void QRZT(Matrix& X, LowerTriangularMatrix& L)
{
REPORT
Tracer et("QRZT(1)");
int n = X.Ncols(); int s = X.Nrows(); L.resize(s);
if (n == 0 || s == 0) { L = 0.0; return; }
Real* xi = X.Store(); int k;
for (int i=0; i<s; i++)
{
Real sum = 0.0;
Real* xi0=xi; k=n; while(k--) { sum += square(*xi++); }
sum = sqrt(sum);
if (sum == 0.0)
{
REPORT
k=n; while(k--) { *xi0++ = 0.0; }
for (int j=i; j<s; j++) L.element(j,i) = 0.0;
}
else
{
L.element(i,i) = sum;
Real* xj0=xi0; k=n; while(k--) { *xj0++ /= sum; }
for (int j=i+1; j<s; j++)
{
sum=0.0;
xi=xi0; Real* xj=xj0; k=n; while(k--) { sum += *xi++ * *xj++; }
xi=xi0; k=n; while(k--) { *xj0++ -= sum * *xi++; }
L.element(j,i) = sum;
}
}
}
}
void QRZT(Matrix& X, LowerTriangularMatrix& L)
{
REPORT
Tracer et("QZT(1)");
int n = X.Ncols(); int s = X.Nrows(); L.ReSize(s);
Real* xi = X.Store(); int k;
for (int i=0; i<s; i++)
{
Real sum = 0.0;
Real* xi0=xi; k=n; while(k--) { sum += square(*xi++); }
sum = sqrt(sum);
L.element(i,i) = sum;
if (sum==0.0) Throw(SingularException(L));
Real* xj0=xi0; k=n; while(k--) { *xj0++ /= sum; }
for (int j=i+1; j<s; j++)
{
sum=0.0;
xi=xi0; Real* xj=xj0; k=n; while(k--) { sum += *xi++ * *xj++; }
xi=xi0; k=n; while(k--) { *xj0++ -= sum * *xi++; }
L.element(j,i) = sum;
}
}
}
void updateQRZT(Matrix& X, LowerTriangularMatrix& L)
{
REPORT
Tracer et("updateQRZT");
int n = X.Ncols(); int s = X.Nrows();
if (s != L.Nrows())
Throw(ProgramException("Incompatible dimensions",X,L));
if (n == 0 || s == 0) return;
Real* xi = X.Store(); int k;
for (int i=0; i<s; i++)
{
Real r = L.element(i,i);
Real sum = 0.0;
Real* xi0=xi; k=n; while(k--) { sum += square(*xi++); }
sum = sqrt(sum + square(r));
if (sum == 0.0)
{
REPORT
k=n; while(k--) { *xi0++ = 0.0; }
for (int j=i; j<s; j++) L.element(j,i) = 0.0;
}
else
{
Real frs = fabs(r) + sum;
Real a0 = sqrt(frs / sum); Real alpha = a0 / frs;
if (r <= 0) { REPORT L.element(i,i) = sum; alpha = -alpha; }
else { REPORT L.element(i,i) = -sum; }
Real* xj0=xi0; k=n; while(k--) { *xj0++ *= alpha; }
for (int j=i+1; j<s; j++)
{
sum = 0.0;
xi=xi0; Real* xj=xj0; k=n; while(k--) { sum += *xi++ * *xj++; }
sum += a0 * L.element(j,i);
xi=xi0; k=n; while(k--) { *xj0++ -= sum * *xi++; }
L.element(j,i) -= sum * a0;
}
}
}
}
