nmrSVD.h

Go to the documentation of this file.

/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-    */
/* ex: set filetype=cpp softtabstop=4 shiftwidth=4 tabstop=4 cindent expandtab: */
 
/*
  Author(s):  Ankur Kapoor, Anton Deguet
  Created on: 2005-10-18
 
  (C) Copyright 2005-2022 Johns Hopkins University (JHU), All Rights Reserved.
 
--- begin cisst license - do not edit ---
 
This software is provided "as is" under an open source license, with
no warranty.  The complete license can be found in license.txt and
http://www.cisst.org/cisst/license.txt.
 
--- end cisst license ---
*/
 

 
 
#ifndef _nmrSVD_h
#define _nmrSVD_h
 
#include <cisstCommon/cmnThrow.h>
#include <cisstVector/vctFixedSizeMatrix.h>
#include <cisstVector/vctDynamicMatrix.h>
#include <cisstNumerical/nmrNetlib.h>
 
// Always include last
#include <cisstNumerical/nmrExport.h>
 

class nmrSVDDynamicData {
 
public:
    typedef vct::size_type size_type;

    typedef vctFixedSizeVector<size_type, 2> nsize_type;
 
protected:
    vctDynamicVector<CISSTNETLIB_DOUBLE> WorkspaceMemory;

    vctDynamicVector<CISSTNETLIB_DOUBLE> OutputMemory;

    vctDynamicMatrixRef<CISSTNETLIB_DOUBLE> UReference;
    vctDynamicMatrixRef<CISSTNETLIB_DOUBLE> VtReference;
    vctDynamicVectorRef<CISSTNETLIB_DOUBLE> SReference;
    vctDynamicVectorRef<CISSTNETLIB_DOUBLE> WorkspaceReference;

    size_type MMember;
    size_type NMember;
    bool StorageOrderMember;

    inline void SetDimension(size_type m,
                             size_type n,
                             bool storageOrder)
    {
        StorageOrderMember = storageOrder;
        MMember = m;
        NMember = n;
    }

    inline void AllocateOutputWorkspace( bool allocateOutput,
                                         bool allocateWorkspace)
    {
 
        // allocate output
        if (allocateOutput) {
            const size_type minmn =(MMember<NMember)? MMember: NMember;
            const size_type outputLength = ( MMember * MMember +
                                             NMember * NMember +
                                             minmn );
            this->OutputMemory.SetSize(outputLength);
            this->UReference.SetRef(MMember, MMember,
                                    (StorageOrderMember) ? MMember : 1,
                                    (StorageOrderMember) ? 1 : MMember,
                                    this->OutputMemory.Pointer(0));
            this->VtReference.SetRef(NMember, NMember,
                                     (StorageOrderMember)? NMember: 1,
                                     (StorageOrderMember)? 1: NMember,
                                     this->OutputMemory.Pointer(MMember * MMember));
            this->SReference.SetRef((MMember<NMember)? MMember:NMember,
                                    this->OutputMemory.Pointer(MMember*MMember + NMember*NMember),
                                    1);
        }
        else {
            this->OutputMemory.SetSize(0);
        }
        // allocate workspace
        if (allocateWorkspace) {
            this->WorkspaceMemory.SetSize( WorkspaceSize( MMember,
                                                          NMember ) );
            this->WorkspaceReference.SetRef(this->WorkspaceMemory);
        }
        else {
            this->WorkspaceMemory.SetSize(0);
        }
    }
 

    template <typename _matrixOwnerTypeU,
              typename _vectorOwnerTypeS,
              typename _matrixOwnerTypeVt>
    inline
    void ThrowUnlessOutputSizeIsCorrect(vctDynamicMatrixBase<_matrixOwnerTypeU, CISSTNETLIB_DOUBLE>& inU,
                                        vctDynamicVectorBase<_vectorOwnerTypeS, CISSTNETLIB_DOUBLE>& inS,
                                        vctDynamicMatrixBase<_matrixOwnerTypeVt, CISSTNETLIB_DOUBLE>& inVt) const
        CISST_THROW(std::runtime_error)
    {
 
