import eigen2 test suite. enable by defining EIGEN_TEST_EIGEN2

only test_prec_inverse4x4 is fixed at the moment. now need to go over all those tests.

Eigen/Array

@@ -1,12 +1,14 @@
 #ifndef EIGEN_ARRAY_MODULE_H
 #define EIGEN_ARRAY_MODULE_H
 
-#ifdef _MSC_VER
+#ifndef EIGEN_NO_EIGEN2_DEPRECATED_WARNINGS
-#pragma message("The inclusion of Eigen/Array is deprecated. \
+  #ifdef _MSC_VER
-The array module is available as soon as Eigen/Core is included.")
+    #pragma message("The inclusion of Eigen/Array is deprecated. \
-#elif __GNUC__
+                     The array module is available as soon as Eigen/Core is included.")
-#warning "The inclusion of Eigen/Array is deprecated. \
+  #elif __GNUC__
-The array module is available as soon as Eigen/Core is included."
+    #warning "The inclusion of Eigen/Array is deprecated. \
+              The array module is available as soon as Eigen/Core is included."
+  #endif
 #endif
 
 #include "Core"

test/CMakeLists.txt

@@ -136,3 +136,8 @@ if(CMAKE_COMPILER_IS_GNUCXX AND NOT CXX_IS_QCC)
 endif()
 ei_add_property(EIGEN_TESTING_SUMMARY "CXX_FLAGS:         ${CMAKE_CXX_FLAGS}\n")
 ei_add_property(EIGEN_TESTING_SUMMARY "Sparse lib flags:  ${SPARSE_LIBS}\n")
+
+option(EIGEN_TEST_EIGEN2 "Run whole Eigen2 test suite against EIGEN2_SUPPORT" OFF)
+if(EIGEN_TEST_EIGEN2)
+  add_subdirectory(eigen2)
+endif()

test/eigen2/CMakeLists.txt

@@ -0,0 +1,132 @@
+add_custom_target(buildtests_eigen2)
+add_custom_target(check_eigen2 COMMAND "ctest")
+add_dependencies(check_eigen2 buildtests_eigen2)
+
+add_definitions("-DEIGEN_NO_EIGEN2_DEPRECATED_WARNINGS")
+
+# Macro to add a test
+#
+# the unique parameter testname must correspond to a file
+# <testname>.cpp which follows this pattern:
+#
+# #include "main.h"
+# void test_<testname>() { ... }
+#
+# this macro add an executable test_<testname> as well as a ctest test
+# named <testname>
+#
+# On platforms with bash simply run:
+#   "ctest -V" or "ctest -V -R <testname>"
+# On other platform use ctest as usual
+#
+macro(ei_add_test_eigen2 testname)
+
+  set(targetname test_eigen2_${testname})
+
+  set(filename ${testname}.cpp)
+  add_executable(${targetname} ${filename})
+  add_dependencies(buildtests_eigen2 ${targetname})
+
+  if(NOT EIGEN_NO_ASSERTION_CHECKING)
+
+    if(MSVC)
+      set_target_properties(${targetname} PROPERTIES COMPILE_FLAGS "/EHsc")
+    else(MSVC)
+      set_target_properties(${targetname} PROPERTIES COMPILE_FLAGS "-fexceptions")
+    endif(MSVC)
+
+    option(EIGEN_DEBUG_ASSERTS "Enable debuging of assertions" OFF)
+    if(EIGEN_DEBUG_ASSERTS)
+      set_target_properties(${targetname} PROPERTIES COMPILE_DEFINITIONS "EIGEN_DEBUG_ASSERTS=1")
+    endif(EIGEN_DEBUG_ASSERTS)
+
+  endif(NOT EIGEN_NO_ASSERTION_CHECKING)
+
+  if(${ARGC} GREATER 1)
+    ei_add_target_property(${targetname} COMPILE_FLAGS "${ARGV1}")
+  endif(${ARGC} GREATER 1)
+
+  ei_add_target_property(${targetname} COMPILE_FLAGS "-DEIGEN_TEST_FUNC=${testname}")
+
+  if(TEST_LIB)
+    target_link_libraries(${targetname} Eigen2)
+  endif(TEST_LIB)
+
+  if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO)
+    target_link_libraries(${targetname} ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO})
+  endif()
+
+  target_link_libraries(${targetname} ${EXTERNAL_LIBS})
+  if(${ARGC} GREATER 2)
+    string(STRIP "${ARGV2}" ARGV2_stripped)
+    string(LENGTH "${ARGV2_stripped}" ARGV2_stripped_length)
+    if(${ARGV2_stripped_length} GREATER 0)
+      target_link_libraries(${targetname} ${ARGV2})
+    endif(${ARGV2_stripped_length} GREATER 0)
+  endif(${ARGC} GREATER 2)
+
+  if(WIN32)
+    add_test(${testname} "${targetname}")
+  else(WIN32)
+    add_test(${testname} "${CMAKE_CURRENT_SOURCE_DIR}/runtest.sh" "${testname}")
+  endif(WIN32)
+
+endmacro(ei_add_test_eigen2)
+
+enable_testing()
+
+if(TEST_LIB)
+  add_definitions("-DEIGEN_EXTERN_INSTANTIATIONS=1")
+endif(TEST_LIB)
+
+ei_add_test_eigen2(meta)
+ei_add_test_eigen2(sizeof)
+ei_add_test_eigen2(dynalloc)
+ei_add_test_eigen2(nomalloc)
+ei_add_test_eigen2(first_aligned)
+ei_add_test_eigen2(mixingtypes)
+ei_add_test_eigen2(packetmath)
+ei_add_test_eigen2(unalignedassert)
+ei_add_test_eigen2(vectorization_logic)
+ei_add_test_eigen2(basicstuff)
+ei_add_test_eigen2(linearstructure)
+ei_add_test_eigen2(cwiseop)
+ei_add_test_eigen2(sum)
+ei_add_test_eigen2(product_small)
+ei_add_test_eigen2(product_large ${EI_OFLAG})
+ei_add_test_eigen2(adjoint)
+ei_add_test_eigen2(submatrices)
+ei_add_test_eigen2(miscmatrices)
+ei_add_test_eigen2(commainitializer)
+ei_add_test_eigen2(smallvectors)
+ei_add_test_eigen2(map)
+ei_add_test_eigen2(array)
+ei_add_test_eigen2(triangular)
+ei_add_test_eigen2(cholesky " " "${GSL_LIBRARIES}")
+ei_add_test_eigen2(lu ${EI_OFLAG})
+ei_add_test_eigen2(determinant ${EI_OFLAG})
+ei_add_test_eigen2(inverse)
+ei_add_test_eigen2(qr)
+ei_add_test_eigen2(eigensolver " " "${GSL_LIBRARIES}")
+ei_add_test_eigen2(svd)
+ei_add_test_eigen2(geometry)
+ei_add_test_eigen2(hyperplane)
+ei_add_test_eigen2(parametrizedline)
+ei_add_test_eigen2(alignedbox)
+ei_add_test_eigen2(regression)
+ei_add_test_eigen2(stdvector)
+ei_add_test_eigen2(newstdvector)
+if(QT4_FOUND)
+  ei_add_test_eigen2(qtvector " " "${QT_QTCORE_LIBRARY}")
+endif(QT4_FOUND)
+if(NOT EIGEN_DEFAULT_TO_ROW_MAJOR)
+  ei_add_test_eigen2(sparse_vector)
+  ei_add_test_eigen2(sparse_basic)
+  ei_add_test_eigen2(sparse_solvers " " "${SPARSE_LIBS}")
+  ei_add_test_eigen2(sparse_product)
+endif()
+ei_add_test_eigen2(swap)
+ei_add_test_eigen2(visitor)
+ei_add_test_eigen2(bug_132)
+
+ei_add_test_eigen2(prec_inverse_4x4 ${EI_OFLAG})

test/eigen2/adjoint.cpp

@@ -0,0 +1,116 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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"
+
+template<typename MatrixType> void adjoint(const MatrixType& m)
+{
+  /* this test covers the following files:
+     Transpose.h Conjugate.h Dot.h
+  */
+
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
+  int rows = m.rows();
+  int cols = m.cols();
+
+  RealScalar largerEps = test_precision<RealScalar>();
+  if (ei_is_same_type<RealScalar,float>::ret)
+    largerEps = RealScalar(1e-3f);
+
+  MatrixType m1 = MatrixType::Random(rows, cols),
+             m2 = MatrixType::Random(rows, cols),
+             m3(rows, cols),
+             mzero = MatrixType::Zero(rows, cols),
+             identity = SquareMatrixType::Identity(rows, rows),
+             square = SquareMatrixType::Random(rows, rows);
+  VectorType v1 = VectorType::Random(rows),
+             v2 = VectorType::Random(rows),
+             v3 = VectorType::Random(rows),
+             vzero = VectorType::Zero(rows);
+
+  Scalar s1 = ei_random<Scalar>(),
+         s2 = ei_random<Scalar>();
+
+  // check basic compatibility of adjoint, transpose, conjugate
+  VERIFY_IS_APPROX(m1.transpose().conjugate().adjoint(),    m1);
+  VERIFY_IS_APPROX(m1.adjoint().conjugate().transpose(),    m1);
+
+  // check multiplicative behavior
+  VERIFY_IS_APPROX((m1.adjoint() * m2).adjoint(),           m2.adjoint() * m1);
+  VERIFY_IS_APPROX((s1 * m1).adjoint(),                     ei_conj(s1) * m1.adjoint());
+
+  // check basic properties of dot, norm, norm2
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  VERIFY(ei_isApprox((s1 * v1 + s2 * v2).dot(v3),   s1 * v1.dot(v3) + s2 * v2.dot(v3), largerEps));
+  VERIFY(ei_isApprox(v3.dot(s1 * v1 + s2 * v2),     ei_conj(s1)*v3.dot(v1)+ei_conj(s2)*v3.dot(v2), largerEps));
+  VERIFY_IS_APPROX(ei_conj(v1.dot(v2)),               v2.dot(v1));
+  VERIFY_IS_APPROX(ei_abs(v1.dot(v1)),                v1.squaredNorm());
+  if(NumTraits<Scalar>::HasFloatingPoint)
+    VERIFY_IS_APPROX(v1.squaredNorm(),                      v1.norm() * v1.norm());
+  VERIFY_IS_MUCH_SMALLER_THAN(ei_abs(vzero.dot(v1)),  static_cast<RealScalar>(1));
+  if(NumTraits<Scalar>::HasFloatingPoint)
+    VERIFY_IS_MUCH_SMALLER_THAN(vzero.norm(),         static_cast<RealScalar>(1));
+
+  // check compatibility of dot and adjoint
+  VERIFY(ei_isApprox(v1.dot(square * v2), (square.adjoint() * v1).dot(v2), largerEps));
+
+  // like in testBasicStuff, test operator() to check const-qualification
+  int r = ei_random<int>(0, rows-1),
+      c = ei_random<int>(0, cols-1);
+  VERIFY_IS_APPROX(m1.conjugate()(r,c), ei_conj(m1(r,c)));
+  VERIFY_IS_APPROX(m1.adjoint()(c,r), ei_conj(m1(r,c)));
+
+  if(NumTraits<Scalar>::HasFloatingPoint)
+  {
+    // check that Random().normalized() works: tricky as the random xpr must be evaluated by
+    // normalized() in order to produce a consistent result.
+    VERIFY_IS_APPROX(VectorType::Random(rows).normalized().norm(), RealScalar(1));
+  }
+
+  // check inplace transpose
+  m3 = m1;
+  m3.transposeInPlace();
+  VERIFY_IS_APPROX(m3,m1.transpose());
+  m3.transposeInPlace();
+  VERIFY_IS_APPROX(m3,m1);
+  
+}
+
+void test_adjoint()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( adjoint(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST( adjoint(Matrix3d()) );
+    CALL_SUBTEST( adjoint(Matrix4f()) );
+    CALL_SUBTEST( adjoint(MatrixXcf(4, 4)) );
+    CALL_SUBTEST( adjoint(MatrixXi(8, 12)) );
+    CALL_SUBTEST( adjoint(MatrixXf(21, 21)) );
+  }
+  // test a large matrix only once
+  CALL_SUBTEST( adjoint(Matrix<float, 100, 100>()) );
+}
+

test/eigen2/alignedbox.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) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// 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/Geometry>
+#include <Eigen/LU>
+#include <Eigen/QR>
+
+template<typename BoxType> void alignedbox(const BoxType& _box)
+{
+  /* this test covers the following files:
+     AlignedBox.h
+  */
+
+  const int dim = _box.dim();
+  typedef typename BoxType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar, BoxType::AmbientDimAtCompileTime, 1> VectorType;
+
+  VectorType p0 = VectorType::Random(dim);
+  VectorType p1 = VectorType::Random(dim);
+  RealScalar s1 = ei_random<RealScalar>(0,1);
+
+  BoxType b0(dim);
+  BoxType b1(VectorType::Random(dim),VectorType::Random(dim));
+  BoxType b2;
+
+  b0.extend(p0);
+  b0.extend(p1);
+  VERIFY(b0.contains(p0*s1+(Scalar(1)-s1)*p1));
+  VERIFY(!b0.contains(p0 + (1+s1)*(p1-p0)));
+
+  (b2 = b0).extend(b1);
+  VERIFY(b2.contains(b0));
+  VERIFY(b2.contains(b1));
+  VERIFY_IS_APPROX(b2.clamp(b0), b0);
+
+  // casting
+  const int Dim = BoxType::AmbientDimAtCompileTime;
+  typedef typename GetDifferentType<Scalar>::type OtherScalar;
+  AlignedBox<OtherScalar,Dim> hp1f = b0.template cast<OtherScalar>();
+  VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),b0);
+  AlignedBox<Scalar,Dim> hp1d = b0.template cast<Scalar>();
+  VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),b0);
+}
+
+void test_alignedbox()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( alignedbox(AlignedBox<float,2>()) );
+    CALL_SUBTEST( alignedbox(AlignedBox<float,3>()) );
+    CALL_SUBTEST( alignedbox(AlignedBox<double,4>()) );
+  }
+}

