コード例 #1
0
ファイル: SVD.hpp プロジェクト: certik/Elemental
inline void
SimpleSingularValuesUpper
( DistMatrix<Complex<Real> >& A,
  DistMatrix<Real,VR,STAR>& s )
{
#ifndef RELEASE
    PushCallStack("svd::SimpleSingularValuesUpper");
#endif
    typedef Complex<Real> C;
    const int m = A.Height();
    const int n = A.Width();
    const int k = std::min( m, n );
    const int offdiagonal = ( m>=n ? 1 : -1 );
    const char uplo = ( m>=n ? 'U' : 'L' );
    const Grid& g = A.Grid();

    // Bidiagonalize A
    DistMatrix<C,STAR,STAR> tP(g), tQ(g);
    Bidiag( A, tP, tQ );

    // Grab copies of the diagonal and sub/super-diagonal of A
    DistMatrix<Real,MD,STAR> d_MD_STAR( g ), 
                             e_MD_STAR( g );
    A.GetRealPartOfDiagonal( d_MD_STAR );
    A.GetRealPartOfDiagonal( e_MD_STAR, offdiagonal );

    // In order to use serial QR kernels, we need the full bidiagonal matrix
    // on each process
    //
    // NOTE: lapack::BidiagQRAlg expects e to be of length k
    DistMatrix<Real,STAR,STAR> d_STAR_STAR( d_MD_STAR );
    DistMatrix<Real,STAR,STAR> eHat_STAR_STAR( k, 1, g );
    DistMatrix<Real,STAR,STAR> e_STAR_STAR( g );
    e_STAR_STAR.View( eHat_STAR_STAR, 0, 0, k-1, 1 );
    e_STAR_STAR = e_MD_STAR;

    // Compute the singular values of the bidiagonal matrix
    lapack::BidiagQRAlg
    ( uplo, k, 0, 0,
      d_STAR_STAR.LocalBuffer(), e_STAR_STAR.LocalBuffer(), 
      (C*)0, 1, (C*)0, 1 );

    // Copy out the appropriate subset of the singular values
    s = d_STAR_STAR;
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #2
0
inline void
GolubReinschUpper
( DistMatrix<F>& A,
  DistMatrix<BASE(F),VR,STAR>& s )
{
#ifndef RELEASE
    CallStackEntry entry("svd::GolubReinschUpper");
#endif
    typedef BASE(F) Real;
    const Int m = A.Height();
    const Int n = A.Width();
    const Int k = Min( m, n );
    const Int offdiagonal = ( m>=n ? 1 : -1 );
    const Grid& g = A.Grid();

    // Bidiagonalize A
    DistMatrix<F,STAR,STAR> tP(g), tQ(g);
    Bidiag( A, tP, tQ );

    // Grab copies of the diagonal and sub/super-diagonal of A
    DistMatrix<Real,MD,STAR> d_MD_STAR(g), e_MD_STAR(g);
    A.GetRealPartOfDiagonal( d_MD_STAR );
    A.GetRealPartOfDiagonal( e_MD_STAR, offdiagonal );

    // In order to use serial DQDS kernels, we need the full bidiagonal matrix
    // on each process
    //
    // NOTE: lapack::BidiagDQDS expects e to be of length k
    DistMatrix<Real,STAR,STAR> d_STAR_STAR( d_MD_STAR ),
                               eHat_STAR_STAR( k, 1, g ),
                               e_STAR_STAR( g );
    View( e_STAR_STAR, eHat_STAR_STAR, 0, 0, k-1, 1 );
    e_STAR_STAR = e_MD_STAR;

    // Compute the singular values of the bidiagonal matrix via DQDS
    lapack::BidiagDQDS( k, d_STAR_STAR.Buffer(), e_STAR_STAR.Buffer() );

