uLAPACK.hpp

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/*
 * Bayes++ the Bayesian Filtering Library
 * Copyright (c) 2002 Michael Stevens
 * See accompanying Bayes++.htm for terms and conditions of use.
 *
 * $Id$
 */

/*
 * uBLAS to LAPACK Interface
 *  Very basic we only functions for information_root_filter supported
 */

/* Filter Matrix Namespace */
namespace Bayesian_filter_matrix
{
namespace LAPACK {

namespace rawLAPACK {
    // LAPACK routines as C callable functions
    extern "C" {

    void dgeqrf_(
            const int & m,
            const int & n,
            double da[],
            const int & lda,
            double dtau[],
            double dwork[],
            const int& ldwork,
            int& info);
    void sgeqrf_(
            const int & m,
            const int & n,
            float da[],
            const int & lda,
            float dtau[],
            float dwork[],
            const int& ldwork,
            int& info);

    void dgetrs_(
            const char& transa,
            const int& n,
            const int& nrhs,
            const double da[],
            const int& lda,
            int ipivot[],
            double db[],
            const int& ldb,
            int& info);
    void sgetrs_(
            const char& transa,
            const int& n,
            const int& nrhs,
            const float da[],
            const int& lda,
            int ipivot[],
            float db[],
            const int& ldb,
            int& info);

    void dgetrf_(
            const int& m,
            const int& n,
            double da[],
            const int& lda,
            int ipivot[],
            int& info);
    void sgetrf_(
            const int& m,
            const int& n,
            float da[],
            const int& lda,
            int ipivot[],
            int& info);

    }// extern "C"

    // Type overloads for C++
    inline void geqrf( const int & m, const int & n, double da[], const int & lda, double dtau[], double dwork[], const int& ldwork, int& info)
    {
        dgeqrf_(m,n,da,lda,dtau,dwork,ldwork,info);
    }
    inline void geqrf( const int & m, const int & n, float da[], const int & lda, float dtau[], float dwork[], const int& ldwork, int& info)
    {
        sgeqrf_(m,n,da,lda,dtau,dwork,ldwork,info);
    }
    inline void getrs( const char& transa, const int& n, const int& nrhs, const double da[], const int& lda, int ipivot[], double db[], const int& ldb, int& info)
    {
        dgetrs_(transa,n,nrhs,da,lda,ipivot,db,ldb,info);
    }
    inline void getrs( const char& transa, const int& n, const int& nrhs, const float da[], const int& lda, int ipivot[], float db[], const int& ldb, int& info)
    {
        sgetrs_(transa,n,nrhs,da,lda,ipivot,db,ldb,info);
    }
    inline void getrf( const int& m, const int& n, double da[], const int& lda, int ipivot[], int& info)
    {
        dgetrf_(m,n,da,lda,ipivot,info);
    }
    inline void getrf( const int& m, const int& n, float da[], const int& lda, int ipivot[], int& info)
    {
        sgetrf_(m,n,da,lda,ipivot,info);
    }
}// namespace rawLAPACK


/* Support types */
typedef boost::numeric::ublas::vector<int> pivot_t;
typedef Bayesian_filter_matrix::DenseVec vector_t;
typedef Bayesian_filter_matrix::DenseColMatrix matrix_t;

/* LAPACK Interface*/



// QR Factorization of a MxN General Matrix A.
//    a       (IN/OUT - matrix(M,N)) On entry, the coefficient matrix A. On exit , the upper triangle and diagonal is the min(M,N) by N upper triangular matrix R.  The lower triangle, together with the tau vector, is the orthogonal matrix Q as a product of min(M,N) elementary reflectors.
//    tau     (OUT - vector (min(M,N))) Vector of the same numerical type as A. The scalar factors of the elementary reflectors.
//    info    (OUT - int)
//   0   : function completed normally
//   < 0 : The ith argument, where i = abs(return value) had an illegal value.
int geqrf (matrix_t& a, vector_t& tau)
{
    int              _m = int(a.size1());
    int              _n = int(a.size2());
    int              _lda = int(a.size1());
    int              _info;

    // make_sure tau's size is greater than or equal to min(m,n)
    if (int(tau.size()) < (_n<_m ? _n : _m) )
        return -104;

    int ldwork = _n*_n;
    vector_t dwork(ldwork);
    rawLAPACK::geqrf (_m, _n, a.data().begin(), _lda, tau.data().begin(), dwork.data().begin(), ldwork, _info);

    return _info;
}

// LU factorization of a general matrix A.  
//    Computes an LU factorization of a general M-by-N matrix A using
//    partial pivoting with row interchanges. Factorization has the form
//    A = P*L*U.
//    a       (IN/OUT - matrix(M,N)) On entry, the coefficient matrix A to be factored. On exit, the factors L and U from the factorization A = P*L*U.
//    ipivot  (OUT - vector(min(M,N))) Integer vector. The row i of A was interchanged with row IPIV(i).
//    info    (OUT - int)
//   0   :  successful exit
//   < 0 :  If INFO = -i, then the i-th argument had an illegal value.
//   > 0 :  If INFO = i, then U(i,i) is exactly zero. The  factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.
int getrf (matrix_t& a, pivot_t& ipivot)
{
    matrix_t::value_type* _a = a.data().begin();
    int _m = int(a.size1());
    int _n = int(a.size2());
    int _lda = _m;  // minor size
    int _info;

    rawLAPACK::getrf (_m, _n,   _a, _lda, ipivot.data().begin(), _info);

    return _info;
}

// Solution to a system using LU factorization 
//   Solves a system of linear equations A*X = B with a general NxN
//   matrix A using the LU factorization computed by GETRF.
//   transa  (IN - char)  'T' for the transpose of A, 'N' otherwise.
//   a       (IN - matrix(M,N)) The factors L and U from the factorization A = P*L*U as computed by GETRF.
//   ipivot  (IN - vector(min(M,N))) Integer vector. The pivot indices from GETRF; row i of A was interchanged with row IPIV(i).
//   b       (IN/OUT - matrix(ldb,NRHS)) Matrix of same numerical type as A. On entry, the right hand side matrix B. On exit, the solution matrix X.
//
//   info    (OUT - int)
//   0   : function completed normally
//   < 0 : The ith argument, where i = abs(return value) had an illegal value.
//   > 0 : if INFO =  i,  U(i,i)  is  exactly  zero;  the  matrix is singular and its inverse could not be computed.
int getrs (char transa, matrix_t& a,
        pivot_t& ipivot, matrix_t& b)
{
    matrix_t::value_type* _a = a.data().begin();
    int a_n = int(a.size1());
    int _lda = a_n;
    int p_n = int(ipivot.size());

    matrix_t::value_type* _b = b.data().begin();
    int b_n = int(b.size1());
    int _ldb = b_n;
    int _nrhs = int(b.size2()); /* B's size2 is the # of vectors on rhs */

    if (a_n != b_n) /*Test to see if AX=B has correct dimensions */
        return -101;
    if (p_n < a_n)     /*Check to see if ipivot is big enough */
        return -102;

    int _info;
    rawLAPACK::getrs (transa, a_n, _nrhs, _a,   _lda, ipivot.data().begin(), 
                _b, _ldb, _info);

    return _info;
} 

}//namespace LAPACK
}//namespace Bayesian_filter_matrix