Fix bug #736: LDLT isPositive returns false for a positive semidefinite matrix

Add unit test covering this case.

1 files changed, 21 insertions, 3 deletions

diff --git a/test/cholesky.cpp b/test/cholesky.cpp
index 378525a83..b980dc572 100644
--- a/test/cholesky.cpp
+++ b/test/cholesky.cpp
@@ -263,8 +263,8 @@ template<typename MatrixType> void cholesky_bug241(const MatrixType& m)
 
 // LDLT is not guaranteed to work for indefinite matrices, but happens to work fine if matrix is diagonal.
 // This test checks that LDLT reports correctly that matrix is indefinite. 
-// See http://forum.kde.org/viewtopic.php?f=74&t=106942
-template<typename MatrixType> void cholesky_indefinite(const MatrixType& m)
+// See http://forum.kde.org/viewtopic.php?f=74&t=106942 and bug 736
+template<typename MatrixType> void cholesky_definiteness(const MatrixType& m)
 {
   eigen_assert(m.rows() == 2 && m.cols() == 2);
   MatrixType mat;
@@ -280,6 +280,24 @@ template<typename MatrixType> void cholesky_indefinite(const MatrixType& m)
     VERIFY(!ldlt.isNegative());
     VERIFY(!ldlt.isPositive());
   }
+  {
+    mat << 0, 0, 0, 0;
+    LDLT<MatrixType> ldlt(mat);
+    VERIFY(ldlt.isNegative());
+    VERIFY(ldlt.isPositive());
+  }
+  {
+    mat << 0, 0, 0, 1;
+    LDLT<MatrixType> ldlt(mat);
+    VERIFY(!ldlt.isNegative());
+    VERIFY(ldlt.isPositive());
+  }
+  {
+    mat << -1, 0, 0, 0;
+    LDLT<MatrixType> ldlt(mat);
+    VERIFY(ldlt.isNegative());
+    VERIFY(!ldlt.isPositive());
+  }
 }
 
 template<typename MatrixType> void cholesky_verify_assert()
@@ -309,7 +327,7 @@ void test_cholesky()
     CALL_SUBTEST_1( cholesky(Matrix<double,1,1>()) );
     CALL_SUBTEST_3( cholesky(Matrix2d()) );
     CALL_SUBTEST_3( cholesky_bug241(Matrix2d()) );
-    CALL_SUBTEST_3( cholesky_indefinite(Matrix2d()) );
+    CALL_SUBTEST_3( cholesky_definiteness(Matrix2d()) );
     CALL_SUBTEST_4( cholesky(Matrix3f()) );
     CALL_SUBTEST_5( cholesky(Matrix4d()) );
     s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE);