/* Version for when blocks are 4 by 4 */
PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4(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 i,j,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
MatScalar *ba = b->a,*aa,*ap,*dk,*uik;
MatScalar *u,*diag,*rtmp,*rtmp_ptr;
PetscBool pivotinblocks = b->pivotinblocks;
PetscReal shift = info->shiftamount;
PetscBool allowzeropivot,zeropivotdetected=PETSC_FALSE;
PetscFunctionBegin;
/* initialization */
allowzeropivot = PetscNot(A->erroriffailure);
ierr = PetscCalloc1(16*mbs,&rtmp);CHKERRQ(ierr);
ierr = PetscMalloc2(mbs,&il,mbs,&jl);CHKERRQ(ierr);
il[0] = 0;
for (i=0; i<mbs; i++) jl[i] = mbs;
ierr = PetscMalloc2(16,&dk,16,&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 = PetscMalloc1(16*ai[mbs],&aa);CHKERRQ(ierr);
ierr = PetscMemcpy(aa,a->a,16*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
ierr = PetscMalloc1(ai[mbs],&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<16; k1++) {
dk[k1] = aa[k*16+k1];
aa[k*16+k1] = aa[j*16+k1];
aa[j*16+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*16; /* ptr to the beginning of j-th block of aa */
for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
for (k=0; k<4; k++) { /* j-th block of aa <- dk^T */
for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*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*16;
for (j = jmin; j < jmax; j++) {
vj = perm_ptr[aj[j]]; /* block col. index */
rtmp_ptr = rtmp + vj*16;
for (i=0; i<16; i++) *rtmp_ptr++ = *ap++;
}
}
/* modify k-th row by adding in those rows i with U(i,k) != 0 */
ierr = PetscMemcpy(dk,rtmp+k*16,16*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*16;
u = ba + ili*16;
uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]);
uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]);
uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]);
uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]);
uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]);
uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]);
uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]);
uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]);
uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]);
uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]);
uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]);
uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]);
uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]);
uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]);
uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]);
uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]);
/* 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] + uik[3]*u[3];
dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
ierr = PetscLogFlops(64.0*4.0);CHKERRQ(ierr);
/* update -U(i,k) */
ierr = PetscMemcpy(ba+ili*16,uik,16*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]*16;
u = ba + j*16;
rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
