From 1aa89fb85548dc425d54d2cbe7f28915c29db13a Mon Sep 17 00:00:00 2001
From: Rasmus Munk Larsen <rmlarsen@google.com>
Date: Fri, 1 Apr 2016 10:27:59 -0700
Subject: 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.

---
 test/lu.cpp | 22 ++++++++++++++++++++--
 1 file changed, 20 insertions(+), 2 deletions(-)

(limited to 'test/lu.cpp')

diff --git a/test/lu.cpp b/test/lu.cpp
index f14435114..31991520d 100644
--- a/test/lu.cpp
+++ b/test/lu.cpp
@@ -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);
-- 
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