PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat C,Mat A,const MatFactorInfo *info)
{
Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
IS perm = b->row;
PetscErrorCode ierr;
const PetscInt *ai,*aj,*perm_ptr,mbs=a->mbs,*bi=b->i,*bj=b->j;
PetscInt *a2anew,i,j,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
MatScalar *ba = b->a,*aa,*ap,*dk,*uik;
MatScalar *u,*diag,*rtmp,*rtmp_ptr;
PetscReal shift = info->shiftamount;
PetscFunctionBegin;
/* initialization */
ierr = PetscMalloc(9*mbs*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr);
ierr = PetscMalloc2(mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr);
for (i=0; i<mbs; i++) {
jl[i] = mbs; il[0] = 0;
}
ierr = PetscMalloc2(9,MatScalar,&dk,9,MatScalar,&uik);CHKERRQ(ierr);
ierr = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
/* check permutation */
if (!a->permute){
ai = a->i; aj = a->j; aa = a->a;
} else {
ai = a->inew; aj = a->jnew;
ierr = PetscMalloc(9*ai[mbs]*sizeof(MatScalar),&aa);CHKERRQ(ierr);
ierr = PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
ierr = PetscMalloc(ai[mbs]*sizeof(PetscInt),&a2anew);CHKERRQ(ierr);
ierr = PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(PetscInt));CHKERRQ(ierr);
for (i=0; i<mbs; i++){
jmin = ai[i]; jmax = ai[i+1];
for (j=jmin; j<jmax; j++){
while (a2anew[j] != j){
k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
for (k1=0; k1<9; k1++){
dk[k1] = aa[k*9+k1];
aa[k*9+k1] = aa[j*9+k1];
aa[j*9+k1] = dk[k1];
}
}
/* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
if (i > aj[j]){
/* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
ap = aa + j*9; /* ptr to the beginning of j-th block of aa */
for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
for (k=0; k<3; k++){ /* j-th block of aa <- dk^T */
for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1];
}
}
}
}
ierr = PetscFree(a2anew);CHKERRQ(ierr);
}
/* for each row k */
for (k = 0; k<mbs; k++){
/*initialize k-th row with elements nonzero in row perm(k) of A */
jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
if (jmin < jmax) {
ap = aa + jmin*9;
for (j = jmin; j < jmax; j++){
vj = perm_ptr[aj[j]]; /* block col. index */
rtmp_ptr = rtmp + vj*9;
for (i=0; i<9; i++) *rtmp_ptr++ = *ap++;
}
}
/* modify k-th row by adding in those rows i with U(i,k) != 0 */
ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr);
i = jl[k]; /* first row to be added to k_th row */
while (i < mbs){
nexti = jl[i]; /* next row to be added to k_th row */
/* compute multiplier */
ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
/* uik = -inv(Di)*U_bar(i,k) */
diag = ba + i*9;
u = ba + ili*9;
uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);
uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);
uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);
/* update D(k) += -U(i,k)^T * U_bar(i,k) */
dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
ierr = PetscLogFlops(27.0*4.0);CHKERRQ(ierr);
/* update -U(i,k) */
ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr);
/* add multiple of row i to k-th row ... */
jmin = ili + 1; jmax = bi[i+1];
if (jmin < jmax){
for (j=jmin; j<jmax; j++) {
/* rtmp += -U(i,k)^T * U_bar(i,j) */
rtmp_ptr = rtmp + bj[j]*9;
u = ba + j*9;
rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
}
ierr = PetscLogFlops(2.0*27.0*(jmax-jmin));CHKERRQ(ierr);
/* ... add i to row list for next nonzero entry */
il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
j = bj[jmin];
jl[i] = jl[j]; jl[j] = i; /* update jl */
}
i = nexti;
}
/* save nonzero entries in k-th row of U ... */
/* invert diagonal block */
diag = ba+k*9;
ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr);
ierr = PetscKernel_A_gets_inverse_A_3(diag,shift);CHKERRQ(ierr);
jmin = bi[k]; jmax = bi[k+1];
if (jmin < jmax) {
for (j=jmin; j<jmax; j++){
vj = bj[j]; /* block col. index of U */
u = ba + j*9;
rtmp_ptr = rtmp + vj*9;
for (k1=0; k1<9; k1++){
*u++ = *rtmp_ptr;
*rtmp_ptr++ = 0.0;
}
}
/* ... add k to row list for first nonzero entry in k-th row */
il[k] = jmin;
i = bj[jmin];
jl[k] = jl[i]; jl[i] = k;
}
}
ierr = PetscFree(rtmp);CHKERRQ(ierr);
ierr = PetscFree2(il,jl);CHKERRQ(ierr);
ierr = PetscFree2(dk,uik);CHKERRQ(ierr);
if (a->permute){
ierr = PetscFree(aa);CHKERRQ(ierr);
}
ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
C->ops->solve = MatSolve_SeqSBAIJ_3_inplace;
C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_inplace;
C->assembled = PETSC_TRUE;
C->preallocated = PETSC_TRUE;
ierr = PetscLogFlops(1.3333*27*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
PetscFunctionReturn(0);