}
ierr = PetscLogFlops(2.0*64.0*(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*16;
ierr = PetscMemcpy(diag,dk,16*sizeof(MatScalar));CHKERRQ(ierr);
if (pivotinblocks) {
ierr = PetscKernel_A_gets_inverse_A_4(diag,shift, allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
} else {
ierr = PetscKernel_A_gets_inverse_A_4_nopivot(diag);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*16;
rtmp_ptr = rtmp + vj*16;
for (k1=0; k1<16; 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_4_inplace;
C->ops->solvetranspose = MatSolve_SeqSBAIJ_4_inplace;
C->assembled = PETSC_TRUE;
C->preallocated = PETSC_TRUE;
ierr = PetscLogFlops(1.3333*64*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
PetscFunctionReturn(0);
}
PetscErrorCode MatCholeskyFactorNumeric_SeqSBAIJ_4_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;
PetscBool pivotinblocks = b->pivotinblocks;
PetscReal shift = info->shiftamount;
PetscBool allowzeropivot,zeropivotdetected=PETSC_FALSE;
PetscFunctionBegin;
/* initialization */
allowzeropivot = PetscNot(A->erroriffailure);
ierr = PetscCalloc1(16*mbs,&rtmp);CHKERRQ(ierr);
ierr = PetscMalloc2(mbs,&il,mbs,&jl);CHKERRQ(ierr);
for (i=0; i<mbs; i++) {
jl[i] = mbs; il[0] = 0;
}
ierr = PetscMalloc2(16,&dk,16,&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*16;
for (j = jmin; j < jmax; j++) {
vj = aj[j]; /* block col. index */
rtmp_ptr = rtmp + vj*16;
for (i=0; i<16; i++) *rtmp_ptr++ = *ap++;
}
}
/* modify k-th row by adding in those rows i with U(i,k) != 0 */
ierr = PetscMemcpy(dk,rtmp+k*16,16*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*16;
u = ba + ili*16;
uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]);
uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]);
uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]);
uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]);
uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]);
uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]);
uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]);
uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]);
uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]);
uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]);
uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]);
uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]);
uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]);
uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]);
uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]);
uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]);
/* 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] + uik[3]*u[3];
dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
ierr = PetscLogFlops(64.0*4.0);CHKERRQ(ierr);
/* update -U(i,k) */
ierr = PetscMemcpy(ba+ili*16,uik,16*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]*16;
u = ba + j*16;
rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
}
