Eigen::LeastSquareDiagonalPreconditioner< Scalar_ > Class Template Reference

Jacobi preconditioner for LeastSquaresConjugateGradient. More...

#include <BasicPreconditioners.h>

Inheritance diagram for Eigen::LeastSquareDiagonalPreconditioner< Scalar_ >:

Public Member Functions
	LeastSquareDiagonalPreconditioner ()
template<typename MatType >
	LeastSquareDiagonalPreconditioner (const MatType &mat)
template<typename MatType >
LeastSquareDiagonalPreconditioner &	analyzePattern (const MatType &)
template<typename MatType >
LeastSquareDiagonalPreconditioner &	factorize (const MatType &mat)
template<typename MatType >
LeastSquareDiagonalPreconditioner &	compute (const MatType &mat)
ComputationInfo	info ()
Public Member Functions inherited from Eigen::DiagonalPreconditioner< Scalar_ >
	DiagonalPreconditioner ()
template<typename MatType >
	DiagonalPreconditioner (const MatType &mat)
EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT
EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT
template<typename MatType >
DiagonalPreconditioner &	analyzePattern (const MatType &)
template<typename MatType >
DiagonalPreconditioner &	factorize (const MatType &mat)
template<typename MatType >
DiagonalPreconditioner &	compute (const MatType &mat)
template<typename Rhs , typename Dest >
void	_solve_impl (const Rhs &b, Dest &x) const
template<typename Rhs >
const Solve< DiagonalPreconditioner, Rhs >	solve (const MatrixBase< Rhs > &b) const
ComputationInfo	info ()

Private Types
typedef Scalar_	Scalar
typedef NumTraits< Scalar >::Real	RealScalar
typedef DiagonalPreconditioner< Scalar_ >	Base

Private Attributes
Vector	m_invdiag

Additional Inherited Members
Public Types inherited from Eigen::DiagonalPreconditioner< Scalar_ >
enum	{ ColsAtCompileTime = Dynamic , MaxColsAtCompileTime = Dynamic }
typedef Vector::StorageIndex	StorageIndex
Protected Attributes inherited from Eigen::DiagonalPreconditioner< Scalar_ >
Vector	m_invdiag
bool	m_isInitialized

Detailed Description

template<typename Scalar_>
class Eigen::LeastSquareDiagonalPreconditioner< Scalar_ >

Jacobi preconditioner for LeastSquaresConjugateGradient.

This class allows to approximately solve for A' A x = A' b problems assuming A' A is a diagonal matrix. In other words, this preconditioner neglects all off diagonal entries and, in Eigen's language, solves for:

(A.adjoint() * A).diagonal().asDiagonal() * x = b

Template Parameters

Scalar_

the type of the scalar.

\implsparsesolverconcept

The diagonal entries are pre-inverted and stored into a dense vector.

See also

class LeastSquaresConjugateGradient, class DiagonalPreconditioner

Member Typedef Documentation

Base

template<typename Scalar_ >

typedef DiagonalPreconditioner<Scalar_> Eigen::LeastSquareDiagonalPreconditioner< Scalar_ >::Base

private

RealScalar

template<typename Scalar_ >

typedef NumTraits<Scalar>::Real Eigen::LeastSquareDiagonalPreconditioner< Scalar_ >::RealScalar

private

Scalar

template<typename Scalar_ >

typedef Scalar_ Eigen::LeastSquareDiagonalPreconditioner< Scalar_ >::Scalar

private

Constructor & Destructor Documentation

LeastSquareDiagonalPreconditioner() [1/2]

template<typename Scalar_ >

Eigen::LeastSquareDiagonalPreconditioner< Scalar_ >::LeastSquareDiagonalPreconditioner ( )

inline

: Base() {}

LeastSquareDiagonalPreconditioner() [2/2]

template<typename Scalar_ >

template<typename MatType >

Eigen::LeastSquareDiagonalPreconditioner< Scalar_ >::LeastSquareDiagonalPreconditioner ( const MatType &  mat )

inlineexplicit

                                                                 : Base() {
    compute(mat);
  }

References Eigen::LeastSquareDiagonalPreconditioner< Scalar_ >::compute().

Member Function Documentation

analyzePattern()

template<typename Scalar_ >

template<typename MatType >

LeastSquareDiagonalPreconditioner& Eigen::LeastSquareDiagonalPreconditioner< Scalar_ >::analyzePattern ( const MatType &  )

inline

                                                                    {
    return *this;
  }

compute()

template<typename Scalar_ >

template<typename MatType >

LeastSquareDiagonalPreconditioner& Eigen::LeastSquareDiagonalPreconditioner< Scalar_ >::compute ( const MatType &  mat )

inline

                                                                 {
    return factorize(mat);
  }

References Eigen::LeastSquareDiagonalPreconditioner< Scalar_ >::factorize().

Referenced by Eigen::LeastSquareDiagonalPreconditioner< Scalar_ >::LeastSquareDiagonalPreconditioner().

factorize()

template<typename Scalar_ >

template<typename MatType >

LeastSquareDiagonalPreconditioner& Eigen::LeastSquareDiagonalPreconditioner< Scalar_ >::factorize ( const MatType &  mat )

inline

                                                                   {
    // Compute the inverse squared-norm of each column of mat
    m_invdiag.resize(mat.cols());
    if (MatType::IsRowMajor) {
      m_invdiag.setZero();
      for (Index j = 0; j < mat.outerSize(); ++j) {
        for (typename MatType::InnerIterator it(mat, j); it; ++it) m_invdiag(it.index()) += numext::abs2(it.value());
      }
      for (Index j = 0; j < mat.cols(); ++j)
        if (numext::real(m_invdiag(j)) > RealScalar(0)) m_invdiag(j) = RealScalar(1) / numext::real(m_invdiag(j));
    } else {
      for (Index j = 0; j < mat.outerSize(); ++j) {
        RealScalar sum = mat.col(j).squaredNorm();
        if (sum > RealScalar(0))
          m_invdiag(j) = RealScalar(1) / sum;
        else
          m_invdiag(j) = RealScalar(1);
      }
    }
    Base::m_isInitialized = true;
    return *this;
  }

References Eigen::numext::abs2(), Eigen::SparseMatrix< Scalar_, Options_, StorageIndex_ >::cols(), j, Eigen::LeastSquareDiagonalPreconditioner< Scalar_ >::m_invdiag, Eigen::DiagonalPreconditioner< Scalar_ >::m_isInitialized, Eigen::SparseMatrix< Scalar_, Options_, StorageIndex_ >::outerSize(), Eigen::PlainObjectBase< Derived >::resize(), Eigen::PlainObjectBase< Derived >::setZero(), and Eigen::SparseMatrixBase< Derived >::squaredNorm().

Referenced by Eigen::LeastSquareDiagonalPreconditioner< Scalar_ >::compute().

info()

template<typename Scalar_ >

ComputationInfo Eigen::LeastSquareDiagonalPreconditioner< Scalar_ >::info ( )

inline

{ return Success; }

References Eigen::Success.

Member Data Documentation

m_invdiag

template<typename Scalar_ >

Vector Eigen::DiagonalPreconditioner< Scalar_ >::m_invdiag

private

Referenced by Eigen::LeastSquareDiagonalPreconditioner< Scalar_ >::factorize().

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The documentation for this class was generated from the following file:

• BasicPreconditioners.h