        // check sizes and storage order
        if (! inU.IsSquare(MMember)) {
            cmnThrow(std::runtime_error("nmrSVDDynamicData: Size of matrix U is incorrect."));
        }
        if (inU.StorageOrder() != StorageOrderMember) {
            cmnThrow(std::runtime_error("nmrSVDDynamicData: Storage order of U is incorrect."));
        }
        if (!inU.IsCompact()) {
            cmnThrow(std::runtime_error("nmrSVDDynamicData: Matrix U must be compact."));
        }
        if (! inVt.IsSquare(NMember)) {
            cmnThrow(std::runtime_error("nmrSVDDynamicData: Size of matrix Vt is incorrect."));
        }
        if (inVt.StorageOrder() != StorageOrderMember) {
            cmnThrow(std::runtime_error("nmrSVDDynamicData: Storage order of Vt is incorrect."));
        }
        if (!inVt.IsCompact()) {
            cmnThrow(std::runtime_error("nmrSVDDynamicData: Matrix Vt must be compact."));
        }
        const size_type minmn = (MMember < NMember)? MMember: NMember;
        if (minmn != inS.size()) {
            cmnThrow(std::runtime_error("nmrSVDDynamicData: Size of vector S is incorrect."));
        }
        if (!inS.IsCompact()) {
            cmnThrow(std::runtime_error("nmrSVDDynamicData: Vector S must be compact."));
        }
    }
 

    template <typename _vectorOwnerTypeWorkspace>
    inline void
    ThrowUnlessWorkspaceSizeIsCorrect(vctDynamicVectorBase<_vectorOwnerTypeWorkspace, CISSTNETLIB_DOUBLE>& inWorkspace) const
        CISST_THROW(std::runtime_error)
    {
 
        const size_type lwork =
            nmrSVDDynamicData::WorkspaceSize(MMember, NMember);
 
        if (lwork > inWorkspace.size()) {
            cmnThrow(std::runtime_error("nmrSVDDynamicData: Workspace is too small."));
        }
 
        if (!inWorkspace.IsCompact()) {
            cmnThrow(std::runtime_error("nmrSVDDynamicData: Workspace must be compact."));
        }
    }
 
public:

    static inline size_type WorkspaceSize(size_type m, size_type n)
    {
        const size_type minmn = (m < n) ? m : n;
        const size_type maxmn = (m > n) ? m : n;
        const size_type lwork_1 = 3 * minmn + maxmn;
        const size_type lwork_2 = 5 * minmn;
        return (lwork_1 > lwork_2) ? lwork_1 : lwork_2;
    }

    template <class _matrixOwnerTypeA>
    static inline
    size_type WorkspaceSize( vctDynamicMatrixBase<_matrixOwnerTypeA, CISSTNETLIB_DOUBLE>& inA)
    {
        return nmrSVDDynamicData::WorkspaceSize(inA.rows(), inA.cols());
    }
 

    template <class _matrixOwnerTypeA>
    static inline
    nsize_type MatrixSSize(const vctDynamicConstMatrixBase<_matrixOwnerTypeA, CISSTNETLIB_DOUBLE> & A)
    {
        nsize_type matrixSize(A.rows(), A.cols());
        return matrixSize;
    }
 

