Re: how do i solve sparse linear equation like A*x=b

Thank you very much!

But what's the function of permutation_t pvector(A.size1())?

And I note that there's sparse matrix and symmetric matrix in ublas, but how can I
express symmetric sparse matrix conveniently?

Also I want to know the performance of ublas::lu_* comparing with other math library.

Best regards!

Yan Yaqin 2004-09-03

----- Original Message ----- 
From: "Paul C. Leopardi" <[email protected]>
To: "General Matrix Template Library (MTL) list" <[email protected]>
Sent: Thursday, September 02, 2004 10:46 PM
Subject: Re: MTL: how do i solve sparse linear equation like A*x=b


> Yan Yaqin,
> See the example below. Best regards
> 
> On Thursday 02 September 2004 11:52, Yan Yaqin wrote:
> > hi,
> > I'm really appreciate for your help, but there's another thing.
> > One parameter for lu_substitute is vector_expression, i'm not familiar with
> > this type, Would you like to provide me a simple real number demo?
> >
> > Thanks and best regards!
> 
> > ls -l
> total 8
> lrwxrwxrwx  1 leopardi users   25 2004-09-03 00:24 boost 
> -> ../boost/boost-1_31/boost
> -rw-r--r--  1 leopardi users 1457 2004-09-03 00:41 sample_solve.cpp
> -rw-r--r--  1 leopardi users 1458 2004-09-03 00:40 sample_solve.cpp~
> 
> > g++ -I. sample_solve.cpp -o sample_solve
> 
> > ./sample_solve
> A: [2,2]((0,1),(2,0))
> B: [2,2]((1,0),(0,-1))
> X: [2,2]((0,-0.5),(1,0))
> 
> > cat sample_solve.cpp
> #include <fstream>
> 
> #include <boost/numeric/ublas/config.hpp>
> #include <boost/numeric/ublas/vector.hpp>
> #include <boost/numeric/ublas/matrix.hpp>
> #include <boost/numeric/ublas/triangular.hpp>
> #include <boost/numeric/ublas/vector_sparse.hpp>
> #include <boost/numeric/ublas/matrix_sparse.hpp>
> #include <boost/numeric/ublas/operation_sparse.hpp>
> #include <boost/numeric/ublas/io.hpp>
> #include <boost/numeric/ublas/operation.hpp>
> #include <boost/numeric/ublas/lu.hpp>
> 
> namespace ublas = boost::numeric::ublas;
> 
> typedef ublas::row_major                           orientation_t;
> typedef ublas::compressed_matrix< double, orientation_t >
>                                                    matrix_t;
> typedef matrix_t::size_type                        matrix_index_t;
> typedef ublas::permutation_matrix<matrix_index_t>  permutation_t;
> 
> // Geometric quotient
> matrix_index_t
> sample_solve (matrix_t& X, const matrix_t& A, const matrix_t& B)
> {
>   // We solve A*X == B
> 
>   matrix_t LU = A;
>   permutation_t pvector(A.size1());
>   matrix_index_t singular = ublas::lu_factorize(LU, pvector);
> 
>   if (! singular)
>   {
>     X = B;
>     ublas::lu_substitute(LU, pvector, X);
>   }
>   return singular;
> }
> 
> main()
> {
>   matrix_t A(2,2);
>   matrix_t B(2,2);
>   matrix_t X(2,2);
> 
>   A(0,1) =     1;
>   A(1,0) = 2;
>   std::cout << "A: " << A << std::endl;
> 
>   B(0,0) = 1;
>   B(1,1) =    -1;
>   std::cout << "B: " << B << std::endl;
> 
>   sample_solve(X,A,B);
>   std::cout << "X: " << X << std::endl;
> }
> >
> 
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