test/eigen2/array.cpp

@@ -0,0 +1,157 @@
+// 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>
+//
+// 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/Array>
+
+template<typename MatrixType> void array(const MatrixType& m)
+{
+  /* this test covers the following files:
+     Array.cpp
+  */
+
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+
+  int rows = m.rows();
+  int cols = m.cols();
+
+  MatrixType m1 = MatrixType::Random(rows, cols),
+             m2 = MatrixType::Random(rows, cols),
+             m3(rows, cols);
+
+  Scalar  s1 = ei_random<Scalar>(),
+          s2 = ei_random<Scalar>();
+
+  // scalar addition
+  VERIFY_IS_APPROX(m1.cwise() + s1, s1 + m1.cwise());
+  VERIFY_IS_APPROX(m1.cwise() + s1, MatrixType::Constant(rows,cols,s1) + m1);
+  VERIFY_IS_APPROX((m1*Scalar(2)).cwise() - s2, (m1+m1) - MatrixType::Constant(rows,cols,s2) );
+  m3 = m1;
+  m3.cwise() += s2;
+  VERIFY_IS_APPROX(m3, m1.cwise() + s2);
+  m3 = m1;
+  m3.cwise() -= s1;
+  VERIFY_IS_APPROX(m3, m1.cwise() - s1);
+
+  // reductions
+  VERIFY_IS_APPROX(m1.colwise().sum().sum(), m1.sum());
+  VERIFY_IS_APPROX(m1.rowwise().sum().sum(), m1.sum());
+  if (!ei_isApprox(m1.sum(), (m1+m2).sum()))
+    VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum());
+  VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(ei_scalar_sum_op<Scalar>()));
+}
+
+template<typename MatrixType> void comparisons(const MatrixType& m)
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+
+  int rows = m.rows();
+  int cols = m.cols();
+
+  int r = ei_random<int>(0, rows-1),
+      c = ei_random<int>(0, cols-1);
+
+  MatrixType m1 = MatrixType::Random(rows, cols),
+             m2 = MatrixType::Random(rows, cols),
+             m3(rows, cols);
+
+  VERIFY(((m1.cwise() + Scalar(1)).cwise() > m1).all());
+  VERIFY(((m1.cwise() - Scalar(1)).cwise() < m1).all());
+  if (rows*cols>1)
+  {
+    m3 = m1;
+    m3(r,c) += 1;
+    VERIFY(! (m1.cwise() < m3).all() );
+    VERIFY(! (m1.cwise() > m3).all() );
+  }
+  
+  // comparisons to scalar
+  VERIFY( (m1.cwise() != (m1(r,c)+1) ).any() );
+  VERIFY( (m1.cwise() > (m1(r,c)-1) ).any() );
+  VERIFY( (m1.cwise() < (m1(r,c)+1) ).any() );
+  VERIFY( (m1.cwise() == m1(r,c) ).any() );
+  
+  // test Select
+  VERIFY_IS_APPROX( (m1.cwise()<m2).select(m1,m2), m1.cwise().min(m2) );
+  VERIFY_IS_APPROX( (m1.cwise()>m2).select(m1,m2), m1.cwise().max(m2) );
+  Scalar mid = (m1.cwise().abs().minCoeff() + m1.cwise().abs().maxCoeff())/Scalar(2);
+  for (int j=0; j<cols; ++j)
+  for (int i=0; i<rows; ++i)
+    m3(i,j) = ei_abs(m1(i,j))<mid ? 0 : m1(i,j);
+  VERIFY_IS_APPROX( (m1.cwise().abs().cwise()<MatrixType::Constant(rows,cols,mid))
+                        .select(MatrixType::Zero(rows,cols),m1), m3);
+  // shorter versions:
+  VERIFY_IS_APPROX( (m1.cwise().abs().cwise()<MatrixType::Constant(rows,cols,mid))
+                        .select(0,m1), m3);
+  VERIFY_IS_APPROX( (m1.cwise().abs().cwise()>=MatrixType::Constant(rows,cols,mid))
+                        .select(m1,0), m3);
+  // even shorter version:
+  VERIFY_IS_APPROX( (m1.cwise().abs().cwise()<mid).select(0,m1), m3);
+  
+  // count
+  VERIFY(((m1.cwise().abs().cwise()+1).cwise()>RealScalar(0.1)).count() == rows*cols);
+  VERIFY_IS_APPROX(((m1.cwise().abs().cwise()+1).cwise()>RealScalar(0.1)).colwise().count(), RowVectorXi::Constant(cols,rows));
+  VERIFY_IS_APPROX(((m1.cwise().abs().cwise()+1).cwise()>RealScalar(0.1)).rowwise().count(), VectorXi::Constant(rows, cols));
+}
+
+template<typename VectorType> void lpNorm(const VectorType& v)
+{
+  VectorType u = VectorType::Random(v.size());
+
+  VERIFY_IS_APPROX(u.template lpNorm<Infinity>(), u.cwise().abs().maxCoeff());
+  VERIFY_IS_APPROX(u.template lpNorm<1>(), u.cwise().abs().sum());
+  VERIFY_IS_APPROX(u.template lpNorm<2>(), ei_sqrt(u.cwise().abs().cwise().square().sum()));
+  VERIFY_IS_APPROX(ei_pow(u.template lpNorm<5>(), typename VectorType::RealScalar(5)), u.cwise().abs().cwise().pow(5).sum());
+}
+
+void test_array()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( array(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST( array(Matrix2f()) );
+    CALL_SUBTEST( array(Matrix4d()) );
+    CALL_SUBTEST( array(MatrixXcf(3, 3)) );
+    CALL_SUBTEST( array(MatrixXf(8, 12)) );
+    CALL_SUBTEST( array(MatrixXi(8, 12)) );
+  }
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( comparisons(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST( comparisons(Matrix2f()) );
+    CALL_SUBTEST( comparisons(Matrix4d()) );
+    CALL_SUBTEST( comparisons(MatrixXf(8, 12)) );
+    CALL_SUBTEST( comparisons(MatrixXi(8, 12)) );
+  }
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( lpNorm(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST( lpNorm(Vector2f()) );
+    CALL_SUBTEST( lpNorm(Vector3d()) );
+    CALL_SUBTEST( lpNorm(Vector4f()) );
+    CALL_SUBTEST( lpNorm(VectorXf(16)) );
+    CALL_SUBTEST( lpNorm(VectorXcd(10)) );
+  }
+}

test/eigen2/basicstuff.cpp

@@ -0,0 +1,123 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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"
+
+template<typename MatrixType> void basicStuff(const MatrixType& m)
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+
+  int rows = m.rows();
+  int cols = m.cols();
+
+  // this test relies a lot on Random.h, and there's not much more that we can do
+  // to test it, hence I consider that we will have tested Random.h
+  MatrixType m1 = MatrixType::Random(rows, cols),
+             m2 = MatrixType::Random(rows, cols),
+             m3(rows, cols),
+             mzero = MatrixType::Zero(rows, cols),
+             identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+                              ::Identity(rows, rows),
+             square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>::Random(rows, rows);
+  VectorType v1 = VectorType::Random(rows),
+             v2 = VectorType::Random(rows),
+             vzero = VectorType::Zero(rows);
+
+  Scalar x = ei_random<Scalar>();
+
+  int r = ei_random<int>(0, rows-1),
+      c = ei_random<int>(0, cols-1);
+
+  m1.coeffRef(r,c) = x;
+  VERIFY_IS_APPROX(x, m1.coeff(r,c));
+  m1(r,c) = x;
+  VERIFY_IS_APPROX(x, m1(r,c));
+  v1.coeffRef(r) = x;
+  VERIFY_IS_APPROX(x, v1.coeff(r));
+  v1(r) = x;
+  VERIFY_IS_APPROX(x, v1(r));
+  v1[r] = x;
+  VERIFY_IS_APPROX(x, v1[r]);
+
+  VERIFY_IS_APPROX(               v1,    v1);
+  VERIFY_IS_NOT_APPROX(           v1,    2*v1);
+  VERIFY_IS_MUCH_SMALLER_THAN(    vzero, v1);
+  if(NumTraits<Scalar>::HasFloatingPoint)
+    VERIFY_IS_MUCH_SMALLER_THAN(  vzero, v1.norm());
+  VERIFY_IS_NOT_MUCH_SMALLER_THAN(v1,    v1);
+  VERIFY_IS_APPROX(               vzero, v1-v1);
+  VERIFY_IS_APPROX(               m1,    m1);
+  VERIFY_IS_NOT_APPROX(           m1,    2*m1);
+  VERIFY_IS_MUCH_SMALLER_THAN(    mzero, m1);
+  VERIFY_IS_NOT_MUCH_SMALLER_THAN(m1,    m1);
+  VERIFY_IS_APPROX(               mzero, m1-m1);
+
+  // always test operator() on each read-only expression class,
+  // in order to check const-qualifiers.
+  // indeed, if an expression class (here Zero) is meant to be read-only,
+  // hence has no _write() method, the corresponding MatrixBase method (here zero())
+  // should return a const-qualified object so that it is the const-qualified
+  // operator() that gets called, which in turn calls _read().
+  VERIFY_IS_MUCH_SMALLER_THAN(MatrixType::Zero(rows,cols)(r,c), static_cast<Scalar>(1));
+
+  // now test copying a row-vector into a (column-)vector and conversely.
+  square.col(r) = square.row(r).eval();
+  Matrix<Scalar, 1, MatrixType::RowsAtCompileTime> rv(rows);
+  Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> cv(rows);
+  rv = square.row(r);
+  cv = square.col(r);
+  VERIFY_IS_APPROX(rv, cv.transpose());
+
+  if(cols!=1 && rows!=1 && MatrixType::SizeAtCompileTime!=Dynamic)
+  {
+    VERIFY_RAISES_ASSERT(m1 = (m2.block(0,0, rows-1, cols-1)));
+  }
+
+  VERIFY_IS_APPROX(m3 = m1,m1);
+  MatrixType m4;
+  VERIFY_IS_APPROX(m4 = m1,m1);
+
+  // test swap
+  m3 = m1;
+  m1.swap(m2);
+  VERIFY_IS_APPROX(m3, m2);
+  if(rows*cols>=3)
+  {
+    VERIFY_IS_NOT_APPROX(m3, m1);
+  }
+}
+
+void test_basicstuff()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( basicStuff(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST( basicStuff(Matrix4d()) );
+    CALL_SUBTEST( basicStuff(MatrixXcf(3, 3)) );
+    CALL_SUBTEST( basicStuff(MatrixXi(8, 12)) );
+    CALL_SUBTEST( basicStuff(MatrixXcd(20, 20)) );
+    CALL_SUBTEST( basicStuff(Matrix<float, 100, 100>()) );
+    CALL_SUBTEST( basicStuff(Matrix<long double,Dynamic,Dynamic>(10,10)) );
+  }
+}

test/eigen2/bug_132.cpp

@@ -0,0 +1,41 @@
+// 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 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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"
+
+void test_bug_132() {
+  enum { size = 100 };
+  MatrixXd A(size, size);
+  VectorXd b(size), c(size);
+  {
+    VectorXd y = A.transpose() * (b-c);  // bug 132: infinite recursion in coeffRef
+    VectorXd z = (b-c).transpose() * A;  // bug 132: infinite recursion in coeffRef
+  }
+
+  // the following ones weren't failing, but let's include them for completeness:
+  {
+    VectorXd y = A * (b-c);
+    VectorXd z = (b-c).transpose() * A.transpose();
+  }
+}

test/eigen2/cholesky.cpp

@@ -0,0 +1,131 @@
+// 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>
+//
+// 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/>.
+
+#define EIGEN_NO_ASSERTION_CHECKING
+#include "main.h"
+#include <Eigen/Cholesky>
+#include <Eigen/LU>
+
+#ifdef HAS_GSL
+#include "gsl_helper.h"
+#endif
+
+template<typename MatrixType> void cholesky(const MatrixType& m)
+{
+  /* this test covers the following files:
+     LLT.h LDLT.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, MatrixType::RowsAtCompileTime> SquareMatrixType;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+
+  MatrixType a0 = MatrixType::Random(rows,cols);
+  VectorType vecB = VectorType::Random(rows), vecX(rows);
+  MatrixType matB = MatrixType::Random(rows,cols), matX(rows,cols);
+  SquareMatrixType symm =  a0 * a0.adjoint();
+  // let's make sure the matrix is not singular or near singular
+  MatrixType a1 = MatrixType::Random(rows,cols);
+  symm += a1 * a1.adjoint();
+
+  #ifdef HAS_GSL
+  if (ei_is_same_type<RealScalar,double>::ret)
+  {
+    typedef GslTraits<Scalar> Gsl;
+    typename Gsl::Matrix gMatA=0, gSymm=0;
+    typename Gsl::Vector gVecB=0, gVecX=0;
+    convert<MatrixType>(symm, gSymm);
+    convert<MatrixType>(symm, gMatA);
+    convert<VectorType>(vecB, gVecB);
+    convert<VectorType>(vecB, gVecX);
+    Gsl::cholesky(gMatA);
+    Gsl::cholesky_solve(gMatA, gVecB, gVecX);
+    VectorType vecX(rows), _vecX, _vecB;
+    convert(gVecX, _vecX);
+    symm.llt().solve(vecB, &vecX);
+    Gsl::prod(gSymm, gVecX, gVecB);
+    convert(gVecB, _vecB);
+    // test gsl itself !
+    VERIFY_IS_APPROX(vecB, _vecB);
+    VERIFY_IS_APPROX(vecX, _vecX);
+
+    Gsl::free(gMatA);
+    Gsl::free(gSymm);
+    Gsl::free(gVecB);
+    Gsl::free(gVecX);
+  }
+  #endif
+
+  {
+    LDLT<SquareMatrixType> ldlt(symm);
+    VERIFY(ldlt.isPositiveDefinite());
+    VERIFY_IS_APPROX(symm, ldlt.matrixL() * ldlt.vectorD().asDiagonal() * ldlt.matrixL().adjoint());
+    ldlt.solve(vecB, &vecX);
+    VERIFY_IS_APPROX(symm * vecX, vecB);
+    ldlt.solve(matB, &matX);
+    VERIFY_IS_APPROX(symm * matX, matB);
+  }
+
+  {
+    LLT<SquareMatrixType> chol(symm);
+    VERIFY(chol.isPositiveDefinite());
+    VERIFY_IS_APPROX(symm, chol.matrixL() * chol.matrixL().adjoint());
+    chol.solve(vecB, &vecX);
+    VERIFY_IS_APPROX(symm * vecX, vecB);
+    chol.solve(matB, &matX);
+    VERIFY_IS_APPROX(symm * matX, matB);
+  }
+
+#if 0 // cholesky is not rank-revealing anyway
+  // test isPositiveDefinite on non definite matrix
+  if (rows>4)
+  {
+    SquareMatrixType symm =  a0.block(0,0,rows,cols-4) * a0.block(0,0,rows,cols-4).adjoint();
+    LLT<SquareMatrixType> chol(symm);
+    VERIFY(!chol.isPositiveDefinite());
+    LDLT<SquareMatrixType> cholnosqrt(symm);
+    VERIFY(!cholnosqrt.isPositiveDefinite());
+  }
+#endif
+}
+
+void test_cholesky()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( cholesky(Matrix<double,1,1>()) );
+    CALL_SUBTEST( cholesky(Matrix2d()) );
+    CALL_SUBTEST( cholesky(Matrix3f()) );
+    CALL_SUBTEST( cholesky(Matrix4d()) );
+    CALL_SUBTEST( cholesky(MatrixXcd(7,7)) );
+    CALL_SUBTEST( cholesky(MatrixXf(17,17)) );
+    CALL_SUBTEST( cholesky(MatrixXd(33,33)) );
+  }
+
+  MatrixXf m = MatrixXf::Zero(10,10);
+  VectorXf b = VectorXf::Zero(10);
+  VERIFY(!m.llt().isPositiveDefinite());
+}

test/eigen2/commainitializer.cpp

@@ -0,0 +1,61 @@
+// 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>
+//
+// 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"
+
+void test_commainitializer()
+{
+  Matrix3d m3;
+  Matrix4d m4;
+
+  VERIFY_RAISES_ASSERT( (m3 << 1, 2, 3, 4, 5, 6, 7, 8) );
+  
+  #ifndef _MSC_VER
+  VERIFY_RAISES_ASSERT( (m3 << 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) );
+  #endif
+
+  double data[] = {1, 2, 3, 4, 5, 6, 7, 8, 9};
+  Matrix3d ref = Map<Matrix<double,3,3,RowMajor> >(data);
+
+  m3 = Matrix3d::Random();
+  m3 << 1, 2, 3, 4, 5, 6, 7, 8, 9;
+  VERIFY_IS_APPROX(m3, ref );
+
+  Vector3d vec[3];
+  vec[0] << 1, 4, 7;
+  vec[1] << 2, 5, 8;
+  vec[2] << 3, 6, 9;
+  m3 = Matrix3d::Random();
+  m3 << vec[0], vec[1], vec[2];
+  VERIFY_IS_APPROX(m3, ref);
+
+  vec[0] << 1, 2, 3;
+  vec[1] << 4, 5, 6;
+  vec[2] << 7, 8, 9;
+  m3 = Matrix3d::Random();
+  m3 << vec[0].transpose(),
+        4, 5, 6,
+        vec[2].transpose();
+  VERIFY_IS_APPROX(m3, ref);
+}