ierr = PetscLogFlops(2.0*64.0*(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*16;
ierr = PetscMemcpy(diag,dk,16*sizeof(MatScalar));CHKERRQ(ierr);
if (pivotinblocks) {
ierr = PetscKernel_A_gets_inverse_A_4(diag,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
} else {
ierr = PetscKernel_A_gets_inverse_A_4_nopivot(diag);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*16;
rtmp_ptr = rtmp + vj*16;
for (k1=0; k1<16; 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_4_NaturalOrdering_inplace;
C->ops->solvetranspose = MatSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_4_NaturalOrdering_inplace;
C->assembled = PETSC_TRUE;
C->preallocated = PETSC_TRUE;
ierr = PetscLogFlops(1.3333*64*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);
}
/*
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_6_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,*d,*w,*wp,u0,u1,u2,u3,u4,u5,u6,u7,u8,u9,u10,u11,u12;
MatScalar u13,u14,u15,u16,u17,u18,u19,u20,u21,u22,u23,u24,u25,u26,u27;
MatScalar u28,u29,u30,u31,u32,u33,u34,u35;
MatScalar d0,d1,d2,d3,d4,d5,d6,d7,d8,d9,d10,d11,d12;
MatScalar d13,d14,d15,d16,d17,d18,d19,d20,d21,d22,d23,d24,d25,d26,d27;
MatScalar d28,d29,d30,d31,d32,d33,d34,d35;
MatScalar m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12;
MatScalar m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25,m26,m27;
MatScalar m28,m29,m30,m31,m32,m33,m34,m35;
PetscReal shift = info->shiftamount;
PetscBool allowzeropivot,zeropivotdetected;
PetscFunctionBegin;
/* initialization */
allowzeropivot = PetscNot(A->erroriffailure);
ierr = PetscCalloc1(36*mbs,&w);CHKERRQ(ierr);
ierr = PetscMalloc2(mbs,&il,mbs,&jl);CHKERRQ(ierr);
for (i=0; i<mbs; i++) {
jl[i] = mbs; il[0] = 0;
}
ierr = PetscMalloc2(36,&dk,36,&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*36;
for (j = jmin; j < jmax; j++) {
vj = aj[j]; /* block col. index */
wp = w + vj*36;
for (i=0; i<36; i++) *wp++ = *ap++;
}
}
/* modify k-th row by adding in those rows i with U(i,k) != 0 */
ierr = PetscMemcpy(dk,w+k*36,36*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) */
d = ba + i*36;
u = ba + ili*36;
u0 = u[0]; u1 = u[1]; u2 = u[2]; u3 = u[3]; u4 = u[4]; u5 = u[5]; u6 = u[6];
u7 = u[7]; u8 = u[8]; u9 = u[9]; u10 = u[10]; u11 = u[11]; u12 = u[12]; u13 = u[13];
u14 = u[14]; u15 = u[15]; u16 = u[16]; u17 = u[17]; u18 = u[18]; u19 = u[19]; u20 = u[20];
u21 = u[21]; u22 = u[22]; u23 = u[23]; u24 = u[24]; u25 = u[25]; u26 = u[26]; u27 = u[27];
u28 = u[28]; u29 = u[29]; u30 = u[30]; u31 = u[31]; u32 = u[32]; u33 = u[33]; u34 = u[34];
u35 = u[35];
d0 = d[0]; d1 = d[1]; d2 = d[2]; d3 = d[3];
d4 = d[4]; d5 = d[5]; d6 = d[6]; d7 = d[7];
d8 = d[8]; d9 = d[9]; d10 = d[10]; d11 = d[11];
d12 = d[12]; d13 = d[13]; d14 = d[14]; d15 = d[15];
d16 = d[16]; d17 = d[17]; d18 = d[18]; d19 = d[19];
d20 = d[20]; d21 = d[21]; d22 = d[22]; d23 = d[23];
d24 = d[24]; d25 = d[25]; d26 = d[26]; d27 = d[27];
d28 = d[28]; d29 = d[29]; d30 = d[30]; d31 = d[31];
