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Allow user to compute only the eigenvalues and not the eigenvectors.

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This commit is contained in:
Jitse Niesen
2010-05-31 18:17:47 +01:00
parent 609941380a
commit 8dc947821b
11 changed files with 235 additions and 155 deletions
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100
Eigen/src/Eigenvalues/EigenSolver.h
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@@ -57,16 +57,16 @@
* this variant of the eigendecomposition the pseudo-eigendecomposition.
*
* Call the function compute() to compute the eigenvalues and eigenvectors of
* a given matrix. Alternatively, you can use the
* EigenSolver(const MatrixType&) constructor which computes the eigenvalues
* and eigenvectors at construction time. Once the eigenvalue and eigenvectors
* are computed, they can be retrieved with the eigenvalues() and
* a given matrix. Alternatively, you can use the
* EigenSolver(const MatrixType&, bool) constructor which computes the
* eigenvalues and eigenvectors at construction time. Once the eigenvalue and
* eigenvectors are computed, they can be retrieved with the eigenvalues() and
* eigenvectors() functions. The pseudoEigenvalueMatrix() and
* pseudoEigenvectors() methods allow the construction of the
* pseudo-eigendecomposition.
*
* The documentation for EigenSolver(const MatrixType&) contains an example of
* the typical use of this class.
* The documentation for EigenSolver(const MatrixType&, bool) contains an
* example of the typical use of this class.
*
* \note The implementation is adapted from
* <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> (public domain).
@@ -78,7 +78,9 @@ template<typename _MatrixType> class EigenSolver
{
public:
/** \brief Synonym for the template parameter \p _MatrixType. */
typedef _MatrixType MatrixType;
enum {
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
@@ -87,12 +89,12 @@ template<typename _MatrixType> class EigenSolver
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
};
/** \brief Scalar type for matrices of type \p _MatrixType. */
/** \brief Scalar type for matrices of type #MatrixType. */
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef typename MatrixType::Index Index;
/** \brief Complex scalar type for \p _MatrixType.
/** \brief Complex scalar type for #MatrixType.
*
* This is \c std::complex<Scalar> if #Scalar is real (e.g.,
* \c float or \c double) and just \c Scalar if #Scalar is
@@ -103,27 +105,27 @@ template<typename _MatrixType> class EigenSolver
/** \brief Type for vector of eigenvalues as returned by eigenvalues().
*
* This is a column vector with entries of type #ComplexScalar.
* The length of the vector is the size of \p _MatrixType.
* The length of the vector is the size of #MatrixType.
*/
typedef Matrix<ComplexScalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> EigenvalueType;
/** \brief Type for matrix of eigenvectors as returned by eigenvectors().
*
* This is a square matrix with entries of type #ComplexScalar.
* The size is the same as the size of \p _MatrixType.
* The size is the same as the size of #MatrixType.
*/
typedef Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime> EigenvectorsType;
/** \brief Default constructor.
*
* The default constructor is useful in cases in which the user intends to
* perform decompositions via EigenSolver::compute(const MatrixType&).
* perform decompositions via EigenSolver::compute(const MatrixType&, bool).
*
* \sa compute() for an example.
*/
EigenSolver() : m_eivec(), m_eivalues(), m_isInitialized(false), m_realSchur(), m_matT(), m_tmp() {}
/** \brief Default Constructor with memory preallocation
/** \brief Default constructor with memory preallocation
*
* Like the default constructor but with preallocation of the internal data
* according to the specified problem \a size.
@@ -133,6 +135,7 @@ template<typename _MatrixType> class EigenSolver
: m_eivec(size, size),
m_eivalues(size),
m_isInitialized(false),
m_eigenvectorsOk(false),
m_realSchur(size),
m_matT(size, size),
m_tmp(size)
@@ -141,6 +144,9 @@ template<typename _MatrixType> class EigenSolver
/** \brief Constructor; computes eigendecomposition of given matrix.
*
* \param[in] matrix Square matrix whose eigendecomposition is to be computed.
* \param[in] computeEigenvectors If true, both the eigenvectors and the
* eigenvalues are computed; if false, only the eigenvalues are
* computed.
