void QRZ(Matrix& X, UpperTriangularMatrix& U)
{
REPORT
Tracer et("QRZ(1)");
int n = X.Nrows(); int s = X.Ncols(); U.ReSize(s); U = 0.0;
Real* xi0 = X.Store(); Real* u0 = U.Store(); Real* u;
int j, k; int J = s; int i = s;
while (i--)
{
Real* xj0 = xi0; Real* xi = xi0; k = n;
if (k) for (;;)
{
u = u0; Real Xi = *xi; Real* xj = xj0;
j = J; while(j--) *u++ += Xi * *xj++;
if (!(--k)) break;
xi += s; xj0 += s;
}
Real sum = sqrt(*u0); *u0 = sum; u = u0+1;
if (sum == 0.0) Throw(SingularException(U));
int J1 = J-1; j = J1; while(j--) *u++ /= sum;
xj0 = xi0; xi = xi0++; k = n;
if (k) for (;;)
{
u = u0+1; Real Xi = *xi; Real* xj = xj0;
Xi /= sum; *xj++ = Xi;
j = J1; while(j--) *xj++ -= *u++ * Xi;
if (!(--k)) break;
xi += s; xj0 += s;
}
u0 += J--;
}
}
void updateQRZ(Matrix& X, UpperTriangularMatrix& U)
{
REPORT
Tracer et("updateQRZ");
int n = X.Nrows(); int s = X.Ncols();
if (s != U.Ncols())
Throw(ProgramException("Incompatible dimensions",X,U));
if (n == 0 || s == 0) return;
Real* xi0 = X.Store(); Real* u0 = U.Store(); Real* u;
RowVector V(s); Real* v0 = V.Store(); Real* v; V = 0.0;
int j, k; int J = s; int i = s;
while (i--)
{
Real* xj0 = xi0; Real* xi = xi0; k = n;
if (k) for (;;)
{
v = v0; Real Xi = *xi; Real* xj = xj0;
j = J; while(j--) *v++ += Xi * *xj++;
if (!(--k)) break;
xi += s; xj0 += s;
}
Real r = *u0;
Real sum = sqrt(*v0 + square(r));
if (sum == 0.0)
{
REPORT
u = u0; v = v0;
j = J; while(j--) { *u++ = 0.0; *v++ = 0.0; }
xj0 = xi0++; k = n;
if (k) for (;;)
{
*xj0 = 0.0;
if (!(--k)) break;
xj0 += s;
}
u0 += J--;
}
else
{
Real frs = fabs(r) + sum;
Real a0 = sqrt(frs / sum); Real alpha = a0 / frs;
if (r <= 0) { REPORT alpha = -alpha; *u0 = sum; }
else { REPORT *u0 = -sum; }
j = J - 1; v = v0 + 1; u = u0 + 1;
while (j--)
{ *v = a0 * *u + alpha * *v; *u -= a0 * *v; ++v; ++u; }
xj0 = xi0; xi = xi0++; k = n;
if (k) for (;;)
{
v = v0 + 1; Real Xi = *xi; Real* xj = xj0;
Xi *= alpha; *xj++ = Xi;
j = J - 1; while(j--) *xj++ -= *v++ * Xi;
if (!(--k)) break;
xi += s; xj0 += s;
}
j = J; v = v0;
while (j--) *v++ = 0.0;
u0 += J--;
}
}
}
