[boost] (Vector) norm functions?

19 Aug 2005

      Should we add functions to evaluate the various norms of a (numeric)
sequence?

//=======================================================================
template < typename Number, typename InputIterator >
Number  norm_1( InputIterator b, InputIterator e )
{
    using std::abs;
    return std::accumulate( b, e, Number(), abs(_1) + abs(_2) );
}

template < typename Number, typename InputIterator >
Number  norm_2( InputIterator b, InputIterator e )
{
    using std::sqrt;
    return sqrt( std::inner_product( b, e, b, Number() ) );
}

template < typename Number, typename InputIterator >
Number  norm_infinity( InputIterator b, InputIterator e )
{
    using std::abs;
    return abs( *std::max_element( b, e, abs(_1) < abs(_2) ) );
}

template < typename Number, typename InputIterator >
Number  norm_x( int n, InputIterator b, InputIterator e )
{
    switch ( n )
    {
    default:
        {
            using std::pow;
            using std::abs;

            Number  r = Number();

            for ( ; b != e ; ++b )
            {
                r += pow( abs(*b), n );
            }

            return root( r, n );
        }
    case 2:
        return norm_2<Number>( b, e );
    case 1:
        return norm_1<Number>( b, e );
    case 0:
        // You can't really have a zero-norm
        // And you can't pass in infinity as a parameter
        // So we have 0 -> infinity
        return norm_infinity<Number>( b, e );
    }
}
//=======================================================================

I just wrote that here, so I don't know if it can work.  I don't know if I
used the bind/lambda stuff correctly, and there's still the problem that the
"root" function doesn't exist.

-- 
Daryle Walker
Mac, Internet, and Video Game Junkie
darylew AT hotmail DOT com