    // Copy out the appropriate subset of the singular values
    s = d_STAR_STAR;
}
コード例 #3
0
ファイル: HermitianTridiag.cpp プロジェクト: hrhill/Elemental
void TestCorrectness
( UpperOrLower uplo, 
  const DistMatrix<F>& A, 
  const DistMatrix<F,STAR,STAR>& t,
        DistMatrix<F>& AOrig,
  bool print, bool display )
{
    typedef Base<F> Real;
    const Grid& g = A.Grid();
    const Int m = AOrig.Height();
    const Real infNormAOrig = HermitianInfinityNorm( uplo, AOrig );
    const Real frobNormAOrig = HermitianFrobeniusNorm( uplo, AOrig );
    if( g.Rank() == 0 )
        cout << "Testing error..." << endl;

    // Grab the diagonal and subdiagonal of the symmetric tridiagonal matrix
    Int subdiagonal = ( uplo==LOWER ? -1 : +1 );
    auto d = A.GetRealPartOfDiagonal();
    auto e = A.GetRealPartOfDiagonal( subdiagonal );
     
    // Grab a full copy of e so that we may fill the opposite subdiagonal 
    DistMatrix<Real,STAR,STAR> e_STAR_STAR( e );
    DistMatrix<Real,MD,STAR> eOpposite(g);
    A.ForceDiagonalAlign( eOpposite, -subdiagonal );
    eOpposite = e_STAR_STAR;
    
    // Zero B and then fill its tridiagonal
    DistMatrix<F> B(g);
    B.AlignWith( A );
    Zeros( B, m, m );
    B.SetRealPartOfDiagonal( d );
    B.SetRealPartOfDiagonal( e, subdiagonal );
    B.SetRealPartOfDiagonal( eOpposite, -subdiagonal );
    if( print )
        Print( B, "Tridiagonal" );
    if( display )
        Display( B, "Tridiagonal" );

    // Reverse the accumulated Householder transforms, ignoring symmetry
    herm_tridiag::ApplyQ( LEFT, uplo, NORMAL, A, t, B );
    herm_tridiag::ApplyQ( RIGHT, uplo, ADJOINT, A, t, B );
    if( print )
        Print( B, "Rotated tridiagonal" );
    if( display )
        Display( B, "Rotated tridiagonal" );

    // Compare the appropriate triangle of AOrig and B
    MakeTriangular( uplo, AOrig );
    MakeTriangular( uplo, B );
    Axpy( F(-1), AOrig, B );
    if( print )
        Print( B, "Error in rotated tridiagonal" );
    if( display )
        Display( B, "Error in rotated tridiagonal" );
    const Real infNormError = HermitianInfinityNorm( uplo, B );
    const Real frobNormError = HermitianFrobeniusNorm( uplo, B );

    // Compute || I - Q Q^H ||
    MakeIdentity( B );
    herm_tridiag::ApplyQ( RIGHT, uplo, ADJOINT, A, t, B );
    DistMatrix<F> QHAdj( g );
    Adjoint( B, QHAdj );
    MakeIdentity( B );
    herm_tridiag::ApplyQ( LEFT, uplo, NORMAL, A, t, B );
    Axpy( F(-1), B, QHAdj );
    herm_tridiag::ApplyQ( RIGHT, uplo, ADJOINT, A, t, B );
    UpdateDiagonal( B, F(-1) );
    const Real infNormQError = InfinityNorm( B );
    const Real frobNormQError = FrobeniusNorm( B ); 

