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diff --git a/test/eigen2/eigen2_eigensolver.cpp b/test/eigen2/eigen2_eigensolver.cpp
new file mode 100644
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+++ b/test/eigen2/eigen2_eigensolver.cpp
@@ -0,0 +1,146 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/QR>
+
+#ifdef HAS_GSL
+#include "gsl_helper.h"
+#endif
+
+template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
+{
+  /* this test covers the following files:
+     EigenSolver.h, SelfAdjointEigenSolver.h (and indirectly: Tridiagonalization.h)
+  */
+  int rows = m.rows();
+  int cols = m.cols();
+
+  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;
+
+  RealScalar largerEps = 10*test_precision<RealScalar>();
+
+  MatrixType a = MatrixType::Random(rows,cols);
+  MatrixType a1 = MatrixType::Random(rows,cols);
+  MatrixType symmA =  a.adjoint() * a + a1.adjoint() * a1;
+
+  MatrixType b = MatrixType::Random(rows,cols);
+  MatrixType b1 = MatrixType::Random(rows,cols);
+  MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1;
+
+  SelfAdjointEigenSolver<MatrixType> eiSymm(symmA);
+  // generalized eigen pb
+  SelfAdjointEigenSolver<MatrixType> eiSymmGen(symmA, symmB);
+
+  #ifdef HAS_GSL
+  if (ei_is_same_type<RealScalar,double>::ret)
+  {
+    typedef GslTraits<Scalar> Gsl;
+    typename Gsl::Matrix gEvec=0, gSymmA=0, gSymmB=0;
+    typename GslTraits<RealScalar>::Vector gEval=0;
+    RealVectorType _eval;
+    MatrixType _evec;
+    convert<MatrixType>(symmA, gSymmA);
+    convert<MatrixType>(symmB, gSymmB);
+    convert<MatrixType>(symmA, gEvec);
+    gEval = GslTraits<RealScalar>::createVector(rows);
+
+    Gsl::eigen_symm(gSymmA, gEval, gEvec);
+    convert(gEval, _eval);
+    convert(gEvec, _evec);
+
+    // test gsl itself !
+    VERIFY((symmA * _evec).isApprox(_evec * _eval.asDiagonal(), largerEps));
+
+    // compare with eigen
+    VERIFY_IS_APPROX(_eval, eiSymm.eigenvalues());
+    VERIFY_IS_APPROX(_evec.cwise().abs(), eiSymm.eigenvectors().cwise().abs());
+
+    // generalized pb
+    Gsl::eigen_symm_gen(gSymmA, gSymmB, gEval, gEvec);
+    convert(gEval, _eval);
+    convert(gEvec, _evec);
+    // test GSL itself:
+    VERIFY((symmA * _evec).isApprox(symmB * (_evec * _eval.asDiagonal()), largerEps));
+
+    // compare with eigen
+    MatrixType normalized_eivec = eiSymmGen.eigenvectors()*eiSymmGen.eigenvectors().colwise().norm().asDiagonal().inverse();
+    VERIFY_IS_APPROX(_eval, eiSymmGen.eigenvalues());
+    VERIFY_IS_APPROX(_evec.cwiseAbs(), normalized_eivec.cwiseAbs());
+
+    Gsl::free(gSymmA);
+    Gsl::free(gSymmB);
+    GslTraits<RealScalar>::free(gEval);
+    Gsl::free(gEvec);
+  }
+  #endif
+
+  VERIFY((symmA * eiSymm.eigenvectors()).isApprox(
+          eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal(), largerEps));
+
+  // generalized eigen problem Ax = lBx
+  VERIFY((symmA * eiSymmGen.eigenvectors()).isApprox(
+          symmB * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
+
+  MatrixType sqrtSymmA = eiSymm.operatorSqrt();
+  VERIFY_IS_APPROX(symmA, sqrtSymmA*sqrtSymmA);
+  VERIFY_IS_APPROX(sqrtSymmA, symmA*eiSymm.operatorInverseSqrt());
+}
+
+template<typename MatrixType> void eigensolver(const MatrixType& m)
+{
+  /* this test covers the following files:
+     EigenSolver.h
+  */
+  int rows = m.rows();
+  int cols = m.cols();
+
+  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;
+
+  // RealScalar largerEps = 10*test_precision<RealScalar>();
+
+  MatrixType a = MatrixType::Random(rows,cols);
+  MatrixType a1 = MatrixType::Random(rows,cols);
+  MatrixType symmA =  a.adjoint() * a + a1.adjoint() * a1;
+
+  EigenSolver<MatrixType> ei0(symmA);
+  VERIFY_IS_APPROX(symmA * ei0.pseudoEigenvectors(), ei0.pseudoEigenvectors() * ei0.pseudoEigenvalueMatrix());
+  VERIFY_IS_APPROX((symmA.template cast<Complex>()) * (ei0.pseudoEigenvectors().template cast<Complex>()),
+    (ei0.pseudoEigenvectors().template cast<Complex>()) * (ei0.eigenvalues().asDiagonal()));
+
+  EigenSolver<MatrixType> ei1(a);
+  VERIFY_IS_APPROX(a * ei1.pseudoEigenvectors(), ei1.pseudoEigenvectors() * ei1.pseudoEigenvalueMatrix());
+  VERIFY_IS_APPROX(a.template cast<Complex>() * ei1.eigenvectors(),
+                   ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
+
+}
+
+void test_eigen2_eigensolver()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    // very important to test a 3x3 matrix since we provide a special path for it
+    CALL_SUBTEST_1( selfadjointeigensolver(Matrix3f()) );
+    CALL_SUBTEST_2( selfadjointeigensolver(Matrix4d()) );
+    CALL_SUBTEST_3( selfadjointeigensolver(MatrixXf(7,7)) );
+    CALL_SUBTEST_4( selfadjointeigensolver(MatrixXcd(5,5)) );
+    CALL_SUBTEST_5( selfadjointeigensolver(MatrixXd(19,19)) );
+
+    CALL_SUBTEST_6( eigensolver(Matrix4f()) );
+    CALL_SUBTEST_5( eigensolver(MatrixXd(17,17)) );
+  }
+}
+