    template <class _matrixOwnerTypeA, class _matrixOwnerTypeS, class _vectorOwnerTypeS>
    static inline
    vctDynamicMatrixBase<_matrixOwnerTypeS, CISSTNETLIB_DOUBLE> &
    UpdateMatrixS(const vctDynamicConstMatrixBase<_matrixOwnerTypeA, CISSTNETLIB_DOUBLE> & A,
                  const vctDynamicConstVectorBase<_vectorOwnerTypeS, CISSTNETLIB_DOUBLE> & vectorS,
                  vctDynamicMatrixBase<_matrixOwnerTypeS, CISSTNETLIB_DOUBLE> & matrixS)
        CISST_THROW(std::runtime_error)
    {
        if ((A.rows() != matrixS.rows()) || (A.cols() != matrixS.cols())) {
            cmnThrow(std::runtime_error("nmrSVDDynamicData::UpdateMatrixS: Size of matrix S is incorrect."));
        }
        matrixS.SetAll(0.0);
        matrixS.Diagonal().Assign(vectorS);
        return matrixS;
    }
 
#ifndef SWIG
#ifndef DOXYGEN
    class Friend {
    private:
        nmrSVDDynamicData & Data;
    public:
        Friend(nmrSVDDynamicData &inData): Data(inData) {
        }
        inline vctDynamicVectorRef<CISSTNETLIB_DOUBLE> & S(void) {
            return Data.SReference;
        }
        inline vctDynamicMatrixRef<CISSTNETLIB_DOUBLE> & U(void) {
            return Data.UReference;
        }
        inline vctDynamicMatrixRef<CISSTNETLIB_DOUBLE> & Vt(void) {
            return Data.VtReference;
        }
        inline vctDynamicVectorRef<CISSTNETLIB_DOUBLE>& Workspace(void){
            return Data.WorkspaceReference;
        }
        inline size_type M(void) {
            return Data.MMember;
        }
        inline size_type N(void) {
            return Data.NMember;
        }
        inline bool StorageOrder(void) {
            return Data.StorageOrderMember;
        }
    };
    friend class Friend;
#endif // DOXYGEN
#endif // SWIG

    nmrSVDDynamicData():
        MMember(static_cast<size_type>(0)),
        NMember(static_cast<size_type>(0)),
        StorageOrderMember(VCT_COL_MAJOR)
    {
        AllocateOutputWorkspace(false, false);
    }

    nmrSVDDynamicData(size_type m, size_type n, bool storageOrder)
    {
        this->Allocate(m, n, storageOrder);
    }

    template <class _matrixOwnerTypeA>
    nmrSVDDynamicData(const vctDynamicMatrixBase<_matrixOwnerTypeA, CISSTNETLIB_DOUBLE> & A)
    {
        this->Allocate(A);
    }

    template <class _matrixOwnerTypeA, class _vectorOwnerTypeWorkspace>
    nmrSVDDynamicData(vctDynamicMatrixBase<_matrixOwnerTypeA, CISSTNETLIB_DOUBLE>& A,
                      vctDynamicVectorBase<_vectorOwnerTypeWorkspace, CISSTNETLIB_DOUBLE>& inWorkspace)
    {
        this->SetRefWorkspace(A, inWorkspace);
    }

    template <typename _matrixOwnerTypeU,
              typename _vectorOwnerTypeS,
              typename _matrixOwnerTypeVt,
              typename _vectorOwnerTypeWorkspace>
    nmrSVDDynamicData(vctDynamicMatrixBase<_matrixOwnerTypeU, CISSTNETLIB_DOUBLE> & inU,
                      vctDynamicVectorBase<_vectorOwnerTypeS, CISSTNETLIB_DOUBLE> & inS,
                      vctDynamicMatrixBase<_matrixOwnerTypeVt, CISSTNETLIB_DOUBLE> & inVt,
                      vctDynamicVectorBase<_vectorOwnerTypeWorkspace, CISSTNETLIB_DOUBLE> & inWorkspace)
    {
        this->SetRef(inU, inS, inVt, inWorkspace);
    }