    if( g.Rank() == 0 )
    {
        cout << "    ||A||_oo = " << infNormAOrig << "\n"
             << "    ||A||_F  = " << frobNormAOrig << "\n"
             << "    || I - Q^H Q ||_oo = " << infNormQError << "\n"
             << "    || I - Q^H Q ||_F  = " << frobNormQError << "\n"
             << "    ||A - Q T Q^H||_oo = " << infNormError << "\n"
             << "    ||A - Q T Q^H||_F  = " << frobNormError << endl;
    }
}
コード例 #4
0
inline void
GolubReinschUpper
( DistMatrix<F>& A, DistMatrix<BASE(F),VR,STAR>& s, DistMatrix<F>& V )
{
#ifndef RELEASE
    CallStackEntry entry("svd::GolubReinschUpper");
#endif
    typedef BASE(F) Real;
    const Int m = A.Height();
    const Int n = A.Width();
    const Int k = Min( m, n );
    const Int offdiagonal = ( m>=n ? 1 : -1 );
    const char uplo = ( m>=n ? 'U' : 'L' );
    const Grid& g = A.Grid();

    // Bidiagonalize A
    DistMatrix<F,STAR,STAR> tP( g ), tQ( g );
    Bidiag( A, tP, tQ );

    // Grab copies of the diagonal and sub/super-diagonal of A
    DistMatrix<Real,MD,STAR> d_MD_STAR(g), e_MD_STAR(g);
    A.GetRealPartOfDiagonal( d_MD_STAR );
    A.GetRealPartOfDiagonal( e_MD_STAR, offdiagonal );

    // NOTE: lapack::BidiagQRAlg expects e to be of length k
    DistMatrix<Real,STAR,STAR> d_STAR_STAR( d_MD_STAR ),
                               eHat_STAR_STAR( k, 1, g ),
                               e_STAR_STAR( g );
    View( e_STAR_STAR, eHat_STAR_STAR, 0, 0, k-1, 1 );
    e_STAR_STAR = e_MD_STAR;

    // Initialize U and VAdj to the appropriate identity matrices
    DistMatrix<F,VC,STAR> U_VC_STAR( g );
    DistMatrix<F,STAR,VC> VAdj_STAR_VC( g );
    U_VC_STAR.AlignWith( A );
    VAdj_STAR_VC.AlignWith( V );
    Identity( U_VC_STAR, m, k );
    Identity( VAdj_STAR_VC, k, n );

    // Compute the SVD of the bidiagonal matrix and accumulate the Givens
    // rotations into our local portion of U and VAdj
    Matrix<F>& ULoc = U_VC_STAR.Matrix();
    Matrix<F>& VAdjLoc = VAdj_STAR_VC.Matrix();
    lapack::BidiagQRAlg
    ( uplo, k, VAdjLoc.Width(), ULoc.Height(),
      d_STAR_STAR.Buffer(), e_STAR_STAR.Buffer(), 
      VAdjLoc.Buffer(), VAdjLoc.LDim(), 
      ULoc.Buffer(), ULoc.LDim() );

    // Make a copy of A (for the Householder vectors) and pull the necessary 
    // portions of U and VAdj into a standard matrix dist.
    DistMatrix<F> B( A );
    if( m >= n )
    {
        DistMatrix<F> AT(g), AB(g);
        DistMatrix<F,VC,STAR> UT_VC_STAR(g), UB_VC_STAR(g);
        PartitionDown( A, AT, AB, n );
        PartitionDown( U_VC_STAR, UT_VC_STAR, UB_VC_STAR, n );
        AT = UT_VC_STAR;
        MakeZeros( AB );
        Adjoint( VAdj_STAR_VC, V );
    }
    else
    {
        DistMatrix<F> VT(g), VB(g);
        DistMatrix<F,STAR,VC> VAdjL_STAR_VC(g), VAdjR_STAR_VC(g);
        PartitionDown( V, VT, VB, m );
        PartitionRight( VAdj_STAR_VC, VAdjL_STAR_VC, VAdjR_STAR_VC, m );
        Adjoint( VAdjL_STAR_VC, VT );
        MakeZeros( VB );
    }

    // Backtransform U and V
    bidiag::ApplyU( LEFT, NORMAL, B, tQ, A );
    bidiag::ApplyV( LEFT, NORMAL, B, tP, V );

