//
// Copyright (c) 2002--2010
// Toon Knapen, Karl Meerbergen, Kresimir Fresl,
// 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_DRIVER_GGEVX_HPP
#define BOOST_NUMERIC_BINDINGS_LAPACK_DRIVER_GGEVX_HPP

#include <boost/assert.hpp>
#include <Core/Utils/numeric/bindings/begin.hpp>
#include <Core/Utils/numeric/bindings/detail/array.hpp>
#include <Core/Utils/numeric/bindings/is_column_major.hpp>
#include <Core/Utils/numeric/bindings/is_complex.hpp>
#include <Core/Utils/numeric/bindings/is_mutable.hpp>
#include <Core/Utils/numeric/bindings/is_real.hpp>
#include <Core/Utils/numeric/bindings/lapack/workspace.hpp>
#include <Core/Utils/numeric/bindings/remove_imaginary.hpp>
#include <Core/Utils/numeric/bindings/size.hpp>
#include <Core/Utils/numeric/bindings/stride.hpp>
#include <Core/Utils/numeric/bindings/traits/detail/utils.hpp>
#include <Core/Utils/numeric/bindings/value_type.hpp>
#include <boost/static_assert.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/type_traits/remove_const.hpp>
#include <boost/utility/enable_if.hpp>

//
// The LAPACK-backend for ggevx is the netlib-compatible backend.
//
#include <Core/Utils/numeric/bindings/lapack/detail/lapack.h>
#include <Core/Utils/numeric/bindings/lapack/detail/lapack_option.hpp>

namespace boost
{
    namespace numeric
    {
        namespace bindings
        {
            namespace lapack
            {
                //
                // The detail namespace contains value-type-overloaded functions that
                // dispatch to the appropriate back-end LAPACK-routine.
                //
                namespace detail
                {
                    //
                    // Overloaded function for dispatching to
                    // * netlib-compatible LAPACK backend (the default), and
                    // * float value-type.
                    //
                    inline std::ptrdiff_t ggevx(const char balanc, const char jobvl,
                                                const char jobvr, const char sense, const fortran_int_t n, float* a,
                                                const fortran_int_t lda, float* b, const fortran_int_t ldb,
                                                float* alphar, float* alphai, float* beta, float* vl,
                                                const fortran_int_t ldvl, float* vr, const fortran_int_t ldvr,
                                                fortran_int_t& ilo, fortran_int_t& ihi, float* lscale, float* rscale,
                                                float& abnrm, float& bbnrm, float* rconde, float* rcondv, float* work,
                                                const fortran_int_t lwork, fortran_int_t* iwork,
                                                fortran_bool_t* bwork)
                    {
                        fortran_int_t info(0);
                        LAPACK_SGGEVX(&balanc, &jobvl, &jobvr, &sense, &n, a, &lda, b, &ldb,
                                      alphar, alphai, beta, vl, &ldvl, vr, &ldvr, &ilo, &ihi, lscale,
                                      rscale, &abnrm, &bbnrm, rconde, rcondv, work, &lwork, iwork,
                                      bwork, &info);
                        return info;
                    }

                    //
                    // Overloaded function for dispatching to
                    // * netlib-compatible LAPACK backend (the default), and
                    // * double value-type.
                    //
                    inline std::ptrdiff_t ggevx(const char balanc, const char jobvl,
                                                const char jobvr, const char sense, const fortran_int_t n, double* a,
                                                const fortran_int_t lda, double* b, const fortran_int_t ldb,
                                                double* alphar, double* alphai, double* beta, double* vl,
                                                const fortran_int_t ldvl, double* vr, const fortran_int_t ldvr,
                                                fortran_int_t& ilo, fortran_int_t& ihi, double* lscale,
                                                double* rscale, double& abnrm, double& bbnrm, double* rconde,
                                                double* rcondv, double* work, const fortran_int_t lwork,
                                                fortran_int_t* iwork, fortran_bool_t* bwork)
                    {
                        fortran_int_t info(0);
                        LAPACK_DGGEVX(&balanc, &jobvl, &jobvr, &sense, &n, a, &lda, b, &ldb,
                                      alphar, alphai, beta, vl, &ldvl, vr, &ldvr, &ilo, &ihi, lscale,
                                      rscale, &abnrm, &bbnrm, rconde, rcondv, work, &lwork, iwork,
                                      bwork, &info);
                        return info;
                    }

                    //
                    // Overloaded function for dispatching to
                    // * netlib-compatible LAPACK backend (the default), and
                    // * complex<float> value-type.
                    //
                    inline std::ptrdiff_t ggevx(const char balanc, const char jobvl,
                                                const char jobvr, const char sense, const fortran_int_t n,
                                                std::complex<float>* a, const fortran_int_t lda,
                                                std::complex<float>* b, const fortran_int_t ldb,
                                                std::complex<float>* alpha, std::complex<float>* beta,
                                                std::complex<float>* vl, const fortran_int_t ldvl,
                                                std::complex<float>* vr, const fortran_int_t ldvr, fortran_int_t& ilo,
                                                fortran_int_t& ihi, float* lscale, float* rscale, float& abnrm,
                                                float& bbnrm, float* rconde, float* rcondv, std::complex<float>* work,
                                                const fortran_int_t lwork, float* rwork, fortran_int_t* iwork,
                                                fortran_bool_t* bwork)
                    {
                        fortran_int_t info(0);
                        LAPACK_CGGEVX(&balanc, &jobvl, &jobvr, &sense, &n, a, &lda, b, &ldb,
                                      alpha, beta, vl, &ldvl, vr, &ldvr, &ilo, &ihi, lscale, rscale,
                                      &abnrm, &bbnrm, rconde, rcondv, work, &lwork, rwork, iwork, bwork,
                                      &info);
                        return info;
                    }