    template <typename _matrixOwnerTypeU,
              typename _vectorOwnerTypeS,
              typename _matrixOwnerTypeVt>
    nmrSVDDynamicData(vctDynamicMatrixBase<_matrixOwnerTypeU, CISSTNETLIB_DOUBLE> & inU,
                      vctDynamicVectorBase<_vectorOwnerTypeS, CISSTNETLIB_DOUBLE> & inS,
                      vctDynamicMatrixBase<_matrixOwnerTypeVt, CISSTNETLIB_DOUBLE> & inVt)
    {
        this->SetRefOutput(inU, inS, inVt);
    }
 

    template <class _matrixOwnerTypeA>
    inline
    void Allocate(const vctDynamicMatrixBase<_matrixOwnerTypeA, CISSTNETLIB_DOUBLE> & A)
    {
        this->Allocate(A.rows(), A.cols(), A.StorageOrder());
    }

    template <class _matrixOwnerTypeA, class _vectorOwnerTypeWorkspace>
    inline
    void SetRefWorkspace(vctDynamicMatrixBase<_matrixOwnerTypeA, CISSTNETLIB_DOUBLE> & A,
                         vctDynamicVectorBase<_vectorOwnerTypeWorkspace, CISSTNETLIB_DOUBLE> & inWorkspace)
    {
        this->SetDimension(A.rows(), A.cols(), A.StorageOrder());
 
        // allocate output and set references
        this->AllocateOutputWorkspace(true, false);
 
        // set reference on user provided workspace
        this->ThrowUnlessWorkspaceSizeIsCorrect(inWorkspace);
        this->WorkspaceReference.SetRef(inWorkspace);
    }

    void Allocate(size_type m, size_type n, bool storageOrder)
    {
        this->SetDimension(m, n, storageOrder);
        this->AllocateOutputWorkspace(true, true);
    }

    template <typename _matrixOwnerTypeU,
              typename _vectorOwnerTypeS,
              typename _matrixOwnerTypeVt,
              typename _vectorOwnerTypeWorkspace>
    void SetRef(vctDynamicMatrixBase<_matrixOwnerTypeU, CISSTNETLIB_DOUBLE> & inU,
                vctDynamicVectorBase<_vectorOwnerTypeS, CISSTNETLIB_DOUBLE> & inS,
                vctDynamicMatrixBase<_matrixOwnerTypeVt, CISSTNETLIB_DOUBLE> & inVt,
                vctDynamicVectorBase<_vectorOwnerTypeWorkspace, CISSTNETLIB_DOUBLE> & inWorkspace)
        CISST_THROW(std::runtime_error)
    {
        this->SetDimension(inU.rows(),inVt.rows(),inU.StorageOrder());
        this->AllocateOutputWorkspace(false, false);
        this->ThrowUnlessOutputSizeIsCorrect(inU, inS, inVt);
        this->ThrowUnlessWorkspaceSizeIsCorrect(inWorkspace);
 
        this->SReference.SetRef(inS);
        this->UReference.SetRef(inU);
        this->VtReference.SetRef(inVt);
        this->WorkspaceReference.SetRef(inWorkspace);
    }
 

    template <typename _matrixOwnerTypeU,
              typename _vectorOwnerTypeS,
              typename _matrixOwnerTypeVt>
    void SetRefOutput(vctDynamicMatrixBase<_matrixOwnerTypeU, CISSTNETLIB_DOUBLE> & inU,
                      vctDynamicVectorBase<_vectorOwnerTypeS, CISSTNETLIB_DOUBLE> & inS,
                      vctDynamicMatrixBase<_matrixOwnerTypeVt, CISSTNETLIB_DOUBLE> & inVt)
        CISST_THROW(std::runtime_error)
    {
        this->SetDimension(inU.rows(), inVt.rows(), inU.StorageOrder());
        this->ThrowUnlessOutputSizeIsCorrect(inU, inS, inVt);
 
        this->SReference.SetRef(inS);
        this->UReference.SetRef(inU);
        this->VtReference.SetRef(inVt);
 