}
/*
MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering -
copied from MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace()
*/
PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
{
Mat C =B;
Mat_SeqBAIJ *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
PetscErrorCode ierr;
PetscInt i,j,k,nz,nzL,row;
const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
MatScalar *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
PetscInt flg;
PetscReal shift = info->shiftamount;
PetscBool allowzeropivot,zeropivotdetected;
PetscFunctionBegin;
allowzeropivot = PetscNot(A->erroriffailure);
/* generate work space needed by the factorization */
ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr);
ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
for (i=0; i<n; i++) {
/* zero rtmp */
/* L part */
nz = bi[i+1] - bi[i];
bjtmp = bj + bi[i];
for (j=0; j<nz; j++) {
ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
}
/* U part */
nz = bdiag[i] - bdiag[i+1];
bjtmp = bj + bdiag[i+1] + 1;
for (j=0; j<nz; j++) {
ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
}
/* load in initial (unfactored row) */
nz = ai[i+1] - ai[i];
ajtmp = aj + ai[i];
v = aa + bs2*ai[i];
for (j=0; j<nz; j++) {
ierr = PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
}
/* elimination */
bjtmp = bj + bi[i];
nzL = bi[i+1] - bi[i];
for (k=0; k<nzL; k++) {
row = bjtmp[k];
pc = rtmp + bs2*row;
for (flg=0,j=0; j<bs2; j++) {
if (pc[j]!=0.0) {
flg = 1;
break;
}
}
if (flg) {
pv = b->a + bs2*bdiag[row];
/* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
ierr = PetscKernel_A_gets_A_times_B_3(pc,pv,mwork);CHKERRQ(ierr);
pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
pv = b->a + bs2*(bdiag[row+1]+1);
nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
for (j=0; j<nz; j++) {
/* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
/* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
v = rtmp + bs2*pj[j];
ierr = PetscKernel_A_gets_A_minus_B_times_C_3(v,pc,pv);CHKERRQ(ierr);
pv += bs2;
}
ierr = PetscLogFlops(54*nz+45);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
}
}
/* finished row so stick it into b->a */
/* L part */
pv = b->a + bs2*bi[i];
pj = b->j + bi[i];
nz = bi[i+1] - bi[i];
for (j=0; j<nz; j++) {
ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
}
/* Mark diagonal and invert diagonal for simplier triangular solves */
pv = b->a + bs2*bdiag[i];
pj = b->j + bdiag[i];
ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
ierr = PetscKernel_A_gets_inverse_A_3(pv,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
if (zeropivotdetected) B->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
/* U part */
pv = b->a + bs2*(bdiag[i+1]+1);
pj = b->j + bdiag[i+1]+1;
nz = bdiag[i] - bdiag[i+1] - 1;
for (j=0; j<nz; j++) {
ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
}
}
ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
C->ops->solve = MatSolve_SeqBAIJ_3_NaturalOrdering;
C->ops->forwardsolve = MatForwardSolve_SeqBAIJ_3_NaturalOrdering;
C->ops->backwardsolve = MatBackwardSolve_SeqBAIJ_3_NaturalOrdering;
C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering;
C->assembled = PETSC_TRUE;
ierr = PetscLogFlops(1.333333333333*3*3*3*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
PetscFunctionReturn(0);
}
PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
{
Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ*)C->data;
PetscErrorCode ierr;
PetscInt i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
PetscInt *ai,*aj,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
MatScalar *ba = b->a,*aa,*ap,*dk,*uik;
MatScalar *u,*diag,*rtmp,*rtmp_ptr;
PetscReal shift = info->shiftamount;
PetscFunctionBegin;
/* initialization */
ierr = PetscMalloc(9*mbs*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr);
ierr = PetscMalloc2(mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr);
for (i=0; i<mbs; i++) {
jl[i] = mbs; il[0] = 0;
}
ierr = PetscMalloc2(9,MatScalar,&dk,9,MatScalar,&uik);CHKERRQ(ierr);
ai = a->i; aj = a->j; aa = a->a;
/* for each row k */
for (k = 0; k<mbs; k++) {
/*initialize k-th row with elements nonzero in row k of A */
jmin = ai[k]; jmax = ai[k+1];
if (jmin < jmax) {
ap = aa + jmin*9;
for (j = jmin; j < jmax; j++) {
vj = aj[j]; /* block col. index */
rtmp_ptr = rtmp + vj*9;
for (i=0; i<9; i++) *rtmp_ptr++ = *ap++;
}
}
/* modify k-th row by adding in those rows i with U(i,k) != 0 */
ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr);
i = jl[k]; /* first row to be added to k_th row */
while (i < mbs) {
