Add a RealQZ class: a generalized Schur decomposition for real matrices

1 files changed, 84 insertions, 0 deletions

diff --git a/test/real_qz.cpp b/test/real_qz.cpp
new file mode 100644
index 000000000..e5b301c94
--- /dev/null
+++ b/test/real_qz.cpp
@@ -0,0 +1,84 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 Alexey Korepanov <kaikaikai@yandex.ru>
+//
+// 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 <limits>
+#include <Eigen/Eigenvalues>
+
+template<typename MatrixType> void real_qz(const MatrixType& m)
+{
+  /* this test covers the following files:
+     RealQZ.h
+  */
+  
+  typedef typename MatrixType::Index Index;
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+  typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType;
+  typedef typename std::complex<typename NumTraits<typename MatrixType::Scalar>::Real> Complex;
+  
+  Index dim = m.cols();
+  
+  MatrixType A = MatrixType::Random(dim,dim),
+             B = MatrixType::Random(dim,dim);
+
+  RealQZ<MatrixType> qz(A,B);
+  
+  VERIFY_IS_EQUAL(qz.info(), Success);
+  // check for zeros
+  bool all_zeros = true;
+  for (Index i=0; i<A.cols(); i++)
+    for (Index j=0; j<i; j++) {
+      if (internal::abs(qz.matrixT()(i,j))!=Scalar(0.0))
+        all_zeros = false;
+      if (j<i-1 && internal::abs(qz.matrixS()(i,j))!=Scalar(0.0))
+        all_zeros = false;
+      if (j==i-1 && j>0 && internal::abs(qz.matrixS()(i,j))!=Scalar(0.0) && internal::abs(qz.matrixS()(i-1,j-1))!=Scalar(0.0))
+        all_zeros = false;
+    }
+  VERIFY_IS_EQUAL(all_zeros, true);
+  VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixS()*qz.matrixZ(), A);
+  VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixT()*qz.matrixZ(), B);
+  VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixQ().adjoint(), MatrixType::Identity(dim,dim));
+  VERIFY_IS_APPROX(qz.matrixZ()*qz.matrixZ().adjoint(), MatrixType::Identity(dim,dim));
+}
+
+void test_real_qz()
+{
+  int s;
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST_1( real_qz(Matrix4f()) );
+    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
+    CALL_SUBTEST_2( real_qz(MatrixXd(s,s)) );
+
+    // some trivial but implementation-wise tricky cases
+    CALL_SUBTEST_2( real_qz(MatrixXd(1,1)) );
+    CALL_SUBTEST_2( real_qz(MatrixXd(2,2)) );
+    CALL_SUBTEST_3( real_qz(Matrix<double,1,1>()) );
+    CALL_SUBTEST_4( real_qz(Matrix2d()) );
+  }
+  
+  EIGEN_UNUSED_VARIABLE(s)
+}