        AllocateOutputWorkspace(false, true);
    }

    inline
    const vctDynamicVectorRef<CISSTNETLIB_DOUBLE>& S(void) const
    { return SReference; }

    inline
    const vctDynamicMatrixRef<CISSTNETLIB_DOUBLE> & U(void) const
    { return UReference; }

    inline
    const vctDynamicMatrixRef<CISSTNETLIB_DOUBLE> & Vt(void) const
    { return VtReference; }
 
};
 
 
 
 

#ifndef SWIG
template <vct::size_type _rows, vct::size_type _cols, bool _storageOrder = VCT_ROW_MAJOR>
class nmrSVDFixedSizeData
{
public:
#ifndef DOXYGEN
    typedef vct::size_type size_type;
 
    enum {M = (_storageOrder == VCT_COL_MAJOR) ? _rows : _cols};
    enum {N = (_storageOrder == VCT_COL_MAJOR) ? _cols : _rows};
    enum {MIN_MN =
          (static_cast<size_type>(M) < static_cast<size_type>(N))
          ?
          static_cast<size_type>(M)
          :
          static_cast<size_type>(N)};
    enum {LWORK_1 =
          (3 * static_cast<size_type>(MIN_MN) + (static_cast<size_type>(M)) > static_cast<size_type>(N))
          ?
          static_cast<size_type>(M)
          :
          static_cast<size_type>(N)};
    enum {LWORK_2 = 5 * MIN_MN};
    enum {LWORK =
          (static_cast<size_type>(LWORK_1) > static_cast<size_type>(LWORK_2))
          ?
          static_cast<size_type>(LWORK_1)
          :
          static_cast<size_type>(LWORK_2)};
#endif // DOXYGEN
    typedef vctFixedSizeMatrix<CISSTNETLIB_DOUBLE, _rows, _cols, _storageOrder> MatrixTypeA;
    typedef vctFixedSizeMatrix<CISSTNETLIB_DOUBLE, _rows, _rows, _storageOrder> MatrixTypeU;
    typedef vctFixedSizeVector<CISSTNETLIB_DOUBLE, MIN_MN> VectorTypeS;
    typedef vctFixedSizeMatrix<CISSTNETLIB_DOUBLE, _rows, _cols, _storageOrder> MatrixTypeS;
    typedef vctFixedSizeMatrix<CISSTNETLIB_DOUBLE, _cols, _cols, _storageOrder> MatrixTypeVt;
    typedef vctFixedSizeVector<CISSTNETLIB_DOUBLE, LWORK> VectorTypeWorkspace;
 
protected:
    MatrixTypeU UMember;                 
    MatrixTypeVt VtMember;               
    VectorTypeS SMember;                 
    VectorTypeWorkspace WorkspaceMember; 
 
public:
#ifndef DOXYGEN
    class Friend {
    private:
        nmrSVDFixedSizeData<_rows, _cols, _storageOrder>& Data;
    public:
        Friend(nmrSVDFixedSizeData<_rows, _cols, _storageOrder> &inData): Data(inData)
        {}
 
        inline VectorTypeS & S(void)
        { return Data.SMember; }
 
        inline MatrixTypeU & U(void)
        { return Data.UMember; }
 
        inline MatrixTypeVt & Vt(void)
        { return Data.VtMember; }
 
        inline VectorTypeWorkspace & Workspace(void)
        { return Data.WorkspaceMember; }
    };
    friend class Friend;
#endif // DOXYGEN

    nmrSVDFixedSizeData() {};

    inline const VectorTypeS & S(void) const
    { return SMember; }

    inline const MatrixTypeU & U(void) const
    { return UMember; }

    inline const MatrixTypeVt & Vt(void) const
    { return VtMember; }

    static inline
    MatrixTypeS & UpdateMatrixS( const VectorTypeS & vectorS,
                                 MatrixTypeS & matrixS )
    {
        matrixS.SetAll(0.0);
        matrixS.Diagonal().Assign(vectorS);
        return matrixS;
    }
};
#endif // SWIG
 
 
 

 

template <class _matrixOwnerType>
inline
CISSTNETLIB_INTEGER nmrSVD(vctDynamicMatrixBase<_matrixOwnerType, CISSTNETLIB_DOUBLE> & A,
                           nmrSVDDynamicData & data)
    CISST_THROW(std::runtime_error)
{
    typename nmrSVDDynamicData::Friend dataFriend(data);
    CISSTNETLIB_INTEGER Info;
    char m_Jobu = 'A';
    char m_Jobvt = 'A';
    CISSTNETLIB_INTEGER m_Lwork =
        static_cast<CISSTNETLIB_INTEGER>(nmrSVDDynamicData::WorkspaceSize(dataFriend.M(),
                                                                          dataFriend.N()));
 
    /* check that storage order matches with Allocate() */
    if (A.StorageOrder() != dataFriend.StorageOrder()) {
        cmnThrow(std::runtime_error("nmrSVD: Storage order used for Allocate was different"));
    }
    /* check sizes */
    if ((dataFriend.M() != A.rows()) || (dataFriend.N() != A.cols())) {
        cmnThrow(std::runtime_error("nmrSVD: Size used for Allocate was different"));
    }
    /* check that the matrices are compact */
    if (! A.IsCompact()) {
        cmnThrow(std::runtime_error("nmrSVD: Requires a compact matrix"));
    }
 
    /* Based on storage order, permute U and Vt as well as dimension */
    CISSTNETLIB_DOUBLE *UPtr, *VtPtr;
    CISSTNETLIB_INTEGER m_Lda, m_Ldu, m_Ldvt;
 
    CISSTNETLIB_INTEGER dfM = static_cast<CISSTNETLIB_INTEGER>(dataFriend.M());
    CISSTNETLIB_INTEGER dfN = static_cast<CISSTNETLIB_INTEGER>(dataFriend.N());
    if (A.IsColMajor()) {
        m_Lda = (1 > dfM) ? 1 : dfM;
        m_Ldu = dfM;
        m_Ldvt = dfN;
        UPtr = dataFriend.U().Pointer();
        VtPtr = dataFriend.Vt().Pointer();
    } else {
        m_Lda = (1 > dfN) ? 1 : dfN;
        m_Ldu = dfN;
        m_Ldvt = dfM;
        UPtr = dataFriend.Vt().Pointer();
        VtPtr = dataFriend.U().Pointer();
    }
 
    // for versions based on gfortran/lapack, CISSTNETLIB_VERSION is
    // defined
#if defined(CISSTNETLIB_VERSION)
#if defined(CISSTNETLIB_VERSION_MAJOR)
#if (CISSTNETLIB_VERSION_MAJOR >= 3)
    cisstNetlib_dgesvd_(&m_Jobu, &m_Jobvt, &m_Ldu, &m_Ldvt,
                        A.Pointer(), &m_Lda, dataFriend.S().Pointer(),
                        UPtr, &m_Ldu,
                        VtPtr, &m_Ldvt,
                        dataFriend.Workspace().Pointer(), &m_Lwork, &Info);
#endif
#else // no major version
    dgesvd_(&m_Jobu, &m_Jobvt, &m_Ldu, &m_Ldvt,
            A.Pointer(), &m_Lda, dataFriend.S().Pointer(),
            UPtr, &m_Ldu,
            VtPtr, &m_Ldvt,
            dataFriend.Workspace().Pointer(), &m_Lwork, &Info);
#endif // CISSTNETLIB_VERSION
#else
    ftnlen jobu_len = (ftnlen)1, jobvt_len = (ftnlen)1;
    la_dzlapack_MP_sgesvd_nat(&m_Jobu, &m_Jobvt, &m_Ldu, &m_Ldvt,
                              A.Pointer(), &m_Lda, dataFriend.S().Pointer(),
                              UPtr, &m_Ldu,
                              VtPtr, &m_Ldvt,
                              dataFriend.Workspace().Pointer(), &m_Lwork, &Info,
                              jobu_len, jobvt_len);
#endif
 
