void updateQRZ(UpperTriangularMatrix& X, UpperTriangularMatrix& U)
{
REPORT
Tracer et("updateQRZ(3)");
int s = X.Ncols();
if (s != U.Ncols())
Throw(ProgramException("Incompatible dimensions",X,U));
if (s == 0) return;
Real* xi0 = X.data(); Real* u = U.data();
for (int i=1; i<=s; ++i)
{
Real r = *u; Real sum = 0.0;
{
Real* xi=xi0; int k=i; int l=s;
while(k--) { sum += square(*xi); xi+= --l;}
}
sum = sqrt(sum + square(r));
if (sum == 0.0) { REPORT X.column(i) = 0.0; *u = 0.0; }
else
{
Real frs = fabs(r) + sum;
Real a0 = sqrt(frs / sum); Real alpha = a0 / frs;
if (r <= 0) { REPORT *u = sum; alpha = -alpha; }
else { REPORT *u = -sum; }
{
Real* xj0=xi0; int k=i; int l=s;
while(k--) { *xj0 *= alpha; --l; xj0 += l;}
}
Real* xj0=xi0; Real* uj=u;
for (int j=i+1; j<=s; ++j)
{
Real sum = 0.0; ++xj0; ++uj;
Real* xi=xi0; Real* xj=xj0; int k=i; int l=s;
while(k--) { sum += *xi * *xj; --l; xi += l; xj += l; }
sum += a0 * *uj;
xi=xi0; xj=xj0; k=i; l=s;
while(k--) { *xj -= sum * *xi; --l; xi += l; xj += l; }
*uj -= sum * a0;
}
}
++xi0; u += s-i+1;
}
}
void updateQRZ(const UpperTriangularMatrix& X, Matrix& MX, Matrix& MU)
{
REPORT
Tracer et("updateQRZ(4)");
int s = X.Ncols();
if (s != MX.Nrows())
Throw(ProgramException("Incompatible dimensions",X,MX));
if (s != MU.Nrows())
Throw(ProgramException("Incompatible dimensions",X,MU));
int t = MX.Ncols();
if (t != MU.Ncols())
Throw(ProgramException("Incompatible dimensions",MX,MU));
if (s == 0) return;
const Real* xi0 = X.data(); Real* mx = MX.data(); Real* muj = MU.data();
for (int i=1; i<=s; ++i)
{
Real sum = 0.0;
{
const Real* xi=xi0; int k=i; int l=s;
while(k--) { sum += square(*xi); xi+= --l;}
}
Real a0 = sqrt(2.0 - sum); Real* mxj0 = mx;
for (int j=1; j<=t; ++j)
{
Real sum = 0.0;
const Real* xi=xi0; Real* mxj=mxj0; int k=i; int l=s;
while(--k) { sum += *xi * *mxj; --l; xi += l; mxj += t; }
sum += *xi * *mxj; // last line of loop
sum += a0 * *muj;
xi=xi0; mxj=mxj0; k=i; l=s;
while(--k) { *mxj -= sum * *xi; --l; xi += l; mxj += t; }
*mxj -= sum * *xi; // last line of loop
*muj -= sum * a0; ++mxj0; ++muj;
}
++xi0;
}
}