*
* This constructor calls compute() to compute the eigenvalues
* and eigenvectors.
@@ -150,23 +156,26 @@ template<typename _MatrixType> class EigenSolver
*
* \sa compute()
*/
EigenSolver(const MatrixType& matrix)
EigenSolver(const MatrixType& matrix, bool computeEigenvectors = true)
: m_eivec(matrix.rows(), matrix.cols()),
m_eivalues(matrix.cols()),
m_isInitialized(false),
m_eigenvectorsOk(false),
m_realSchur(matrix.cols()),
m_matT(matrix.rows(), matrix.cols()),
m_tmp(matrix.cols())
{
compute(matrix);
compute(matrix, computeEigenvectors);
}
/** \brief Returns the eigenvectors of given matrix.
*
* \returns %Matrix whose columns are the (possibly complex) eigenvectors.
*
* \pre Either the constructor EigenSolver(const MatrixType&) or the
* member function compute(const MatrixType&) has been called before.
* \pre Either the constructor
* EigenSolver(const MatrixType&,bool) or the member function
* compute(const MatrixType&, bool) has been called before, and
* \p computeEigenvectors was set to true (the default).
*
* Column \f$ k \f$ of the returned matrix is an eigenvector corresponding
* to eigenvalue number \f$ k \f$ as returned by eigenvalues(). The
@@ -185,9 +194,10 @@ template<typename _MatrixType> class EigenSolver
*
* \returns Const reference to matrix whose columns are the pseudo-eigenvectors.
*
* \pre Either the constructor EigenSolver(const MatrixType&) or
* the member function compute(const MatrixType&) has been called
* before.
* \pre Either the constructor
* EigenSolver(const MatrixType&,bool) or the member function
* compute(const MatrixType&, bool) has been called before, and
* \p computeEigenvectors was set to true (the default).
*
* The real matrix \f$ V \f$ returned by this function and the
* block-diagonal matrix \f$ D \f$ returned by pseudoEigenvalueMatrix()
@@ -201,6 +211,7 @@ template<typename _MatrixType> class EigenSolver
const MatrixType& pseudoEigenvectors() const
{
ei_assert(m_isInitialized && "EigenSolver is not initialized.");
ei_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
return m_eivec;
}
@@ -208,8 +219,9 @@ template<typename _MatrixType> class EigenSolver
*
* \returns A block-diagonal matrix.
*
* \pre Either the constructor EigenSolver(const MatrixType&) or the
* member function compute(const MatrixType&) has been called before.
* \pre Either the constructor
* EigenSolver(const MatrixType&,bool) or the member function
* compute(const MatrixType&, bool) has been called before.
*
* The matrix \f$ D \f$ returned by this function is real and
* block-diagonal. The blocks on the diagonal are either 1-by-1 or 2-by-2
@@ -226,8 +238,9 @@ template<typename _MatrixType> class EigenSolver
*
* \returns A const reference to the column vector containing the eigenvalues.
*
* \pre Either the constructor EigenSolver(const MatrixType&) or the
* member function compute(const MatrixType&) has been called before.
* \pre Either the constructor
* EigenSolver(const MatrixType&,bool) or the member function
* compute(const MatrixType&, bool) has been called before.
*
* The eigenvalues are repeated according to their algebraic multiplicity,
* so there are as many eigenvalues as rows in the matrix.
@@ -247,34 +260,40 @@ template<typename _MatrixType> class EigenSolver
/** \brief Computes eigendecomposition of given matrix.
*
* \param[in] matrix Square matrix whose eigendecomposition is to be computed.
* \param[in] computeEigenvectors If true, both the eigenvectors and the
* eigenvalues are computed; if false, only the eigenvalues are
* computed.
* \returns Reference to \c *this
*
* This function computes the eigenvalues and eigenvectors of \p matrix.
* The eigenvalues() and eigenvectors() functions can be used to retrieve
* the computed eigendecomposition.
* This function computes the eigenvalues of the real matrix \p matrix.