    return Info;
}

template <class _matrixOwnerTypeA,
          class _matrixOwnerTypeU,
          class _vectorOwnerTypeS,
          class _matrixOwnerTypeVt,
          class _vectorOwnerTypeWorkspace>
inline
CISSTNETLIB_INTEGER nmrSVD(vctDynamicMatrixBase<_matrixOwnerTypeA, CISSTNETLIB_DOUBLE> & A,
                           vctDynamicMatrixBase<_matrixOwnerTypeU, CISSTNETLIB_DOUBLE> & U,
                           vctDynamicVectorBase<_vectorOwnerTypeS, CISSTNETLIB_DOUBLE> & S,
                           vctDynamicMatrixBase<_matrixOwnerTypeVt, CISSTNETLIB_DOUBLE> & Vt,
                           vctDynamicVectorBase<_vectorOwnerTypeWorkspace, CISSTNETLIB_DOUBLE> & Workspace)
{
    nmrSVDDynamicData svdData(U, S, Vt, Workspace);
    CISSTNETLIB_INTEGER ret_value = nmrSVD(A, svdData);
    return ret_value;
}

template <class _matrixOwnerTypeA,
          class _matrixOwnerTypeU,
          class _vectorOwnerTypeS,
          class _matrixOwnerTypeVt>
inline
CISSTNETLIB_INTEGER nmrSVD(vctDynamicMatrixBase<_matrixOwnerTypeA, CISSTNETLIB_DOUBLE>& A,
                           vctDynamicMatrixBase<_matrixOwnerTypeU, CISSTNETLIB_DOUBLE>& U,
                           vctDynamicVectorBase<_vectorOwnerTypeS, CISSTNETLIB_DOUBLE>& S,
                           vctDynamicMatrixBase<_matrixOwnerTypeVt, CISSTNETLIB_DOUBLE>& Vt)
{
    nmrSVDDynamicData svdData(U, S, Vt);
    CISSTNETLIB_INTEGER ret_value = nmrSVD(A, svdData);
    return ret_value;
}
 
 
#ifndef SWIG // don't have fixed size containers in Python

template <vct::size_type _rows, vct::size_type _cols, vct::size_type _minmn,
          vct::size_type _work, bool _storageOrder>
inline
CISSTNETLIB_INTEGER nmrSVD(vctFixedSizeMatrix<CISSTNETLIB_DOUBLE, _rows, _cols, _storageOrder> & A,
                           vctFixedSizeMatrix<CISSTNETLIB_DOUBLE, _rows, _rows, _storageOrder> & U,
                           vctFixedSizeVector<CISSTNETLIB_DOUBLE, _minmn> & S,
                           vctFixedSizeMatrix<CISSTNETLIB_DOUBLE, _cols, _cols, _storageOrder> & Vt,
                           vctFixedSizeVector<CISSTNETLIB_DOUBLE, _work> & workspace)
{
#if CMN_ASSERT_IS_DEFINED
    const CISSTNETLIB_INTEGER minmn =
        static_cast<CISSTNETLIB_INTEGER>(nmrSVDFixedSizeData<_rows, _cols, _storageOrder>::MIN_MN);
#endif
    //Assert if requirement is greater than size provided!
    CMN_ASSERT(minmn <= static_cast<CISSTNETLIB_INTEGER>(_minmn));
    CISSTNETLIB_INTEGER ldu = (_storageOrder == VCT_COL_MAJOR) ? _rows : _cols;
    CISSTNETLIB_INTEGER lda = (1 > ldu) ? 1 : ldu;
    CISSTNETLIB_INTEGER ldvt = (_storageOrder == VCT_COL_MAJOR) ? _cols : _rows;
    CISSTNETLIB_INTEGER lwork =
        static_cast<CISSTNETLIB_INTEGER>(nmrSVDFixedSizeData<_rows, _cols, _storageOrder>::LWORK);
    //Assert if requirement is greater than size provided!
    CMN_ASSERT(lwork <= static_cast<CISSTNETLIB_INTEGER>(_work));
    char jobu = 'A';
    char jobvt = 'A';
    CISSTNETLIB_INTEGER info;
    CISSTNETLIB_DOUBLE *UPtr, *VtPtr;
    if (_storageOrder == VCT_COL_MAJOR) {
        UPtr = U.Pointer();
        VtPtr = Vt.Pointer();
    } else {
        UPtr = Vt.Pointer();
        VtPtr = U.Pointer();
    }
 
