/// \ingroup newmat
///@{
/// \file nm_misc.cpp
/// Miscellaneous programs.
#define WANT_MATH
#include "include.h"
#include "newmatap.h"
#ifdef use_namespace
namespace NEWMAT {
#endif
#ifdef DO_REPORT
#define REPORT { static ExeCounter ExeCount(__LINE__,21); ++ExeCount; }
#else
#define REPORT {}
#endif
ReturnMatrix Helmert(int n, bool full)
{
REPORT
Tracer et("Helmert ");
if (n <= 0) Throw(ProgramException("Dimension <= 0 "));
Matrix H;
if (full) H.resize(n,n); else H.resize(n-1,n);
H = 0.0;
for (int i = 1; i < n; ++i)
{
Real f = 1.0 / sqrt((Real)i * (i+1));
H.submatrix(i,i,1,i) = -f; H(i,i+1) = f * i;
}
if (full) { H.row(n) = 1.0 / sqrt((Real)n); }
H.release(); return H.for_return();
}
// Multiply X by n-1 x n matrix to give n-1 contrasts
// Return a ColumnVector
ReturnMatrix Helmert(const ColumnVector& X, bool full)
{
REPORT
Tracer et("Helmert * CV");
int n = X.nrows();
if (n == 0) Throw(ProgramException("X Vector of length 0", X));
Real sum = 0.0; ColumnVector Y;
if (full) Y.resize(n); else Y.resize(n-1);
for (int i = 1; i < n; ++i)
{ sum += X(i); Y(i) = (i * X(i+1) - sum) / sqrt((Real)i * (i+1)); }
if (full) { sum += X(n); Y(n) = sum / sqrt((Real)n); }
Y.release(); return Y.for_return();
}
// same as above for X a ColumnVector, length n, element j = 1; otherwise 0
ReturnMatrix Helmert(int n, int j, bool full)
{
REPORT
Tracer et("Helmert:single element ");
if (n <= 0) Throw(ProgramException("X Vector of length <= 0"));
if (j > n || j <= 0)
Throw(ProgramException("Out of range element number "));
ColumnVector Y; if (full) Y.resize(n); else Y.resize(n-1);
Y = 0.0;
if (j > 1) Y(j-1) = sqrt((Real)(j-1) / (Real)j);
for (int i = j; i < n; ++i) Y(i) = - 1.0 / sqrt((Real)i * (i+1));
if (full) Y(n) = 1.0 / sqrt((Real)n);
Y.release(); return Y.for_return();
}
ReturnMatrix Helmert_transpose(const ColumnVector& Y, bool full)
{
REPORT
Tracer et("Helmert_transpose * CV ");
int n = Y.nrows(); Real sum;
if (full) sum = Y(n) / sqrt((Real)n); else { sum = 0.0; ++n; }
ColumnVector X(n);
for (int i = n-1; i > 0; --i)
{
Real Yi = Y(i) / sqrt((Real)i * (i+1));
X(i+1) = i * Yi + sum; sum -= Yi;
}
X(1) = sum;
X.release(); return X.for_return();
}
// same as above but want only j-th element
Real Helmert_transpose(const ColumnVector& Y, int j, bool full)
{
REPORT
Tracer et("Helmert_transpose:single element ");
int n = Y.nrows(); Real sum;
if (full) sum = Y(n) / sqrt((Real)n); else { sum = 0.0; ++n; }
if (j > n || j <= 0) Throw(IndexException(j, Y));
for (int i = n-1; i > 0; --i)
{
Real Yi = Y(i) / sqrt((Real)i * (i+1));
if (i+1 == j) return i * Yi + sum;
sum -= Yi;
}
return sum;
}
ReturnMatrix Helmert(const Matrix& X, bool full)
{
REPORT
Tracer et("Helmert * Matrix");
int m = X.nrows(); int n = X.ncols();
if (m == 0) Throw(ProgramException("Matrix has 0 rows ", X));
Matrix Y;
if (full) Y.resize(m,n); else Y.resize(m-1, n);
for (int j = 1; j <= n; ++j)
{
ColumnVector CV = X.Column(j);
Y.Column(j) = Helmert(CV, full);
}
Y.release(); return Y.for_return();
}
ReturnMatrix Helmert_transpose(const Matrix& Y, bool full)
{
REPORT
Tracer et("Helmert_transpose * Matrix ");
int m = Y.nrows(); int n = Y.ncols(); if (!full) ++m;
Matrix X(m, n);
for (int j = 1; j <= n; ++j)
{
ColumnVector CV = Y.Column(j);
X.Column(j) = Helmert_transpose(CV, full);
}
X.release(); return X.for_return();
}
#ifdef use_namespace
}
#endif
///@}
syntax highlighted by Code2HTML, v. 0.9.1