d32 = d[32]; d33 = d[33]; d34 = d[34]; d35 = d[35];
m0 = uik[0] = -(d0*u0 + d6*u1 + d12*u2 + d18*u3 + d24*u4 + d30*u5);
m1 = uik[1] = -(d1*u0 + d7*u1 + d13*u2 + d19*u3 + d25*u4 + d31*u5);
m2 = uik[2] = -(d2*u0 + d8*u1 + d14*u2 + d20*u3 + d26*u4 + d32*u5);
m3 = uik[3] = -(d3*u0 + d9*u1 + d15*u2 + d21*u3 + d27*u4 + d33*u5);
m4 = uik[4] = -(d4*u0+ d10*u1 + d16*u2 + d22*u3 + d28*u4 + d34*u5);
m5 = uik[5] = -(d5*u0+ d11*u1 + d17*u2 + d23*u3 + d29*u4 + d35*u5);
m6 = uik[6] = -(d0*u6 + d6*u7 + d12*u8 + d18*u9 + d24*u10 + d30*u11);
m7 = uik[7] = -(d1*u6 + d7*u7 + d13*u8 + d19*u9 + d25*u10 + d31*u11);
m8 = uik[8] = -(d2*u6 + d8*u7 + d14*u8 + d20*u9 + d26*u10 + d32*u11);
m9 = uik[9] = -(d3*u6 + d9*u7 + d15*u8 + d21*u9 + d27*u10 + d33*u11);
m10 = uik[10]= -(d4*u6+ d10*u7 + d16*u8 + d22*u9 + d28*u10 + d34*u11);
m11 = uik[11]= -(d5*u6+ d11*u7 + d17*u8 + d23*u9 + d29*u10 + d35*u11);
m12 = uik[12] = -(d0*u12 + d6*u13 + d12*u14 + d18*u15 + d24*u16 + d30*u17);
m13 = uik[13] = -(d1*u12 + d7*u13 + d13*u14 + d19*u15 + d25*u16 + d31*u17);
m14 = uik[14] = -(d2*u12 + d8*u13 + d14*u14 + d20*u15 + d26*u16 + d32*u17);
m15 = uik[15] = -(d3*u12 + d9*u13 + d15*u14 + d21*u15 + d27*u16 + d33*u17);
m16 = uik[16] = -(d4*u12+ d10*u13 + d16*u14 + d22*u15 + d28*u16 + d34*u17);
m17 = uik[17] = -(d5*u12+ d11*u13 + d17*u14 + d23*u15 + d29*u16 + d35*u17);
m18 = uik[18] = -(d0*u18 + d6*u19 + d12*u20 + d18*u21 + d24*u22 + d30*u23);
m19 = uik[19] = -(d1*u18 + d7*u19 + d13*u20 + d19*u21 + d25*u22 + d31*u23);
m20 = uik[20] = -(d2*u18 + d8*u19 + d14*u20 + d20*u21 + d26*u22 + d32*u23);
m21 = uik[21] = -(d3*u18 + d9*u19 + d15*u20 + d21*u21 + d27*u22 + d33*u23);
m22 = uik[22] = -(d4*u18+ d10*u19 + d16*u20 + d22*u21 + d28*u22 + d34*u23);
m23 = uik[23] = -(d5*u18+ d11*u19 + d17*u20 + d23*u21 + d29*u22 + d35*u23);
m24 = uik[24] = -(d0*u24 + d6*u25 + d12*u26 + d18*u27 + d24*u28 + d30*u29);
m25 = uik[25] = -(d1*u24 + d7*u25 + d13*u26 + d19*u27 + d25*u28 + d31*u29);
m26 = uik[26] = -(d2*u24 + d8*u25 + d14*u26 + d20*u27 + d26*u28 + d32*u29);
m27 = uik[27] = -(d3*u24 + d9*u25 + d15*u26 + d21*u27 + d27*u28 + d33*u29);
m28 = uik[28] = -(d4*u24+ d10*u25 + d16*u26 + d22*u27 + d28*u28 + d34*u29);
m29 = uik[29] = -(d5*u24+ d11*u25 + d17*u26 + d23*u27 + d29*u28 + d35*u29);
m30 = uik[30] = -(d0*u30 + d6*u31 + d12*u32 + d18*u33 + d24*u34 + d30*u35);
m31 = uik[31] = -(d1*u30 + d7*u31 + d13*u32 + d19*u33 + d25*u34 + d31*u35);
m32 = uik[32] = -(d2*u30 + d8*u31 + d14*u32 + d20*u33 + d26*u34 + d32*u35);
m33 = uik[33] = -(d3*u30 + d9*u31 + d15*u32 + d21*u33 + d27*u34 + d33*u35);
m34 = uik[34] = -(d4*u30+ d10*u31 + d16*u32 + d22*u33 + d28*u34 + d34*u35);
m35 = uik[35] = -(d5*u30+ d11*u31 + d17*u32 + d23*u33 + d29*u34 + d35*u35);
/* update D(k) += -U(i,k)^T * U_bar(i,k) */
dk[0] += m0*u0 + m1*u1 + m2*u2 + m3*u3 + m4*u4 + m5*u5;
dk[1] += m6*u0 + m7*u1 + m8*u2 + m9*u3+ m10*u4+ m11*u5;
dk[2] += m12*u0+ m13*u1+ m14*u2+ m15*u3+ m16*u4+ m17*u5;