    // Copy out the appropriate subset of the singular values
    s = d_STAR_STAR;
}
コード例 #5
0
inline void
GolubReinschUpper_FLA
( DistMatrix<F>& A, DistMatrix<BASE(F),VR,STAR>& s, DistMatrix<F>& V )
{
#ifndef RELEASE
    CallStackEntry entry("svd::GolubReinschUpper_FLA");
#endif
    typedef BASE(F) Real;
    const Int m = A.Height();
    const Int n = A.Width();
    const Int k = Min( m, n );
    const Int offdiagonal = ( m>=n ? 1 : -1 );
    const Grid& g = A.Grid();

    // Bidiagonalize A
    DistMatrix<F,STAR,STAR> tP(g), tQ(g);
    Bidiag( A, tP, tQ );

    // Grab copies of the diagonal and sub/super-diagonal of A
    DistMatrix<Real,MD,STAR> d_MD_STAR(g), e_MD_STAR(g);
    A.GetRealPartOfDiagonal( d_MD_STAR );
    A.GetRealPartOfDiagonal( e_MD_STAR, offdiagonal );

    // In order to use serial QR kernels, we need the full bidiagonal matrix
    // on each process
    DistMatrix<Real,STAR,STAR> d_STAR_STAR( d_MD_STAR ),
                               e_STAR_STAR( e_MD_STAR );

    // Initialize U and VAdj to the appropriate identity matrices
    DistMatrix<F,VC,STAR> U_VC_STAR(g), V_VC_STAR(g);
    U_VC_STAR.AlignWith( A );
    V_VC_STAR.AlignWith( V );
    Identity( U_VC_STAR, m, k );
    Identity( V_VC_STAR, n, k );

    FlaSVD
    ( k, U_VC_STAR.LocalHeight(), V_VC_STAR.LocalHeight(),
      d_STAR_STAR.Buffer(), e_STAR_STAR.Buffer(),
      U_VC_STAR.Buffer(), U_VC_STAR.LDim(),
      V_VC_STAR.Buffer(), V_VC_STAR.LDim() );

    // Make a copy of A (for the Householder vectors) and pull the necessary 
    // portions of U and V into a standard matrix dist.
    DistMatrix<F> B( A );
    if( m >= n )
    {
        DistMatrix<F> AT(g), AB(g);
        DistMatrix<F,VC,STAR> UT_VC_STAR(g), UB_VC_STAR(g);
        PartitionDown( A, AT, AB, n );
        PartitionDown( U_VC_STAR, UT_VC_STAR, UB_VC_STAR, n );
        AT = UT_VC_STAR;
        MakeZeros( AB );
        V = V_VC_STAR;
    }
    else
    {
        DistMatrix<F> VT(g), VB(g);
        DistMatrix<F,VC,STAR> VT_VC_STAR(g), VB_VC_STAR(g);
        PartitionDown( V, VT, VB, m );
        PartitionDown( V_VC_STAR, VT_VC_STAR, VB_VC_STAR, m );
        VT = VT_VC_STAR;
        MakeZeros( VB );
    }

    // Backtransform U and V
    bidiag::ApplyU( LEFT, NORMAL, B, tQ, A );
    bidiag::ApplyV( LEFT, NORMAL, B, tP, V );

    // Copy out the appropriate subset of the singular values
    s = d_STAR_STAR;
}
コード例 #6
0
void TestCorrectness
( bool print,
  UpperOrLower uplo, 
  const DistMatrix<F>& A, 
  const DistMatrix<F,STAR,STAR>& t,
        DistMatrix<F>& AOrig )
{
    typedef BASE(F) Real;
    const Grid& g = A.Grid();
    const Int m = AOrig.Height();

    Int subdiagonal = ( uplo==LOWER ? -1 : +1 );

    if( g.Rank() == 0 )
        cout << "Testing error..." << endl;