nexti = jl[i]; /* next row to be added to k_th row */
/* compute multiplier */
ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
/* uik = -inv(Di)*U_bar(i,k) */
diag = ba + i*9;
u = ba + ili*9;
uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);
uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);
uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);
/* update D(k) += -U(i,k)^T * U_bar(i,k) */
dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
ierr = PetscLogFlops(27.0*4.0);CHKERRQ(ierr);
/* update -U(i,k) */
ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr);
/* add multiple of row i to k-th row ... */
jmin = ili + 1; jmax = bi[i+1];
if (jmin < jmax) {
for (j=jmin; j<jmax; j++) {
/* rtmp += -U(i,k)^T * U_bar(i,j) */
rtmp_ptr = rtmp + bj[j]*9;
u = ba + j*9;
rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
}
ierr = PetscLogFlops(2.0*27.0*(jmax-jmin));CHKERRQ(ierr);
/* ... add i to row list for next nonzero entry */
il[i] = jmin; /* update il(i) in column k+1, ... mbs-1 */
j = bj[jmin];
jl[i] = jl[j]; jl[j] = i; /* update jl */
}
i = nexti;
}
/* save nonzero entries in k-th row of U ... */
/* invert diagonal block */
diag = ba+k*9;
ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr);
ierr = PetscKernel_A_gets_inverse_A_3(diag,shift);CHKERRQ(ierr);
jmin = bi[k]; jmax = bi[k+1];
if (jmin < jmax) {
for (j=jmin; j<jmax; j++) {
vj = bj[j]; /* block col. index of U */
u = ba + j*9;
rtmp_ptr = rtmp + vj*9;
for (k1=0; k1<9; k1++) {
*u++ = *rtmp_ptr;
*rtmp_ptr++ = 0.0;
}
}
/* ... add k to row list for first nonzero entry in k-th row */
il[k] = jmin;
i = bj[jmin];
jl[k] = jl[i]; jl[i] = k;
}
}
ierr = PetscFree(rtmp);CHKERRQ(ierr);
ierr = PetscFree2(il,jl);CHKERRQ(ierr);
ierr = PetscFree2(dk,uik);CHKERRQ(ierr);
C->ops->solve = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
C->ops->solvetranspose = MatSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_3_NaturalOrdering_inplace;
C->assembled = PETSC_TRUE;
C->preallocated = PETSC_TRUE;
ierr = PetscLogFlops(1.3333*27*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
PetscFunctionReturn(0);
}
PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
{
Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
PetscErrorCode ierr;
PetscInt i,j,n = a->mbs,*bi = b->i,*bj = b->j;
PetscInt *ajtmpold,*ajtmp,nz,row;
PetscInt *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
MatScalar *pv,*v,*rtmp,*pc,*w,*x;
MatScalar p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
MatScalar p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
MatScalar *ba = b->a,*aa = a->a;
PetscReal shift = info->shiftamount;
PetscBool allowzeropivot,zeropivotdetected;
PetscFunctionBegin;
ierr = PetscMalloc1(9*(n+1),&rtmp);CHKERRQ(ierr);
allowzeropivot = PetscNot(A->erroriffailure);
for (i=0; i<n; i++) {
nz = bi[i+1] - bi[i];
ajtmp = bj + bi[i];
for (j=0; j<nz; j++) {
x = rtmp+9*ajtmp[j];
x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
}
/* load in initial (unfactored row) */
nz = ai[i+1] - ai[i];
ajtmpold = aj + ai[i];
v = aa + 9*ai[i];
for (j=0; j<nz; j++) {
x = rtmp+9*ajtmpold[j];
x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
v += 9;
}
row = *ajtmp++;
while (row < i) {
pc = rtmp + 9*row;
p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
pv = ba + 9*diag_offset[row];
pj = bj + diag_offset[row] + 1;
x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
nz = bi[row+1] - diag_offset[row] - 1;
pv += 9;
for (j=0; j<nz; j++) {
x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
x = rtmp + 9*pj[j];
x[0] -= m1*x1 + m4*x2 + m7*x3;
x[1] -= m2*x1 + m5*x2 + m8*x3;
x[2] -= m3*x1 + m6*x2 + m9*x3;
x[3] -= m1*x4 + m4*x5 + m7*x6;
x[4] -= m2*x4 + m5*x5 + m8*x6;
x[5] -= m3*x4 + m6*x5 + m9*x6;
x[6] -= m1*x7 + m4*x8 + m7*x9;
x[7] -= m2*x7 + m5*x8 + m8*x9;
x[8] -= m3*x7 + m6*x8 + m9*x9;
pv += 9;
}
ierr = PetscLogFlops(54.0*nz+36.0);CHKERRQ(ierr);
}
row = *ajtmp++;
}
/* finished row so stick it into b->a */
pv = ba + 9*bi[i];
pj = bj + bi[i];
nz = bi[i+1] - bi[i];
for (j=0; j<nz; j++) {
x = rtmp+9*pj[j];
pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
pv += 9;
}
/* invert diagonal block */
w = ba + 9*diag_offset[i];
ierr = PetscKernel_A_gets_inverse_A_3(w,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
}
ierr = PetscFree(rtmp);CHKERRQ(ierr);
C->ops->solve = MatSolve_SeqBAIJ_3_NaturalOrdering_inplace;
C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace;
C->assembled = PETSC_TRUE;
ierr = PetscLogFlops(1.333333333333*3*3*3*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
PetscFunctionReturn(0);
}
