From 8905331427725871757 X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: f78e5,94e9c2bbb0060b48 X-Google-Attributes: gidf78e5,public X-Google-ArrivalTime: 2002-08-25 17:10:04 PST Return-Path: X-Authentication-Warning: mulga.cs.mu.OZ.AU: fjh set sender to devnull@stump.algebra.com using -f Path: archiver1.google.com!news1.google.com!newsfeed.stanford.edu!comp-std-cpp-robomod!not-for-mail X-Robomod: STUMP, ichudov@algebra.com (Igor Chudov) Delivered-To: std-c++@ncar.ucar.edu From: ros0230@iperbole.bologna.it (Natale Fietta) Newsgroups: comp.std.c++ Subject: Re: Proposals for small vectors? Organization: NETTuno Message-ID: <3d6752fb.4893595@news.iperbole.bologna.it> References: <87bs7yps0l.fsf_-_@grue.ucsd.edu> Reply-To: ros0230@iperbole.bologna.it X-Trace: panco.nettuno.it 1030181947 9368 193.207.3.36 (24 Aug 2002 09:39:07 GMT) X-Complaints-To: news@nettuno.it NNTP-Posting-Date: 24 Aug 2002 09:39:07 GMT X-Newsreader: Forte Free Agent 1.21/32.243 Approved: Fergus Henderson , moderator of comp.std.c++ Date: Sun, 25 Aug 2002 19:09:10 CST Lines: 160 Xref: archiver1.google.com comp.std.c++:13374 On Mon, 19 Aug 2002 19:37:58 GMT, Walter Landry wrote: >Natale Fietta wrote: >> Note: for some API matrixes are transposed, so i must use M*V >> instead of V*M. because using the wrong multiplication order can be >> a difficult bug to find (and also a pain to write if the same >> program must be compiled for both conventions) i usually define both >> V*M and M*V to be equivalent to the only geometrically correct >> multiplication for the currently selected API. >Well, this is where I think the tensor notation will help you. V*M >would be something like V(i)*M(i,j), or equivalently as M(i,j)*V(i). >Similarly, M*V -> M(j,i)*V(i) or V(i)*M(j,i). The indices keep things >in order. Maybe i have poorly described my situation: the fact that sometime i miswrite U=V*M instead of U=M*V is a lesser problem, the main problem is that when i write U=V*M i want it to mean U(j)=V(i)*M(i,j) if i select some API, but instead to mean U(j)=V(i)*M(j,i) if i select a different API. so i think the tensorial formalism do not solve the situation. >> Not only, i also want to multiply two matrixes of this form using the >> minimal needed number of operations, like as >> C00 = A00*B00 + A01*B10 + A02*B20 instead of >> C00 = A00*B00 + A01*B10 + A02*B20 + A03*B30 > >Well, you could do > >Index<'i',3> i; >Index<'j',3> j; >Index<'k',3> k; if i understand it correctly this must be Index<'k',4> k; >C(i,k)=A(i,j)*B(j,k); >C(i,3)+=A(i,3); maybe is also need C(3,k)=A(3,k); if the previous value of C is not an homogeneous transformation. My question: but this do not make all advantages of expression templates not appliables ? I do mean, if i want to do A=B*C*D*E using normal matrix multiplication i can write (i hope tensor syntax is correct, i am still learning this formalism) A(i,j)=B(i,k)*C(k,l)*D(l,m)*E(m,j); and have the wonderful template optimization. but if i use the special optimized form of multiplication implemented with two (or three) line of code for each single multiplication it is not possible to combine them all in a single optimizable expression, am i wrong ? >> i am not interested in a vector class without the ability to access >> components with a .x or .x() or GetX() syntax or similar (the .x is >> my favourite). > >I'm sure that you can add a non-member function of your own named >GetX() that does the right thing. Yes, it was a very poor objection, forget of it. Sometime i also use this trick: class MyVector { float data[3]; public: float& x; float& y; float& z; MyVector() : x(data[0]), y(data[1]), z(data[2]) {} } Alas, this is not feasible with vectors if i want a memory layout compatile with C API's... >template >double GetX(const T &t) > { > return t(0); > } It is only syntactic sugar, but i do prefer v.GetX() instead of GetX(v). >> Also note that often videogames console do not have very standard >> conforming C++ compilers, so a library that do not work even on >> MSVC++6 in out of my range of usefulness. > >I'm sure that the library could be made to have the same interface and >still work with broken compilers. It just wouldn't use expression >templates, removing some of its nice aspects. This is very unfortunate, because the main reason i can convince myself (and my coworkers) to learn and use tensors can be to take advantage of this optimization. as far as i can actually see they do not give other significative advantages in my application domain. Probably a non-tensorial small-matrix library implemented to take full advantage of expression template can be more useful for me (maybe, if i found sufficient spare time, i can attempt to write one). >> Sorry, this tensorial formalism only confuse me... :-( > >Wherever you see an index (i.e. i, j, or k), substitute a loop. So >the previous example would be equivavlent to I am starting to understand it, but it is difficult for me to get used to this formalism, the loss of abstraction is unwanted, i usually think of matrix multiplications as "black boxes", i bother to understand they only when i implement the operator*, instead this formalism force me to remember how they work each time i write an expression, i suppose this is very unusual for people out of the numeric community (it is surely very unusual for me). >> Yes, but i do also use (less often) this: >> >> A00 A01 A02 A03 B0 >> A10 A11 A12 A13 * B1 >> A20 A21 A22 A23 B2 >> A30 A31 A32 A33 1 >> >> performing the full multiplication and returning as result: >> Vector(C.x/C.w, C.y/C.w, C.z/C.w) //C.w is C3 > >In that case, you can write > >Index<'i',3> i; >Index<'j',3> j; > >C(i)=(A(i,j)*B(j) + A(i,3)) / (A(3,j)*B(j) + A(3,3)); > >And it will use the minimum number of operations (Really!). To me it seem that this do calculate C.w three times, so it is not the minimal number of operations ;-) >Tensor notation is really a powerful tool. Yes, i am fully convinced tensor are a powerful tool. indeed i am only half-convinced they are worthwhile in my application domain. >Also, relating to POD's, for a non-constant vector C, &(C(0)) would >give you a pointer to the beginning of the vector. What about arrays of vectors ? as i said to Uwe Schnitker i often pass arrays of vectors to C API's. Regards, Natale Fietta --- [ comp.std.c++ is moderated. To submit articles, try just posting with ] [ your news-reader. If that fails, use mailto:std-c++@ncar.ucar.edu ] [ --- Please see the FAQ before posting. --- ] [ FAQ: http://www.jamesd.demon.co.uk/csc/faq.html ]