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Subject: Re: [boost] [qvm] few q's for emil
From: Jeffrey Lee Hellrung, Jr. (jeffrey.hellrung_at_[hidden])
Date: 20110718 14:14:13
On Mon, Jul 18, 2011 at 12:24 AM, Emil Dotchevski
<emildotchevski_at_[hidden]>wrote:
> On Sun, Jul 17, 2011 at 9:16 PM, Jeffrey Lee Hellrung, Jr.
> <jeffrey.hellrung_at_[hidden]> wrote:
>
[...]
> > First, it doesn't look like you support readonly or writeonly
> structures,
>
> The library doesn't require that ::w is defined. The library itself
> does define some types that are readonly.
>
Ah, okay; that wasn't clear in the docs on v_traits, IIRC :/
> or structures for which writing is effected through a proxy reference.
> > E.g., v_traits<V>::r<I>(v) and v_traits<V>::w<I>(v) must always be
> > supported, and v_traits<V>::w<I>(v) must return a referencetononconst.
>
> Yes, ::w must return a mutable reference. However, it is not required
> that ::w is defined for each and every element. For example, diag_m
> maps a vector as a square matrix that has the vector as its diagonal,
> and zeroes in all other elements. In this case, ::r is defined for all
> elements, but ::w is defined only for the diagonal elements, returning
> mutable references to the vector elements.
>
Make sense.
> > 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?
> > Why do you require the dimension of vectors (and, likely, matrices; I
> > haven't checked) to be strictly greater than 0? Sometimes a
> 0dimensional
> > vector is convenient to have when writing dimensionindependent code.
>
> I wasn't aware of that. What can you do with a zero dimensional vector?
>
Not much, to be sure (all zerodim 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.
> > I noticed that among the vector operations is a cross product for
> 3vectors,
> > but no cross product for vectors of other dimensions. Such a construct
> is
> > useful for computing normals to hyperplanes in Ddimensional space. I
> can
> > help you add it if you think it fits.
>
> Sure.
>
I'll browse the code.
> > 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...?
> I think a signed volume function would fit in well with the matrix
> > operations. I can help you add this, too.
>
> OK.
>
> > Hmmm...how do you compute the magnitude of a vector given the scalar
> > requirements defined at
> >
> > http://www.revergestudios.com/boostqvm/scalar_requirements.html
> >
> > ? Seems like you would need a square root function, and possibly even a
> > conjugation function if you want to support complex scalar types...
>
> 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?
 Jeff
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