                    //
                    // Overloaded function for dispatching to
                    // * netlib-compatible LAPACK backend (the default), and
                    // * complex<double> value-type.
                    //
                    inline std::ptrdiff_t ggevx(const char balanc, const char jobvl,
                                                const char jobvr, const char sense, const fortran_int_t n,
                                                std::complex<double>* a, const fortran_int_t lda,
                                                std::complex<double>* b, const fortran_int_t ldb,
                                                std::complex<double>* alpha, std::complex<double>* beta,
                                                std::complex<double>* vl, const fortran_int_t ldvl,
                                                std::complex<double>* vr, const fortran_int_t ldvr,
                                                fortran_int_t& ilo, fortran_int_t& ihi, double* lscale,
                                                double* rscale, double& abnrm, double& bbnrm, double* rconde,
                                                double* rcondv, std::complex<double>* work, const fortran_int_t lwork,
                                                double* rwork, fortran_int_t* iwork, fortran_bool_t* bwork)
                    {
                        fortran_int_t info(0);
                        LAPACK_ZGGEVX(&balanc, &jobvl, &jobvr, &sense, &n, a, &lda, b, &ldb,
                                      alpha, beta, vl, &ldvl, vr, &ldvr, &ilo, &ihi, lscale, rscale,
                                      &abnrm, &bbnrm, rconde, rcondv, work, &lwork, rwork, iwork, bwork,
                                      &info);
                        return info;
                    }
                } // namespace detail

                //
                // Value-type based template class. Use this class if you need a type
                // for dispatching to ggevx.
                //
                template <typename Value, typename Enable = void>
                struct ggevx_impl
                {
                };

                //
                // This implementation is enabled if Value is a real type.
                //
                template <typename Value>
                struct ggevx_impl<Value, typename boost::enable_if<is_real<Value>>::type>
                {
                    typedef Value value_type;
                    typedef typename remove_imaginary<Value>::type real_type;