test/eigen2/cwiseop.cpp

@@ -0,0 +1,173 @@
+// 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>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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 <functional>
+#include <Eigen/Array>
+
+using namespace std;
+
+template<typename Scalar> struct AddIfNull {
+    const Scalar operator() (const Scalar a, const Scalar b) const {return a<=1e-3 ? b : a;}
+    enum { Cost = NumTraits<Scalar>::AddCost };
+};
+
+template<typename MatrixType> void cwiseops(const MatrixType& m)
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+
+  int rows = m.rows();
+  int cols = m.cols();
+
+  MatrixType m1 = MatrixType::Random(rows, cols),
+             m2 = MatrixType::Random(rows, cols),
+             m3(rows, cols),
+             m4(rows, cols),
+             mzero = MatrixType::Zero(rows, cols),
+             mones = MatrixType::Ones(rows, cols),
+             identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+                              ::Identity(rows, rows),
+             square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>::Random(rows, rows);
+  VectorType v1 = VectorType::Random(rows),
+             v2 = VectorType::Random(rows),
+             vzero = VectorType::Zero(rows),
+             vones = VectorType::Ones(rows),
+             v3(rows);
+
+  int r = ei_random<int>(0, rows-1),
+      c = ei_random<int>(0, cols-1);
+  
+  Scalar s1 = ei_random<Scalar>();
+  
+  // test Zero, Ones, Constant, and the set* variants
+  m3 = MatrixType::Constant(rows, cols, s1);
+  for (int j=0; j<cols; ++j)
+    for (int i=0; i<rows; ++i)
+    {
+      VERIFY_IS_APPROX(mzero(i,j), Scalar(0));
+      VERIFY_IS_APPROX(mones(i,j), Scalar(1));
+      VERIFY_IS_APPROX(m3(i,j), s1);
+    }
+  VERIFY(mzero.isZero());
+  VERIFY(mones.isOnes());
+  VERIFY(m3.isConstant(s1));
+  VERIFY(identity.isIdentity());
+  VERIFY_IS_APPROX(m4.setConstant(s1), m3);
+  VERIFY_IS_APPROX(m4.setConstant(rows,cols,s1), m3);
+  VERIFY_IS_APPROX(m4.setZero(), mzero);
+  VERIFY_IS_APPROX(m4.setZero(rows,cols), mzero);
+  VERIFY_IS_APPROX(m4.setOnes(), mones);
+  VERIFY_IS_APPROX(m4.setOnes(rows,cols), mones);
+  m4.fill(s1);
+  VERIFY_IS_APPROX(m4, m3);
+  
+  VERIFY_IS_APPROX(v3.setConstant(rows, s1), VectorType::Constant(rows,s1));
+  VERIFY_IS_APPROX(v3.setZero(rows), vzero);
+  VERIFY_IS_APPROX(v3.setOnes(rows), vones);
+
+  m2 = m2.template binaryExpr<AddIfNull<Scalar> >(mones);
+
+  VERIFY_IS_APPROX(m1.cwise().pow(2), m1.cwise().abs2());
+  VERIFY_IS_APPROX(m1.cwise().pow(2), m1.cwise().square());
+  VERIFY_IS_APPROX(m1.cwise().pow(3), m1.cwise().cube());
+
+  VERIFY_IS_APPROX(m1 + mones, m1.cwise()+Scalar(1));
+  VERIFY_IS_APPROX(m1 - mones, m1.cwise()-Scalar(1));
+  m3 = m1; m3.cwise() += 1;
+  VERIFY_IS_APPROX(m1 + mones, m3);
+  m3 = m1; m3.cwise() -= 1;
+  VERIFY_IS_APPROX(m1 - mones, m3);
+
+  VERIFY_IS_APPROX(m2, m2.cwise() * mones);
+  VERIFY_IS_APPROX(m1.cwise() * m2,  m2.cwise() * m1);
+  m3 = m1;
+  m3.cwise() *= m2;
+  VERIFY_IS_APPROX(m3, m1.cwise() * m2);
+  
+  VERIFY_IS_APPROX(mones,    m2.cwise()/m2);
+  if(NumTraits<Scalar>::HasFloatingPoint)
+  {
+    VERIFY_IS_APPROX(m1.cwise() / m2,    m1.cwise() * (m2.cwise().inverse()));
+    m3 = m1.cwise().abs().cwise().sqrt();
+    VERIFY_IS_APPROX(m3.cwise().square(), m1.cwise().abs());
+    VERIFY_IS_APPROX(m1.cwise().square().cwise().sqrt(), m1.cwise().abs());
+    VERIFY_IS_APPROX(m1.cwise().abs().cwise().log().cwise().exp() , m1.cwise().abs());
+
+    VERIFY_IS_APPROX(m1.cwise().pow(2), m1.cwise().square());
+    m3 = (m1.cwise().abs().cwise()<=RealScalar(0.01)).select(mones,m1);
+    VERIFY_IS_APPROX(m3.cwise().pow(-1), m3.cwise().inverse());
+    m3 = m1.cwise().abs();
+    VERIFY_IS_APPROX(m3.cwise().pow(RealScalar(0.5)), m3.cwise().sqrt());
+    
+//     VERIFY_IS_APPROX(m1.cwise().tan(), m1.cwise().sin().cwise() / m1.cwise().cos());
+    VERIFY_IS_APPROX(mones, m1.cwise().sin().cwise().square() + m1.cwise().cos().cwise().square());
+    m3 = m1;
+    m3.cwise() /= m2;
+    VERIFY_IS_APPROX(m3, m1.cwise() / m2);
+  }
+
+  // check min
+  VERIFY_IS_APPROX( m1.cwise().min(m2), m2.cwise().min(m1) );
+  VERIFY_IS_APPROX( m1.cwise().min(m1+mones), m1 );
+  VERIFY_IS_APPROX( m1.cwise().min(m1-mones), m1-mones );
+
+  // check max
+  VERIFY_IS_APPROX( m1.cwise().max(m2), m2.cwise().max(m1) );
+  VERIFY_IS_APPROX( m1.cwise().max(m1-mones), m1 );
+  VERIFY_IS_APPROX( m1.cwise().max(m1+mones), m1+mones );
+  
+  VERIFY( (m1.cwise() == m1).all() );
+  VERIFY( (m1.cwise() != m2).any() );
+  VERIFY(!(m1.cwise() == (m1+mones)).any() );
+  if (rows*cols>1)
+  {
+    m3 = m1;
+    m3(r,c) += 1;
+    VERIFY( (m1.cwise() == m3).any() );
+    VERIFY( !(m1.cwise() == m3).all() );
+  }
+  VERIFY( (m1.cwise().min(m2).cwise() <= m2).all() );
+  VERIFY( (m1.cwise().max(m2).cwise() >= m2).all() );
+  VERIFY( (m1.cwise().min(m2).cwise() < (m1+mones)).all() );
+  VERIFY( (m1.cwise().max(m2).cwise() > (m1-mones)).all() );
+
+  VERIFY( (m1.cwise()<m1.unaryExpr(bind2nd(plus<Scalar>(), Scalar(1)))).all() );
+  VERIFY( !(m1.cwise()<m1.unaryExpr(bind2nd(minus<Scalar>(), Scalar(1)))).all() );
+  VERIFY( !(m1.cwise()>m1.unaryExpr(bind2nd(plus<Scalar>(), Scalar(1)))).any() );
+}
+
+void test_cwiseop()
+{
+  for(int i = 0; i < g_repeat ; i++) {
+    CALL_SUBTEST( cwiseops(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST( cwiseops(Matrix4d()) );
+    CALL_SUBTEST( cwiseops(MatrixXf(3, 3)) );
+    CALL_SUBTEST( cwiseops(MatrixXf(22, 22)) );
+    CALL_SUBTEST( cwiseops(MatrixXi(8, 12)) );
+    CALL_SUBTEST( cwiseops(MatrixXd(20, 20)) );
+  }
+}

test/eigen2/determinant.cpp

@@ -0,0 +1,76 @@
+// 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 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// 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/LU>
+
+template<typename MatrixType> void determinant(const MatrixType& m)
+{
+  /* this test covers the following files:
+     Determinant.h
+  */
+  int size = m.rows();
+
+  MatrixType m1(size, size), m2(size, size);
+  m1.setRandom();
+  m2.setRandom();
+  typedef typename MatrixType::Scalar Scalar;
+  Scalar x = ei_random<Scalar>();
+  VERIFY_IS_APPROX(MatrixType::Identity(size, size).determinant(), Scalar(1));
+  VERIFY_IS_APPROX((m1*m2).determinant(), m1.determinant() * m2.determinant());
+  if(size==1) return;
+  int i = ei_random<int>(0, size-1);
+  int j;
+  do {
+    j = ei_random<int>(0, size-1);
+  } while(j==i);
+  m2 = m1;
+  m2.row(i).swap(m2.row(j));
+  VERIFY_IS_APPROX(m2.determinant(), -m1.determinant());
+  m2 = m1;
+  m2.col(i).swap(m2.col(j));
+  VERIFY_IS_APPROX(m2.determinant(), -m1.determinant());
+  VERIFY_IS_APPROX(m2.determinant(), m2.transpose().determinant());
+  VERIFY_IS_APPROX(ei_conj(m2.determinant()), m2.adjoint().determinant());
+  m2 = m1;
+  m2.row(i) += x*m2.row(j);
+  VERIFY_IS_APPROX(m2.determinant(), m1.determinant());
+  m2 = m1;
+  m2.row(i) *= x;
+  VERIFY_IS_APPROX(m2.determinant(), m1.determinant() * x);
+}
+
+void test_determinant()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( determinant(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST( determinant(Matrix<double, 2, 2>()) );
+    CALL_SUBTEST( determinant(Matrix<double, 3, 3>()) );
+    CALL_SUBTEST( determinant(Matrix<double, 4, 4>()) );
+    CALL_SUBTEST( determinant(Matrix<std::complex<double>, 10, 10>()) );
+    CALL_SUBTEST( determinant(MatrixXd(20, 20)) );
+  }
+  CALL_SUBTEST( determinant(MatrixXd(200, 200)) );
+}

test/eigen2/dynalloc.cpp

@@ -0,0 +1,147 @@
+// 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>
+//
+// 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"
+
+#if EIGEN_ARCH_WANTS_ALIGNMENT
+#define ALIGNMENT 16
+#else
+#define ALIGNMENT 1
+#endif
+
+void check_handmade_aligned_malloc()
+{
+  for(int i = 1; i < 1000; i++)
+  {
+    char *p = (char*)ei_handmade_aligned_malloc(i);
+    VERIFY(std::size_t(p)%ALIGNMENT==0);
+    // if the buffer is wrongly allocated this will give a bad write --> check with valgrind
+    for(int j = 0; j < i; j++) p[j]=0;
+    ei_handmade_aligned_free(p);
+  }
+}
+
+void check_aligned_malloc()
+{
+  for(int i = 1; i < 1000; i++)
+  {
+    char *p = (char*)ei_aligned_malloc(i);
+    VERIFY(std::size_t(p)%ALIGNMENT==0);
+    // if the buffer is wrongly allocated this will give a bad write --> check with valgrind
+    for(int j = 0; j < i; j++) p[j]=0;
+    ei_aligned_free(p);
+  }
+}
+
+void check_aligned_new()
+{
+  for(int i = 1; i < 1000; i++)
+  {
+    float *p = ei_aligned_new<float>(i);
+    VERIFY(std::size_t(p)%ALIGNMENT==0);
+    // if the buffer is wrongly allocated this will give a bad write --> check with valgrind
+    for(int j = 0; j < i; j++) p[j]=0;
+    ei_aligned_delete(p,i);
+  }
+}
+
+void check_aligned_stack_alloc()
+{
+  for(int i = 1; i < 1000; i++)
+  {
+    float *p = ei_aligned_stack_new(float,i);
+    VERIFY(std::size_t(p)%ALIGNMENT==0);
+    // if the buffer is wrongly allocated this will give a bad write --> check with valgrind
+    for(int j = 0; j < i; j++) p[j]=0;
+    ei_aligned_stack_delete(float,p,i);
+  }
+}
+
+
+// test compilation with both a struct and a class...
+struct MyStruct
+{
+  EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+  char dummychar;
+  Vector4f avec;
+};
+
+class MyClassA
+{
+  public:
+    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+    char dummychar;
+    Vector4f avec;
+};
+
+template<typename T> void check_dynaligned()
+{
+  T* obj = new T;
+  VERIFY(std::size_t(obj)%ALIGNMENT==0);
+  delete obj;
+}
+
+void test_dynalloc()
+{
+  // low level dynamic memory allocation
+  CALL_SUBTEST(check_handmade_aligned_malloc());
+  CALL_SUBTEST(check_aligned_malloc());
+  CALL_SUBTEST(check_aligned_new());
+  CALL_SUBTEST(check_aligned_stack_alloc());
+
+  for (int i=0; i<g_repeat*100; ++i)
+  {
+    CALL_SUBTEST( check_dynaligned<Vector4f>() );
+    CALL_SUBTEST( check_dynaligned<Vector2d>() );
+    CALL_SUBTEST( check_dynaligned<Matrix4f>() );
+    CALL_SUBTEST( check_dynaligned<Vector4d>() );
+    CALL_SUBTEST( check_dynaligned<Vector4i>() );
+  }
+  
+  // check static allocation, who knows ?
+  {
+    MyStruct foo0;  VERIFY(std::size_t(foo0.avec.data())%ALIGNMENT==0);
+    MyClassA fooA;  VERIFY(std::size_t(fooA.avec.data())%ALIGNMENT==0);
+  }
+
+  // dynamic allocation, single object
+  for (int i=0; i<g_repeat*100; ++i)
+  {
+    MyStruct *foo0 = new MyStruct();  VERIFY(std::size_t(foo0->avec.data())%ALIGNMENT==0);
+    MyClassA *fooA = new MyClassA();  VERIFY(std::size_t(fooA->avec.data())%ALIGNMENT==0);
+    delete foo0;
+    delete fooA;
+  }
+
+  // dynamic allocation, array
+  const int N = 10;
+  for (int i=0; i<g_repeat*100; ++i)
+  {
+    MyStruct *foo0 = new MyStruct[N];  VERIFY(std::size_t(foo0->avec.data())%ALIGNMENT==0);
+    MyClassA *fooA = new MyClassA[N];  VERIFY(std::size_t(fooA->avec.data())%ALIGNMENT==0);
+    delete[] foo0;
+    delete[] fooA;
+  }
+  
+}

test/eigen2/eigensolver.cpp

@@ -0,0 +1,162 @@
+// 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>
+//
+// 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/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().eval(), 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().eval()), largerEps));
+
+    // compare with eigen
+//     std::cerr << _eval.transpose() << "\n" << eiSymmGen.eigenvalues().transpose() << "\n\n";
+//     std::cerr << _evec.format(6) << "\n\n" << eiSymmGen.eigenvectors().format(6) << "\n\n\n";
+    VERIFY_IS_APPROX(_eval, eiSymmGen.eigenvalues());
+    VERIFY_IS_APPROX(_evec.cwise().abs(), eiSymmGen.eigenvectors().cwise().abs());
+
+    Gsl::free(gSymmA);
+    Gsl::free(gSymmB);
+    GslTraits<RealScalar>::free(gEval);
+    Gsl::free(gEvec);
+  }
+  #endif
+
+  VERIFY((symmA * eiSymm.eigenvectors()).isApprox(
+          eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal().eval(), largerEps));
+
+  // generalized eigen problem Ax = lBx
+  VERIFY((symmA * eiSymmGen.eigenvectors()).isApprox(
+          symmB * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal().eval()), 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().eval());
+
+}
+
+void test_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( selfadjointeigensolver(Matrix3f()) );
+    CALL_SUBTEST( selfadjointeigensolver(Matrix4d()) );
+    CALL_SUBTEST( selfadjointeigensolver(MatrixXf(7,7)) );
+    CALL_SUBTEST( selfadjointeigensolver(MatrixXcd(5,5)) );
+    CALL_SUBTEST( selfadjointeigensolver(MatrixXd(19,19)) );
+
+    CALL_SUBTEST( eigensolver(Matrix4f()) );
+    CALL_SUBTEST( eigensolver(MatrixXd(17,17)) );
+  }
+}
+

test/eigen2/first_aligned.cpp

@@ -0,0 +1,64 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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"
+
+template<typename Scalar>
+void test_first_aligned_helper(Scalar *array, int size)
+{
+  const int packet_size = sizeof(Scalar) * ei_packet_traits<Scalar>::size;
+  VERIFY(((std::size_t(array) + sizeof(Scalar) * ei_alignmentOffset(array, size)) % packet_size) == 0);
+}
+
+template<typename Scalar>
+void test_none_aligned_helper(Scalar *array, int size)
+{
+  VERIFY(ei_packet_traits<Scalar>::size == 1 || ei_alignmentOffset(array, size) == size);
+}
+
+struct some_non_vectorizable_type { float x; };
+
+void test_first_aligned()
+{
+  EIGEN_ALIGN_128 float array_float[100];
+  test_first_aligned_helper(array_float, 50);
+  test_first_aligned_helper(array_float+1, 50);
+  test_first_aligned_helper(array_float+2, 50);
+  test_first_aligned_helper(array_float+3, 50);
+  test_first_aligned_helper(array_float+4, 50);
+  test_first_aligned_helper(array_float+5, 50);
+  
+  EIGEN_ALIGN_128 double array_double[100];
+  test_first_aligned_helper(array_double, 50);
+  test_first_aligned_helper(array_double+1, 50);
+  test_first_aligned_helper(array_double+2, 50);
+  
+  double *array_double_plus_4_bytes = (double*)(std::size_t(array_double)+4);
+  test_none_aligned_helper(array_double_plus_4_bytes, 50);
+  test_none_aligned_helper(array_double_plus_4_bytes+1, 50);
+  
+  some_non_vectorizable_type array_nonvec[100];
+  test_first_aligned_helper(array_nonvec, 100);
+  test_none_aligned_helper(array_nonvec, 100);
+}

