void Print(const UpperTriangularMatrix& X)
{
++PCN;
cout << "\nMatrix type: " << X.Type().Value() << " (";
cout << X.Nrows() << ", ";
cout << X.Ncols() << ")\n\n";
if (X.IsZero()) { cout << "All elements are zero\n" << flush; return; }
int nr=X.Nrows(); int nc=X.Ncols();
for (int i=1; i<=nr; i++)
{
int j;
for (j=1; j<i; j++) cout << "\t";
for (j=i; j<=nc; j++) cout << X(i,j) << "\t";
cout << "\n";
}
cout << flush; ++PCZ;
}
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;
}
}
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--;
}
}
}