    // Grab the diagonal and subdiagonal of the symmetric tridiagonal matrix
    DistMatrix<Real,MD,STAR> d(g);
    DistMatrix<Real,MD,STAR> e(g);
    A.GetRealPartOfDiagonal( d );
    A.GetRealPartOfDiagonal( e, subdiagonal );
     
    // Grab a full copy of e so that we may fill the opposite subdiagonal 
    DistMatrix<Real,STAR,STAR> e_STAR_STAR(g);
    DistMatrix<Real,MD,STAR> eOpposite(g);
    e_STAR_STAR = e;
    eOpposite.AlignWithDiagonal( A.DistData(), -subdiagonal );
    eOpposite = e_STAR_STAR;
    
    // Zero B and then fill its tridiagonal
    DistMatrix<F> B(g);
    B.AlignWith( A );
    Zeros( B, m, m );
    B.SetRealPartOfDiagonal( d );
    B.SetRealPartOfDiagonal( e, subdiagonal );
    B.SetRealPartOfDiagonal( eOpposite, -subdiagonal );
    if( print )
        Print( B, "Tridiagonal" );

    // Reverse the accumulated Householder transforms, ignoring symmetry
    hermitian_tridiag::ApplyQ( LEFT, uplo, NORMAL, A, t, B );
    hermitian_tridiag::ApplyQ( RIGHT, uplo, ADJOINT, A, t, B );
    if( print )
        Print( B, "Rotated tridiagonal" );

    // Compare the appropriate triangle of AOrig and B
    MakeTriangular( uplo, AOrig );
    MakeTriangular( uplo, B );
    Axpy( F(-1), AOrig, B );
    if( print )
        Print( B, "Error in rotated tridiagonal" );

    const Real infNormOfAOrig = HermitianInfinityNorm( uplo, AOrig );
    const Real frobNormOfAOrig = HermitianFrobeniusNorm( uplo, AOrig );
    const Real infNormOfError = HermitianInfinityNorm( uplo, B );
    const Real frobNormOfError = HermitianFrobeniusNorm( uplo, B );
    if( g.Rank() == 0 )
    {
        cout << "    ||AOrig||_1 = ||AOrig||_oo = " << infNormOfAOrig << "\n"
             << "    ||AOrig||_F                = " << frobNormOfAOrig << "\n"
             << "    ||AOrig - Q^H A Q||_oo     = " << infNormOfError << "\n"
             << "    ||AOrig - Q^H A Q||_F      = " << frobNormOfError << endl;
    }
}
コード例 #7
0
ファイル: HermitianTridiag.cpp プロジェクト: jimgoo/Elemental
void TestCorrectness
( bool print,
  UpperOrLower uplo, 
  const DistMatrix<Complex<R> >& A, 
  const DistMatrix<Complex<R>,STAR,STAR>& t,
        DistMatrix<Complex<R> >& AOrig )
{
    typedef Complex<R> C;
    const Grid& g = A.Grid();
    const int m = AOrig.Height();

    int subdiagonal = ( uplo==LOWER ? -1 : +1 );

    if( g.Rank() == 0 )
        cout << "Testing error..." << endl;

    // Grab the diagonal and subdiagonal of the symmetric tridiagonal matrix
    DistMatrix<R,MD,STAR> d(g);
    DistMatrix<R,MD,STAR> e(g);
    A.GetRealPartOfDiagonal( d );
    A.GetRealPartOfDiagonal( e, subdiagonal );
     
    // Grab a full copy of e so that we may fill the opposite subdiagonal 
    DistMatrix<R,STAR,STAR> e_STAR_STAR(g);
    DistMatrix<R,MD,STAR> eOpposite(g);
    e_STAR_STAR = e;
    eOpposite.AlignWithDiagonal( A, -subdiagonal );
    eOpposite = e_STAR_STAR;
    