test/eigen2/geometry.cpp

@@ -0,0 +1,446 @@
+// 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>
+//
+// 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/Geometry>
+#include <Eigen/LU>
+#include <Eigen/SVD>
+
+template<typename Scalar> void geometry(void)
+{
+  /* this test covers the following files:
+     Cross.h Quaternion.h, Transform.cpp
+  */
+
+  typedef Matrix<Scalar,2,2> Matrix2;
+  typedef Matrix<Scalar,3,3> Matrix3;
+  typedef Matrix<Scalar,4,4> Matrix4;
+  typedef Matrix<Scalar,2,1> Vector2;
+  typedef Matrix<Scalar,3,1> Vector3;
+  typedef Matrix<Scalar,4,1> Vector4;
+  typedef Quaternion<Scalar> Quaternionx;
+  typedef AngleAxis<Scalar> AngleAxisx;
+  typedef Transform<Scalar,2> Transform2;
+  typedef Transform<Scalar,3> Transform3;
+  typedef Scaling<Scalar,2> Scaling2;
+  typedef Scaling<Scalar,3> Scaling3;
+  typedef Translation<Scalar,2> Translation2;
+  typedef Translation<Scalar,3> Translation3;
+
+  Scalar largeEps = test_precision<Scalar>();
+  if (ei_is_same_type<Scalar,float>::ret)
+    largeEps = 1e-2f;
+
+  Vector3 v0 = Vector3::Random(),
+    v1 = Vector3::Random(),
+    v2 = Vector3::Random();
+  Vector2 u0 = Vector2::Random();
+  Matrix3 matrot1;
+
+  Scalar a = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
+
+  // cross product
+  VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v1), Scalar(1));
+  Matrix3 m;
+  m << v0.normalized(),
+      (v0.cross(v1)).normalized(),
+      (v0.cross(v1).cross(v0)).normalized();
+  VERIFY(m.isUnitary());
+
+  // Quaternion: Identity(), setIdentity();
+  Quaternionx q1, q2;
+  q2.setIdentity();
+  VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs());
+  q1.coeffs().setRandom();
+  VERIFY_IS_APPROX(q1.coeffs(), (q1*q2).coeffs());
+
+  // unitOrthogonal
+  VERIFY_IS_MUCH_SMALLER_THAN(u0.unitOrthogonal().dot(u0), Scalar(1));
+  VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1));
+  VERIFY_IS_APPROX(u0.unitOrthogonal().norm(), Scalar(1));
+  VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), Scalar(1));
+
+
+  VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0);
+  VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(M_PI), v0.unitOrthogonal()) * v0);
+  VERIFY_IS_APPROX(ei_cos(a)*v0.squaredNorm(), v0.dot(AngleAxisx(a, v0.unitOrthogonal()) * v0));
+  m = AngleAxisx(a, v0.normalized()).toRotationMatrix().adjoint();
+  VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxisx(a, v0.normalized()));
+  VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxisx(a, v0.normalized()) * m);
+
+  q1 = AngleAxisx(a, v0.normalized());
+  q2 = AngleAxisx(a, v1.normalized());
+
+  // angular distance
+  Scalar refangle = ei_abs(AngleAxisx(q1.inverse()*q2).angle());
+  if (refangle>Scalar(M_PI))
+    refangle = Scalar(2)*Scalar(M_PI) - refangle;
+  
+  if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps)
+  {
+    VERIFY(ei_isApprox(q1.angularDistance(q2), refangle, largeEps));
+  }
+
+  // rotation matrix conversion
+  VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2);
+  VERIFY_IS_APPROX(q1 * q2 * v2,
+    q1.toRotationMatrix() * q2.toRotationMatrix() * v2);
+
+  VERIFY( (q2*q1).isApprox(q1*q2, largeEps) || !(q2 * q1 * v2).isApprox(
+    q1.toRotationMatrix() * q2.toRotationMatrix() * v2));
+
+  q2 = q1.toRotationMatrix();
+  VERIFY_IS_APPROX(q1*v1,q2*v1);
+
+  matrot1 = AngleAxisx(Scalar(0.1), Vector3::UnitX())
+          * AngleAxisx(Scalar(0.2), Vector3::UnitY())
+          * AngleAxisx(Scalar(0.3), Vector3::UnitZ());
+  VERIFY_IS_APPROX(matrot1 * v1,
+       AngleAxisx(Scalar(0.1), Vector3(1,0,0)).toRotationMatrix()
+    * (AngleAxisx(Scalar(0.2), Vector3(0,1,0)).toRotationMatrix()
+    * (AngleAxisx(Scalar(0.3), Vector3(0,0,1)).toRotationMatrix() * v1)));
+
+  // angle-axis conversion
+  AngleAxisx aa = q1;
+  VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
+  VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1);
+
+  // from two vector creation
+  VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized());
+  VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized());
+
+  // inverse and conjugate
+  VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1);
+  VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1);
+
+  // AngleAxis
+  VERIFY_IS_APPROX(AngleAxisx(a,v1.normalized()).toRotationMatrix(),
+    Quaternionx(AngleAxisx(a,v1.normalized())).toRotationMatrix());
+
+  AngleAxisx aa1;
+  m = q1.toRotationMatrix();
+  aa1 = m;
+  VERIFY_IS_APPROX(AngleAxisx(m).toRotationMatrix(),
+    Quaternionx(m).toRotationMatrix());
+
+  // Transform
+  // TODO complete the tests !
+  a = 0;
+  while (ei_abs(a)<Scalar(0.1))
+    a = ei_random<Scalar>(-Scalar(0.4)*Scalar(M_PI), Scalar(0.4)*Scalar(M_PI));
+  q1 = AngleAxisx(a, v0.normalized());
+  Transform3 t0, t1, t2;
+  // first test setIdentity() and Identity()
+  t0.setIdentity();
+  VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
+  t0.matrix().setZero();
+  t0 = Transform3::Identity();
+  VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
+
+  t0.linear() = q1.toRotationMatrix();
+  t1.setIdentity();
+  t1.linear() = q1.toRotationMatrix();
+
+  v0 << 50, 2, 1;//= ei_random_matrix<Vector3>().cwiseProduct(Vector3(10,2,0.5));
+  t0.scale(v0);
+  t1.prescale(v0);
+
+  VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).norm(), v0.x());
+  //VERIFY(!ei_isApprox((t1 * Vector3(1,0,0)).norm(), v0.x()));
+
+  t0.setIdentity();
+  t1.setIdentity();
+  v1 << 1, 2, 3;
+  t0.linear() = q1.toRotationMatrix();
+  t0.pretranslate(v0);
+  t0.scale(v1);
+  t1.linear() = q1.conjugate().toRotationMatrix();
+  t1.prescale(v1.cwise().inverse());
+  t1.translate(-v0);
+
+  VERIFY((t0.matrix() * t1.matrix()).isIdentity(test_precision<Scalar>()));
+
+  t1.fromPositionOrientationScale(v0, q1, v1);
+  VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
+  VERIFY_IS_APPROX(t1*v1, t0*v1);
+
+  t0.setIdentity(); t0.scale(v0).rotate(q1.toRotationMatrix());
+  t1.setIdentity(); t1.scale(v0).rotate(q1);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  t0.setIdentity(); t0.scale(v0).rotate(AngleAxisx(q1));
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  VERIFY_IS_APPROX(t0.scale(a).matrix(), t1.scale(Vector3::Constant(a)).matrix());
+  VERIFY_IS_APPROX(t0.prescale(a).matrix(), t1.prescale(Vector3::Constant(a)).matrix());
+
+  // More transform constructors, operator=, operator*=
+
+  Matrix3 mat3 = Matrix3::Random();
+  Matrix4 mat4;
+  mat4 << mat3 , Vector3::Zero() , Vector4::Zero().transpose();
+  Transform3 tmat3(mat3), tmat4(mat4);
+  tmat4.matrix()(3,3) = Scalar(1);
+  VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix());
+
+  Scalar a3 = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
+  Vector3 v3 = Vector3::Random().normalized();
+  AngleAxisx aa3(a3, v3);
+  Transform3 t3(aa3);
+  Transform3 t4;
+  t4 = aa3;
+  VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
+  t4.rotate(AngleAxisx(-a3,v3));
+  VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());
+  t4 *= aa3;
+  VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
+
+  v3 = Vector3::Random();
+  Translation3 tv3(v3);
+  Transform3 t5(tv3);
+  t4 = tv3;
+  VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
+  t4.translate(-v3);
+  VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());
+  t4 *= tv3;
+  VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
+
+  Scaling3 sv3(v3);
+  Transform3 t6(sv3);
+  t4 = sv3;
+  VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
+  t4.scale(v3.cwise().inverse());
+  VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());
+  t4 *= sv3;
+  VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
+
+  // matrix * transform
+  VERIFY_IS_APPROX(Transform3(t3.matrix()*t4).matrix(), Transform3(t3*t4).matrix());
+
+  // chained Transform product
+  VERIFY_IS_APPROX(((t3*t4)*t5).matrix(), (t3*(t4*t5)).matrix());
+
+  // check that Transform product doesn't have aliasing problems
+  t5 = t4;
+  t5 = t5*t5;
+  VERIFY_IS_APPROX(t5, t4*t4);
+
+  // 2D transformation
+  Transform2 t20, t21;
+  Vector2 v20 = Vector2::Random();
+  Vector2 v21 = Vector2::Random();
+  for (int k=0; k<2; ++k)
+    if (ei_abs(v21[k])<Scalar(1e-3)) v21[k] = Scalar(1e-3);
+  t21.setIdentity();
+  t21.linear() = Rotation2D<Scalar>(a).toRotationMatrix();
+  VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(),
+    t21.pretranslate(v20).scale(v21).matrix());
+
+  t21.setIdentity();
+  t21.linear() = Rotation2D<Scalar>(-a).toRotationMatrix();
+  VERIFY( (t20.fromPositionOrientationScale(v20,a,v21)
+        * (t21.prescale(v21.cwise().inverse()).translate(-v20))).matrix().isIdentity(test_precision<Scalar>()) );
+
+  // Transform - new API
+  // 3D
+  t0.setIdentity();
+  t0.rotate(q1).scale(v0).translate(v0);
+  // mat * scaling and mat * translation
+  t1 = (Matrix3(q1) * Scaling3(v0)) * Translation3(v0);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  // mat * transformation and scaling * translation
+  t1 = Matrix3(q1) * (Scaling3(v0) * Translation3(v0));
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  t0.setIdentity();
+  t0.prerotate(q1).prescale(v0).pretranslate(v0);
+  // translation * scaling and transformation * mat
+  t1 = (Translation3(v0) * Scaling3(v0)) * Matrix3(q1);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  // scaling * mat and translation * mat
+  t1 = Translation3(v0) * (Scaling3(v0) * Matrix3(q1));
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  t0.setIdentity();
+  t0.scale(v0).translate(v0).rotate(q1);
+  // translation * mat and scaling * transformation
+  t1 = Scaling3(v0) * (Translation3(v0) * Matrix3(q1));
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  // transformation * scaling
+  t0.scale(v0);
+  t1 = t1 * Scaling3(v0);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  // transformation * translation
+  t0.translate(v0);
+  t1 = t1 * Translation3(v0);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  // translation * transformation
+  t0.pretranslate(v0);
+  t1 = Translation3(v0) * t1;
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // transform * quaternion
+  t0.rotate(q1);
+  t1 = t1 * q1;
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // translation * quaternion
+  t0.translate(v1).rotate(q1);
+  t1 = t1 * (Translation3(v1) * q1);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // scaling * quaternion
+  t0.scale(v1).rotate(q1);
+  t1 = t1 * (Scaling3(v1) * q1);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // quaternion * transform
+  t0.prerotate(q1);
+  t1 = q1 * t1;
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // quaternion * translation
+  t0.rotate(q1).translate(v1);
+  t1 = t1 * (q1 * Translation3(v1));
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // quaternion * scaling
+  t0.rotate(q1).scale(v1);
+  t1 = t1 * (q1 * Scaling3(v1));
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+  // translation * vector
+  t0.setIdentity();
+  t0.translate(v0);
+  VERIFY_IS_APPROX(t0 * v1, Translation3(v0) * v1);
+
+  // scaling * vector
+  t0.setIdentity();
+  t0.scale(v0);
+  VERIFY_IS_APPROX(t0 * v1, Scaling3(v0) * v1);
+
+  // test transform inversion
+  t0.setIdentity();
+  t0.translate(v0);
+  t0.linear().setRandom();
+  VERIFY_IS_APPROX(t0.inverse(Affine), t0.matrix().inverse());
+  t0.setIdentity();
+  t0.translate(v0).rotate(q1);
+  VERIFY_IS_APPROX(t0.inverse(Isometry), t0.matrix().inverse());
+
+  // test extract rotation and scaling
+  t0.setIdentity();
+  t0.translate(v0).rotate(q1).scale(v1);
+  VERIFY_IS_APPROX(t0.rotation() * v1, Matrix3(q1) * v1);
+
+  Matrix3 mat_rotation, mat_scaling;
+  t0.setIdentity();
+  t0.translate(v0).rotate(q1).scale(v1);
+  t0.computeRotationScaling(&mat_rotation, &mat_scaling);
+  VERIFY_IS_APPROX(t0.linear(), mat_rotation * mat_scaling);
+  VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
+  VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
+  t0.computeScalingRotation(&mat_scaling, &mat_rotation);
+  VERIFY_IS_APPROX(t0.linear(), mat_scaling * mat_rotation);
+  VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
+  VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
+
+  // test casting
+  Transform<float,3> t1f = t1.template cast<float>();
+  VERIFY_IS_APPROX(t1f.template cast<Scalar>(),t1);
+  Transform<double,3> t1d = t1.template cast<double>();
+  VERIFY_IS_APPROX(t1d.template cast<Scalar>(),t1);
+
+  Translation3 tr1(v0);
+  Translation<float,3> tr1f = tr1.template cast<float>();
+  VERIFY_IS_APPROX(tr1f.template cast<Scalar>(),tr1);
+  Translation<double,3> tr1d = tr1.template cast<double>();
+  VERIFY_IS_APPROX(tr1d.template cast<Scalar>(),tr1);
+
+  Scaling3 sc1(v0);
+  Scaling<float,3> sc1f = sc1.template cast<float>();
+  VERIFY_IS_APPROX(sc1f.template cast<Scalar>(),sc1);
+  Scaling<double,3> sc1d = sc1.template cast<double>();
+  VERIFY_IS_APPROX(sc1d.template cast<Scalar>(),sc1);
+
+  Quaternion<float> q1f = q1.template cast<float>();
+  VERIFY_IS_APPROX(q1f.template cast<Scalar>(),q1);
+  Quaternion<double> q1d = q1.template cast<double>();
+  VERIFY_IS_APPROX(q1d.template cast<Scalar>(),q1);
+
+  AngleAxis<float> aa1f = aa1.template cast<float>();
+  VERIFY_IS_APPROX(aa1f.template cast<Scalar>(),aa1);
+  AngleAxis<double> aa1d = aa1.template cast<double>();
+  VERIFY_IS_APPROX(aa1d.template cast<Scalar>(),aa1);
+
+  Rotation2D<Scalar> r2d1(ei_random<Scalar>());
+  Rotation2D<float> r2d1f = r2d1.template cast<float>();
+  VERIFY_IS_APPROX(r2d1f.template cast<Scalar>(),r2d1);
+  Rotation2D<double> r2d1d = r2d1.template cast<double>();
+  VERIFY_IS_APPROX(r2d1d.template cast<Scalar>(),r2d1);
+
+  m = q1;
+//   m.col(1) = Vector3(0,ei_random<Scalar>(),ei_random<Scalar>()).normalized();
+//   m.col(0) = Vector3(-1,0,0).normalized();
+//   m.col(2) = m.col(0).cross(m.col(1));
+  #define VERIFY_EULER(I,J,K, X,Y,Z) { \
+    Vector3 ea = m.eulerAngles(I,J,K); \
+    Matrix3 m1 = Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z())); \
+    VERIFY_IS_APPROX(m,  Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z()))); \
+  }
+  VERIFY_EULER(0,1,2, X,Y,Z);
+  VERIFY_EULER(0,1,0, X,Y,X);
+  VERIFY_EULER(0,2,1, X,Z,Y);
+  VERIFY_EULER(0,2,0, X,Z,X);
+
+  VERIFY_EULER(1,2,0, Y,Z,X);
+  VERIFY_EULER(1,2,1, Y,Z,Y);
+  VERIFY_EULER(1,0,2, Y,X,Z);
+  VERIFY_EULER(1,0,1, Y,X,Y);
+
+  VERIFY_EULER(2,0,1, Z,X,Y);
+  VERIFY_EULER(2,0,2, Z,X,Z);
+  VERIFY_EULER(2,1,0, Z,Y,X);
+  VERIFY_EULER(2,1,2, Z,Y,Z);
+
+  // colwise/rowwise cross product
+  mat3.setRandom();
+  Vector3 vec3 = Vector3::Random();
+  Matrix3 mcross;
+  int i = ei_random<int>(0,2);
+  mcross = mat3.colwise().cross(vec3);
+  VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3));
+  mcross = mat3.rowwise().cross(vec3);
+  VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3));
+
+
+}
+
+void test_geometry()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( geometry<float>() );
+    CALL_SUBTEST( geometry<double>() );
+  }
+}

