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Add rcond method to LDLT.

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This commit is contained in:
Rasmus Munk Larsen 2016-04-01 16:48:38 -07:00
parent f54137606e
commit 9d51f7c457
2 changed files with 59 additions and 12 deletions
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54
Eigen/src/Cholesky/LDLT.h
View File

@ -13,7 +13,7 @@
#ifndef EIGEN_LDLT_H
#define EIGEN_LDLT_H
namespace Eigen {
namespace Eigen {
namespace internal {
template<typename MatrixType, int UpLo> struct LDLT_Traits;
@ -73,11 +73,11 @@ template<typename _MatrixType, int _UpLo> class LDLT
* The default constructor is useful in cases in which the user intends to
* perform decompositions via LDLT::compute(const MatrixType&).
*/
LDLT()
: m_matrix(),
m_transpositions(),
LDLT()
: m_matrix(),
m_transpositions(),
m_sign(internal::ZeroSign),
m_isInitialized(false)
m_isInitialized(false)
{}
/** \brief Default Constructor with memory preallocation
@ -168,7 +168,7 @@ template<typename _MatrixType, int _UpLo> class LDLT
* \note_about_checking_solutions
*
* More precisely, this method solves \f$ A x = b \f$ using the decomposition \f$ A = P^T L D L^* P \f$
* by solving the systems \f$ P^T y_1 = b \f$, \f$ L y_2 = y_1 \f$, \f$ D y_3 = y_2 \f$,
* by solving the systems \f$ P^T y_1 = b \f$, \f$ L y_2 = y_1 \f$, \f$ D y_3 = y_2 \f$,
* \f$ L^* y_4 = y_3 \f$ and \f$ P x = y_4 \f$ in succession. If the matrix \f$ A \f$ is singular, then
* \f$ D \f$ will also be singular (all the other matrices are invertible). In that case, the
* least-square solution of \f$ D y_3 = y_2 \f$ is computed. This does not mean that this function
@ -192,6 +192,15 @@ template<typename _MatrixType, int _UpLo> class LDLT
template<typename InputType>
LDLT& compute(const EigenBase<InputType>& matrix);
/** \returns an estimate of the reciprocal condition number of the matrix of
* which *this is the LDLT decomposition.
*/
RealScalar rcond() const
{
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return ConditionEstimator<LDLT<MatrixType, UpLo>, true >::rcond(m_l1_norm, *this);
}
template <typename Derived>
LDLT& rankUpdate(const MatrixBase<Derived>& w, const RealScalar& alpha=1);
@ -220,7 +229,7 @@ template<typename _MatrixType, int _UpLo> class LDLT
eigen_assert(m_isInitialized && "LDLT is not initialized.");
return Success;
}
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename RhsType, typename DstType>
EIGEN_DEVICE_FUNC
@ -228,7 +237,7 @@ template<typename _MatrixType, int _UpLo> class LDLT
#endif
protected:
static void check_template_parameters()
{
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
@ -241,6 +250,7 @@ template<typename _MatrixType, int _UpLo> class LDLT
* is not stored), and the diagonal entries correspond to D.
*/
MatrixType m_matrix;
RealScalar m_l1_norm;
TranspositionType m_transpositions;
TmpMatrixType m_temporary;
internal::SignMatrix m_sign;
@ -314,7 +324,7 @@ template<> struct ldlt_inplace<Lower>
if(rs>0)
A21.noalias() -= A20 * temp.head(k);
}
// In some previous versions of Eigen (e.g., 3.2.1), the scaling was omitted if the pivot
// was smaller than the cutoff value. However, since LDLT is not rank-revealing
// we should only make sure that we do not introduce INF or NaN values.
@ -433,12 +443,32 @@ template<typename InputType>
LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::compute(const EigenBase<InputType>& a)
{
check_template_parameters();
eigen_assert(a.rows()==a.cols());
const Index size = a.rows();
m_matrix = a.derived();
// Compute matrix L1 norm = max abs column sum.
m_l1_norm = RealScalar(0);
if (_UpLo == Lower) {
for (int col = 0; col < size; ++col) {
const RealScalar abs_col_sum = m_matrix.col(col).tail(size - col).cwiseAbs().sum() +
m_matrix.row(col).tail(col).cwiseAbs().sum();
if (abs_col_sum > m_l1_norm) {
m_l1_norm = abs_col_sum;
}
}
} else {
for (int col = 0; col < a.cols(); ++col) {
const RealScalar abs_col_sum = m_matrix.col(col).tail(col).cwiseAbs().sum() +
m_matrix.row(col).tail(size - col).cwiseAbs().sum();
if (abs_col_sum > m_l1_norm) {
m_l1_norm = abs_col_sum;
}
}
}
m_transpositions.resize(size);
m_isInitialized = false;
m_temporary.resize(size);
@ -466,7 +496,7 @@ LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::rankUpdate(const MatrixBase<Deri
eigen_assert(m_matrix.rows()==size);
}
else
{
{
m_matrix.resize(size,size);
m_matrix.setZero();
m_transpositions.resize(size);
@ -505,7 +535,7 @@ void LDLT<_MatrixType,_UpLo>::_solve_impl(const RhsType &rhs, DstType &dst) cons
// diagonal element is not well justified and leads to numerical issues in some cases.
// Moreover, Lapack's xSYTRS routines use 0 for the tolerance.
RealScalar tolerance = RealScalar(1) / NumTraits<RealScalar>::highest();
for (Index i = 0; i < vecD.size(); ++i)
{
if(abs(vecD(i)) > tolerance)

17
test/cholesky.cpp
View File

@ -160,6 +160,15 @@ template<typename MatrixType> void cholesky(const MatrixType& m)
matX = ldltlo.solve(matB);
VERIFY_IS_APPROX(symm * matX, matB);
// Verify that the estimated condition number is within a factor of 10 of the
// truth.
const MatrixType symmLo_inverse = ldltlo.solve(MatrixType::Identity(rows,cols));
RealScalar rcond = (RealScalar(1) / matrix_l1_norm<MatrixType, Lower>(symmLo)) /
matrix_l1_norm<MatrixType, Lower>(symmLo_inverse);
RealScalar rcond_est = ldltlo.rcond();
VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10);
LDLT<SquareMatrixType,Upper> ldltup(symmUp);
VERIFY_IS_APPROX(symm, ldltup.reconstructedMatrix());
vecX = ldltup.solve(vecB);
@ -167,6 +176,14 @@ template<typename MatrixType> void cholesky(const MatrixType& m)
matX = ldltup.solve(matB);
VERIFY_IS_APPROX(symm * matX, matB);
// Verify that the estimated condition number is within a factor of 10 of the
// truth.
const MatrixType symmUp_inverse = ldltup.solve(MatrixType::Identity(rows,cols));
rcond = (RealScalar(1) / matrix_l1_norm<MatrixType, Upper>(symmUp)) /
matrix_l1_norm<MatrixType, Upper>(symmUp_inverse);
rcond_est = ldltup.rcond();
VERIFY(rcond_est > rcond / 10 && rcond_est < rcond * 10);
VERIFY_IS_APPROX(MatrixType(ldltlo.matrixL().transpose().conjugate()), MatrixType(ldltlo.matrixU()));
VERIFY_IS_APPROX(MatrixType(ldltlo.matrixU().transpose().conjugate()), MatrixType(ldltlo.matrixL()));
VERIFY_IS_APPROX(MatrixType(ldltup.matrixL().transpose().conjugate()), MatrixType(ldltup.matrixU()));