Actual source code: sbaijfact4.c
2: #include <../src/mat/impls/sbaij/seq/sbaij.h>
3: #include <petsc/private/kernels/blockinvert.h>
5: /*
6: Version for when blocks are 3 by 3 Using natural ordering
7: */
8: PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
9: {
10: Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
11: PetscInt i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
12: PetscInt *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
13: MatScalar *ba = b->a,*aa,*ap,*dk,*uik;
14: MatScalar *u,*diag,*rtmp,*rtmp_ptr;
15: PetscReal shift = info->shiftamount;
16: PetscBool allowzeropivot,zeropivotdetected;
18: /* initialization */
19: allowzeropivot = PetscNot(A->erroriffailure);
20: PetscCalloc1(9*mbs,&rtmp);
21: PetscMalloc2(mbs,&il,mbs,&jl);
22: il[0] = 0;
23: for (i=0; i<mbs; i++) jl[i] = mbs;
25: PetscMalloc2(9,&dk,9,&uik);
26: ai = a->i; aj = a->j; aa = a->a;
28: /* for each row k */
29: for (k = 0; k<mbs; k++) {
31: /*initialize k-th row with elements nonzero in row k of A */
32: jmin = ai[k]; jmax = ai[k+1];
33: if (jmin < jmax) {
34: ap = aa + jmin*9;
35: for (j = jmin; j < jmax; j++) {
36: vj = aj[j]; /* block col. index */
37: rtmp_ptr = rtmp + vj*9;
38: for (i=0; i<9; i++) *rtmp_ptr++ = *ap++;
39: }
40: }
42: /* modify k-th row by adding in those rows i with U(i,k) != 0 */
43: PetscArraycpy(dk,rtmp+k*9,9);
44: i = jl[k]; /* first row to be added to k_th row */
46: while (i < mbs) {
47: nexti = jl[i]; /* next row to be added to k_th row */
49: /* compute multiplier */
50: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
52: /* uik = -inv(Di)*U_bar(i,k) */
53: diag = ba + i*9;
54: u = ba + ili*9;
56: uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
57: uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
58: uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);
60: uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
61: uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
62: uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);
64: uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
65: uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
66: uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);
68: /* update D(k) += -U(i,k)^T * U_bar(i,k) */
69: dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
70: dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
71: dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
73: dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
74: dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
75: dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
77: dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
78: dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
79: dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
81: PetscLogFlops(27.0*4.0);
83: /* update -U(i,k) */
84: PetscArraycpy(ba+ili*9,uik,9);
86: /* add multiple of row i to k-th row ... */
87: jmin = ili + 1; jmax = bi[i+1];
88: if (jmin < jmax) {
89: for (j=jmin; j<jmax; j++) {
90: /* rtmp += -U(i,k)^T * U_bar(i,j) */
91: rtmp_ptr = rtmp + bj[j]*9;
92: u = ba + j*9;
93: rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
94: rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
95: rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
97: rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
98: rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
99: rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
101: rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
102: rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
103: rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
104: }
105: PetscLogFlops(2.0*27.0*(jmax-jmin));
107: /* ... add i to row list for next nonzero entry */
108: il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
109: j = bj[jmin];
110: jl[i] = jl[j]; jl[j] = i; /* update jl */
111: }
112: i = nexti;
113: }
115: /* save nonzero entries in k-th row of U ... */
117: /* invert diagonal block */
118: diag = ba+k*9;
119: PetscArraycpy(diag,dk,9);
120: PetscKernel_A_gets_inverse_A_3(diag,shift,allowzeropivot,&zeropivotdetected);
121: if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
123: jmin = bi[k]; jmax = bi[k+1];
124: if (jmin < jmax) {
125: for (j=jmin; j<jmax; j++) {
126: vj = bj[j]; /* block col. index of U */
127: u = ba + j*9;
128: rtmp_ptr = rtmp + vj*9;
129: for (k1=0; k1<9; k1++) {
130: *u++ = *rtmp_ptr;
131: *rtmp_ptr++ = 0.0;
132: }
133: }
135: /* ... add k to row list for first nonzero entry in k-th row */
136: il[k] = jmin;
137: i = bj[jmin];
138: jl[k] = jl[i]; jl[i] = k;
139: }
140: }
142: PetscFree(rtmp);
143: PetscFree2(il,jl);
144: PetscFree2(dk,uik);
146: C->ops->solve = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
147: C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
148: C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
149: C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
151: C->assembled = PETSC_TRUE;
152: C->preallocated = PETSC_TRUE;
154: PetscLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
155: return 0;
156: }