Matrix inverse( Matrix const & matrix )
{
assert( matrix.rows() == matrix.cols() );
auto [ p, lu ] = decompose( matrix, Strategy::LUP );
std::vector< Matrix > xSolutions;
xSolutions.reserve( lu.rows() );
for ( std::size_t i{ 0 }; i < lu.rows(); ++i )
{
Matrix m{ lu.rows(), 1 };
m( i, 0 ) = 1;
m = p * m;
supstitution::forward( lu, m );
supstitution::backward( lu, m );
xSolutions.emplace_back( m );
}
for ( std::size_t i{ 0 }; i < lu.rows(); ++i )
{
for ( std::size_t j{ 0 }; j < lu.cols(); ++j )
{
lu( i, j ) = xSolutions[ j ]( i, 0 );
}
}
Matrix identity{ Matrix::Identity( lu.rows() ) };
if ( lu.hasNan() || lu.hasInf() )
{
LOG_ERROR( "Matirx does not have inverse." );
}
return lu;
}
bool
isReal(const MatrixBase& exp)
{
return !hasNaN(exp) && ! hasInf(exp);
}
