boost::numeric::ublas::triangular_matrix< T, boost::numeric::ublas::lower >
cholesky_decomposition( const boost::numeric::ublas::symmetric_matrix< T, boost::numeric::ublas::upper >& A)
{
std::clog<<"flat::cholesky_decomposition"<<std::endl<<std::flush;
assert(A.size1()==A.size2());
//Cholesky Decomposition
//Numerical Recipes in C++ (Second Edition), page 100
std::vector< T > d( A.size1() );
T sum;
boost::numeric::ublas::triangular_matrix< T, boost::numeric::ublas::lower > L( A.size1(), A.size2() );
for( size_t i = 0; i < A.size1(); i++ )
{
for( size_t j = 0; j < i; j++ )
{ sum = A(i,j);
for(size_t k = 0; k < j; ++k)
sum -= L(i,k)*L(j,k);
L(i,j) = sum / L(j,j);
}
sum = A(i,i);
for(size_t k = 0; k < i; ++k)
sum -= L(i,k) * L(i,k);
assert( sum > 0 );
L(i,i) = std::sqrt( sum );
}
/*for( size_t i = 0; i < A.size1(); i++ )
for( size_t j = i; j < A.size1(); j++ )
{
sum = A(i,j);
for( int k = int(i)-1; k >= 0; k-- )
sum -= A(i,k) * A(j,k);
if( i == j )
{
std::cerr << "choleski sum " << sum << std::endl;
assert( sum > 0 ); // is A really positive definite?
d[i] = std::sqrt( sum );
} else L(j,i) = sum / d[i];
}
for( size_t i = 0; i < A.size1(); ++i ) L(i,i) = d[i];
*/
std::clog<<"flat::cholesky_decomposition\t|complete"<<std::endl<<std::flush;
return L;
};
void FillMatrix(boost::numeric::ublas::symmetric_matrix<_TReal> &matrix, const size_t cities, const size_t index)
{
matrix.resize(cities, cities);
for (size_t i = 0; i < matrix.size1(); ++i)
{
for (size_t j = 0; j <= i; ++j)
matrix(i, j) = index;
}
}
void BasketProduct::setCorrelations(boost::numeric::ublas::symmetric_matrix<double, boost::numeric::ublas::lower> corr) {
for(int i=0;i<corr.size1();i++) {
for(int j=0;j<corr.size2();j++) {
if(abs(corr(i,j))>1) {
throw out_of_range("La corrélation doit être comprise entre -1 et +1");
}
}
}
correlations = corr;
}
boost::numeric::ublas::matrix< T > pseudoinverse( const boost::numeric::ublas::symmetric_matrix< coord_t, boost::numeric::ublas::upper >& X )
{
using namespace boost::numeric::ublas;
std::clog << "flat::pseudoinverse" << "\t| computing ..."//<<std::endl<<V
<< std::endl << std::flush;
// TODO regularizer. right name?
triangular_matrix< T, lower > L( cholesky_decomposition< T >( X ) );
std::clog << "flat::pseudoinverse" << "\t| L" << std::endl
<< L << std::endl << std::flush;
auto Xinverse = solve( L, solve( L, identity_matrix< T >( X.size1() ), lower_tag() ), lower_tag() );
std::clog << "flat::pseudoinverse" << "\t| complete - pseudoinverse of V " << std::endl
<< Xinverse << std::endl;
return Xinverse;
}
BOOST_UBLAS_INLINE
int matrix_storage_size (const ublas::symmetric_matrix<T,F1,F2,A> &m) {
return (int) ((m.size1() * (m.size1() + 1)) / 2);
}
// Ideally, this template should handle a non-square symmetric_matrix
// using upper and lower.
template <typename T> inline T norm_max(ublas::symmetric_matrix<T>& M) {
size_t n1 = M.size1(); size_t n2 = M.size2(); T m = 0;
for (size_t i=0; i<n1; i++) for (size_t j=i; j<n2; j++)
m = max(M(i,j),m);
return m;
}