    // Zero B and then fill its tridiagonal
    DistMatrix<C> B(g);
    B.AlignWith( A );
    Zeros( m, m, B );
    B.SetRealPartOfDiagonal( d );
    B.SetRealPartOfDiagonal( e, subdiagonal );
    B.SetRealPartOfDiagonal( eOpposite, -subdiagonal );

    // Reverse the accumulated Householder transforms, ignoring symmetry
    if( uplo == LOWER )
    {
        ApplyPackedReflectors
        ( LEFT, LOWER, VERTICAL, BACKWARD, 
          UNCONJUGATED, subdiagonal, A, t, B );
        ApplyPackedReflectors
        ( RIGHT, LOWER, VERTICAL, BACKWARD, 
          CONJUGATED, subdiagonal, A, t, B );
    }
    else
    {
        ApplyPackedReflectors
        ( LEFT, UPPER, VERTICAL, FORWARD, 
          UNCONJUGATED, subdiagonal, A, t, B );
        ApplyPackedReflectors
        ( RIGHT, UPPER, VERTICAL, FORWARD, 
          CONJUGATED, subdiagonal, A, t, B );
    }

    // Compare the appropriate triangle of AOrig and B
    MakeTriangular( uplo, AOrig );
    MakeTriangular( uplo, B );
    Axpy( C(-1), AOrig, B );

    const R infNormOfAOrig = HermitianNorm( uplo, AOrig, INFINITY_NORM );
    const R frobNormOfAOrig = HermitianNorm( uplo, AOrig, FROBENIUS_NORM );
    const R infNormOfError = HermitianNorm( uplo, B, INFINITY_NORM );
    const R frobNormOfError = HermitianNorm( uplo, B, FROBENIUS_NORM );
    if( g.Rank() == 0 )
    {
        cout << "    ||AOrig||_1 = ||AOrig||_oo = " << infNormOfAOrig << "\n"
             << "    ||AOrig||_F                = " << frobNormOfAOrig << "\n"
             << "    ||AOrig - Q^H A Q||_oo     = " << infNormOfError << "\n"
             << "    ||AOrig - Q^H A Q||_F      = " << frobNormOfError << endl;
    }
}
コード例 #8
0
ファイル: SVD.hpp プロジェクト: certik/Elemental
inline void
SimpleSVDUpper
( DistMatrix<Complex<double> >& A,
  DistMatrix<double,VR,STAR>& s,
  DistMatrix<Complex<double> >& V )
{
#ifndef RELEASE
    PushCallStack("svd::SimpleSVDUpper");
#endif
    typedef double Real;
    typedef Complex<Real> C;

    const int m = A.Height();
    const int n = A.Width();
    const int k = std::min( m, n );
    const int offdiagonal = ( m>=n ? 1 : -1 );
    const char uplo = ( m>=n ? 'U' : 'L' );
    const Grid& g = A.Grid();

    // Bidiagonalize A
    DistMatrix<C,STAR,STAR> tP( g ), tQ( g );
    Bidiag( A, tP, tQ );

    // Grab copies of the diagonal and sub/super-diagonal of A
    DistMatrix<Real,MD,STAR> d_MD_STAR( g ),
                             e_MD_STAR( g );
    A.GetRealPartOfDiagonal( d_MD_STAR );
    A.GetRealPartOfDiagonal( e_MD_STAR, offdiagonal );

    // In order to use serial QR kernels, we need the full bidiagonal matrix
    // on each process
    DistMatrix<Real,STAR,STAR> d_STAR_STAR( d_MD_STAR ),
                               e_STAR_STAR( e_MD_STAR );

    // Initialize U and VAdj to the appropriate identity matrices
    DistMatrix<C,VC,STAR> U_VC_STAR( g );
    DistMatrix<C,VC,STAR> V_VC_STAR( g );
    U_VC_STAR.AlignWith( A );
    V_VC_STAR.AlignWith( V );
    Identity( m, k, U_VC_STAR );
    Identity( n, k, V_VC_STAR );

