void dFactorLDLT (dReal *A, dReal *d, int n, int nskip1)
{
int i,j;
dReal sum,*ell,*dee,dd,p1,p2,q1,q2,Z11,m11,Z21,m21,Z22,m22;
if (n < 1) return;
for (i=0; i<=n-2; i += 2) {
/* solve L*(D*l)=a, l is scaled elements in 2 x i block at A(i,0) */
dSolveL1_2 (A,A+i*nskip1,i,nskip1);
/* scale the elements in a 2 x i block at A(i,0), and also */
/* compute Z = the outer product matrix that we'll need. */
Z11 = 0;
Z21 = 0;
Z22 = 0;
ell = A+i*nskip1;
dee = d;
for (j=i-6; j >= 0; j -= 6) {
p1 = ell[0];
p2 = ell[nskip1];
dd = dee[0];
q1 = p1*dd;
q2 = p2*dd;
ell[0] = q1;
ell[nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
p1 = ell[1];
p2 = ell[1+nskip1];
dd = dee[1];
q1 = p1*dd;
q2 = p2*dd;
ell[1] = q1;
ell[1+nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
p1 = ell[2];
p2 = ell[2+nskip1];
dd = dee[2];
q1 = p1*dd;
q2 = p2*dd;
ell[2] = q1;
ell[2+nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
p1 = ell[3];
p2 = ell[3+nskip1];
dd = dee[3];
q1 = p1*dd;
q2 = p2*dd;
ell[3] = q1;
ell[3+nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
p1 = ell[4];
p2 = ell[4+nskip1];
dd = dee[4];
q1 = p1*dd;
q2 = p2*dd;
ell[4] = q1;
ell[4+nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
p1 = ell[5];
p2 = ell[5+nskip1];
dd = dee[5];
q1 = p1*dd;
q2 = p2*dd;
ell[5] = q1;
ell[5+nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
ell += 6;
dee += 6;
}
/* compute left-over iterations */
j += 6;
for (; j > 0; j--) {
p1 = ell[0];
p2 = ell[nskip1];
dd = dee[0];
q1 = p1*dd;
q2 = p2*dd;
ell[0] = q1;
ell[nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
ell++;
dee++;
}
/* solve for diagonal 2 x 2 block at A(i,i) */
Z11 = ell[0] - Z11;
Z21 = ell[nskip1] - Z21;
Z22 = ell[1+nskip1] - Z22;
dee = d + i;
/* factorize 2 x 2 block Z,dee */
/* factorize row 1 */
dee[0] = dRecip(Z11);
/* factorize row 2 */
sum = 0;
q1 = Z21;
q2 = q1 * dee[0];
Z21 = q2;
sum += q1*q2;
dee[1] = dRecip(Z22 - sum);
/* done factorizing 2 x 2 block */
ell[nskip1] = Z21;
}
/* compute the (less than 2) rows at the bottom */
switch (n-i) {
case 0:
break;
case 1:
dSolveL1_1 (A,A+i*nskip1,i,nskip1);
/* scale the elements in a 1 x i block at A(i,0), and also */
/* compute Z = the outer product matrix that we'll need. */
Z11 = 0;
ell = A+i*nskip1;
dee = d;
for (j=i-6; j >= 0; j -= 6) {
p1 = ell[0];
dd = dee[0];
q1 = p1*dd;
ell[0] = q1;
m11 = p1*q1;
Z11 += m11;
p1 = ell[1];
dd = dee[1];
q1 = p1*dd;
ell[1] = q1;
m11 = p1*q1;
Z11 += m11;
p1 = ell[2];
dd = dee[2];
q1 = p1*dd;
ell[2] = q1;
m11 = p1*q1;
Z11 += m11;
p1 = ell[3];
dd = dee[3];
q1 = p1*dd;
ell[3] = q1;
m11 = p1*q1;
Z11 += m11;
p1 = ell[4];
dd = dee[4];
q1 = p1*dd;
ell[4] = q1;
m11 = p1*q1;
Z11 += m11;
p1 = ell[5];
dd = dee[5];
q1 = p1*dd;
ell[5] = q1;
m11 = p1*q1;
Z11 += m11;
ell += 6;
dee += 6;
}
/* compute left-over iterations */
j += 6;
for (; j > 0; j--) {
p1 = ell[0];
dd = dee[0];
q1 = p1*dd;
ell[0] = q1;
m11 = p1*q1;
Z11 += m11;
ell++;
dee++;
}
/* solve for diagonal 1 x 1 block at A(i,i) */
Z11 = ell[0] - Z11;
dee = d + i;
/* factorize 1 x 1 block Z,dee */
/* factorize row 1 */
dee[0] = dRecip(Z11);
/* done factorizing 1 x 1 block */
break;
default: *((char*)0)=0; /* this should never happen! */
}
}
void _dFactorLDLT (dReal *A, dReal *d, int n, int nskip1)
{
int i,j;
dReal sum,*ell,*dee,dd,p1,p2,q1,q2,Z11,m11,Z21,m21,Z22,m22;
if (n < 1) return;
for (i=0; i<=n-2; i += 2) {
/* solve L*(D*l)=a, l is scaled elements in 2 x i block at A(i,0) */
