From a16a36ecf2596fadffd6474d059c334baa905c06 Mon Sep 17 00:00:00 2001
From: Jitse Niesen <jitse@maths.leeds.ac.uk>
Date: Fri, 2 Apr 2010 14:32:20 +0100
Subject: Add tests for real and complex Schur; extend test for Hessenberg.
 Make a minor correction to the ComplexSchur class.

---
 test/schur_real.cpp | 75 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 75 insertions(+)
 create mode 100644 test/schur_real.cpp

(limited to 'test/schur_real.cpp')

diff --git a/test/schur_real.cpp b/test/schur_real.cpp
new file mode 100644
index 000000000..77ef5e2dc
--- /dev/null
+++ b/test/schur_real.cpp
@@ -0,0 +1,75 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#include "main.h"
+#include <Eigen/Eigenvalues>
+
+template<typename MatrixType> void verifyIsQuasiTriangular(const MatrixType& T)
+{
+  const int size = T.cols();
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+
+  // The "zeros" in the real Schur decomposition are only approximately zero
+  RealScalar norm = T.norm();
+
+  // Check T is lower Hessenberg
+  for(int row = 2; row < size; ++row) {
+    for(int col = 0; col < row - 1; ++col) {
+      VERIFY_IS_MUCH_SMALLER_THAN(T(row,col), norm);
+    }
+  }
+
+  // Check that any non-zero on the subdiagonal is followed by a zero and is
+  // part of a 2x2 diagonal block with imaginary eigenvalues.
+  for(int row = 1; row < size; ++row) {
+    if (!test_ei_isMuchSmallerThan(T(row,row-1), norm)) {
+      VERIFY(row == size-1 || test_ei_isMuchSmallerThan(T(row+1,row), norm));
+      Scalar tr = T(row-1,row-1) + T(row,row);
+      Scalar det = T(row-1,row-1) * T(row,row) - T(row-1,row) * T(row,row-1);
+      VERIFY(4 * det > tr * tr);
+    }
+  }
+}
+
+template<typename MatrixType> void schur(int size = MatrixType::ColsAtCompileTime)
+{
+  // Test basic functionality: T is quasi-triangular and A = U T U*
+  for(int counter = 0; counter < g_repeat; ++counter) {
+    MatrixType A = MatrixType::Random(size, size);
+    RealSchur<MatrixType> schurOfA(A);
+    MatrixType U = schurOfA.matrixU();
+    MatrixType T = schurOfA.matrixT();
+    verifyIsQuasiTriangular(T);
+    VERIFY_IS_APPROX(A, U * T * U.transpose());
+  }
+}
+
+void test_schur_real()
+{
+  CALL_SUBTEST_1(( schur<Matrix4f>() ));
+  CALL_SUBTEST_2(( schur<MatrixXd>(ei_random<int>(1,50)) ));
+  CALL_SUBTEST_3(( schur<Matrix<float, 1, 1> >() ));
+  CALL_SUBTEST_4(( schur<Matrix<double, 3, 3, Eigen::RowMajor> >() ));
+}
-- 
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