    // Compute the SVD of the bidiagonal matrix and accumulate the Givens
    // rotations into our local portion of U and V
    // NOTE: This _only_ works in the case where m >= n
    const int numAccum = 32;
    const int maxNumIts = 30;
    const int bAlg = 512;
    std::vector<C> GBuffer( (k-1)*numAccum ),
                   HBuffer( (k-1)*numAccum );
    FLA_Bsvd_v_opz_var1
    ( k, U_VC_STAR.LocalHeight(), V_VC_STAR.LocalHeight(), 
      numAccum, maxNumIts,
      d_STAR_STAR.LocalBuffer(), 1,
      e_STAR_STAR.LocalBuffer(), 1,
      &GBuffer[0], 1, k-1,
      &HBuffer[0], 1, k-1,
      U_VC_STAR.LocalBuffer(), 1, U_VC_STAR.LocalLDim(),
      V_VC_STAR.LocalBuffer(), 1, V_VC_STAR.LocalLDim(),
      bAlg );

    // Make a copy of A (for the Householder vectors) and pull the necessary 
    // portions of U and V into a standard matrix dist.
    DistMatrix<C> B( A );
    if( m >= n )
    {
        DistMatrix<C> AT( g ),
                      AB( g );
        DistMatrix<C,VC,STAR> UT_VC_STAR( g ), 
                              UB_VC_STAR( g );
        PartitionDown( A, AT,
                          AB, n );
        PartitionDown( U_VC_STAR, UT_VC_STAR,
                                  UB_VC_STAR, n );
        AT = UT_VC_STAR;
        MakeZeros( AB );
        V = V_VC_STAR;
    }
    else
    {
        DistMatrix<C> VT( g ), 
                      VB( g );
        DistMatrix<C,VC,STAR> VT_VC_STAR( g ), 
                              VB_VC_STAR( g );
        PartitionDown( V, VT, 
                          VB, m );
        PartitionDown
        ( V_VC_STAR, VT_VC_STAR, 
                     VB_VC_STAR, m );
        VT = VT_VC_STAR;
        MakeZeros( VB );
    }

    // Backtransform U and V
    if( m >= n )
    {
        ApplyPackedReflectors
        ( LEFT, LOWER, VERTICAL, BACKWARD, UNCONJUGATED, 0, B, tQ, A );
        ApplyPackedReflectors
        ( LEFT, UPPER, HORIZONTAL, BACKWARD, UNCONJUGATED, 1, B, tP, V );
    }
    else
    {
        ApplyPackedReflectors
        ( LEFT, LOWER, VERTICAL, BACKWARD, UNCONJUGATED, -1, B, tQ, A );
        ApplyPackedReflectors
        ( LEFT, UPPER, HORIZONTAL, BACKWARD, UNCONJUGATED, 0, B, tP, V );
    }

    // Copy out the appropriate subset of the singular values
    s = d_STAR_STAR;
#ifndef RELEASE
    PopCallStack();
#endif
}
コード例 #9
0
ファイル: SVD.hpp プロジェクト: certik/Elemental
inline void
SimpleSVDUpper
( DistMatrix<Complex<Real> >& A,
  DistMatrix<Real,VR,STAR>& s,
  DistMatrix<Complex<Real> >& V )
{
#ifndef RELEASE
    PushCallStack("svd::SimpleSVDUpper");
#endif
    typedef Complex<Real> C;
    const int m = A.Height();
    const int n = A.Width();
    const int k = std::min( m, n );
    const int offdiagonal = ( m>=n ? 1 : -1 );
    const char uplo = ( m>=n ? 'U' : 'L' );
    const Grid& g = A.Grid();

    // Bidiagonalize A
    DistMatrix<C,STAR,STAR> tP( g ), tQ( g );
    Bidiag( A, tP, tQ );