                    //
                    // Static member function for user-defined workspaces, that
                    // * Deduces the required arguments for dispatching to LAPACK, and
                    // * Asserts that most arguments make sense.
                    //
                    template <typename MatrixA, typename MatrixB, typename VectorALPHAR,
                              typename VectorALPHAI, typename VectorBETA, typename MatrixVL,
                              typename MatrixVR, typename VectorLSCALE, typename VectorRSCALE,
                              typename VectorRCONDE, typename VectorRCONDV, typename WORK,
                              typename IWORK, typename BWORK>
                    static std::ptrdiff_t invoke(const char balanc, const char jobvl,
                                                 const char jobvr, const char sense, MatrixA& a, MatrixB& b,
                                                 VectorALPHAR& alphar, VectorALPHAI& alphai, VectorBETA& beta,
                                                 MatrixVL& vl, MatrixVR& vr, fortran_int_t& ilo,
                                                 fortran_int_t& ihi, VectorLSCALE& lscale,
                                                 VectorRSCALE& rscale, real_type& abnrm, real_type& bbnrm,
                                                 VectorRCONDE& rconde, VectorRCONDV& rcondv, detail::workspace3<
                                                     WORK, IWORK, BWORK> work)
                    {
                        namespace bindings = ::boost::numeric::bindings;
                        BOOST_STATIC_ASSERT((bindings::is_column_major<MatrixA>::value));
                        BOOST_STATIC_ASSERT((bindings::is_column_major<MatrixB>::value));
                        BOOST_STATIC_ASSERT((bindings::is_column_major<MatrixVL>::value));
                        BOOST_STATIC_ASSERT((bindings::is_column_major<MatrixVR>::value));
                        BOOST_STATIC_ASSERT((boost::is_same<typename remove_const<
                                                                typename bindings::value_type<MatrixA>::type>::type,
                                                            typename remove_const<typename bindings::value_type<
                                                                MatrixB>::type>::type>::value));
                        BOOST_STATIC_ASSERT((boost::is_same<typename remove_const<
                                                                typename bindings::value_type<MatrixA>::type>::type,
                                                            typename remove_const<typename bindings::value_type<
                                                                VectorALPHAR>::type>::type>::value));
                        BOOST_STATIC_ASSERT((boost::is_same<typename remove_const<
                                                                typename bindings::value_type<MatrixA>::type>::type,
                                                            typename remove_const<typename bindings::value_type<
                                                                VectorALPHAI>::type>::type>::value));
                        BOOST_STATIC_ASSERT((boost::is_same<typename remove_const<
                                                                typename bindings::value_type<MatrixA>::type>::type,
                                                            typename remove_const<typename bindings::value_type<
                                                                VectorBETA>::type>::type>::value));
                        BOOST_STATIC_ASSERT((boost::is_same<typename remove_const<
                                                                typename bindings::value_type<MatrixA>::type>::type,
                                                            typename remove_const<typename bindings::value_type<
                                                                MatrixVL>::type>::type>::value));
                        BOOST_STATIC_ASSERT((boost::is_same<typename remove_const<
                                                                typename bindings::value_type<MatrixA>::type>::type,
                                                            typename remove_const<typename bindings::value_type<
                                                                MatrixVR>::type>::type>::value));
                        BOOST_STATIC_ASSERT((boost::is_same<typename remove_const<
                                                                typename bindings::value_type<MatrixA>::type>::type,
                                                            typename remove_const<typename bindings::value_type<
                                                                VectorLSCALE>::type>::type>::value));
                        BOOST_STATIC_ASSERT((boost::is_same<typename remove_const<
                                                                typename bindings::value_type<MatrixA>::type>::type,
                                                            typename remove_const<typename bindings::value_type<
                                                                VectorRSCALE>::type>::type>::value));
                        BOOST_STATIC_ASSERT((boost::is_same<typename remove_const<
                                                                typename bindings::value_type<MatrixA>::type>::type,
                                                            typename remove_const<typename bindings::value_type<
                                                                VectorRCONDE>::type>::type>::value));
                        BOOST_STATIC_ASSERT((boost::is_same<typename remove_const<
                                                                typename bindings::value_type<MatrixA>::type>::type,
                                                            typename remove_const<typename bindings::value_type<
                                                                VectorRCONDV>::type>::type>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<MatrixA>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<MatrixB>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<VectorALPHAR>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<VectorALPHAI>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<VectorBETA>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<MatrixVL>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<MatrixVR>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<VectorLSCALE>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<VectorRSCALE>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<VectorRCONDE>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<VectorRCONDV>::value));
                        BOOST_ASSERT(bindings::size(alphai) >= bindings::size_column(a));
                        BOOST_ASSERT(bindings::size(alphar) >= bindings::size_column(a));
                        BOOST_ASSERT(bindings::size(work.select(fortran_int_t())) >=
                            min_size_iwork(sense, bindings::size_column(a)));
                        BOOST_ASSERT(bindings::size(work.select(fortran_bool_t())) >=
                            min_size_bwork(sense, bindings::size_column(a)));
                        BOOST_ASSERT(bindings::size(work.select(real_type())) >=
                            min_size_work(balanc, jobvl, jobvr, sense,
                                          bindings::size_column(a)));
                        BOOST_ASSERT(bindings::size_column(a) >= 0);
                        BOOST_ASSERT(bindings::size_minor(a) == 1 ||
                            bindings::stride_minor(a) == 1);
                        BOOST_ASSERT(bindings::size_minor(b) == 1 ||
                            bindings::stride_minor(b) == 1);
                        BOOST_ASSERT(bindings::size_minor(vl) == 1 ||
                            bindings::stride_minor(vl) == 1);
                        BOOST_ASSERT(bindings::size_minor(vr) == 1 ||
                            bindings::stride_minor(vr) == 1);
                        BOOST_ASSERT(bindings::stride_major(a) >= std::max<std::ptrdiff_t>(1,
                                                                                           bindings::size_column(a)));
                        BOOST_ASSERT(bindings::stride_major(b) >= std::max<std::ptrdiff_t>(1,
                                                                                           bindings::size_column(a)));
                        BOOST_ASSERT(balanc == 'N' || balanc == 'P' || balanc == 'S' ||
                            balanc == 'B');
                        BOOST_ASSERT(jobvl == 'N' || jobvl == 'V');
                        BOOST_ASSERT(jobvr == 'N' || jobvr == 'V');
                        BOOST_ASSERT(sense == 'N' || sense == 'E' || sense == 'V' ||
                            sense == 'B');
                        return detail::ggevx(balanc, jobvl, jobvr, sense,
                                             bindings::size_column(a), bindings::begin_value(a),
                                             bindings::stride_major(a), bindings::begin_value(b),
                                             bindings::stride_major(b), bindings::begin_value(alphar),
                                             bindings::begin_value(alphai), bindings::begin_value(beta),
                                             bindings::begin_value(vl), bindings::stride_major(vl),
                                             bindings::begin_value(vr), bindings::stride_major(vr), ilo,
                                             ihi, bindings::begin_value(lscale),
                                             bindings::begin_value(rscale), abnrm, bbnrm,
                                             bindings::begin_value(rconde), bindings::begin_value(rcondv),
                                             bindings::begin_value(work.select(real_type())),
                                             bindings::size(work.select(real_type())),
                                             bindings::begin_value(work.select(fortran_int_t())),
                                             bindings::begin_value(work.select(fortran_bool_t())));
                    }

