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//$$ hholder.cpp QR decomposition
// Copyright (C) 1991,2,3,4: R B Davies
#define WANT_MATH
#include "include.h"
#include "config.h"
#include "newmatap.h"
#ifdef use_namespace
namespace NEWMAT {
#endif
#ifdef DO_REPORT
#define REPORT { static ExeCounter ExeCount(__LINE__,16); ++ExeCount; }
#else
#define REPORT {}
#endif
/*************************** QR decompositions ***************************/
inline Real square(Real x) { return x*x; }
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 QRZT(const Matrix& X, Matrix& Y, Matrix& M)
{
REPORT
Tracer et("QRZT(2)");
int n = X.Ncols(); int s = X.Nrows(); int t = Y.Nrows();
if (Y.Ncols() != n)
{ Throw(ProgramException("Unequal row lengths",X,Y)); }
M.ReSize(t,s);
Real* xi = X.Store(); int k;
for (int i=0; i<s; i++)
{
Real* xj0 = Y.Store(); Real* xi0 = xi;
for (int j=0; j<t; j++)
{
Real sum=0.0;
xi=xi0; Real* xj=xj0; k=n; while(k--) { sum += *xi++ * *xj++; }
xi=xi0; k=n; while(k--) { *xj0++ -= sum * *xi++; }
M.element(j,i) = sum;
}
}
}
/*
void QRZ(Matrix& X, UpperTriangularMatrix& U)
{
Tracer et("QRZ(1)");
int n = X.Nrows(); int s = X.Ncols(); U.ReSize(s);
Real* xi0 = X.Store(); int k;
for (int i=0; i<s; i++)
{
Real sum = 0.0;
Real* xi = xi0; k=n; while(k--) { sum += square(*xi); xi+=s; }
sum = sqrt(sum);
U.element(i,i) = sum;
if (sum==0.0) Throw(SingularException(U));
Real* xj0=xi0; k=n; while(k--) { *xj0 /= sum; xj0+=s; }
xj0 = xi0;
for (int j=i+1; j<s; j++)
{
sum=0.0;
xi=xi0; k=n; xj0++; Real* xj=xj0;
while(k--) { sum += *xi * *xj; xi+=s; xj+=s; }
xi=xi0; k=n; xj=xj0;
while(k--) { *xj -= sum * *xi; xj+=s; xi+=s; }
U.element(i,j) = sum;
}
xi0++;
}
}
*/
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 QRZ(const Matrix& X, Matrix& Y, Matrix& M)
{
REPORT
Tracer et("QRZ(2)");
int n = X.Nrows(); int s = X.Ncols(); int t = Y.Ncols();
if (Y.Nrows() != n)
{ Throw(ProgramException("Unequal column lengths",X,Y)); }
M.ReSize(s,t); M = 0;Real* m0 = M.Store(); Real* m;
Real* xi0 = X.Store();
int j, k; int i = s;
while (i--)
{
Real* xj0 = Y.Store(); Real* xi = xi0; k = n;
if (k) for (;;)
{
m = m0; Real Xi = *xi; Real* xj = xj0;
j = t; while(j--) *m++ += Xi * *xj++;
if (!(--k)) break;
xi += s; xj0 += t;
}
xj0 = Y.Store(); xi = xi0++; k = n;
if (k) for (;;)
{
m = m0; Real Xi = *xi; Real* xj = xj0;
j = t; while(j--) *xj++ -= *m++ * Xi;
if (!(--k)) break;
xi += s; xj0 += t;
}
m0 += t;
}
}
/*
void QRZ(const Matrix& X, Matrix& Y, Matrix& M)
{
Tracer et("QRZ(2)");
int n = X.Nrows(); int s = X.Ncols(); int t = Y.Ncols();
if (Y.Nrows() != n)
{ Throw(ProgramException("Unequal column lengths",X,Y)); }
M.ReSize(s,t);
Real* xi0 = X.Store(); int k;
for (int i=0; i<s; i++)
{
Real* xj0 = Y.Store();
for (int j=0; j<t; j++)
{
Real sum=0.0;
Real* xi=xi0; Real* xj=xj0; k=n;
while(k--) { sum += *xi * *xj; xi+=s; xj+=t; }
xi=xi0; k=n; xj=xj0++;
while(k--) { *xj -= sum * *xi; xj+=t; xi+=s; }
M.element(i,j) = sum;
}
xi0++;
}
}
*/
#ifdef use_namespace
}
#endif
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