Re: do you support MTL?

Hi, I meant to write earlier - you will finds a successful implimentation of a (in general non commutative) abstract templated polynomial class in the package libalgebra in http://coropa.sourceforge.net/#latest 

It is tested and has worked in a number of quite stressful settings including arbitrary precision integer coefficients (using gmp) and several non-commuting symbols. In the end the main difficulty was porting gmp to windows.

It can certainly handle ordinary polynomials (set the number of letters to one) and the case of many commutting symbols (ie the abelian case) can be very easily  accomodated in the same way (but more easily) than we have created lie product and tensor prduct - but is actually simpler. The code is not fantastic but and was a first attemtp to create a design to work robustly; it might not be as efficient as one would hope.

Dont know if this is helpful to you or not.

Are you using mtl to model the polynomials directly (as vectors) and overloading the class to produce multiplication of polynomials. Or did you implicitly create your own vector class to describe each polynomial and only use the mtl for vectors of polynomials.

I have used MTL to do abstract multiplications and it did well but really I think it is generally easier to overload and use map classes and stl features directly to impliment sparseness.


Terry
  ----- Original Message ----- 
  From: Xu Bin 
  To: General Matrix Template Library (MTL) list 
  Sent: Friday, May 12, 2006 6:04 PM
  Subject: Re: MTL: do you support MTL?





  On 5/10/06, Irek Szczesniak <[email protected]> wrote: 
    Hi Peter,

    Thank you for your email and resolving my problems.  I implemented the
    operators for the polynomial type, and now I'm able to multiply 
    vectors and matrixes of polynomials.  I'm attaching a complete program
    at the bottom of this email.

    Because I have the basic functionality going (a product of polynomial
    vectors and matrixes), I think I will plugh ahead harnessing MTL. 

    I'm looking forward to the release of the new MTL.


    Best,
    Irek

    Peter Gottschling wrote:

    > Hi Irek,
    >
    > Thank you for your interest in MTL and sorry for the trouble you run 
    > into.  The problem is that nobody developed MTL for some years.
    > When we restarted it (with different authors), we saw many things
    > principally different.  Therefore, we decided to restart from the
    > beginning (which unfortunately goes slower than expected).
    > Therefore I tend to keep the maintenance efforts on MTL 2.xx minimal
    > (to not delay the delivery of the new version even further).
    >
    > However, the idea of polynomials as scalar types is interesting and
    > I tried to figure out your problems.  There were severals issues and
    > not everything was MTL's fault ;-)
    > 1. print_all_matrix is implemented as std::cout << x ..., it better 
    > should be 'using std::cout; cout << x; ...'
    > - there are several such functions and we will fix this one day
    > - one can work around by defining the << operator in std namespace
    > 2. print_vector used iterator -> I changed it to const_iterator in 
    > the hope that all relevant vectors have this
    > 3. instead of defining * and + operator for map it works better to
    > define a new type that derives from map (which is needed by
    > 4. anyway)
    > 4. the utilization of scale(v, 0) requires that polynomial is 
    > constructible from int or double
    >
    > I add some code that solved the syntactical problems.  The
    > implementation of the numerical part I leave to you although that is
    > the more interesting.  I would appreciate if you can keep me 
    > up-to-date occasionally (better directly to me instead of the list).
    >
    > Best,
    > Peter

    ********************************************************************

    #include <iostream> 
    #include <map>
    #include <vector>
    #include <mtl/matrix.h>
    #include <mtl/mtl.h>
    #include <mtl/utils.h>
    #include <mtl/blais.h>
    #include <mtl/sparse1D.h>

    using namespace mtl;
    using namespace std;

    struct polynomial : map<int, double>
    {
      typedef map<int, double> base;

      polynomial() : base() {}

      polynomial(double c0) : base()
      { 
        (*this)[0]= c0;
      }
    };


    typedef matrix<polynomial,
                    rectangle<>,
                    array< dense<> >,
                    row_major>::type Mat;


    polynomial 
    operator *(const polynomial &p1, const polynomial &p2)
    {
      polynomial result;

      for(polynomial::const_iterator i = p1.begin(); i != p1.end(); ++i)
        for(polynomial::const_iterator j = p2.begin (); j != p2.end(); ++j)
          result[i->first + j->first] += i->second * j->second;

      return result;
    }


    polynomial&
    operator +=(polynomial &p1, const polynomial &p2)
    {
      for(polynomial::const_iterator i = p2.begin(); i != p2.end(); ++i)
        p1[i->first] += i->second;
      return p1;
    }


    polynomial
    operator +(const polynomial &p1, const polynomial &p2)
    {
      polynomial result = p1;
      result += p2;
      return result;
    }


    namespace std
    {
      ostream &operator << (ostream &out, const polynomial &p)
      {
        for(polynomial::const_reverse_iterator i = p.rbegin(); i !=
    p.rend();)
          {
           out << i->second;

           if (i->first)
             out << "*x^" << i->first;;

           if (++i != p.rend())
             cout << " + "; 
          }

        return out;
      }
    }

    int
    main()
    {
      Mat A(3, 3);

      A(0, 0) = polynomial();
      A(1, 1) = polynomial();
      A(2, 2) = polynomial();

      A(0, 0)[2] = 1;
      A(1, 1)[1] = 1; 
      A(2, 2)[0] = 1;

      dense1D<polynomial> c(3), result(3);

      c[0][0] = 1;
      c[1][1] = 3;
      c[2][2] = 2;

      mult(A, c, result);

      print_all_matrix(A);

      print_vector(result); 

      return 0;
    }
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  -- 
  xubin

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