dk[3] += m18*u0+ m19*u1+ m20*u2+ m21*u3+ m22*u4+ m23*u5;
dk[4] += m24*u0+ m25*u1+ m26*u2+ m27*u3+ m28*u4+ m29*u5;
dk[5] += m30*u0+ m31*u1+ m32*u2+ m33*u3+ m34*u4+ m35*u5;
dk[6] += m0*u6 + m1*u7 + m2*u8 + m3*u9 + m4*u10 + m5*u11;
dk[7] += m6*u6 + m7*u7 + m8*u8 + m9*u9+ m10*u10+ m11*u11;
dk[8] += m12*u6+ m13*u7+ m14*u8+ m15*u9+ m16*u10+ m17*u11;
dk[9] += m18*u6+ m19*u7+ m20*u8+ m21*u9+ m22*u10+ m23*u11;
dk[10]+= m24*u6+ m25*u7+ m26*u8+ m27*u9+ m28*u10+ m29*u11;
dk[11]+= m30*u6+ m31*u7+ m32*u8+ m33*u9+ m34*u10+ m35*u11;
dk[12]+= m0*u12 + m1*u13 + m2*u14 + m3*u15 + m4*u16 + m5*u17;
dk[13]+= m6*u12 + m7*u13 + m8*u14 + m9*u15+ m10*u16+ m11*u17;
dk[14]+= m12*u12+ m13*u13+ m14*u14+ m15*u15+ m16*u16+ m17*u17;
dk[15]+= m18*u12+ m19*u13+ m20*u14+ m21*u15+ m22*u16+ m23*u17;
dk[16]+= m24*u12+ m25*u13+ m26*u14+ m27*u15+ m28*u16+ m29*u17;
dk[17]+= m30*u12+ m31*u13+ m32*u14+ m33*u15+ m34*u16+ m35*u17;
dk[18]+= m0*u18 + m1*u19 + m2*u20 + m3*u21 + m4*u22 + m5*u23;
dk[19]+= m6*u18 + m7*u19 + m8*u20 + m9*u21+ m10*u22+ m11*u23;
dk[20]+= m12*u18+ m13*u19+ m14*u20+ m15*u21+ m16*u22+ m17*u23;
dk[21]+= m18*u18+ m19*u19+ m20*u20+ m21*u21+ m22*u22+ m23*u23;
dk[22]+= m24*u18+ m25*u19+ m26*u20+ m27*u21+ m28*u22+ m29*u23;
dk[23]+= m30*u18+ m31*u19+ m32*u20+ m33*u21+ m34*u22+ m35*u23;
dk[24]+= m0*u24 + m1*u25 + m2*u26 + m3*u27 + m4*u28 + m5*u29;
dk[25]+= m6*u24 + m7*u25 + m8*u26 + m9*u27+ m10*u28+ m11*u29;
dk[26]+= m12*u24+ m13*u25+ m14*u26+ m15*u27+ m16*u28+ m17*u29;
dk[27]+= m18*u24+ m19*u25+ m20*u26+ m21*u27+ m22*u28+ m23*u29;
dk[28]+= m24*u24+ m25*u25+ m26*u26+ m27*u27+ m28*u28+ m29*u29;
dk[29]+= m30*u24+ m31*u25+ m32*u26+ m33*u27+ m34*u28+ m35*u29;
dk[30]+= m0*u30 + m1*u31 + m2*u32 + m3*u33 + m4*u34 + m5*u35;
dk[31]+= m6*u30 + m7*u31 + m8*u32 + m9*u33+ m10*u34+ m11*u35;
dk[32]+= m12*u30+ m13*u31+ m14*u32+ m15*u33+ m16*u34+ m17*u35;
dk[33]+= m18*u30+ m19*u31+ m20*u32+ m21*u33+ m22*u34+ m23*u35;
dk[34]+= m24*u30+ m25*u31+ m26*u32+ m27*u33+ m28*u34+ m29*u35;
dk[35]+= m30*u30+ m31*u31+ m32*u32+ m33*u33+ m34*u34+ m35*u35;
ierr = PetscLogFlops(216.0*4.0);CHKERRQ(ierr);
/* update -U(i,k) */
ierr = PetscMemcpy(ba+ili*36,uik,36*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++) {
/* w += -U(i,k)^T * U_bar(i,j) */
wp = w + bj[j]*36;
u = ba + j*36;
u0 = u[0]; u1 = u[1]; u2 = u[2]; u3 = u[3]; u4 = u[4]; u5 = u[5]; u6 = u[6];
u7 = u[7]; u8 = u[8]; u9 = u[9]; u10 = u[10]; u11 = u[11]; u12 = u[12]; u13 = u[13];
u14 = u[14]; u15 = u[15]; u16 = u[16]; u17 = u[17]; u18 = u[18]; u19 = u[19]; u20 = u[20];
u21 = u[21]; u22 = u[22]; u23 = u[23]; u24 = u[24]; u25 = u[25]; u26 = u[26]; u27 = u[27];
u28 = u[28]; u29 = u[29]; u30 = u[30]; u31 = u[31]; u32 = u[32]; u33 = u[33]; u34 = u[34];
u35 = u[35];
wp[0] += m0*u0 + m1*u1 + m2*u2 + m3*u3 + m4*u4 + m5*u5;
wp[1] += m6*u0 + m7*u1 + m8*u2 + m9*u3+ m10*u4+ m11*u5;
wp[2] += m12*u0+ m13*u1+ m14*u2+ m15*u3+ m16*u4+ m17*u5;
wp[3] += m18*u0+ m19*u1+ m20*u2+ m21*u3+ m22*u4+ m23*u5;
