On Mon, Jul 18, 2011 at 11:14 AM, Jeffrey Lee Hellrung, Jr. <jeffrey.hellrung@gmail.com> wrote:
On Mon, Jul 18, 2011 at 12:24 AM, Emil Dotchevski
as could proxy structures (c*v could be a proxy vector where w<0>(c*v) = 1 is equivalent to w<0>(v) = 1/c).
This requirement means that none of the boost::qvm functions can return temporary objects for proxies. The mutable proxies Boost QVM avoid temporary objects by clever type casting. This helps control the abstraction penalty of the library.
I don't understand. Can you elaborate?
For example, here is the col_m function which maps a vector type A as a matrix-column: template <class A> typename boost::enable_if_c< is_v<A>::value, qvm_detail::col_m_<A> &>::type BOOST_QVM_INLINE_TRIVIAL col_m( A & a ) { return reinterpret_cast<typename qvm_detail::col_m_<A> &>(a); } The v_traits<col_m_>::r and v_traits<col_m_>::w functions cast back to A (which is stored as v_traits<col_m_>::OriginalVector) before accessing its elements: template <int Row,int Col> static BOOST_QVM_INLINE_CRITICAL scalar_type & w( this_matrix & x ) { BOOST_QVM_STATIC_ASSERT(Col==0); BOOST_QVM_STATIC_ASSERT(Row>=0); BOOST_QVM_STATIC_ASSERT(Row<rows); return v_traits<OriginalVector>::template w<Row>(reinterpret_cast<OriginalVector &>(x)); } This technique avoids the creation of temporaries which are often the source of abstraction penalties.
Why do you require the dimension of vectors (and, likely, matrices; I haven't checked) to be strictly greater than 0? Sometimes a 0-dimensional vector is convenient to have when writing dimension-independent code.
I wasn't aware of that. What can you do with a zero dimensional vector?
Not much, to be sure (all zero-dim vectors of a given scalar type, at least, would be equal). I can't give a concrete example at the moment, but I seem to remember some recursion on dimension I've done where the base case was simpler to express at 0 than at 1.
In principle I'm not against lifting this requirement, but I want to make sure it's needed first. Doesn't this only affect the specialization of v_traits? I mean, you can still write recursive template meta programs that use zero as the base case as long as they don't define zero size in a v_traits specialization.
What algorithm do you use for computing determinants?
The general case is pretty straight forward recursion, defined in boost/qvm/detail/determinant_impl.hpp. However, the library comes with a code generator (libs/qvm/gen.cpp) capable of defining overloads for any specific size, unrolling the recursion.
The code generator is used instead of template metaprogramming, again to control the abstraction penalty of the library.
I'll take a look. I ask because I believe for 4x4 and larger matrices, a dynamic programming solution ends up significantly reducing the number of operations over the O(n!) recursive solution. But, I believe, for matrices larger than 5x5, still other techniques take fewer operations. Still, dynamic programming might improve the 4x4 and 5x5 cases. But maybe you've already looked into this...?
No I have not. The determinant computations are currently pretty straight-forward, save the use of an off-line code generator.
I guess that the documentation isn't clear but boost/qvm/math.hpp defines function templates that correspond to the functions from <math.h>. The templates are specialized for float and double, but can be specialized for any other scalar. That said, I don't have tests using any other scalar type. Perhaps a fixed point scalar should be implemented to make sure there isn't something missing.
Are complex scalar types within the scope of the library?
I think so. I've certainly been very careful to design a type system that permits non-trivial scalar types. Emil Dotchevski Reverge Studios, Inc. http://www.revergestudios.com/reblog/index.php?n=ReCode