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Add matrix condition estimator module that implements the Higham/Hager algorithm from http://www.maths.manchester.ac.uk/~higham/narep/narep135.pdf used in LPACK. Add rcond() methods to FullPivLU and PartialPivLU.

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This commit is contained in:
Rasmus Munk Larsen
2016-04-01 10:27:59 -07:00
parent 1b40abbf99
commit 1aa89fb855
5 changed files with 332 additions and 10 deletions
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13
Eigen/src/LU/FullPivLU.h
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@@ -231,6 +231,15 @@ template<typename _MatrixType> class FullPivLU
return Solve<FullPivLU, Rhs>(*this, b.derived());
}
/** \returns an estimate of the reciprocal condition number of the matrix of which *this is
the LU decomposition.
*/
inline RealScalar rcond() const
{
eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
return ConditionEstimator<FullPivLU<_MatrixType> >::rcond(m_l1_norm, *this);
}
/** \returns the determinant of the matrix of which
* *this is the LU decomposition. It has only linear complexity
* (that is, O(n) where n is the dimension of the square matrix)
@@ -410,6 +419,7 @@ template<typename _MatrixType> class FullPivLU
IntColVectorType m_rowsTranspositions;
IntRowVectorType m_colsTranspositions;
Index m_det_pq, m_nonzero_pivots;
RealScalar m_l1_norm;
RealScalar m_maxpivot, m_prescribedThreshold;
bool m_isInitialized, m_usePrescribedThreshold;
};
@@ -455,11 +465,12 @@ FullPivLU<MatrixType>& FullPivLU<MatrixType>::compute(const EigenBase<InputType>
// the permutations are stored as int indices, so just to be sure:
eigen_assert(matrix.rows()<=NumTraits<int>::highest() && matrix.cols()<=NumTraits<int>::highest());
m_isInitialized = true;
m_lu = matrix.derived();
m_l1_norm = m_lu.cwiseAbs().colwise().sum().maxCoeff();
computeInPlace();
m_isInitialized = true;
return *this;
}

19
Eigen/src/LU/PartialPivLU.h
View File

@@ -76,7 +76,6 @@ template<typename _MatrixType> class PartialPivLU
typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType;
typedef typename MatrixType::PlainObject PlainObject;
/**
* \brief Default Constructor.
*
@@ -152,6 +151,15 @@ template<typename _MatrixType> class PartialPivLU
return Solve<PartialPivLU, Rhs>(*this, b.derived());
}
/** \returns an estimate of the reciprocal condition number of the matrix of which *this is
the LU decomposition.
*/
inline RealScalar rcond() const
{
eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
return ConditionEstimator<PartialPivLU<_MatrixType> >::rcond(m_l1_norm, *this);
}
/** \returns the inverse of the matrix of which *this is the LU decomposition.
*
* \warning The matrix being decomposed here is assumed to be invertible. If you need to check for
@@ -178,7 +186,7 @@ template<typename _MatrixType> class PartialPivLU
*
* \sa MatrixBase::determinant()
*/
typename internal::traits<MatrixType>::Scalar determinant() const;
Scalar determinant() const;
MatrixType reconstructedMatrix() const;
@@ -247,6 +255,7 @@ template<typename _MatrixType> class PartialPivLU
PermutationType m_p;
TranspositionType m_rowsTranspositions;
Index m_det_p;
RealScalar m_l1_norm;
bool m_isInitialized;
};
@@ -256,6 +265,7 @@ PartialPivLU<MatrixType>::PartialPivLU()
m_p(),
m_rowsTranspositions(),
m_det_p(0),
m_l1_norm(0),
m_isInitialized(false)
{
}
@@ -266,6 +276,7 @@ PartialPivLU<MatrixType>::PartialPivLU(Index size)
m_p(size),
m_rowsTranspositions(size),
m_det_p(0),
m_l1_norm(0),
m_isInitialized(false)
{
}
@@ -277,6 +288,7 @@ PartialPivLU<MatrixType>::PartialPivLU(const EigenBase<InputType>& matrix)
m_p(matrix.rows()),
m_rowsTranspositions(matrix.rows()),
m_det_p(0),
m_l1_norm(0),
m_isInitialized(false)
{
compute(matrix.derived());
@@ -467,6 +479,7 @@ PartialPivLU<MatrixType>& PartialPivLU<MatrixType>::compute(const EigenBase<Inpu
eigen_assert(matrix.rows()<NumTraits<int>::highest());
m_lu = matrix.derived();
m_l1_norm = m_lu.cwiseAbs().colwise().sum().maxCoeff();
eigen_assert(matrix.rows() == matrix.cols() && "PartialPivLU is only for square (and moreover invertible) matrices");
const Index size = matrix.rows();
@@ -484,7 +497,7 @@ PartialPivLU<MatrixType>& PartialPivLU<MatrixType>::compute(const EigenBase<Inpu
}
template<typename MatrixType>
typename internal::traits<MatrixType>::Scalar PartialPivLU<MatrixType>::determinant() const
typename PartialPivLU<MatrixType>::Scalar PartialPivLU<MatrixType>::determinant() const
{
eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
return Scalar(m_det_p) * m_lu.diagonal().prod();