wp[4] += m24*u0+ m25*u1+ m26*u2+ m27*u3+ m28*u4+ m29*u5;
wp[5] += m30*u0+ m31*u1+ m32*u2+ m33*u3+ m34*u4+ m35*u5;
wp[6] += m0*u6 + m1*u7 + m2*u8 + m3*u9 + m4*u10 + m5*u11;
wp[7] += m6*u6 + m7*u7 + m8*u8 + m9*u9+ m10*u10+ m11*u11;
wp[8] += m12*u6+ m13*u7+ m14*u8+ m15*u9+ m16*u10+ m17*u11;
wp[9] += m18*u6+ m19*u7+ m20*u8+ m21*u9+ m22*u10+ m23*u11;
wp[10]+= m24*u6+ m25*u7+ m26*u8+ m27*u9+ m28*u10+ m29*u11;
wp[11]+= m30*u6+ m31*u7+ m32*u8+ m33*u9+ m34*u10+ m35*u11;
wp[12]+= m0*u12 + m1*u13 + m2*u14 + m3*u15 + m4*u16 + m5*u17;
wp[13]+= m6*u12 + m7*u13 + m8*u14 + m9*u15+ m10*u16+ m11*u17;
wp[14]+= m12*u12+ m13*u13+ m14*u14+ m15*u15+ m16*u16+ m17*u17;
wp[15]+= m18*u12+ m19*u13+ m20*u14+ m21*u15+ m22*u16+ m23*u17;
wp[16]+= m24*u12+ m25*u13+ m26*u14+ m27*u15+ m28*u16+ m29*u17;
wp[17]+= m30*u12+ m31*u13+ m32*u14+ m33*u15+ m34*u16+ m35*u17;
wp[18]+= m0*u18 + m1*u19 + m2*u20 + m3*u21 + m4*u22 + m5*u23;
wp[19]+= m6*u18 + m7*u19 + m8*u20 + m9*u21+ m10*u22+ m11*u23;
wp[20]+= m12*u18+ m13*u19+ m14*u20+ m15*u21+ m16*u22+ m17*u23;
wp[21]+= m18*u18+ m19*u19+ m20*u20+ m21*u21+ m22*u22+ m23*u23;
wp[22]+= m24*u18+ m25*u19+ m26*u20+ m27*u21+ m28*u22+ m29*u23;
wp[23]+= m30*u18+ m31*u19+ m32*u20+ m33*u21+ m34*u22+ m35*u23;
wp[24]+= m0*u24 + m1*u25 + m2*u26 + m3*u27 + m4*u28 + m5*u29;
wp[25]+= m6*u24 + m7*u25 + m8*u26 + m9*u27+ m10*u28+ m11*u29;
wp[26]+= m12*u24+ m13*u25+ m14*u26+ m15*u27+ m16*u28+ m17*u29;
wp[27]+= m18*u24+ m19*u25+ m20*u26+ m21*u27+ m22*u28+ m23*u29;
wp[28]+= m24*u24+ m25*u25+ m26*u26+ m27*u27+ m28*u28+ m29*u29;
wp[29]+= m30*u24+ m31*u25+ m32*u26+ m33*u27+ m34*u28+ m35*u29;
wp[30]+= m0*u30 + m1*u31 + m2*u32 + m3*u33 + m4*u34 + m5*u35;
wp[31]+= m6*u30 + m7*u31 + m8*u32 + m9*u33+ m10*u34+ m11*u35;
wp[32]+= m12*u30+ m13*u31+ m14*u32+ m15*u33+ m16*u34+ m17*u35;
wp[33]+= m18*u30+ m19*u31+ m20*u32+ m21*u33+ m22*u34+ m23*u35;
wp[34]+= m24*u30+ m25*u31+ m26*u32+ m27*u33+ m28*u34+ m29*u35;
wp[35]+= m30*u30+ m31*u31+ m32*u32+ m33*u33+ m34*u34+ m35*u35;
}
ierr = PetscLogFlops(2.0*216.0*(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 */
d = ba+k*36;
ierr = PetscMemcpy(d,dk,36*sizeof(MatScalar));CHKERRQ(ierr);
ierr = PetscKernel_A_gets_inverse_A_6(d,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
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*36;
wp = w + vj*36;
for (k1=0; k1<36; k1++) {
*u++ = *wp;
*wp++ = 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(w);CHKERRQ(ierr);
ierr = PetscFree2(il,jl);CHKERRQ(ierr);
ierr = PetscFree2(dk,uik);CHKERRQ(ierr);
C->ops->solve = MatSolve_SeqSBAIJ_6_NaturalOrdering_inplace;
C->ops->solvetranspose = MatSolve_SeqSBAIJ_6_NaturalOrdering_inplace;
C->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_6_NaturalOrdering_inplace;
C->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_6_NaturalOrdering_inplace;
C->assembled = PETSC_TRUE;
C->preallocated = PETSC_TRUE;
ierr = PetscLogFlops(1.3333*216*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
PetscFunctionReturn(0);
}