test/eigen2/gsl_helper.h

@@ -0,0 +1,190 @@
+// 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>
+//
+// 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/>.
+
+#ifndef EIGEN_GSL_HELPER
+#define EIGEN_GSL_HELPER
+
+#include <Eigen/Core>
+
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_multifit.h>
+#include <gsl/gsl_eigen.h>
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_complex.h>
+#include <gsl/gsl_complex_math.h>
+
+namespace Eigen {
+
+template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex> struct GslTraits
+{
+  typedef gsl_matrix* Matrix;
+  typedef gsl_vector* Vector;
+  static Matrix createMatrix(int rows, int cols) { return gsl_matrix_alloc(rows,cols); }
+  static Vector createVector(int size) { return gsl_vector_alloc(size); }
+  static void free(Matrix& m) { gsl_matrix_free(m); m=0; }
+  static void free(Vector& m) { gsl_vector_free(m); m=0; }
+  static void prod(const Matrix& m, const Vector& v, Vector& x) { gsl_blas_dgemv(CblasNoTrans,1,m,v,0,x); }
+  static void cholesky(Matrix& m) { gsl_linalg_cholesky_decomp(m); }
+  static void cholesky_solve(const Matrix& m, const Vector& b, Vector& x) { gsl_linalg_cholesky_solve(m,b,x); }
+  static void eigen_symm(const Matrix& m, Vector& eval, Matrix& evec)
+  {
+    gsl_eigen_symmv_workspace * w = gsl_eigen_symmv_alloc(m->size1);
+    Matrix a = createMatrix(m->size1, m->size2);
+    gsl_matrix_memcpy(a, m);
+    gsl_eigen_symmv(a,eval,evec,w);
+    gsl_eigen_symmv_sort(eval, evec, GSL_EIGEN_SORT_VAL_ASC);
+    gsl_eigen_symmv_free(w);
+    free(a);
+  }
+  static void eigen_symm_gen(const Matrix& m, const Matrix& _b, Vector& eval, Matrix& evec)
+  {
+    gsl_eigen_gensymmv_workspace * w = gsl_eigen_gensymmv_alloc(m->size1);
+    Matrix a = createMatrix(m->size1, m->size2);
+    Matrix b = createMatrix(_b->size1, _b->size2);
+    gsl_matrix_memcpy(a, m);
+    gsl_matrix_memcpy(b, _b);
+    gsl_eigen_gensymmv(a,b,eval,evec,w);
+    gsl_eigen_symmv_sort(eval, evec, GSL_EIGEN_SORT_VAL_ASC);
+    gsl_eigen_gensymmv_free(w);
+    free(a);
+  }
+};
+
+template<typename Scalar> struct GslTraits<Scalar,true>
+{
+  typedef gsl_matrix_complex* Matrix;
+  typedef gsl_vector_complex* Vector;
+  static Matrix createMatrix(int rows, int cols) { return gsl_matrix_complex_alloc(rows,cols); }
+  static Vector createVector(int size) { return gsl_vector_complex_alloc(size); }
+  static void free(Matrix& m) { gsl_matrix_complex_free(m); m=0; }
+  static void free(Vector& m) { gsl_vector_complex_free(m); m=0; }
+  static void cholesky(Matrix& m) { gsl_linalg_complex_cholesky_decomp(m); }
+  static void cholesky_solve(const Matrix& m, const Vector& b, Vector& x) { gsl_linalg_complex_cholesky_solve(m,b,x); }
+  static void prod(const Matrix& m, const Vector& v, Vector& x)
+  { gsl_blas_zgemv(CblasNoTrans,gsl_complex_rect(1,0),m,v,gsl_complex_rect(0,0),x); }
+  static void eigen_symm(const Matrix& m, gsl_vector* &eval, Matrix& evec)
+  {
+    gsl_eigen_hermv_workspace * w = gsl_eigen_hermv_alloc(m->size1);
+    Matrix a = createMatrix(m->size1, m->size2);
+    gsl_matrix_complex_memcpy(a, m);
+    gsl_eigen_hermv(a,eval,evec,w);
+    gsl_eigen_hermv_sort(eval, evec, GSL_EIGEN_SORT_VAL_ASC);
+    gsl_eigen_hermv_free(w);
+    free(a);
+  }
+  static void eigen_symm_gen(const Matrix& m, const Matrix& _b, gsl_vector* &eval, Matrix& evec)
+  {
+    gsl_eigen_genhermv_workspace * w = gsl_eigen_genhermv_alloc(m->size1);
+    Matrix a = createMatrix(m->size1, m->size2);
+    Matrix b = createMatrix(_b->size1, _b->size2);
+    gsl_matrix_complex_memcpy(a, m);
+    gsl_matrix_complex_memcpy(b, _b);
+    gsl_eigen_genhermv(a,b,eval,evec,w);
+    gsl_eigen_hermv_sort(eval, evec, GSL_EIGEN_SORT_VAL_ASC);
+    gsl_eigen_genhermv_free(w);
+    free(a);
+  }
+};
+
+template<typename MatrixType>
+void convert(const MatrixType& m, gsl_matrix* &res)
+{
+//   if (res)
+//     gsl_matrix_free(res);
+  res = gsl_matrix_alloc(m.rows(), m.cols());
+  for (int i=0 ; i<m.rows() ; ++i)
+    for (int j=0 ; j<m.cols(); ++j)
+      gsl_matrix_set(res, i, j, m(i,j));
+}
+
+template<typename MatrixType>
+void convert(const gsl_matrix* m, MatrixType& res)
+{
+  res.resize(int(m->size1), int(m->size2));
+  for (int i=0 ; i<res.rows() ; ++i)
+    for (int j=0 ; j<res.cols(); ++j)
+      res(i,j) = gsl_matrix_get(m,i,j);
+}
+
+template<typename VectorType>
+void convert(const VectorType& m, gsl_vector* &res)
+{
+  if (res) gsl_vector_free(res);
+  res = gsl_vector_alloc(m.size());
+  for (int i=0 ; i<m.size() ; ++i)
+      gsl_vector_set(res, i, m[i]);
+}
+
+template<typename VectorType>
+void convert(const gsl_vector* m, VectorType& res)
+{
+  res.resize (m->size);
+  for (int i=0 ; i<res.rows() ; ++i)
+    res[i] = gsl_vector_get(m, i);
+}
+
+template<typename MatrixType>
+void convert(const MatrixType& m, gsl_matrix_complex* &res)
+{
+  res = gsl_matrix_complex_alloc(m.rows(), m.cols());
+  for (int i=0 ; i<m.rows() ; ++i)
+    for (int j=0 ; j<m.cols(); ++j)
+    {
+      gsl_matrix_complex_set(res, i, j,
+        gsl_complex_rect(m(i,j).real(), m(i,j).imag()));
+    }
+}
+
+template<typename MatrixType>
+void convert(const gsl_matrix_complex* m, MatrixType& res)
+{
+  res.resize(int(m->size1), int(m->size2));
+  for (int i=0 ; i<res.rows() ; ++i)
+    for (int j=0 ; j<res.cols(); ++j)
+      res(i,j) = typename MatrixType::Scalar(
+        GSL_REAL(gsl_matrix_complex_get(m,i,j)),
+        GSL_IMAG(gsl_matrix_complex_get(m,i,j)));
+}
+
+template<typename VectorType>
+void convert(const VectorType& m, gsl_vector_complex* &res)
+{
+  res = gsl_vector_complex_alloc(m.size());
+  for (int i=0 ; i<m.size() ; ++i)
+      gsl_vector_complex_set(res, i, gsl_complex_rect(m[i].real(), m[i].imag()));
+}
+
+template<typename VectorType>
+void convert(const gsl_vector_complex* m, VectorType& res)
+{
+  res.resize(m->size);
+  for (int i=0 ; i<res.rows() ; ++i)
+    res[i] = typename VectorType::Scalar(
+        GSL_REAL(gsl_vector_complex_get(m, i)),
+        GSL_IMAG(gsl_vector_complex_get(m, i)));
+}
+
+}
+
+#endif // EIGEN_GSL_HELPER

test/eigen2/hyperplane.cpp

@@ -0,0 +1,141 @@
+// 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>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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/Geometry>
+#include <Eigen/LU>
+#include <Eigen/QR>
+
+template<typename HyperplaneType> void hyperplane(const HyperplaneType& _plane)
+{
+  /* this test covers the following files:
+     Hyperplane.h
+  */
+
+  const int dim = _plane.dim();
+  typedef typename HyperplaneType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 1> VectorType;
+  typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime,
+                         HyperplaneType::AmbientDimAtCompileTime> MatrixType;
+
+  VectorType p0 = VectorType::Random(dim);
+  VectorType p1 = VectorType::Random(dim);
+
+  VectorType n0 = VectorType::Random(dim).normalized();
+  VectorType n1 = VectorType::Random(dim).normalized();
+
+  HyperplaneType pl0(n0, p0);
+  HyperplaneType pl1(n1, p1);
+  HyperplaneType pl2 = pl1;
+
+  Scalar s0 = ei_random<Scalar>();
+  Scalar s1 = ei_random<Scalar>();
+
+  VERIFY_IS_APPROX( n1.dot(n1), Scalar(1) );
+
+  VERIFY_IS_MUCH_SMALLER_THAN( pl0.absDistance(p0), Scalar(1) );
+  VERIFY_IS_APPROX( pl1.signedDistance(p1 + n1 * s0), s0 );
+  VERIFY_IS_MUCH_SMALLER_THAN( pl1.signedDistance(pl1.projection(p0)), Scalar(1) );
+  VERIFY_IS_MUCH_SMALLER_THAN( pl1.absDistance(p1 +  pl1.normal().unitOrthogonal() * s1), Scalar(1) );
+
+  // transform
+  if (!NumTraits<Scalar>::IsComplex)
+  {
+    MatrixType rot = MatrixType::Random(dim,dim).qr().matrixQ();
+    Scaling<Scalar,HyperplaneType::AmbientDimAtCompileTime> scaling(VectorType::Random());
+    Translation<Scalar,HyperplaneType::AmbientDimAtCompileTime> translation(VectorType::Random());
+
+    pl2 = pl1;
+    VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot).absDistance(rot * p1), Scalar(1) );
+    pl2 = pl1;
+    VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot,Isometry).absDistance(rot * p1), Scalar(1) );
+    pl2 = pl1;
+    VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling).absDistance((rot*scaling) * p1), Scalar(1) );
+    pl2 = pl1;
+    VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling*translation)
+                                 .absDistance((rot*scaling*translation) * p1), Scalar(1) );
+    pl2 = pl1;
+    VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*translation,Isometry)
+                                 .absDistance((rot*translation) * p1), Scalar(1) );
+  }
+
+  // casting
+  const int Dim = HyperplaneType::AmbientDimAtCompileTime;
+  typedef typename GetDifferentType<Scalar>::type OtherScalar;
+  Hyperplane<OtherScalar,Dim> hp1f = pl1.template cast<OtherScalar>();
+  VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),pl1);
+  Hyperplane<Scalar,Dim> hp1d = pl1.template cast<Scalar>();
+  VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),pl1);
+}
+
+template<typename Scalar> void lines()
+{
+  typedef Hyperplane<Scalar, 2> HLine;
+  typedef ParametrizedLine<Scalar, 2> PLine;
+  typedef Matrix<Scalar,2,1> Vector;
+  typedef Matrix<Scalar,3,1> CoeffsType;
+
+  for(int i = 0; i < 10; i++)
+  {
+    Vector center = Vector::Random();
+    Vector u = Vector::Random();
+    Vector v = Vector::Random();
+    Scalar a = ei_random<Scalar>();
+    while (ei_abs(a-1) < 1e-4) a = ei_random<Scalar>();
+    while (u.norm() < 1e-4) u = Vector::Random();
+    while (v.norm() < 1e-4) v = Vector::Random();
+
+    HLine line_u = HLine::Through(center + u, center + a*u);
+    HLine line_v = HLine::Through(center + v, center + a*v);
+
+    // the line equations should be normalized so that a^2+b^2=1
+    VERIFY_IS_APPROX(line_u.normal().norm(), Scalar(1));
+    VERIFY_IS_APPROX(line_v.normal().norm(), Scalar(1));
+
+    Vector result = line_u.intersection(line_v);
+
+    // the lines should intersect at the point we called "center"
+    VERIFY_IS_APPROX(result, center);
+
+    // check conversions between two types of lines
+    PLine pl(line_u); // gcc 3.3 will commit suicide if we don't name this variable
+    CoeffsType converted_coeffs(HLine(pl).coeffs());
+    converted_coeffs *= line_u.coeffs()(0)/converted_coeffs(0);
+    VERIFY(line_u.coeffs().isApprox(converted_coeffs));
+  }
+}
+
+void test_hyperplane()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( hyperplane(Hyperplane<float,2>()) );
+    CALL_SUBTEST( hyperplane(Hyperplane<float,3>()) );
+    CALL_SUBTEST( hyperplane(Hyperplane<double,4>()) );
+    CALL_SUBTEST( hyperplane(Hyperplane<std::complex<double>,5>()) );
+    CALL_SUBTEST( lines<float>() );
+    CALL_SUBTEST( lines<double>() );
+  }
+}

test/eigen2/inverse.cpp

@@ -0,0 +1,78 @@
+// 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>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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/LU>
+
+template<typename MatrixType> void inverse(const MatrixType& m)
+{
+  /* this test covers the following files:
+     Inverse.h
+  */
+  int rows = m.rows();
+  int cols = m.cols();
+
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
+
+  MatrixType m1 = MatrixType::Random(rows, cols),
+             m2(rows, cols),
+             mzero = MatrixType::Zero(rows, cols),
+             identity = MatrixType::Identity(rows, rows);
+
+  while(ei_abs(m1.determinant()) < RealScalar(0.1) && rows <= 8)
+  {
+    m1 = MatrixType::Random(rows, cols);
+  }
+
+  m2 = m1.inverse();
+  VERIFY_IS_APPROX(m1, m2.inverse() );
+
+  m1.computeInverse(&m2);
+  VERIFY_IS_APPROX(m1, m2.inverse() );
+
+  VERIFY_IS_APPROX((Scalar(2)*m2).inverse(), m2.inverse()*Scalar(0.5));
+
+  VERIFY_IS_APPROX(identity, m1.inverse() * m1 );
+  VERIFY_IS_APPROX(identity, m1 * m1.inverse() );
+
+  VERIFY_IS_APPROX(m1, m1.inverse().inverse() );
+
+  // since for the general case we implement separately row-major and col-major, test that
+  VERIFY_IS_APPROX(m1.transpose().inverse(), m1.inverse().transpose());
+}
+
+void test_inverse()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( inverse(Matrix<double,1,1>()) );
+    CALL_SUBTEST( inverse(Matrix2d()) );
+    CALL_SUBTEST( inverse(Matrix3f()) );
+    CALL_SUBTEST( inverse(Matrix4f()) );
+    CALL_SUBTEST( inverse(MatrixXf(8,8)) );
+    CALL_SUBTEST( inverse(MatrixXcd(7,7)) );
+  }
+}

test/eigen2/linearstructure.cpp

@@ -0,0 +1,99 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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"
+
+template<typename MatrixType> void linearStructure(const MatrixType& m)
+{
+  /* this test covers the following files:
+     Sum.h Difference.h Opposite.h ScalarMultiple.h
+  */
+
+  typedef typename MatrixType::Scalar Scalar;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+
+  int rows = m.rows();
+  int cols = m.cols();
+
+  // this test relies a lot on Random.h, and there's not much more that we can do
+  // to test it, hence I consider that we will have tested Random.h
+  MatrixType m1 = MatrixType::Random(rows, cols),
+             m2 = MatrixType::Random(rows, cols),
+             m3(rows, cols),
+             mzero = MatrixType::Zero(rows, cols);
+
+  Scalar s1 = ei_random<Scalar>();
+  while (ei_abs(s1)<1e-3) s1 = ei_random<Scalar>();
+
+  int r = ei_random<int>(0, rows-1),
+      c = ei_random<int>(0, cols-1);
+
+  VERIFY_IS_APPROX(-(-m1),                  m1);
+  VERIFY_IS_APPROX(m1+m1,                   2*m1);
+  VERIFY_IS_APPROX(m1+m2-m1,                m2);
+  VERIFY_IS_APPROX(-m2+m1+m2,               m1);
+  VERIFY_IS_APPROX(m1*s1,                   s1*m1);
+  VERIFY_IS_APPROX((m1+m2)*s1,              s1*m1+s1*m2);
+  VERIFY_IS_APPROX((-m1+m2)*s1,             -s1*m1+s1*m2);
+  m3 = m2; m3 += m1;
+  VERIFY_IS_APPROX(m3,                      m1+m2);
+  m3 = m2; m3 -= m1;
+  VERIFY_IS_APPROX(m3,                      m2-m1);
+  m3 = m2; m3 *= s1;
+  VERIFY_IS_APPROX(m3,                      s1*m2);
+  if(NumTraits<Scalar>::HasFloatingPoint)
+  {
+    m3 = m2; m3 /= s1;
+    VERIFY_IS_APPROX(m3,                    m2/s1);
+  }
+
+  // again, test operator() to check const-qualification
+  VERIFY_IS_APPROX((-m1)(r,c), -(m1(r,c)));
+  VERIFY_IS_APPROX((m1-m2)(r,c), (m1(r,c))-(m2(r,c)));
+  VERIFY_IS_APPROX((m1+m2)(r,c), (m1(r,c))+(m2(r,c)));
+  VERIFY_IS_APPROX((s1*m1)(r,c), s1*(m1(r,c)));
+  VERIFY_IS_APPROX((m1*s1)(r,c), (m1(r,c))*s1);
+  if(NumTraits<Scalar>::HasFloatingPoint)
+    VERIFY_IS_APPROX((m1/s1)(r,c), (m1(r,c))/s1);
+
+  // use .block to disable vectorization and compare to the vectorized version
+  VERIFY_IS_APPROX(m1+m1.block(0,0,rows,cols), m1+m1);
+  VERIFY_IS_APPROX(m1.cwise() * m1.block(0,0,rows,cols), m1.cwise() * m1);
+  VERIFY_IS_APPROX(m1 - m1.block(0,0,rows,cols), m1 - m1);
+  VERIFY_IS_APPROX(m1.block(0,0,rows,cols) * s1, m1 * s1);
+}
+
+void test_linearstructure()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( linearStructure(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST( linearStructure(Matrix2f()) );
+    CALL_SUBTEST( linearStructure(Vector3d()) );
+    CALL_SUBTEST( linearStructure(Matrix4d()) );
+    CALL_SUBTEST( linearStructure(MatrixXcf(3, 3)) );
+    CALL_SUBTEST( linearStructure(MatrixXf(8, 12)) );
+    CALL_SUBTEST( linearStructure(MatrixXi(8, 12)) );
+    CALL_SUBTEST( linearStructure(MatrixXcd(20, 20)) );
+  }
+}