* The eigenvalues() function can be used to retrieve them. If
* \p computeEigenvectors is true, then the eigenvectors are also computed
* and can be retrieved by calling eigenvectors().
*
* The matrix is first reduced to real Schur form using the RealSchur
* class. The Schur decomposition is then used to compute the eigenvalues
* and eigenvectors.
*
* The cost of the computation is dominated by the cost of the Schur
* decomposition, which is very approximately \f$ 25n^3 \f$ where
* \f$ n \f$ is the size of the matrix.
* The cost of the computation is dominated by the cost of the
* Schur decomposition, which is very approximately \f$ 25n^3 \f$
* (where \f$ n \f$ is the size of the matrix) if \p computeEigenvectors
* is true, and \f$ 10n^3 \f$ if \p computeEigenvectors is false.
*
* This method reuses of the allocated data in the EigenSolver object.
*
* Example: \include EigenSolver_compute.cpp
* Output: \verbinclude EigenSolver_compute.out
*/
EigenSolver& compute(const MatrixType& matrix);
EigenSolver& compute(const MatrixType& matrix, bool computeEigenvectors = true);
private:
void computeEigenvectors();
void doComputeEigenvectors();
protected:
MatrixType m_eivec;
EigenvalueType m_eivalues;
bool m_isInitialized;
bool m_eigenvectorsOk;
RealSchur<MatrixType> m_realSchur;
MatrixType m_matT;
@@ -286,7 +305,7 @@ template<typename MatrixType>
MatrixType EigenSolver<MatrixType>::pseudoEigenvalueMatrix() const
{
ei_assert(m_isInitialized && "EigenSolver is not initialized.");
Index n = m_eivec.cols();
Index n = m_eivalues.rows();
MatrixType matD = MatrixType::Zero(n,n);
for (Index i=0; i<n; ++i)
{
@@ -306,6 +325,7 @@ template<typename MatrixType>
typename EigenSolver<MatrixType>::EigenvectorsType EigenSolver<MatrixType>::eigenvectors() const
{
ei_assert(m_isInitialized && "EigenSolver is not initialized.");
ei_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
Index n = m_eivec.cols();
EigenvectorsType matV(n,n);
for (Index j=0; j<n; ++j)
@@ -332,14 +352,15 @@ typename EigenSolver<MatrixType>::EigenvectorsType EigenSolver<MatrixType>::eige
}
template<typename MatrixType>
EigenSolver<MatrixType>& EigenSolver<MatrixType>::compute(const MatrixType& matrix)
EigenSolver<MatrixType>& EigenSolver<MatrixType>::compute(const MatrixType& matrix, bool computeEigenvectors)
{
assert(matrix.cols() == matrix.rows());
// Reduce to real Schur form.
m_realSchur.compute(matrix);
m_realSchur.compute(matrix, computeEigenvectors);
m_matT = m_realSchur.matrixT();
m_eivec = m_realSchur.matrixU();
if (computeEigenvectors)
m_eivec = m_realSchur.matrixU();
// Compute eigenvalues from matT
m_eivalues.resize(matrix.cols());
@@ -362,9 +383,12 @@ EigenSolver<MatrixType>& EigenSolver<MatrixType>::compute(const MatrixType& matr
}
// Compute eigenvectors.
computeEigenvectors();
if (computeEigenvectors)
doComputeEigenvectors();
m_isInitialized = true;
m_eigenvectorsOk = computeEigenvectors;
return *this;
}
@@ -389,7 +413,7 @@ std::complex<Scalar> cdiv(Scalar xr, Scalar xi, Scalar yr, Scalar yi)
template<typename MatrixType>
void EigenSolver<MatrixType>::computeEigenvectors()
void EigenSolver<MatrixType>::doComputeEigenvectors()
{
const Index size = m_eivec.cols();
const Scalar eps = NumTraits<Scalar>::epsilon();
@@ -404,7 +428,7 @@ void EigenSolver<MatrixType>::computeEigenvectors()
// Backsubstitute to find vectors of upper triangular form
if (norm == 0.0)
{
return;
return;
}
for (Index n = size-1; n >= 0; n--)