                    //
                    // Static member function that
                    // * Figures out the minimal workspace requirements, and passes
                    //   the results to the user-defined workspace overload of the
                    //   invoke static member function
                    // * Enables the unblocked algorithm (BLAS level 2)
                    //
                    template <typename MatrixA, typename MatrixB, typename VectorALPHAR,
                              typename VectorALPHAI, typename VectorBETA, typename MatrixVL,
                              typename MatrixVR, typename VectorLSCALE, typename VectorRSCALE,
                              typename VectorRCONDE, typename VectorRCONDV>
                    static std::ptrdiff_t invoke(const char balanc, const char jobvl,
                                                 const char jobvr, const char sense, MatrixA& a, MatrixB& b,
                                                 VectorALPHAR& alphar, VectorALPHAI& alphai, VectorBETA& beta,
                                                 MatrixVL& vl, MatrixVR& vr, fortran_int_t& ilo,
                                                 fortran_int_t& ihi, VectorLSCALE& lscale,
                                                 VectorRSCALE& rscale, real_type& abnrm, real_type& bbnrm,
                                                 VectorRCONDE& rconde, VectorRCONDV& rcondv, minimal_workspace)
                    {
                        namespace bindings = ::boost::numeric::bindings;
                        bindings::detail::array<real_type> tmp_work(min_size_work(balanc,
                                                                                  jobvl, jobvr, sense,
                                                                                  bindings::size_column(a)));
                        bindings::detail::array<fortran_int_t> tmp_iwork(
                            min_size_iwork(sense, bindings::size_column(a)));
                        bindings::detail::array<fortran_bool_t> tmp_bwork(min_size_bwork(
                            sense, bindings::size_column(a)));
                        return invoke(balanc, jobvl, jobvr, sense, a, b, alphar, alphai,
                                      beta, vl, vr, ilo, ihi, lscale, rscale, abnrm, bbnrm, rconde,
                                      rcondv, workspace(tmp_work, tmp_iwork, tmp_bwork));
                    }

                    //
                    // Static member function that
                    // * Figures out the optimal workspace requirements, and passes
                    //   the results to the user-defined workspace overload of the
                    //   invoke static member
                    // * Enables the blocked algorithm (BLAS level 3)
                    //
                    template <typename MatrixA, typename MatrixB, typename VectorALPHAR,
                              typename VectorALPHAI, typename VectorBETA, typename MatrixVL,
                              typename MatrixVR, typename VectorLSCALE, typename VectorRSCALE,
                              typename VectorRCONDE, typename VectorRCONDV>
                    static std::ptrdiff_t invoke(const char balanc, const char jobvl,
                                                 const char jobvr, const char sense, MatrixA& a, MatrixB& b,
                                                 VectorALPHAR& alphar, VectorALPHAI& alphai, VectorBETA& beta,
                                                 MatrixVL& vl, MatrixVR& vr, fortran_int_t& ilo,
                                                 fortran_int_t& ihi, VectorLSCALE& lscale,
                                                 VectorRSCALE& rscale, real_type& abnrm, real_type& bbnrm,
                                                 VectorRCONDE& rconde, VectorRCONDV& rcondv, optimal_workspace)
                    {
                        namespace bindings = ::boost::numeric::bindings;
                        real_type opt_size_work;
                        bindings::detail::array<fortran_int_t> tmp_iwork(
                            min_size_iwork(sense, bindings::size_column(a)));
                        bindings::detail::array<fortran_bool_t> tmp_bwork(min_size_bwork(
                            sense, bindings::size_column(a)));
                        detail::ggevx(balanc, jobvl, jobvr, sense,
                                      bindings::size_column(a), bindings::begin_value(a),
                                      bindings::stride_major(a), bindings::begin_value(b),
                                      bindings::stride_major(b), bindings::begin_value(alphar),
                                      bindings::begin_value(alphai), bindings::begin_value(beta),
                                      bindings::begin_value(vl), bindings::stride_major(vl),
                                      bindings::begin_value(vr), bindings::stride_major(vr), ilo,
                                      ihi, bindings::begin_value(lscale),
                                      bindings::begin_value(rscale), abnrm, bbnrm,
                                      bindings::begin_value(rconde), bindings::begin_value(rcondv),
                                      &opt_size_work, -1, bindings::begin_value(tmp_iwork),
                                      bindings::begin_value(tmp_bwork));
                        bindings::detail::array<real_type> tmp_work(
                            traits::detail::to_int(opt_size_work));
                        return invoke(balanc, jobvl, jobvr, sense, a, b, alphar, alphai,
                                      beta, vl, vr, ilo, ihi, lscale, rscale, abnrm, bbnrm, rconde,
                                      rcondv, workspace(tmp_work, tmp_iwork, tmp_bwork));
                    }

                    //
                    // Static member function that returns the minimum size of
                    // workspace-array work.
                    //
                    static std::ptrdiff_t min_size_work(const char balanc, const char jobvl,
                                                        const char jobvr, const char sense, const std::ptrdiff_t n)
                    {
                        if (balanc == 'S' || balanc == 'B' || jobvl == 'V' || jobvr == 'V')
                            return std::max<std::ptrdiff_t>(1, 6 * n);
                        if (sense == 'E')
                            return std::max<std::ptrdiff_t>(1, 10 * n);
                        if (sense == 'V' || sense == 'B')
                            return 2 * n * n + 8 * n + 16;
                        return std::max<std::ptrdiff_t>(1, 2 * n);
                    }

                    //
                    // Static member function that returns the minimum size of
                    // workspace-array iwork.
                    //
                    static std::ptrdiff_t min_size_iwork(const char sense,
                                                         const std::ptrdiff_t n)
                    {
                        if (sense == 'E')
                            return 0;
                        else
                            return n + 6;
                    }

