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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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30
Eigen/src/Cholesky/LDLT.h
View File

@ -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);
@ -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;
@ -439,6 +449,26 @@ LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::compute(const EigenBase<InputTyp
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);

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()));