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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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22
test/lu.cpp
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@@ -11,6 +11,11 @@
#include <Eigen/LU>
using namespace std;
template<typename MatrixType>
typename MatrixType::RealScalar matrix_l1_norm(const MatrixType& m) {
return m.cwiseAbs().colwise().sum().maxCoeff();
}
template<typename MatrixType> void lu_non_invertible()
{
typedef typename MatrixType::Index Index;
@@ -143,7 +148,13 @@ template<typename MatrixType> void lu_invertible()
m3 = MatrixType::Random(size,size);
m2 = lu.solve(m3);
VERIFY_IS_APPROX(m3, m1*m2);
VERIFY_IS_APPROX(m2, lu.inverse()*m3);
MatrixType m1_inverse = lu.inverse();
VERIFY_IS_APPROX(m2, m1_inverse*m3);
// Test condition number estimation.
RealScalar rcond = RealScalar(1) / matrix_l1_norm(m1) / matrix_l1_norm(m1_inverse);
// Verify that the estimate is within a factor of 10 of the truth.
VERIFY(lu.rcond() > rcond / 10 && lu.rcond() < rcond * 10);
// test solve with transposed
lu.template _solve_impl_transposed<false>(m3, m2);
@@ -170,6 +181,7 @@ template<typename MatrixType> void lu_partial_piv()
PartialPivLU.h
*/
typedef typename MatrixType::Index Index;
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
Index size = internal::random<Index>(1,4);
MatrixType m1(size, size), m2(size, size), m3(size, size);
@@ -181,7 +193,13 @@ template<typename MatrixType> void lu_partial_piv()
m3 = MatrixType::Random(size,size);
m2 = plu.solve(m3);
VERIFY_IS_APPROX(m3, m1*m2);
VERIFY_IS_APPROX(m2, plu.inverse()*m3);
MatrixType m1_inverse = plu.inverse();
VERIFY_IS_APPROX(m2, m1_inverse*m3);
// Test condition number estimation.
RealScalar rcond = RealScalar(1) / matrix_l1_norm(m1) / matrix_l1_norm(m1_inverse);
// Verify that the estimate is within a factor of 10 of the truth.
VERIFY(plu.rcond() > rcond / 10 && plu.rcond() < rcond * 10);
// test solve with transposed
plu.template _solve_impl_transposed<false>(m3, m2);