                    //
                    // Static member function that returns the minimum size of
                    // workspace-array bwork.
                    //
                    static std::ptrdiff_t min_size_bwork(const char sense,
                                                         const std::ptrdiff_t n)
                    {
                        if (sense == 'N')
                            return 0;
                        else
                            return n;
                    }
                };

                //
                // This implementation is enabled if Value is a complex type.
                //
                template <typename Value>
                struct ggevx_impl<Value, typename boost::enable_if<is_complex<Value>>::type>
                {
                    typedef Value value_type;
                    typedef typename remove_imaginary<Value>::type real_type;

                    //
                    // Static member function for user-defined workspaces, that
                    // * Deduces the required arguments for dispatching to LAPACK, and
                    // * Asserts that most arguments make sense.
                    //
                    template <typename MatrixA, typename MatrixB, typename VectorALPHA,
                              typename VectorBETA, typename MatrixVL, typename MatrixVR,
                              typename VectorLSCALE, typename VectorRSCALE,
                              typename VectorRCONDE, typename VectorRCONDV, typename WORK,
                              typename RWORK, typename IWORK, typename BWORK>
                    static std::ptrdiff_t invoke(const char balanc, const char jobvl,
                                                 const char jobvr, const char sense, MatrixA& a, MatrixB& b,
                                                 VectorALPHA& alpha, VectorBETA& beta, MatrixVL& vl, MatrixVR& vr,
                                                 fortran_int_t& ilo, fortran_int_t& ihi,
                                                 VectorLSCALE& lscale, VectorRSCALE& rscale, real_type& abnrm,
                                                 real_type& bbnrm, VectorRCONDE& rconde, VectorRCONDV& rcondv,
                                                 detail::workspace4<WORK, RWORK, IWORK, BWORK> work)
                    {
                        namespace bindings = ::boost::numeric::bindings;
                        BOOST_STATIC_ASSERT((bindings::is_column_major<MatrixA>::value));
                        BOOST_STATIC_ASSERT((bindings::is_column_major<MatrixB>::value));
                        BOOST_STATIC_ASSERT((bindings::is_column_major<MatrixVL>::value));
                        BOOST_STATIC_ASSERT((bindings::is_column_major<MatrixVR>::value));
                        BOOST_STATIC_ASSERT((boost::is_same<typename remove_const<
                                                                typename bindings::value_type<VectorLSCALE>::type>::type
                                                            ,
                                                            typename remove_const<typename bindings::value_type<
                                                                VectorRSCALE>::type>::type>::value));
                        BOOST_STATIC_ASSERT((boost::is_same<typename remove_const<
                                                                typename bindings::value_type<VectorLSCALE>::type>::type
                                                            ,
                                                            typename remove_const<typename bindings::value_type<
                                                                VectorRCONDE>::type>::type>::value));
                        BOOST_STATIC_ASSERT((boost::is_same<typename remove_const<
                                                                typename bindings::value_type<VectorLSCALE>::type>::type
                                                            ,
                                                            typename remove_const<typename bindings::value_type<
                                                                VectorRCONDV>::type>::type>::value));
                        BOOST_STATIC_ASSERT((boost::is_same<typename remove_const<
                                                                typename bindings::value_type<MatrixA>::type>::type,
                                                            typename remove_const<typename bindings::value_type<
                                                                MatrixB>::type>::type>::value));
                        BOOST_STATIC_ASSERT((boost::is_same<typename remove_const<
                                                                typename bindings::value_type<MatrixA>::type>::type,
                                                            typename remove_const<typename bindings::value_type<
                                                                VectorALPHA>::type>::type>::value));
                        BOOST_STATIC_ASSERT((boost::is_same<typename remove_const<
                                                                typename bindings::value_type<MatrixA>::type>::type,
                                                            typename remove_const<typename bindings::value_type<
                                                                VectorBETA>::type>::type>::value));
                        BOOST_STATIC_ASSERT((boost::is_same<typename remove_const<
                                                                typename bindings::value_type<MatrixA>::type>::type,
                                                            typename remove_const<typename bindings::value_type<
                                                                MatrixVL>::type>::type>::value));
                        BOOST_STATIC_ASSERT((boost::is_same<typename remove_const<
                                                                typename bindings::value_type<MatrixA>::type>::type,
                                                            typename remove_const<typename bindings::value_type<
                                                                MatrixVR>::type>::type>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<MatrixA>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<MatrixB>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<VectorALPHA>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<VectorBETA>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<MatrixVL>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<MatrixVR>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<VectorLSCALE>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<VectorRSCALE>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<VectorRCONDE>::value));
                        BOOST_STATIC_ASSERT((bindings::is_mutable<VectorRCONDV>::value));
                        BOOST_ASSERT(bindings::size(alpha) >= bindings::size_column(a));
                        BOOST_ASSERT(bindings::size(beta) >= bindings::size_column(a));
                        BOOST_ASSERT(bindings::size(work.select(fortran_int_t())) >=
                            min_size_iwork(sense, bindings::size_column(a)));
                        BOOST_ASSERT(bindings::size(work.select(fortran_bool_t())) >=
                            min_size_bwork(sense, bindings::size_column(a)));
                        BOOST_ASSERT(bindings::size(work.select(real_type())) >=
                            min_size_rwork(balanc, bindings::size_column(a)));
                        BOOST_ASSERT(bindings::size(work.select(value_type())) >=
                            min_size_work(sense, bindings::size_column(a)));
                        BOOST_ASSERT(bindings::size_column(a) >= 0);
                        BOOST_ASSERT(bindings::size_minor(a) == 1 ||
                            bindings::stride_minor(a) == 1);
                        BOOST_ASSERT(bindings::size_minor(b) == 1 ||
                            bindings::stride_minor(b) == 1);
                        BOOST_ASSERT(bindings::size_minor(vl) == 1 ||
                            bindings::stride_minor(vl) == 1);
                        BOOST_ASSERT(bindings::size_minor(vr) == 1 ||
                            bindings::stride_minor(vr) == 1);
                        BOOST_ASSERT(bindings::stride_major(a) >= std::max<std::ptrdiff_t>(1,
                                                                                           bindings::size_column(a)));
                        BOOST_ASSERT(bindings::stride_major(b) >= std::max<std::ptrdiff_t>(1,
                                                                                           bindings::size_column(a)));
                        BOOST_ASSERT(balanc == 'N' || balanc == 'P' || balanc == 'S' ||
                            balanc == 'B');
                        BOOST_ASSERT(jobvl == 'N' || jobvl == 'V');
                        BOOST_ASSERT(jobvr == 'N' || jobvr == 'V');
                        BOOST_ASSERT(sense == 'N' || sense == 'E' || sense == 'V' ||
                            sense == 'B');
                        return detail::ggevx(balanc, jobvl, jobvr, sense,
                                             bindings::size_column(a), bindings::begin_value(a),
                                             bindings::stride_major(a), bindings::begin_value(b),
                                             bindings::stride_major(b), bindings::begin_value(alpha),
                                             bindings::begin_value(beta), bindings::begin_value(vl),
                                             bindings::stride_major(vl), bindings::begin_value(vr),
                                             bindings::stride_major(vr), ilo, ihi,
                                             bindings::begin_value(lscale), bindings::begin_value(rscale),
                                             abnrm, bbnrm, bindings::begin_value(rconde),
                                             bindings::begin_value(rcondv),
                                             bindings::begin_value(work.select(value_type())),
                                             bindings::size(work.select(value_type())),
                                             bindings::begin_value(work.select(real_type())),
                                             bindings::begin_value(work.select(fortran_int_t())),
                                             bindings::begin_value(work.select(fortran_bool_t())));
                    }

