typename make_triangular_matrix<SymMatrix, boost::numeric::ublas::lower>::type
cholesky_decomposition(SymMatrix const & A)
{
assert(A.size1() == A.size2());
auto L = matrix_lower_trianle(A);
for(size_t i = 0; i != A.size1(); ++ i)
{
for(size_t j = 0; j != i; ++ j)
{
for(size_t k = 0; k != j; ++ k)
{
L(i, j) -= L(i, k) * L(j, k);
}
L(i, j) /= L(j, j);
using ural::square;
L(i, i) -= square(L(i, j));
}
assert(L(i, i) >= 0);
using std::sqrt;
L(i, i) = sqrt(L(i, i));
}
return L;
}
bool isPSD (const SymMatrix &M)
/* Check a Matrix is both Symetric and Positive Semi Definite
* Creates a temporary copy
*
* Numerics of Algorithm:
* Use UdUfactor and checks reciprocal condition number >=0
* Algorithms using UdUfactor will will therefore succeed if isPSD(M) is true
* Do NOT assume because isPSD is true that M will appear to be PSD to other numerical algorithms
* Return:
* true iff M isSymetric and is PSD by the above algorithm
*/
{
RowMatrix UD(M.size1(),M.size1());
RowMatrix::value_type rcond = UdUfactor(UD, M);
return rcond >= 0.;
}