dSolveL1_2 (A,A+i*nskip1,i,nskip1);
/* scale the elements in a 2 x i block at A(i,0), and also */
/* compute Z = the outer product matrix that we'll need. */
Z11 = 0;
Z21 = 0;
Z22 = 0;
ell = A+i*nskip1;
dee = d;
#pragma kaapi loop \
reduction(reduce_sum:Z11, reduce_sum:Z21, reduce_sum:Z22)
for (j=i-6; j >= 0; j -= 6, ell += 6, dee += 6) {
dReal _Z11 = 0;
dReal _Z21 = 0;
dReal _Z22 = 0;
p1 = ell[0];
p2 = ell[nskip1];
dd = dee[0];
q1 = p1*dd;
q2 = p2*dd;
ell[0] = q1;
ell[nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
p1 = ell[1];
p2 = ell[1+nskip1];
dd = dee[1];
q1 = p1*dd;
q2 = p2*dd;
ell[1] = q1;
ell[1+nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
p1 = ell[2];
p2 = ell[2+nskip1];
dd = dee[2];
q1 = p1*dd;
q2 = p2*dd;
ell[2] = q1;
ell[2+nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
p1 = ell[3];
p2 = ell[3+nskip1];
dd = dee[3];
q1 = p1*dd;
q2 = p2*dd;
ell[3] = q1;
ell[3+nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
p1 = ell[4];
p2 = ell[4+nskip1];
dd = dee[4];
q1 = p1*dd;
q2 = p2*dd;
ell[4] = q1;
ell[4+nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
p1 = ell[5];
p2 = ell[5+nskip1];
dd = dee[5];
q1 = p1*dd;
q2 = p2*dd;
ell[5] = q1;
ell[5+nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
}
/* xkaapi does not yet update affine variables */
fixme_skip:
if ((i - 6) >= 0)
{
static const int step = 6;
const int range_size = (i - 6 + 1) - 0;
int niter = range_size / step;
if (range_size % step) niter += 1;
j = (i - 6) - niter * 6;
ell = (A + i * nskip1) + niter * 6;
dee = d + niter * 6;
}
else
{
j = i - 6;
}
/* compute left-over iterations */
j += 6;
for (; j > 0; j--) {
p1 = ell[0];
p2 = ell[nskip1];
dd = dee[0];
q1 = p1*dd;
q2 = p2*dd;
ell[0] = q1;
ell[nskip1] = q2;
m11 = p1*q1;
m21 = p2*q1;
m22 = p2*q2;
Z11 += m11;
Z21 += m21;
Z22 += m22;
ell++;
dee++;
}
/* solve for diagonal 2 x 2 block at A(i,i) */
Z11 = ell[0] - Z11;
Z21 = ell[nskip1] - Z21;
Z22 = ell[1+nskip1] - Z22;
dee = d + i;
/* factorize 2 x 2 block Z,dee */
/* factorize row 1 */
dee[0] = dRecip(Z11);
/* factorize row 2 */
sum = 0;
q1 = Z21;
q2 = q1 * dee[0];
Z21 = q2;
sum += q1*q2;
dee[1] = dRecip(Z22 - sum);
/* done factorizing 2 x 2 block */
ell[nskip1] = Z21;
}
/* compute the (less than 2) rows at the bottom */
switch (n-i) {
case 0:
break;
case 1:
dSolveL1_1 (A,A+i*nskip1,i,nskip1);
/* scale the elements in a 1 x i block at A(i,0), and also */
/* compute Z = the outer product matrix that we'll need. */
Z11 = 0;
ell = A+i*nskip1;
dee = d;
for (j=i-6; j >= 0; j -= 6) {
p1 = ell[0];
dd = dee[0];
q1 = p1*dd;
ell[0] = q1;
m11 = p1*q1;
Z11 += m11;
p1 = ell[1];
dd = dee[1];
q1 = p1*dd;
ell[1] = q1;
m11 = p1*q1;
Z11 += m11;
p1 = ell[2];
dd = dee[2];
q1 = p1*dd;
ell[2] = q1;
m11 = p1*q1;
Z11 += m11;
p1 = ell[3];
dd = dee[3];
q1 = p1*dd;
ell[3] = q1;
m11 = p1*q1;
Z11 += m11;
p1 = ell[4];
dd = dee[4];
q1 = p1*dd;
ell[4] = q1;
m11 = p1*q1;
Z11 += m11;
p1 = ell[5];
dd = dee[5];
q1 = p1*dd;
ell[5] = q1;
m11 = p1*q1;
Z11 += m11;
ell += 6;
dee += 6;
}
/* compute left-over iterations */
j += 6;
for (; j > 0; j--) {
p1 = ell[0];
dd = dee[0];
q1 = p1*dd;
ell[0] = q1;
m11 = p1*q1;
Z11 += m11;
ell++;
dee++;
}
/* solve for diagonal 1 x 1 block at A(i,i) */
Z11 = ell[0] - Z11;
dee = d + i;
/* factorize 1 x 1 block Z,dee */
/* factorize row 1 */
dee[0] = dRecip(Z11);
/* done factorizing 1 x 1 block */
break;
default: *((char*)0)=0; /* this should never happen! */
}
}