                    //
                    // Static member function that
                    // * Figures out the minimal workspace requirements, and passes
                    //   the results to the user-defined workspace overload of the
                    //   invoke static member function
                    // * Enables the unblocked algorithm (BLAS level 2)
                    //
                    template <typename MatrixA, typename MatrixB, typename VectorALPHA,
                              typename VectorBETA, typename MatrixVL, typename MatrixVR,
                              typename VectorLSCALE, typename VectorRSCALE,
                              typename VectorRCONDE, typename VectorRCONDV>
                    static std::ptrdiff_t invoke(const char balanc, const char jobvl,
                                                 const char jobvr, const char sense, MatrixA& a, MatrixB& b,
                                                 VectorALPHA& alpha, VectorBETA& beta, MatrixVL& vl, MatrixVR& vr,
                                                 fortran_int_t& ilo, fortran_int_t& ihi,
                                                 VectorLSCALE& lscale, VectorRSCALE& rscale, real_type& abnrm,
                                                 real_type& bbnrm, VectorRCONDE& rconde, VectorRCONDV& rcondv,
                                                 minimal_workspace)
                    {
                        namespace bindings = ::boost::numeric::bindings;
                        bindings::detail::array<value_type> tmp_work(min_size_work(sense,
                                                                                   bindings::size_column(a)));
                        bindings::detail::array<real_type> tmp_rwork(min_size_rwork(
                            balanc, bindings::size_column(a)));
                        bindings::detail::array<fortran_int_t> tmp_iwork(
                            min_size_iwork(sense, bindings::size_column(a)));
                        bindings::detail::array<fortran_bool_t> tmp_bwork(min_size_bwork(
                            sense, bindings::size_column(a)));
                        return invoke(balanc, jobvl, jobvr, sense, a, b, alpha, beta, vl, vr,
                                      ilo, ihi, lscale, rscale, abnrm, bbnrm, rconde, rcondv,
                                      workspace(tmp_work, tmp_rwork, tmp_iwork, tmp_bwork));
                    }