test/eigen2/lu.cpp

@@ -0,0 +1,141 @@
+// 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 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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/LU>
+
+template<typename Derived>
+void doSomeRankPreservingOperations(Eigen::MatrixBase<Derived>& m)
+{
+  typedef typename Derived::RealScalar RealScalar;
+  for(int a = 0; a < 3*(m.rows()+m.cols()); a++)
+  {
+    RealScalar d = Eigen::ei_random<RealScalar>(-1,1);
+    int i = Eigen::ei_random<int>(0,m.rows()-1); // i is a random row number
+    int j;
+    do {
+      j = Eigen::ei_random<int>(0,m.rows()-1);
+    } while (i==j); // j is another one (must be different)
+    m.row(i) += d * m.row(j);
+
+    i = Eigen::ei_random<int>(0,m.cols()-1); // i is a random column number
+    do {
+      j = Eigen::ei_random<int>(0,m.cols()-1);
+    } while (i==j); // j is another one (must be different)
+    m.col(i) += d * m.col(j);
+  }
+}
+
+template<typename MatrixType> void lu_non_invertible()
+{
+  /* this test covers the following files:
+     LU.h
+  */
+  // NOTE there seems to be a problem with too small sizes -- could easily lie in the doSomeRankPreservingOperations function
+  int rows = ei_random<int>(20,200), cols = ei_random<int>(20,200), cols2 = ei_random<int>(20,200);
+  int rank = ei_random<int>(1, std::min(rows, cols)-1);
+
+  MatrixType m1(rows, cols), m2(cols, cols2), m3(rows, cols2), k(1,1);
+  m1 = MatrixType::Random(rows,cols);
+  if(rows <= cols)
+    for(int i = rank; i < rows; i++) m1.row(i).setZero();
+  else
+    for(int i = rank; i < cols; i++) m1.col(i).setZero();
+  doSomeRankPreservingOperations(m1);
+
+  LU<MatrixType> lu(m1);
+  typename LU<MatrixType>::KernelResultType m1kernel = lu.kernel();
+  typename LU<MatrixType>::ImageResultType m1image = lu.image();
+
+  VERIFY(rank == lu.rank());
+  VERIFY(cols - lu.rank() == lu.dimensionOfKernel());
+  VERIFY(!lu.isInjective());
+  VERIFY(!lu.isInvertible());
+  VERIFY(lu.isSurjective() == (lu.rank() == rows));
+  VERIFY((m1 * m1kernel).isMuchSmallerThan(m1));
+  VERIFY(m1image.lu().rank() == rank);
+  MatrixType sidebyside(m1.rows(), m1.cols() + m1image.cols());
+  sidebyside << m1, m1image;
+  VERIFY(sidebyside.lu().rank() == rank);
+  m2 = MatrixType::Random(cols,cols2);
+  m3 = m1*m2;
+  m2 = MatrixType::Random(cols,cols2);
+  lu.solve(m3, &m2);
+  VERIFY_IS_APPROX(m3, m1*m2);
+  m3 = MatrixType::Random(rows,cols2);
+  VERIFY(!lu.solve(m3, &m2));
+}
+
+template<typename MatrixType> void lu_invertible()
+{
+  /* this test covers the following files:
+     LU.h
+  */
+  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+  int size = ei_random<int>(10,200);
+
+  MatrixType m1(size, size), m2(size, size), m3(size, size);
+  m1 = MatrixType::Random(size,size);
+
+  if (ei_is_same_type<RealScalar,float>::ret)
+  {
+    // let's build a matrix more stable to inverse
+    MatrixType a = MatrixType::Random(size,size*2);
+    m1 += a * a.adjoint();
+  }
+
+  LU<MatrixType> lu(m1);
+  VERIFY(0 == lu.dimensionOfKernel());
+  VERIFY(size == lu.rank());
+  VERIFY(lu.isInjective());
+  VERIFY(lu.isSurjective());
+  VERIFY(lu.isInvertible());
+  VERIFY(lu.image().lu().isInvertible());
+  m3 = MatrixType::Random(size,size);
+  lu.solve(m3, &m2);
+  VERIFY_IS_APPROX(m3, m1*m2);
+  VERIFY_IS_APPROX(m2, lu.inverse()*m3);
+  m3 = MatrixType::Random(size,size);
+  VERIFY(lu.solve(m3, &m2));
+}
+
+void test_lu()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( lu_non_invertible<MatrixXf>() );
+    CALL_SUBTEST( lu_non_invertible<MatrixXd>() );
+    CALL_SUBTEST( lu_non_invertible<MatrixXcf>() );
+    CALL_SUBTEST( lu_non_invertible<MatrixXcd>() );
+    CALL_SUBTEST( lu_invertible<MatrixXf>() );
+    CALL_SUBTEST( lu_invertible<MatrixXd>() );
+    CALL_SUBTEST( lu_invertible<MatrixXcf>() );
+    CALL_SUBTEST( lu_invertible<MatrixXcd>() );
+  }
+
+  MatrixXf m = MatrixXf::Zero(10,10);
+  VectorXf b = VectorXf::Zero(10);
+  VectorXf x = VectorXf::Random(10);
+  VERIFY(m.lu().solve(b,&x));
+  VERIFY(x.isZero());
+}

test/eigen2/main.h

@@ -0,0 +1,313 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// 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 <cstdlib>
+#include <ctime>
+#include <iostream>
+#include <string>
+#include <vector>
+
+#ifndef EIGEN_TEST_FUNC
+#error EIGEN_TEST_FUNC must be defined
+#endif
+
+#define DEFAULT_REPEAT 10
+
+namespace Eigen
+{
+  static std::vector<std::string> g_test_stack;
+  static int g_repeat;
+}
+
+#define EI_PP_MAKE_STRING2(S) #S
+#define EI_PP_MAKE_STRING(S) EI_PP_MAKE_STRING2(S)
+
+#define EI_PP_CAT2(a,b) a ## b
+#define EI_PP_CAT(a,b) EI_PP_CAT2(a,b)
+
+#ifndef EIGEN_NO_ASSERTION_CHECKING
+
+  namespace Eigen
+  {
+    static const bool should_raise_an_assert = false;
+
+    // Used to avoid to raise two exceptions at a time in which
+    // case the exception is not properly caught.
+    // This may happen when a second exceptions is raise in a destructor.
+    static bool no_more_assert = false;
+
+    struct ei_assert_exception
+    {
+      ei_assert_exception(void) {}
+      ~ei_assert_exception() { Eigen::no_more_assert = false; }
+    };
+  }
+
+  // If EIGEN_DEBUG_ASSERTS is defined and if no assertion is raised while
+  // one should have been, then the list of excecuted assertions is printed out.
+  //
+  // EIGEN_DEBUG_ASSERTS is not enabled by default as it
+  // significantly increases the compilation time
+  // and might even introduce side effects that would hide
+  // some memory errors.
+  #ifdef EIGEN_DEBUG_ASSERTS
+
+    namespace Eigen
+    {
+      static bool ei_push_assert = false;
+      static std::vector<std::string> ei_assert_list;
+    }
+
+    #define ei_assert(a)                       \
+      if( (!(a)) && (!no_more_assert) )     \
+      {                                     \
+        Eigen::no_more_assert = true;       \
+        throw Eigen::ei_assert_exception(); \
+      }                                     \
+      else if (Eigen::ei_push_assert)       \
+      {                                     \
+        ei_assert_list.push_back(std::string(EI_PP_MAKE_STRING(__FILE__)" ("EI_PP_MAKE_STRING(__LINE__)") : "#a) ); \
+      }
+
+    #define VERIFY_RAISES_ASSERT(a)                                               \
+      {                                                                           \
+        Eigen::no_more_assert = false;                                            \
+        try {                                                                     \
+          Eigen::ei_assert_list.clear();                                          \
+          Eigen::ei_push_assert = true;                                           \
+          a;                                                                      \
+          Eigen::ei_push_assert = false;                                          \
+          std::cerr << "One of the following asserts should have been raised:\n"; \
+          for (uint ai=0 ; ai<ei_assert_list.size() ; ++ai)                       \
+            std::cerr << "  " << ei_assert_list[ai] << "\n";                      \
+          VERIFY(Eigen::should_raise_an_assert && # a);                           \
+        } catch (Eigen::ei_assert_exception e) {                                  \
+          Eigen::ei_push_assert = false; VERIFY(true);                            \
+        }                                                                         \
+      }
+
+  #else // EIGEN_DEBUG_ASSERTS
+
+    #define ei_assert(a) \
+      if( (!(a)) && (!no_more_assert) )     \
+      {                                     \
+        Eigen::no_more_assert = true;       \
+        throw Eigen::ei_assert_exception(); \
+      }
+
+    #define VERIFY_RAISES_ASSERT(a) {                             \
+        Eigen::no_more_assert = false;                            \
+        try { a; VERIFY(Eigen::should_raise_an_assert && # a); }  \
+        catch (Eigen::ei_assert_exception e) { VERIFY(true); }    \
+      }
+
+  #endif // EIGEN_DEBUG_ASSERTS
+
+  #define EIGEN_USE_CUSTOM_ASSERT
+
+#else // EIGEN_NO_ASSERTION_CHECKING
+
+  #define VERIFY_RAISES_ASSERT(a) {}
+
+#endif // EIGEN_NO_ASSERTION_CHECKING
+
+
+#define EIGEN_INTERNAL_DEBUGGING
+#define EIGEN_NICE_RANDOM
+#include <Eigen/Array>
+
+
+#define VERIFY(a) do { if (!(a)) { \
+    std::cerr << "Test " << g_test_stack.back() << " failed in "EI_PP_MAKE_STRING(__FILE__) << " (" << EI_PP_MAKE_STRING(__LINE__) << ")" \
+      << std::endl << "    " << EI_PP_MAKE_STRING(a) << std::endl << std::endl; \
+    std::exit(2); \
+  } } while (0)
+
+#define VERIFY_IS_APPROX(a, b) VERIFY(test_isApprox(a, b))
+#define VERIFY_IS_NOT_APPROX(a, b) VERIFY(!test_isApprox(a, b))
+#define VERIFY_IS_MUCH_SMALLER_THAN(a, b) VERIFY(test_isMuchSmallerThan(a, b))
+#define VERIFY_IS_NOT_MUCH_SMALLER_THAN(a, b) VERIFY(!test_isMuchSmallerThan(a, b))
+#define VERIFY_IS_APPROX_OR_LESS_THAN(a, b) VERIFY(test_isApproxOrLessThan(a, b))
+#define VERIFY_IS_NOT_APPROX_OR_LESS_THAN(a, b) VERIFY(!test_isApproxOrLessThan(a, b))
+
+#define CALL_SUBTEST(FUNC) do { \
+    g_test_stack.push_back(EI_PP_MAKE_STRING(FUNC)); \
+    FUNC; \
+    g_test_stack.pop_back(); \
+  } while (0)
+
+namespace Eigen {
+
+template<typename T> inline typename NumTraits<T>::Real test_precision();
+template<> inline int test_precision<int>() { return 0; }
+template<> inline float test_precision<float>() { return 1e-3f; }
+template<> inline double test_precision<double>() { return 1e-6; }
+template<> inline float test_precision<std::complex<float> >() { return test_precision<float>(); }
+template<> inline double test_precision<std::complex<double> >() { return test_precision<double>(); }
+template<> inline long double test_precision<long double>() { return 1e-6; }
+
+inline bool test_isApprox(const int& a, const int& b)
+{ return internal::isApprox(a, b, test_precision<int>()); }
+inline bool test_isMuchSmallerThan(const int& a, const int& b)
+{ return internal::isMuchSmallerThan(a, b, test_precision<int>()); }
+inline bool test_isApproxOrLessThan(const int& a, const int& b)
+{ return internal::isApproxOrLessThan(a, b, test_precision<int>()); }
+
+inline bool test_isApprox(const float& a, const float& b)
+{ return internal::isApprox(a, b, test_precision<float>()); }
+inline bool test_isMuchSmallerThan(const float& a, const float& b)
+{ return internal::isMuchSmallerThan(a, b, test_precision<float>()); }
+inline bool test_isApproxOrLessThan(const float& a, const float& b)
+{ return internal::isApproxOrLessThan(a, b, test_precision<float>()); }
+
+inline bool test_isApprox(const double& a, const double& b)
+{ return internal::isApprox(a, b, test_precision<double>()); }
+inline bool test_isMuchSmallerThan(const double& a, const double& b)
+{ return internal::isMuchSmallerThan(a, b, test_precision<double>()); }
+inline bool test_isApproxOrLessThan(const double& a, const double& b)
+{ return internal::isApproxOrLessThan(a, b, test_precision<double>()); }
+
+inline bool test_isApprox(const std::complex<float>& a, const std::complex<float>& b)
+{ return internal::isApprox(a, b, test_precision<std::complex<float> >()); }
+inline bool test_isMuchSmallerThan(const std::complex<float>& a, const std::complex<float>& b)
+{ return internal::isMuchSmallerThan(a, b, test_precision<std::complex<float> >()); }
+
+inline bool test_isApprox(const std::complex<double>& a, const std::complex<double>& b)
+{ return internal::isApprox(a, b, test_precision<std::complex<double> >()); }
+inline bool test_isMuchSmallerThan(const std::complex<double>& a, const std::complex<double>& b)
+{ return internal::isMuchSmallerThan(a, b, test_precision<std::complex<double> >()); }
+
+inline bool test_isApprox(const long double& a, const long double& b)
+{ return internal::isApprox(a, b, test_precision<long double>()); }
+inline bool test_isMuchSmallerThan(const long double& a, const long double& b)
+{ return internal::isMuchSmallerThan(a, b, test_precision<long double>()); }
+inline bool test_isApproxOrLessThan(const long double& a, const long double& b)
+{ return internal::isApproxOrLessThan(a, b, test_precision<long double>()); }
+
+template<typename Type1, typename Type2>
+inline bool test_isApprox(const Type1& a, const Type2& b)
+{
+  return a.isApprox(b, test_precision<typename Type1::Scalar>());
+}
+
+template<typename Derived1, typename Derived2>
+inline bool test_isMuchSmallerThan(const MatrixBase<Derived1>& m1,
+                                   const MatrixBase<Derived2>& m2)
+{
+  return m1.isMuchSmallerThan(m2, test_precision<typename internal::traits<Derived1>::Scalar>());
+}
+
+template<typename Derived>
+inline bool test_isMuchSmallerThan(const MatrixBase<Derived>& m,
+                                   const typename NumTraits<typename internal::traits<Derived>::Scalar>::Real& s)
+{
+  return m.isMuchSmallerThan(s, test_precision<typename internal::traits<Derived>::Scalar>());
+}
+
+} // end namespace Eigen
+
+template<typename T> struct GetDifferentType;
+
+template<> struct GetDifferentType<float> { typedef double type; };
+template<> struct GetDifferentType<double> { typedef float type; };
+template<typename T> struct GetDifferentType<std::complex<T> >
+{ typedef std::complex<typename GetDifferentType<T>::type> type; };
+
+// forward declaration of the main test function
+void EI_PP_CAT(test_,EIGEN_TEST_FUNC)();
+
+using namespace Eigen;
+
+int main(int argc, char *argv[])
+{
+    bool has_set_repeat = false;
+    bool has_set_seed = false;
+    bool need_help = false;
+    unsigned int seed = 0;
+    int repeat = DEFAULT_REPEAT;
+
+    for(int i = 1; i < argc; i++)
+    {
+      if(argv[i][0] == 'r')
+      {
+        if(has_set_repeat)
+        {
+          std::cout << "Argument " << argv[i] << " conflicting with a former argument" << std::endl;
+          return 1;
+        }
+        repeat = std::atoi(argv[i]+1);
+        has_set_repeat = true;
+        if(repeat <= 0)
+        {
+          std::cout << "Invalid \'repeat\' value " << argv[i]+1 << std::endl;
+          return 1;
+        }
+      }
+      else if(argv[i][0] == 's')
+      {
+        if(has_set_seed)
+        {
+          std::cout << "Argument " << argv[i] << " conflicting with a former argument" << std::endl;
+          return 1;
+        }
+        seed = int(std::strtoul(argv[i]+1, 0, 10));
+        has_set_seed = true;
+        bool ok = seed!=0;
+        if(!ok)
+        {
+          std::cout << "Invalid \'seed\' value " << argv[i]+1 << std::endl;
+          return 1;
+        }
+      }
+      else
+      {
+        need_help = true;
+      }
+    }
+
+    if(need_help)
+    {
+      std::cout << "This test application takes the following optional arguments:" << std::endl;
+      std::cout << "  rN     Repeat each test N times (default: " << DEFAULT_REPEAT << ")" << std::endl;
+      std::cout << "  sN     Use N as seed for random numbers (default: based on current time)" << std::endl;
+      return 1;
+    }
+
+    if(!has_set_seed) seed = (unsigned int) std::time(NULL);
+    if(!has_set_repeat) repeat = DEFAULT_REPEAT;
+
+    std::cout << "Initializing random number generator with seed " << seed << std::endl;
+	std::srand(seed);
+    std::cout << "Repeating each test " << repeat << " times" << std::endl;
+
+    Eigen::g_repeat = repeat;
+    Eigen::g_test_stack.push_back(EI_PP_MAKE_STRING(EIGEN_TEST_FUNC));
+
+    EI_PP_CAT(test_,EIGEN_TEST_FUNC)();
+    return 0;
+}
+
+
+