    // Grab copies of the diagonal and sub/super-diagonal of A
    DistMatrix<Real,MD,STAR> d_MD_STAR( g ),
                             e_MD_STAR( g );
    A.GetRealPartOfDiagonal( d_MD_STAR );
    A.GetRealPartOfDiagonal( e_MD_STAR, offdiagonal );

    // NOTE: lapack::BidiagQRAlg expects e to be of length k
    DistMatrix<Real,STAR,STAR> d_STAR_STAR( d_MD_STAR );
    DistMatrix<Real,STAR,STAR> eHat_STAR_STAR( k, 1, g );
    DistMatrix<Real,STAR,STAR> e_STAR_STAR( g );
    e_STAR_STAR.View( eHat_STAR_STAR, 0, 0, k-1, 1 );
    e_STAR_STAR = e_MD_STAR;

    // Initialize U and VAdj to the appropriate identity matrices
    DistMatrix<C,VC,STAR> U_VC_STAR( g );
    DistMatrix<C,STAR,VC> VAdj_STAR_VC( g );
    U_VC_STAR.AlignWith( A );
    VAdj_STAR_VC.AlignWith( V );
    Identity( m, k, U_VC_STAR );
    Identity( k, n, VAdj_STAR_VC );

    // Compute the SVD of the bidiagonal matrix and accumulate the Givens
    // rotations into our local portion of U and VAdj
    Matrix<C>& ULocal = U_VC_STAR.LocalMatrix();
    Matrix<C>& VAdjLocal = VAdj_STAR_VC.LocalMatrix();
    lapack::BidiagQRAlg
    ( uplo, k, VAdjLocal.Width(), ULocal.Height(),
      d_STAR_STAR.LocalBuffer(), e_STAR_STAR.LocalBuffer(), 
      VAdjLocal.Buffer(), VAdjLocal.LDim(), 
      ULocal.Buffer(), ULocal.LDim() );

    // Make a copy of A (for the Householder vectors) and pull the necessary 
    // portions of U and VAdj into a standard matrix dist.
    DistMatrix<C> B( A );
    if( m >= n )
    {
        DistMatrix<C> AT( g ),
                      AB( g );
        DistMatrix<C,VC,STAR> UT_VC_STAR( g ),
                              UB_VC_STAR( g );
        PartitionDown( A, AT,
                          AB, n );
        PartitionDown( U_VC_STAR, UT_VC_STAR,
                                  UB_VC_STAR, n );
        AT = UT_VC_STAR;
        MakeZeros( AB );
        Adjoint( VAdj_STAR_VC, V );
    }
    else
    {
        DistMatrix<C> VT( g ), 
                      VB( g );
        DistMatrix<C,STAR,VC> VAdjL_STAR_VC( g ), VAdjR_STAR_VC( g );
        PartitionDown( V, VT, 
                          VB, m );
        PartitionRight( VAdj_STAR_VC, VAdjL_STAR_VC, VAdjR_STAR_VC, m );
        Adjoint( VAdjL_STAR_VC, VT );
        MakeZeros( VB );
    }

    // Backtransform U and V
    if( m >= n )
    {
        ApplyPackedReflectors
        ( LEFT, LOWER, VERTICAL, BACKWARD, UNCONJUGATED, 0, B, tQ, A );
        ApplyPackedReflectors
        ( LEFT, UPPER, HORIZONTAL, BACKWARD, UNCONJUGATED, 1, B, tP, V );
    }
    else
    {
        ApplyPackedReflectors
        ( LEFT, LOWER, VERTICAL, BACKWARD, UNCONJUGATED, -1, B, tQ, A );
        ApplyPackedReflectors
        ( LEFT, UPPER, HORIZONTAL, BACKWARD, UNCONJUGATED, 0, B, tP, V );
    }

    // Copy out the appropriate subset of the singular values
    s = d_STAR_STAR;
#ifndef RELEASE
    PopCallStack();
#endif
}