//
//  Copyright (c) 2003 Toon Knapen, Karl Meerbergen, and Kresimir Fresl
//  Copyright (c) 2008 Thomas Klimpel and Rutger ter Borg
//
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
//
// THIS FILE IS AUTOMATICALLY GENERATED
// PLEASE DO NOT EDIT!
//

#ifndef BOOST_NUMERIC_BINDINGS_LAPACK_GELSD_HPP
#define BOOST_NUMERIC_BINDINGS_LAPACK_GELSD_HPP

#include <boost/numeric/bindings/lapack/lapack.h>

namespace boost {
namespace numeric {
namespace bindings {
namespace lapack {

//
//  CGELSD computes the minimum-norm solution to a real linear least
//  squares problem:
//      minimize 2-norm(| b - A*x |)
//  using the singular value decomposition (SVD) of A. A is an M-by-N
//  matrix which may be rank-deficient.
//
//  Several right hand side vectors b and solution vectors x can be
//  handled in a single call; they are stored as the columns of the
//  M-by-NRHS right hand side matrix B and the N-by-NRHS solution
//  matrix X.
//
//  The problem is solved in three steps:
//  (1) Reduce the coefficient matrix A to bidiagonal form with
//      Householder tranformations, reducing the original problem
//      into a "bidiagonal least squares problem" (BLS)
//  (2) Solve the BLS using a divide and conquer approach.
//  (3) Apply back all the Householder tranformations to solve
//      the original least squares problem.
//
//  The effective rank of A is determined by treating as zero those
//  singular values which are less than RCOND times the largest singular
//  value.
//
//  The divide and conquer algorithm makes very mild assumptions about
//  floating point arithmetic. It will work on machines with a guard
//  digit in add/subtract, or on those binary machines without guard
//  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
//  Cray-2. It could conceivably fail on hexadecimal or decimal machines
//  without guard digits, but we know of none.
//

namespace detail {
    // inline overloads
    inline void gelsd( int const m, int const n, int const nrhs, fcomplex_t* a, 
            int const lda, fcomplex_t* b, int const ldb, float* s, 
            float const rcond, int* rank, fcomplex_t* work, int const lwork, 
            float* rwork, int* iwork, int* info ) {
        LAPACK_CGELSD( &m, &n, &nrhs, a, &lda, b, &ldb, s, 
                &rcond, rank, work, &lwork, rwork, iwork, info );
    }
    inline void gelsd( int const m, int const n, int const nrhs, double const* a, 
            int const lda, double* b, int const ldb, double* s, 
            double const rcond, int* rank, double* work, int const lwork, 
            int* iwork, int* info ) {
        LAPACK_DGELSD( &m, &n, &nrhs, a, &lda, b, &ldb, s, 
                &rcond, rank, work, &lwork, iwork, info );
    }
    inline void gelsd( int const m, int const n, int const nrhs, float const* a, 
            int const lda, float* b, int const ldb, float* s, 
            float const rcond, int* rank, float* work, int const lwork, 
            int* iwork, int* info ) {
        LAPACK_SGELSD( &m, &n, &nrhs, a, &lda, b, &ldb, s, 
                &rcond, rank, work, &lwork, iwork, info );
    }
    inline void gelsd( int const m, int const n, int const nrhs, dcomplex_t const* a, 
            int const lda, dcomplex_t* b, int const ldb, double* s, 
            double const rcond, int* rank, dcomplex_t* work, int const lwork, 
            double* rwork, int* iwork, int* info ) {
        LAPACK_ZGELSD( &m, &n, &nrhs, a, &lda, b, &ldb, s, 
                &rcond, rank, work, &lwork, rwork, iwork, info );
    }
}


}}}} // namespace boost::numeric::bindings::lapack

#endif