test/eigen2/map.cpp

@@ -0,0 +1,129 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2007-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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"
+
+template<typename VectorType> void map_class_vector(const VectorType& m)
+{
+  typedef typename VectorType::Scalar Scalar;
+
+  int size = m.size();
+
+  // test Map.h
+  Scalar* array1 = ei_aligned_new<Scalar>(size);
+  Scalar* array2 = ei_aligned_new<Scalar>(size);
+  Scalar* array3 = new Scalar[size+1];
+  Scalar* array3unaligned = std::size_t(array3)%16 == 0 ? array3+1 : array3;
+  
+  Map<VectorType, Aligned>(array1, size) = VectorType::Random(size);
+  Map<VectorType>(array2, size) = Map<VectorType>(array1, size);
+  Map<VectorType>(array3unaligned, size) = Map<VectorType>(array1, size);
+  VectorType ma1 = Map<VectorType>(array1, size);
+  VectorType ma2 = Map<VectorType, Aligned>(array2, size);
+  VectorType ma3 = Map<VectorType>(array3unaligned, size);
+  VERIFY_IS_APPROX(ma1, ma2);
+  VERIFY_IS_APPROX(ma1, ma3);
+  
+  ei_aligned_delete(array1, size);
+  ei_aligned_delete(array2, size);
+  delete[] array3;
+}
+
+template<typename MatrixType> void map_class_matrix(const MatrixType& m)
+{
+  typedef typename MatrixType::Scalar Scalar;
+
+  int rows = m.rows(), cols = m.cols(), size = rows*cols;
+
+  // test Map.h
+  Scalar* array1 = ei_aligned_new<Scalar>(size);
+  for(int i = 0; i < size; i++) array1[i] = Scalar(1);
+  Scalar* array2 = ei_aligned_new<Scalar>(size);
+  for(int i = 0; i < size; i++) array2[i] = Scalar(1);
+  Scalar* array3 = new Scalar[size+1];
+  for(int i = 0; i < size+1; i++) array3[i] = Scalar(1);
+  Scalar* array3unaligned = std::size_t(array3)%16 == 0 ? array3+1 : array3;
+  Map<MatrixType, Aligned>(array1, rows, cols) = MatrixType::Ones(rows,cols);
+  Map<MatrixType>(array2, rows, cols) = Map<MatrixType>(array1, rows, cols);
+  Map<MatrixType>(array3unaligned, rows, cols) = Map<MatrixType>(array1, rows, cols);
+  MatrixType ma1 = Map<MatrixType>(array1, rows, cols);
+  MatrixType ma2 = Map<MatrixType, Aligned>(array2, rows, cols);
+  VERIFY_IS_APPROX(ma1, ma2);
+  MatrixType ma3 = Map<MatrixType>(array3unaligned, rows, cols);
+  VERIFY_IS_APPROX(ma1, ma3);
+  
+  ei_aligned_delete(array1, size);
+  ei_aligned_delete(array2, size);
+  delete[] array3;
+}
+
+template<typename VectorType> void map_static_methods(const VectorType& m)
+{
+  typedef typename VectorType::Scalar Scalar;
+
+  int size = m.size();
+
+  // test Map.h
+  Scalar* array1 = ei_aligned_new<Scalar>(size);
+  Scalar* array2 = ei_aligned_new<Scalar>(size);
+  Scalar* array3 = new Scalar[size+1];
+  Scalar* array3unaligned = std::size_t(array3)%16 == 0 ? array3+1 : array3;
+  
+  VectorType::MapAligned(array1, size) = VectorType::Random(size);
+  VectorType::Map(array2, size) = VectorType::Map(array1, size);
+  VectorType::Map(array3unaligned, size) = VectorType::Map(array1, size);
+  VectorType ma1 = VectorType::Map(array1, size);
+  VectorType ma2 = VectorType::MapAligned(array2, size);
+  VectorType ma3 = VectorType::Map(array3unaligned, size);
+  VERIFY_IS_APPROX(ma1, ma2);
+  VERIFY_IS_APPROX(ma1, ma3);
+  
+  ei_aligned_delete(array1, size);
+  ei_aligned_delete(array2, size);
+  delete[] array3;
+}
+
+
+void test_map()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( map_class_vector(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST( map_class_vector(Vector4d()) );
+    CALL_SUBTEST( map_class_vector(RowVector4f()) );
+    CALL_SUBTEST( map_class_vector(VectorXcf(8)) );
+    CALL_SUBTEST( map_class_vector(VectorXi(12)) );
+
+    CALL_SUBTEST( map_class_matrix(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST( map_class_matrix(Matrix4d()) );
+    CALL_SUBTEST( map_class_matrix(Matrix<float,3,5>()) );
+    CALL_SUBTEST( map_class_matrix(MatrixXcf(ei_random<int>(1,10),ei_random<int>(1,10))) );
+    CALL_SUBTEST( map_class_matrix(MatrixXi(ei_random<int>(1,10),ei_random<int>(1,10))) );
+
+    CALL_SUBTEST( map_static_methods(Matrix<double, 1, 1>()) );
+    CALL_SUBTEST( map_static_methods(Vector3f()) );
+    CALL_SUBTEST( map_static_methods(RowVector3d()) );
+    CALL_SUBTEST( map_static_methods(VectorXcd(8)) );
+    CALL_SUBTEST( map_static_methods(VectorXf(12)) );
+  }
+}

test/eigen2/meta.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) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// 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"
+
+void test_meta()
+{
+  typedef float & FloatRef;
+  typedef const float & ConstFloatRef;
+  
+  VERIFY((ei_meta_if<(3<4),ei_meta_true, ei_meta_false>::ret::ret));
+  VERIFY(( ei_is_same_type<float,float>::ret));
+  VERIFY((!ei_is_same_type<float,double>::ret));
+  VERIFY((!ei_is_same_type<float,float&>::ret));
+  VERIFY((!ei_is_same_type<float,const float&>::ret));
+  
+  VERIFY(( ei_is_same_type<float,ei_cleantype<const float&>::type >::ret));
+  VERIFY(( ei_is_same_type<float,ei_cleantype<const float*>::type >::ret));
+  VERIFY(( ei_is_same_type<float,ei_cleantype<const float*&>::type >::ret));
+  VERIFY(( ei_is_same_type<float,ei_cleantype<float**>::type >::ret));
+  VERIFY(( ei_is_same_type<float,ei_cleantype<float**&>::type >::ret));
+  VERIFY(( ei_is_same_type<float,ei_cleantype<float* const *&>::type >::ret));
+  VERIFY(( ei_is_same_type<float,ei_cleantype<float* const>::type >::ret));
+
+  VERIFY(( ei_is_same_type<float*,ei_unconst<const float*>::type >::ret));
+  VERIFY(( ei_is_same_type<float&,ei_unconst<const float&>::type >::ret));
+  VERIFY(( ei_is_same_type<float&,ei_unconst<ConstFloatRef>::type >::ret));
+  
+  VERIFY(( ei_is_same_type<float&,ei_unconst<float&>::type >::ret));
+  VERIFY(( ei_is_same_type<float,ei_unref<float&>::type >::ret));
+  VERIFY(( ei_is_same_type<const float,ei_unref<const float&>::type >::ret));
+  VERIFY(( ei_is_same_type<float,ei_unpointer<float*>::type >::ret));
+  VERIFY(( ei_is_same_type<const float,ei_unpointer<const float*>::type >::ret));
+  VERIFY(( ei_is_same_type<float,ei_unpointer<float* const >::type >::ret));
+  
+  VERIFY(ei_meta_sqrt<1>::ret == 1);
+  #define VERIFY_META_SQRT(X) VERIFY(ei_meta_sqrt<X>::ret == int(ei_sqrt(double(X))))
+  VERIFY_META_SQRT(2);
+  VERIFY_META_SQRT(3);
+  VERIFY_META_SQRT(4);
+  VERIFY_META_SQRT(5);
+  VERIFY_META_SQRT(6);
+  VERIFY_META_SQRT(8);
+  VERIFY_META_SQRT(9);
+  VERIFY_META_SQRT(15);
+  VERIFY_META_SQRT(16);
+  VERIFY_META_SQRT(17);
+  VERIFY_META_SQRT(255);
+  VERIFY_META_SQRT(256);
+  VERIFY_META_SQRT(257);
+  VERIFY_META_SQRT(1023);
+  VERIFY_META_SQRT(1024);
+  VERIFY_META_SQRT(1025);
+}

test/eigen2/miscmatrices.cpp

@@ -0,0 +1,63 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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"
+
+template<typename MatrixType> void miscMatrices(const MatrixType& m)
+{
+  /* this test covers the following files:
+     DiagonalMatrix.h Ones.h
+  */
+
+  typedef typename MatrixType::Scalar Scalar;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+  typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType;
+  int rows = m.rows();
+  int cols = m.cols();
+
+  int r = ei_random<int>(0, rows-1), r2 = ei_random<int>(0, rows-1), c = ei_random<int>(0, cols-1);
+  VERIFY_IS_APPROX(MatrixType::Ones(rows,cols)(r,c), static_cast<Scalar>(1));
+  MatrixType m1 = MatrixType::Ones(rows,cols);
+  VERIFY_IS_APPROX(m1(r,c), static_cast<Scalar>(1));
+  VectorType v1 = VectorType::Random(rows);
+  v1[0];
+  Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+  square = v1.asDiagonal();
+  if(r==r2) VERIFY_IS_APPROX(square(r,r2), v1[r]);
+  else VERIFY_IS_MUCH_SMALLER_THAN(square(r,r2), static_cast<Scalar>(1));
+  square = MatrixType::Zero(rows, rows);
+  square.diagonal() = VectorType::Ones(rows);
+  VERIFY_IS_APPROX(square, MatrixType::Identity(rows, rows));
+}
+
+void test_miscmatrices()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( miscMatrices(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST( miscMatrices(Matrix4d()) );
+    CALL_SUBTEST( miscMatrices(MatrixXcf(3, 3)) );
+    CALL_SUBTEST( miscMatrices(MatrixXi(8, 12)) );
+    CALL_SUBTEST( miscMatrices(MatrixXcd(20, 20)) );
+  }
+}

test/eigen2/mixingtypes.cpp

@@ -0,0 +1,88 @@
+// 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>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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/>.
+
+#ifndef EIGEN_NO_STATIC_ASSERT
+#define EIGEN_NO_STATIC_ASSERT // turn static asserts into runtime asserts in order to check them
+#endif
+
+#ifndef EIGEN_DONT_VECTORIZE
+#define EIGEN_DONT_VECTORIZE // SSE intrinsics aren't designed to allow mixing types
+#endif
+
+#include "main.h"
+
+
+template<int SizeAtCompileType> void mixingtypes(int size = SizeAtCompileType)
+{
+  typedef Matrix<float, SizeAtCompileType, SizeAtCompileType> Mat_f;
+  typedef Matrix<double, SizeAtCompileType, SizeAtCompileType> Mat_d;
+  typedef Matrix<std::complex<float>, SizeAtCompileType, SizeAtCompileType> Mat_cf;
+  typedef Matrix<std::complex<double>, SizeAtCompileType, SizeAtCompileType> Mat_cd;
+  typedef Matrix<float, SizeAtCompileType, 1> Vec_f;
+  typedef Matrix<double, SizeAtCompileType, 1> Vec_d;
+  typedef Matrix<std::complex<float>, SizeAtCompileType, 1> Vec_cf;
+  typedef Matrix<std::complex<double>, SizeAtCompileType, 1> Vec_cd;
+
+  Mat_f mf(size,size);
+  Mat_d md(size,size);
+  Mat_cf mcf(size,size);
+  Mat_cd mcd(size,size);
+  Vec_f vf(size,1);
+  Vec_d vd(size,1);
+  Vec_cf vcf(size,1);
+  Vec_cd vcd(size,1);
+
+  mf+mf;
+  VERIFY_RAISES_ASSERT(mf+md);
+  VERIFY_RAISES_ASSERT(mf+mcf);
+  VERIFY_RAISES_ASSERT(vf=vd);
+  VERIFY_RAISES_ASSERT(vf+=vd);
+  VERIFY_RAISES_ASSERT(mcd=md);
+
+  mf*mf;
+  md*mcd;
+  mcd*md;
+  mf*vcf;
+  mcf*vf;
+  mcf *= mf;
+  vcd = md*vcd;
+  vcf = mcf*vf;
+  VERIFY_RAISES_ASSERT(mf*md);
+  VERIFY_RAISES_ASSERT(mcf*mcd);
+  VERIFY_RAISES_ASSERT(mcf*vcd);
+  VERIFY_RAISES_ASSERT(vcf = mf*vf);
+
+  vf.dot(vf);
+  VERIFY_RAISES_ASSERT(vd.dot(vf));
+  VERIFY_RAISES_ASSERT(vcf.dot(vf)); // yeah eventually we should allow this but i'm too lazy to make that change now in Dot.h
+}                                    // especially as that might be rewritten as cwise product .sum() which would make that automatic.
+
+void test_mixingtypes()
+{
+  // check that our operator new is indeed called:
+  CALL_SUBTEST(mixingtypes<3>());
+  CALL_SUBTEST(mixingtypes<4>());
+  CALL_SUBTEST(mixingtypes<Dynamic>(20));
+}

