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Fix bug #326 : expose tridiagonal eigensolver to end-users through ComputeFromTridiagonal()

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Desire NUENTSA 2013-07-18 10:32:31 +02:00
parent 6fab4012a3
commit 736fe99fbf
2 changed files with 117 additions and 51 deletions
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159
Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
View File

@ -20,6 +20,8 @@ class GeneralizedSelfAdjointEigenSolver;
namespace internal {
template<typename SolverType,int Size,bool IsComplex> struct direct_selfadjoint_eigenvalues;
template<typename MatrixType, typename DiagType, typename SubDiagType>
ComputationInfo computeFromTridiagonal_impl(DiagType& diag, SubDiagType& subdiag, const typename MatrixType::Index maxIterations, bool computeEigenvectors, MatrixType& eivec);
}
/** \eigenvalues_module \ingroup Eigenvalues_Module
@ -98,6 +100,7 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
*/
typedef typename internal::plain_col_type<MatrixType, RealScalar>::type RealVectorType;
typedef Tridiagonalization<MatrixType> TridiagonalizationType;
typedef typename TridiagonalizationType::SubDiagonalType SubDiagonalType;
/** \brief Default constructor for fixed-size matrices.
*
@ -207,6 +210,19 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
*/
SelfAdjointEigenSolver& computeDirect(const MatrixType& matrix, int options = ComputeEigenvectors);
/**
*\brief Computes the eigen decomposition from a tridiagonal symmetric matrix
*
* \param[in] diag The vector containing the diagonal of the matrix.
* \param[in] subdiag The subdiagonal of the matrix.
* \returns Reference to \c *this
*
* This function assumes that the matrix has been reduced to tridiagonal form.
*
* \sa compute(const MatrixType&, int) for more information
*/
SelfAdjointEigenSolver& computeFromTridiagonal(const RealVectorType& diag, const SubDiagonalType& subdiag , int options=ComputeEigenvectors);
/** \brief Returns the eigenvectors of given matrix.
*
* \returns A const reference to the matrix whose columns are the eigenvectors.
@ -415,58 +431,8 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
mat.template triangularView<Lower>() /= scale;
m_subdiag.resize(n-1);
internal::tridiagonalization_inplace(mat, diag, m_subdiag, computeEigenvectors);
Index end = n-1;
Index start = 0;
Index iter = 0; // total number of iterations
while (end>0)
{
for (Index i = start; i<end; ++i)
if (internal::isMuchSmallerThan(abs(m_subdiag[i]),(abs(diag[i])+abs(diag[i+1]))))
m_subdiag[i] = 0;
// find the largest unreduced block
while (end>0 && m_subdiag[end-1]==0)
{
end--;
}
if (end<=0)
break;
// if we spent too many iterations, we give up
iter++;
if(iter > m_maxIterations * n) break;
start = end - 1;
while (start>0 && m_subdiag[start-1]!=0)
start--;
internal::tridiagonal_qr_step<MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor>(diag.data(), m_subdiag.data(), start, end, computeEigenvectors ? m_eivec.data() : (Scalar*)0, n);
}
if (iter <= m_maxIterations * n)
m_info = Success;
else
m_info = NoConvergence;
// Sort eigenvalues and corresponding vectors.
// TODO make the sort optional ?
// TODO use a better sort algorithm !!
if (m_info == Success)
{
for (Index i = 0; i < n-1; ++i)
{
Index k;
m_eivalues.segment(i,n-i).minCoeff(&k);
if (k > 0)
{
std::swap(m_eivalues[i], m_eivalues[k+i]);
if(computeEigenvectors)
m_eivec.col(i).swap(m_eivec.col(k+i));
}
}
}
m_info = internal::computeFromTridiagonal_impl(diag, m_subdiag, m_maxIterations, computeEigenvectors, m_eivec);
// scale back the eigen values