                    //
                    // Static member function that
                    // * Figures out the optimal workspace requirements, and passes
                    //   the results to the user-defined workspace overload of the
                    //   invoke static member
                    // * Enables the blocked algorithm (BLAS level 3)
                    //
                    template <typename MatrixA, typename MatrixB, typename VectorALPHA,
                              typename VectorBETA, typename MatrixVL, typename MatrixVR,
                              typename VectorLSCALE, typename VectorRSCALE,
                              typename VectorRCONDE, typename VectorRCONDV>
                    static std::ptrdiff_t invoke(const char balanc, const char jobvl,
                                                 const char jobvr, const char sense, MatrixA& a, MatrixB& b,
                                                 VectorALPHA& alpha, VectorBETA& beta, MatrixVL& vl, MatrixVR& vr,
                                                 fortran_int_t& ilo, fortran_int_t& ihi,
                                                 VectorLSCALE& lscale, VectorRSCALE& rscale, real_type& abnrm,
                                                 real_type& bbnrm, VectorRCONDE& rconde, VectorRCONDV& rcondv,
                                                 optimal_workspace)
                    {
                        namespace bindings = ::boost::numeric::bindings;
                        value_type opt_size_work;
                        bindings::detail::array<real_type> tmp_rwork(min_size_rwork(
                            balanc, bindings::size_column(a)));
                        bindings::detail::array<fortran_int_t> tmp_iwork(
                            min_size_iwork(sense, bindings::size_column(a)));
                        bindings::detail::array<fortran_bool_t> tmp_bwork(min_size_bwork(
                            sense, bindings::size_column(a)));
                        detail::ggevx(balanc, jobvl, jobvr, sense,
                                      bindings::size_column(a), bindings::begin_value(a),
                                      bindings::stride_major(a), bindings::begin_value(b),
                                      bindings::stride_major(b), bindings::begin_value(alpha),
                                      bindings::begin_value(beta), bindings::begin_value(vl),
                                      bindings::stride_major(vl), bindings::begin_value(vr),
                                      bindings::stride_major(vr), ilo, ihi,
                                      bindings::begin_value(lscale), bindings::begin_value(rscale),
                                      abnrm, bbnrm, bindings::begin_value(rconde),
                                      bindings::begin_value(rcondv), &opt_size_work, -1,
                                      bindings::begin_value(tmp_rwork),
                                      bindings::begin_value(tmp_iwork),
                                      bindings::begin_value(tmp_bwork));
                        bindings::detail::array<value_type> tmp_work(
                            traits::detail::to_int(opt_size_work));
                        return invoke(balanc, jobvl, jobvr, sense, a, b, alpha, beta, vl, vr,
                                      ilo, ihi, lscale, rscale, abnrm, bbnrm, rconde, rcondv,
                                      workspace(tmp_work, tmp_rwork, tmp_iwork, tmp_bwork));
                    }

                    //
                    // Static member function that returns the minimum size of
                    // workspace-array work.
                    //
                    static std::ptrdiff_t min_size_work(const char sense,
                                                        const std::ptrdiff_t n)
                    {
                        if (sense == 'N')
                            return std::max<std::ptrdiff_t>(1, 2 * n);
                        else
                        {
                            if (sense == 'E')
                                return std::max<std::ptrdiff_t>(1, 4 * n);
                            else
                                return std::max<std::ptrdiff_t>(1, 2 * n * n + 2 * n);
                        }
                    }

                    //
                    // Static member function that returns the minimum size of
                    // workspace-array rwork.
                    //
                    static std::ptrdiff_t min_size_rwork(const char balanc,
                                                         const std::ptrdiff_t n)
                    {
                        if (balanc == 'S' || balanc == 'B')
                            return std::max<std::ptrdiff_t>(1, 6 * n);
                        else
                            return std::max<std::ptrdiff_t>(1, 2 * n);
                    }

                    //
                    // Static member function that returns the minimum size of
                    // workspace-array iwork.
                    //
                    static std::ptrdiff_t min_size_iwork(const char sense,
                                                         const std::ptrdiff_t n)
                    {
                        if (sense == 'E')
                            return 0;
                        else
                            return n + 2;
                    }

                    //
                    // Static member function that returns the minimum size of
                    // workspace-array bwork.
                    //
                    static std::ptrdiff_t min_size_bwork(const char sense,
                                                         const std::ptrdiff_t n)
                    {
                        if (sense == 'N')
                            return 0;
                        else
                            return n;
                    }
                };


                //
                // Functions for direct use. These functions are overloaded for temporaries,
                // so that wrapped types can still be passed and used for write-access. In
                // addition, if applicable, they are overloaded for user-defined workspaces.
                // Calls to these functions are passed to the ggevx_impl classes. In the
                // documentation, most overloads are collapsed to avoid a large number of
                // prototypes which are very similar.
                //

                //
                // Overloaded function for ggevx. Its overload differs for
                // * User-defined workspace
                //
                template <typename MatrixA, typename MatrixB, typename VectorALPHAR,
                          typename VectorALPHAI, typename VectorBETA, typename MatrixVL,
                          typename MatrixVR, typename VectorLSCALE, typename VectorRSCALE,
                          typename VectorRCONDE, typename VectorRCONDV, typename Workspace>
                inline typename boost::enable_if<detail::is_workspace<Workspace>,
                                                 std::ptrdiff_t>::type
                ggevx(const char balanc, const char jobvl, const char jobvr,
                      const char sense, MatrixA& a, MatrixB& b, VectorALPHAR& alphar,
                      VectorALPHAI& alphai, VectorBETA& beta, MatrixVL& vl, MatrixVR& vr,
                      fortran_int_t& ilo, fortran_int_t& ihi, VectorLSCALE& lscale,
                      VectorRSCALE& rscale, typename remove_imaginary<
                          typename bindings::value_type<MatrixA>::type>::type& abnrm,
                      typename remove_imaginary<typename bindings::value_type<
                          MatrixA>::type>::type& bbnrm, VectorRCONDE& rconde,
                      VectorRCONDV& rcondv, Workspace work)
                {
                    return ggevx_impl<typename bindings::value_type<
                        MatrixA>::type>::invoke(balanc, jobvl, jobvr, sense, a, b,
                                                alphar, alphai, beta, vl, vr, ilo, ihi, lscale, rscale, abnrm,
                                                bbnrm, rconde, rcondv, work);
                }

