163         }
164         ierr = PetscLogFlops(2.0*125.0*(jmax-jmin));CHKERRQ(ierr);
165 
166         /* ... add i to row list for next nonzero entry */
167         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
168         j     = bj[jmin];
169         jl[i] = jl[j]; jl[j] = i; /* update jl */
170       }
171       i = nexti;
172     }
173 
174     /* save nonzero entries in k-th row of U ... */
175 
176     /* invert diagonal block */
177     d    = ba+k*25;
178     ierr = PetscMemcpy(d,dk,25*sizeof(MatScalar));CHKERRQ(ierr);
179     ierr = PetscKernel_A_gets_inverse_A_5(d,ipvt,work,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
180     if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
181 
182     jmin = bi[k]; jmax = bi[k+1];
183     if (jmin < jmax) {
184       for (j=jmin; j<jmax; j++) {
185         vj       = bj[j];      /* block col. index of U */
186         u        = ba + j*25;
187         rtmp_ptr = rtmp + vj*25;
188         for (k1=0; k1<25; k1++) {
189           *u++        = *rtmp_ptr;
190           *rtmp_ptr++ = 0.0;
191         }
192       }
193 
194       /* ... add k to row list for first nonzero entry in k-th row */
195       il[k] = jmin;
196       i     = bj[jmin];
197       jl[k] = jl[i]; jl[i] = k;
198     }
199   }
200 
201   ierr = PetscFree(rtmp);CHKERRQ(ierr);
202   ierr = PetscFree2(il,jl);CHKERRQ(ierr);
203   ierr = PetscFree2(dk,uik);CHKERRQ(ierr);
204 
205   C->ops->solve          = MatSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
206   C->ops->solvetranspose = MatSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
207   C->ops->forwardsolve   = MatForwardSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
208   C->ops->backwardsolve  = MatBackwardSolve_SeqSBAIJ_5_NaturalOrdering_inplace;
209   C->assembled           = PETSC_TRUE;
210   C->preallocated        = PETSC_TRUE;
211 
212   ierr = PetscLogFlops(1.3333*125*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
213   PetscFunctionReturn(0);
214 }
215