m_eivalues *= scale;
@ -476,8 +442,99 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
return *this;
}
template<typename MatrixType>
SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
::computeFromTridiagonal(const RealVectorType& diag, const SubDiagonalType& subdiag , int options)
{
//TODO : Add an option to scale the values beforehand
bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors;
m_eivalues = diag;
m_subdiag = subdiag;
if (computeEigenvectors)
{
m_eivec.setIdentity(diag.size(), diag.size());
}
m_info = computeFromTridiagonal_impl(m_eivalues, m_subdiag, m_maxIterations, computeEigenvectors, m_eivec);
m_isInitialized = true;
m_eigenvectorsOk = computeEigenvectors;
return *this;
}
namespace internal {
/**
* \internal
* \brief Compute the eigendecomposition from a tridiagonal matrix
*
* \param[in,out] diag : On input, the diagonal of the matrix, on output the eigenvalues
* \param[in] subdiag : The subdiagonal part of the matrix.
* \param[in,out] : On input, the maximum number of iterations, on output, the effective number of iterations.
* \param[out] eivec : The matrix to store the eigenvectors... if needed. allocated on input
* \returns \c Success or \c NoConvergence
*/
template<typename MatrixType, typename DiagType, typename SubDiagType>
ComputationInfo computeFromTridiagonal_impl(DiagType& diag, SubDiagType& subdiag, const typename MatrixType::Index maxIterations, bool computeEigenvectors, MatrixType& eivec)
{
using std::abs;
ComputationInfo info;
typedef typename MatrixType::Index Index;
typedef typename MatrixType::Scalar Scalar;
Index n = diag.size();
Index end = n-1;
Index start = 0;
Index iter = 0; // total number of iterations
while (end>0)
{
for (Index i = start; i<end; ++i)
if (internal::isMuchSmallerThan(abs(subdiag[i]),(abs(diag[i])+abs(diag[i+1]))))
subdiag[i] = 0;
// find the largest unreduced block
while (end>0 && subdiag[end-1]==0)
{
end--;
}
if (end<=0)
break;
// if we spent too many iterations, we give up
iter++;
if(iter > maxIterations * n) break;
start = end - 1;
while (start>0 && subdiag[start-1]!=0)
start--;
internal::tridiagonal_qr_step<MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor>(diag.data(), subdiag.data(), start, end, computeEigenvectors ? eivec.data() : (Scalar*)0, n);
}
if (iter <= maxIterations * n)
info = Success;
else
info = NoConvergence;
// Sort eigenvalues and corresponding vectors.
// TODO make the sort optional ?
// TODO use a better sort algorithm !!
if (info == Success)
{
for (Index i = 0; i < n-1; ++i)
{
Index k;
diag.segment(i,n-i).minCoeff(&k);
if (k > 0)
{
std::swap(diag[i], diag[k+i]);
if(computeEigenvectors)
eivec.col(i).swap(eivec.col(k+i));
}
}
}
return info;
}
template<typename SolverType,int Size,bool IsComplex> struct direct_selfadjoint_eigenvalues
{

9
test/eigensolver_selfadjoint.cpp
View File

@ -99,6 +99,15 @@ template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
// FIXME tridiag.matrixQ().adjoint() does not work
VERIFY_IS_APPROX(MatrixType(symmA.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint());
// Test computation of eigenvalues from tridiagonal matrix
if(rows > 1)
{
SelfAdjointEigenSolver<MatrixType> eiSymmTridiag;
eiSymmTridiag.computeFromTridiagonal(tridiag.matrixT().diagonal(), tridiag.matrixT().diagonal(-1), ComputeEigenvectors);
VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmTridiag.eigenvalues());
VERIFY_IS_APPROX(tridiag.matrixT(), eiSymmTridiag.eigenvectors().real() * eiSymmTridiag.eigenvalues().asDiagonal() * eiSymmTridiag.eigenvectors().real().transpose());
}
if (rows > 1)
{
// Test matrix with NaN