                //
                // Overloaded function for ggevx. Its overload differs for
                // * Default workspace-type (optimal)
                //
                template <typename MatrixA, typename MatrixB, typename VectorALPHAR,
                          typename VectorALPHAI, typename VectorBETA, typename MatrixVL,
                          typename MatrixVR, typename VectorLSCALE, typename VectorRSCALE,
                          typename VectorRCONDE, typename VectorRCONDV>
                inline typename boost::disable_if<detail::is_workspace<VectorRCONDV>,
                                                  std::ptrdiff_t>::type
                ggevx(const char balanc, const char jobvl, const char jobvr,
                      const char sense, MatrixA& a, MatrixB& b, VectorALPHAR& alphar,
                      VectorALPHAI& alphai, VectorBETA& beta, MatrixVL& vl, MatrixVR& vr,
                      fortran_int_t& ilo, fortran_int_t& ihi, VectorLSCALE& lscale,
                      VectorRSCALE& rscale, typename remove_imaginary<
                          typename bindings::value_type<MatrixA>::type>::type& abnrm,
                      typename remove_imaginary<typename bindings::value_type<
                          MatrixA>::type>::type& bbnrm, VectorRCONDE& rconde,
                      VectorRCONDV& rcondv)
                {
                    return ggevx_impl<typename bindings::value_type<
                        MatrixA>::type>::invoke(balanc, jobvl, jobvr, sense, a, b,
                                                alphar, alphai, beta, vl, vr, ilo, ihi, lscale, rscale, abnrm,
                                                bbnrm, rconde, rcondv, optimal_workspace());
                }

                //
                // Overloaded function for ggevx. Its overload differs for
                // * User-defined workspace
                //
                template <typename MatrixA, typename MatrixB, typename VectorALPHA,
                          typename VectorBETA, typename MatrixVL, typename MatrixVR,
                          typename VectorLSCALE, typename VectorRSCALE, typename VectorRCONDE,
                          typename VectorRCONDV, typename Workspace>
                inline typename boost::enable_if<detail::is_workspace<Workspace>,
                                                 std::ptrdiff_t>::type
                ggevx(const char balanc, const char jobvl, const char jobvr,
                      const char sense, MatrixA& a, MatrixB& b, VectorALPHA& alpha,
                      VectorBETA& beta, MatrixVL& vl, MatrixVR& vr, fortran_int_t& ilo,
                      fortran_int_t& ihi, VectorLSCALE& lscale, VectorRSCALE& rscale,
                      typename remove_imaginary<typename bindings::value_type<
                          MatrixA>::type>::type& abnrm, typename remove_imaginary<
                          typename bindings::value_type<MatrixA>::type>::type& bbnrm,
                      VectorRCONDE& rconde, VectorRCONDV& rcondv, Workspace work)
                {
                    return ggevx_impl<typename bindings::value_type<
                        MatrixA>::type>::invoke(balanc, jobvl, jobvr, sense, a, b,
                                                alpha, beta, vl, vr, ilo, ihi, lscale, rscale, abnrm, bbnrm,
                                                rconde, rcondv, work);
                }

                //
                // Overloaded function for ggevx. Its overload differs for
                // * Default workspace-type (optimal)
                //
                template <typename MatrixA, typename MatrixB, typename VectorALPHA,
                          typename VectorBETA, typename MatrixVL, typename MatrixVR,
                          typename VectorLSCALE, typename VectorRSCALE, typename VectorRCONDE,
                          typename VectorRCONDV>
                inline typename boost::disable_if<detail::is_workspace<VectorRCONDV>,
                                                  std::ptrdiff_t>::type
                ggevx(const char balanc, const char jobvl, const char jobvr,
                      const char sense, MatrixA& a, MatrixB& b, VectorALPHA& alpha,
                      VectorBETA& beta, MatrixVL& vl, MatrixVR& vr, fortran_int_t& ilo,
                      fortran_int_t& ihi, VectorLSCALE& lscale, VectorRSCALE& rscale,
                      typename remove_imaginary<typename bindings::value_type<
                          MatrixA>::type>::type& abnrm, typename remove_imaginary<
                          typename bindings::value_type<MatrixA>::type>::type& bbnrm,
                      VectorRCONDE& rconde, VectorRCONDV& rcondv)
                {
                    return ggevx_impl<typename bindings::value_type<
                        MatrixA>::type>::invoke(balanc, jobvl, jobvr, sense, a, b,
                                                alpha, beta, vl, vr, ilo, ihi, lscale, rscale, abnrm, bbnrm,
                                                rconde, rcondv, optimal_workspace());
                }
            } // namespace lapack
        } // namespace bindings
    } // namespace numeric
} // namespace boost

#endif
