// 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();
}