/**
* \ingroup eigen
* Eigenvectors
* \param m \f$m\f$
* \return a variable matrix with the
* eigenvectors of \f$m\f$ stored in its columns.
*/
dmatrix eigenvectors(const dmatrix &m)
{
if (m.rowsize() != m.colsize())
{
cerr <<
"error -- non square matrix passed to dmatrix eigenvectors(const dmatrix& m)\n";
ad_exit(1);
}
int rmin = m.rowmin();
int rmax = m.rowmax();
dmatrix evecs(rmin, rmax, rmin, rmax);
dvector evals(rmin, rmax);
eigens(m, evecs, evals);
return evecs;
}
/** Eigenvalues.
\param m Input matrix (unchanged on return).
\return Vector of eigenvalues.
*/
dvector eigenvalues(const dmatrix& m)
{
if (m.rowsize()!=m.colsize())
{
cerr << "error -- non square matrix passed to "
"dvector eigen(const dmatrix& m)\n";
ad_exit(1);
}
dmatrix m1=symmetrize(m);
m1.colshift(1); // set minimum column and row indices to 1
m1.rowshift(1);
int n=m1.rowsize();
dvector diag(1,n);
dvector off_diag(1,n);
tri_dag(m1,diag,off_diag);
get_eigen(diag,off_diag,m1); // eigenvalues are returned in diag
// eigenvalues are returned in columns of z
return diag;
}
dvariable mult_likelihood(const dmatrix &o, const dvar_matrix &p, dvar_matrix &nu,
const dvariable &log_vn)
{
// kludge to ensure observed and predicted matrixes are the same size
if(o.colsize()!=p.colsize() || o.rowsize()!=p.rowsize())
{
cerr<<"Error in multivariate_t_likelihood, observed and predicted matrixes"
" are not the same size\n";
ad_exit(1);
}
dvariable vn = mfexp(log_vn);
dvariable ff = 0.0;
int r1 = o.rowmin();
int r2 = o.rowmax();
int c1 = o.colmin();
int c2 = o.colmax();
for(int i = r1; i <= r2; i++ )
{
dvar_vector sobs = vn * o(i)/sum(o(i)); //scale observed numbers by effective sample size.
ff -= gammln(vn);
for(int j = c1; j <= c2; j++ )
{
if( value(sobs(j)) > 0.0 )
ff += gammln(sobs(j));
}
ff -= sobs * log(TINY + p(i));
dvar_vector o1=o(i)/sum(o(i));
dvar_vector p1=p(i)/sum(p(i));
nu(i) = elem_div(o1-p1,sqrt(elem_prod(p1,1.-p1)/vn));
}
// exit(1);
return ff;
}