    // for versions based on gfortran/lapack, CISSTNETLIB_VERSION is
    // defined
#if defined(CISSTNETLIB_VERSION)
    /* call the LAPACK C function */
#if defined(CISSTNETLIB_VERSION_MAJOR)
#if (CISSTNETLIB_VERSION_MAJOR >= 3)
    cisstNetlib_dgesvd_(&jobu, &jobvt, &ldu, &ldvt,
                        A.Pointer(), &lda, S.Pointer(),
                        UPtr, &ldu,
                        VtPtr, &ldvt,
                        workspace.Pointer(), &lwork, &info);
#endif
#else // no major version
      dgesvd_(&jobu, &jobvt, &ldu, &ldvt,
              A.Pointer(), &lda, S.Pointer(),
              UPtr, &ldu,
              VtPtr, &ldvt,
              workspace.Pointer(), &lwork, &info);
#endif // CISSTNETLIB_VERSION
#else
    ftnlen jobu_len = (ftnlen)1, jobvt_len = (ftnlen)1;
    la_dzlapack_MP_sgesvd_nat(&jobu, &jobvt, &ldu, &ldvt,
                              A.Pointer(), &lda, S.Pointer(),
                              UPtr, &ldu,
                              VtPtr, &ldvt,
                              workspace.Pointer(), &lwork, &info,
                              jobu_len, jobvt_len);
#endif
 
    return info;
}

template <vct::size_type _rows, vct::size_type _cols, vct::size_type _minmn, bool _storageOrder>
inline
CISSTNETLIB_INTEGER nmrSVD(vctFixedSizeMatrix<CISSTNETLIB_DOUBLE, _rows, _cols, _storageOrder> & A,
                           vctFixedSizeMatrix<CISSTNETLIB_DOUBLE, _rows, _rows, _storageOrder> & U,
                           vctFixedSizeVector<CISSTNETLIB_DOUBLE, _minmn> & S,
                           vctFixedSizeMatrix<CISSTNETLIB_DOUBLE, _cols, _cols, _storageOrder> & Vt)
{
    typename nmrSVDFixedSizeData<_rows, _cols, _storageOrder>::VectorTypeWorkspace workspace;
    const CISSTNETLIB_INTEGER ret_value = nmrSVD(A, U, S, Vt, workspace);
    return ret_value;
}
 

template <vct::size_type _rows, vct::size_type _cols, bool _storageOrder>
inline
CISSTNETLIB_INTEGER nmrSVD(vctFixedSizeMatrix<CISSTNETLIB_DOUBLE, _rows, _cols, _storageOrder> & A,
                           nmrSVDFixedSizeData<_rows, _cols, _storageOrder> & data)
{
    typename nmrSVDFixedSizeData<_rows, _cols, _storageOrder>::Friend dataFriend(data);
    CISSTNETLIB_INTEGER ret_value = nmrSVD( A, dataFriend.U(), dataFriend.S(),
                                            dataFriend.Vt(), dataFriend.Workspace() );
    return ret_value;
}
#endif // SWIG

 
#endif