test/eigen2/newstdvector.cpp

@@ -0,0 +1,164 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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/>.
+
+#define EIGEN_USE_NEW_STDVECTOR
+#include "main.h"
+#include <Eigen/StdVector>
+#include <Eigen/Geometry>
+
+template<typename MatrixType>
+void check_stdvector_matrix(const MatrixType& m)
+{
+  int rows = m.rows();
+  int cols = m.cols();
+  MatrixType x = MatrixType::Random(rows,cols), y = MatrixType::Random(rows,cols);
+  std::vector<MatrixType,Eigen::aligned_allocator<MatrixType> > v(10, MatrixType(rows,cols)), w(20, y);
+  v[5] = x;
+  w[6] = v[5];
+  VERIFY_IS_APPROX(w[6], v[5]);
+  v = w;
+  for(int i = 0; i < 20; i++)
+  {
+    VERIFY_IS_APPROX(w[i], v[i]);
+  }
+
+  v.resize(21);
+  v[20] = x;
+  VERIFY_IS_APPROX(v[20], x);
+  v.resize(22,y);
+  VERIFY_IS_APPROX(v[21], y);
+  v.push_back(x);
+  VERIFY_IS_APPROX(v[22], x);
+  VERIFY((std::size_t)&(v[22]) == (std::size_t)&(v[21]) + sizeof(MatrixType));
+
+  // do a lot of push_back such that the vector gets internally resized
+  // (with memory reallocation)
+  MatrixType* ref = &w[0];
+  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+    v.push_back(w[i%w.size()]);
+  for(unsigned int i=23; i<v.size(); ++i)
+  {
+    VERIFY(v[i]==w[(i-23)%w.size()]);
+  }
+}
+
+template<typename TransformType>
+void check_stdvector_transform(const TransformType&)
+{
+  typedef typename TransformType::MatrixType MatrixType;
+  TransformType x(MatrixType::Random()), y(MatrixType::Random());
+  std::vector<TransformType,Eigen::aligned_allocator<TransformType> > v(10), w(20, y);
+  v[5] = x;
+  w[6] = v[5];
+  VERIFY_IS_APPROX(w[6], v[5]);
+  v = w;
+  for(int i = 0; i < 20; i++)
+  {
+    VERIFY_IS_APPROX(w[i], v[i]);
+  }
+
+  v.resize(21);
+  v[20] = x;
+  VERIFY_IS_APPROX(v[20], x);
+  v.resize(22,y);
+  VERIFY_IS_APPROX(v[21], y);
+  v.push_back(x);
+  VERIFY_IS_APPROX(v[22], x);
+  VERIFY((std::size_t)&(v[22]) == (std::size_t)&(v[21]) + sizeof(TransformType));
+
+  // do a lot of push_back such that the vector gets internally resized
+  // (with memory reallocation)
+  TransformType* ref = &w[0];
+  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+    v.push_back(w[i%w.size()]);
+  for(unsigned int i=23; i<v.size(); ++i)
+  {
+    VERIFY(v[i].matrix()==w[(i-23)%w.size()].matrix());
+  }
+}
+
+template<typename QuaternionType>
+void check_stdvector_quaternion(const QuaternionType&)
+{
+  typedef typename QuaternionType::Coefficients Coefficients;
+  QuaternionType x(Coefficients::Random()), y(Coefficients::Random());
+  std::vector<QuaternionType,Eigen::aligned_allocator<QuaternionType> > v(10), w(20, y);
+  v[5] = x;
+  w[6] = v[5];
+  VERIFY_IS_APPROX(w[6], v[5]);
+  v = w;
+  for(int i = 0; i < 20; i++)
+  {
+    VERIFY_IS_APPROX(w[i], v[i]);
+  }
+
+  v.resize(21);
+  v[20] = x;
+  VERIFY_IS_APPROX(v[20], x);
+  v.resize(22,y);
+  VERIFY_IS_APPROX(v[21], y);
+  v.push_back(x);
+  VERIFY_IS_APPROX(v[22], x);
+  VERIFY((std::size_t)&(v[22]) == (std::size_t)&(v[21]) + sizeof(QuaternionType));
+
+  // do a lot of push_back such that the vector gets internally resized
+  // (with memory reallocation)
+  QuaternionType* ref = &w[0];
+  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+    v.push_back(w[i%w.size()]);
+  for(unsigned int i=23; i<v.size(); ++i)
+  {
+    VERIFY(v[i].coeffs()==w[(i-23)%w.size()].coeffs());
+  }
+}
+
+void test_newstdvector()
+{
+  // some non vectorizable fixed sizes
+  CALL_SUBTEST(check_stdvector_matrix(Vector2f()));
+  CALL_SUBTEST(check_stdvector_matrix(Matrix3f()));
+  CALL_SUBTEST(check_stdvector_matrix(Matrix3d()));
+
+  // some vectorizable fixed sizes
+  CALL_SUBTEST(check_stdvector_matrix(Matrix2f()));
+  CALL_SUBTEST(check_stdvector_matrix(Vector4f()));
+  CALL_SUBTEST(check_stdvector_matrix(Matrix4f()));
+  CALL_SUBTEST(check_stdvector_matrix(Matrix4d()));
+
+  // some dynamic sizes
+  CALL_SUBTEST(check_stdvector_matrix(MatrixXd(1,1)));
+  CALL_SUBTEST(check_stdvector_matrix(VectorXd(20)));
+  CALL_SUBTEST(check_stdvector_matrix(RowVectorXf(20)));
+  CALL_SUBTEST(check_stdvector_matrix(MatrixXcf(10,10)));
+
+  // some Transform
+  CALL_SUBTEST(check_stdvector_transform(Transform2f()));
+  CALL_SUBTEST(check_stdvector_transform(Transform3f()));
+  CALL_SUBTEST(check_stdvector_transform(Transform3d()));
+  //CALL_SUBTEST(check_stdvector_transform(Transform4d()));
+
+  // some Quaternion
+  CALL_SUBTEST(check_stdvector_quaternion(Quaternionf()));
+  CALL_SUBTEST(check_stdvector_quaternion(Quaterniond()));
+}

test/eigen2/nomalloc.cpp

@@ -0,0 +1,78 @@
+// 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>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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/>.
+
+// this hack is needed to make this file compiles with -pedantic (gcc)
+#ifdef __GNUC__
+#define throw(X)
+#endif
+// discard stack allocation as that too bypasses malloc
+#define EIGEN_STACK_ALLOCATION_LIMIT 0
+// any heap allocation will raise an assert
+#define EIGEN_NO_MALLOC
+
+#include "main.h"
+
+template<typename MatrixType> void nomalloc(const MatrixType& m)
+{
+  /* this test check no dynamic memory allocation are issued with fixed-size matrices
+  */
+
+  typedef typename MatrixType::Scalar Scalar;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+
+  int rows = m.rows();
+  int cols = m.cols();
+
+  MatrixType m1 = MatrixType::Random(rows, cols),
+             m2 = MatrixType::Random(rows, cols),
+             m3(rows, cols),
+             mzero = MatrixType::Zero(rows, cols),
+             identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+                              ::Identity(rows, rows),
+             square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+                              ::Random(rows, rows);
+  VectorType v1 = VectorType::Random(rows),
+             v2 = VectorType::Random(rows),
+             vzero = VectorType::Zero(rows);
+
+  Scalar s1 = ei_random<Scalar>();
+
+  int r = ei_random<int>(0, rows-1),
+      c = ei_random<int>(0, cols-1);
+
+  VERIFY_IS_APPROX((m1+m2)*s1,              s1*m1+s1*m2);
+  VERIFY_IS_APPROX((m1+m2)(r,c), (m1(r,c))+(m2(r,c)));
+  VERIFY_IS_APPROX(m1.cwise() * m1.block(0,0,rows,cols), m1.cwise() * m1);
+  VERIFY_IS_APPROX((m1*m1.transpose())*m2,  m1*(m1.transpose()*m2));
+}
+
+void test_nomalloc()
+{
+  // check that our operator new is indeed called:
+  VERIFY_RAISES_ASSERT(MatrixXd dummy = MatrixXd::Random(3,3));
+  CALL_SUBTEST( nomalloc(Matrix<float, 1, 1>()) );
+  CALL_SUBTEST( nomalloc(Matrix4d()) );
+  CALL_SUBTEST( nomalloc(Matrix<float,32,32>()) );
+}

test/eigen2/packetmath.cpp

@@ -0,0 +1,147 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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"
+
+// using namespace Eigen;
+
+template<typename Scalar> bool areApprox(const Scalar* a, const Scalar* b, int size)
+{
+  for (int i=0; i<size; ++i)
+    if (!ei_isApprox(a[i],b[i])) return false;
+  return true;
+}
+
+#define CHECK_CWISE(REFOP, POP) { \
+  for (int i=0; i<PacketSize; ++i) \
+    ref[i] = REFOP(data1[i], data1[i+PacketSize]); \
+  ei_pstore(data2, POP(ei_pload(data1), ei_pload(data1+PacketSize))); \
+  VERIFY(areApprox(ref, data2, PacketSize) && #POP); \
+}
+
+#define REF_ADD(a,b) ((a)+(b))
+#define REF_SUB(a,b) ((a)-(b))
+#define REF_MUL(a,b) ((a)*(b))
+#define REF_DIV(a,b) ((a)/(b))
+
+namespace std {
+
+template<> const complex<float>& min(const complex<float>& a, const complex<float>& b)
+{ return a.real() < b.real() ? a : b; }
+
+template<> const complex<float>& max(const complex<float>& a, const complex<float>& b)
+{ return a.real() < b.real() ? b : a; }
+
+}
+
+template<typename Scalar> void packetmath()
+{
+  typedef typename ei_packet_traits<Scalar>::type Packet;
+  const int PacketSize = ei_packet_traits<Scalar>::size;
+
+  const int size = PacketSize*4;
+  EIGEN_ALIGN_128 Scalar data1[ei_packet_traits<Scalar>::size*4];
+  EIGEN_ALIGN_128 Scalar data2[ei_packet_traits<Scalar>::size*4];
+  EIGEN_ALIGN_128 Packet packets[PacketSize*2];
+  EIGEN_ALIGN_128 Scalar ref[ei_packet_traits<Scalar>::size*4];
+  for (int i=0; i<size; ++i)
+  {
+    data1[i] = ei_random<Scalar>();
+    data2[i] = ei_random<Scalar>();
+  }
+
+  ei_pstore(data2, ei_pload(data1));
+  VERIFY(areApprox(data1, data2, PacketSize) && "aligned load/store");
+
+  for (int offset=0; offset<PacketSize; ++offset)
+  {
+    ei_pstore(data2, ei_ploadu(data1+offset));
+    VERIFY(areApprox(data1+offset, data2, PacketSize) && "ei_ploadu");
+  }
+
+  for (int offset=0; offset<PacketSize; ++offset)
+  {
+    ei_pstoreu(data2+offset, ei_pload(data1));
+    VERIFY(areApprox(data1, data2+offset, PacketSize) && "ei_pstoreu");
+  }
+
+  for (int offset=0; offset<PacketSize; ++offset)
+  {
+    packets[0] = ei_pload(data1);
+    packets[1] = ei_pload(data1+PacketSize);
+         if (offset==0) ei_palign<0>(packets[0], packets[1]);
+    else if (offset==1) ei_palign<1>(packets[0], packets[1]);
+    else if (offset==2) ei_palign<2>(packets[0], packets[1]);
+    else if (offset==3) ei_palign<3>(packets[0], packets[1]);
+    ei_pstore(data2, packets[0]);
+
+    for (int i=0; i<PacketSize; ++i)
+      ref[i] = data1[i+offset];
+
+    typedef Matrix<Scalar, PacketSize, 1> Vector;
+    VERIFY(areApprox(ref, data2, PacketSize) && "ei_palign");
+  }
+
+  CHECK_CWISE(REF_ADD,  ei_padd);
+  CHECK_CWISE(REF_SUB,  ei_psub);
+  CHECK_CWISE(REF_MUL,  ei_pmul);
+  #ifndef EIGEN_VECTORIZE_ALTIVEC
+  if (!ei_is_same_type<Scalar,int>::ret)
+    CHECK_CWISE(REF_DIV,  ei_pdiv);
+  #endif
+  CHECK_CWISE(std::min, ei_pmin);
+  CHECK_CWISE(std::max, ei_pmax);
+
+  for (int i=0; i<PacketSize; ++i)
+    ref[i] = data1[0];
+  ei_pstore(data2, ei_pset1(data1[0]));
+  VERIFY(areApprox(ref, data2, PacketSize) && "ei_pset1");
+
+  VERIFY(ei_isApprox(data1[0], ei_pfirst(ei_pload(data1))) && "ei_pfirst");
+
+  ref[0] = 0;
+  for (int i=0; i<PacketSize; ++i)
+    ref[0] += data1[i];
+  VERIFY(ei_isApprox(ref[0], ei_predux(ei_pload(data1))) && "ei_predux");
+
+  for (int j=0; j<PacketSize; ++j)
+  {
+    ref[j] = 0;
+    for (int i=0; i<PacketSize; ++i)
+      ref[j] += data1[i+j*PacketSize];
+    packets[j] = ei_pload(data1+j*PacketSize);
+  }
+  ei_pstore(data2, ei_preduxp(packets));
+  VERIFY(areApprox(ref, data2, PacketSize) && "ei_preduxp");
+}
+
+void test_packetmath()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( packetmath<float>() );
+    CALL_SUBTEST( packetmath<double>() );
+    CALL_SUBTEST( packetmath<int>() );
+    CALL_SUBTEST( packetmath<std::complex<float> >() );
+  }
+}

test/eigen2/parametrizedline.cpp

@@ -0,0 +1,77 @@
+// 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>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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/Geometry>
+#include <Eigen/LU>
+#include <Eigen/QR>
+
+template<typename LineType> void parametrizedline(const LineType& _line)
+{
+  /* this test covers the following files:
+     ParametrizedLine.h
+  */
+
+  const int dim = _line.dim();
+  typedef typename LineType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar, LineType::AmbientDimAtCompileTime, 1> VectorType;
+  typedef Matrix<Scalar, LineType::AmbientDimAtCompileTime,
+                         LineType::AmbientDimAtCompileTime> MatrixType;
+
+  VectorType p0 = VectorType::Random(dim);
+  VectorType p1 = VectorType::Random(dim);
+
+  VectorType d0 = VectorType::Random(dim).normalized();
+
+  LineType l0(p0, d0);
+
+  Scalar s0 = ei_random<Scalar>();
+  Scalar s1 = ei_abs(ei_random<Scalar>());
+
+  VERIFY_IS_MUCH_SMALLER_THAN( l0.distance(p0), RealScalar(1) );
+  VERIFY_IS_MUCH_SMALLER_THAN( l0.distance(p0+s0*d0), RealScalar(1) );
+  VERIFY_IS_APPROX( (l0.projection(p1)-p1).norm(), l0.distance(p1) );
+  VERIFY_IS_MUCH_SMALLER_THAN( l0.distance(l0.projection(p1)), RealScalar(1) );
+  VERIFY_IS_APPROX( Scalar(l0.distance((p0+s0*d0) + d0.unitOrthogonal() * s1)), s1 );
+
+  // casting
+  const int Dim = LineType::AmbientDimAtCompileTime;
+  typedef typename GetDifferentType<Scalar>::type OtherScalar;
+  ParametrizedLine<OtherScalar,Dim> hp1f = l0.template cast<OtherScalar>();
+  VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),l0);
+  ParametrizedLine<Scalar,Dim> hp1d = l0.template cast<Scalar>();
+  VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),l0);
+}
+
+void test_parametrizedline()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( parametrizedline(ParametrizedLine<float,2>()) );
+    CALL_SUBTEST( parametrizedline(ParametrizedLine<float,3>()) );
+    CALL_SUBTEST( parametrizedline(ParametrizedLine<double,4>()) );
+    CALL_SUBTEST( parametrizedline(ParametrizedLine<std::complex<double>,5>()) );
+  }
+}

test/eigen2/prec_inverse_4x4.cpp

@@ -0,0 +1,99 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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/LU>
+#include <algorithm>
+
+template<typename T> std::string type_name() { return "other"; }
+template<> std::string type_name<float>() { return "float"; }
+template<> std::string type_name<double>() { return "double"; }
+template<> std::string type_name<int>() { return "int"; }
+template<> std::string type_name<std::complex<float> >() { return "complex<float>"; }
+template<> std::string type_name<std::complex<double> >() { return "complex<double>"; }
+template<> std::string type_name<std::complex<int> >() { return "complex<int>"; }
+
+#define EIGEN_DEBUG_VAR(x) std::cerr << #x << " = " << x << std::endl;
+
+template<typename T> inline typename NumTraits<T>::Real epsilon()
+{
+ return std::numeric_limits<typename NumTraits<T>::Real>::epsilon();
+}
+
+template<typename MatrixType> void inverse_permutation_4x4()
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename MatrixType::RealScalar RealScalar;
+  Vector4i indices(0,1,2,3);
+  for(int i = 0; i < 24; ++i)
+  {
+    MatrixType m = MatrixType::Zero();
+    m(indices(0),0) = 1;
+    m(indices(1),1) = 1;
+    m(indices(2),2) = 1;
+    m(indices(3),3) = 1;
+    MatrixType inv = m.inverse();
+    double error = double( (m*inv-MatrixType::Identity()).norm() / epsilon<Scalar>() );
+    VERIFY(error == 0.0);
+    std::next_permutation(indices.data(),indices.data()+4);
+  }
+}
+
+template<typename MatrixType> void inverse_general_4x4(int repeat)
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename MatrixType::RealScalar RealScalar;
+  double error_sum = 0., error_max = 0.;
+  for(int i = 0; i < repeat; ++i)
+  {
+    MatrixType m;
+    RealScalar absdet;
+    do {
+      m = MatrixType::Random();
+      absdet = internal::abs(m.determinant());
+    } while(absdet < 10 * epsilon<Scalar>());
+    MatrixType inv = m.inverse();
+    double error = double( (m*inv-MatrixType::Identity()).norm() * absdet / epsilon<Scalar>() );
+    error_sum += error;
+    error_max = std::max(error_max, error);
+  }
+  std::cerr << "inverse_general_4x4, Scalar = " << type_name<Scalar>() << std::endl;
+  double error_avg = error_sum / repeat;
+  EIGEN_DEBUG_VAR(error_avg);
+  EIGEN_DEBUG_VAR(error_max);
+  VERIFY(error_avg < (NumTraits<Scalar>::IsComplex ? 8.0 : 1.25));
+  VERIFY(error_max < (NumTraits<Scalar>::IsComplex ? 64.0 : 20.0));
+}
+
+void test_prec_inverse_4x4()
+{
+  CALL_SUBTEST((inverse_permutation_4x4<Matrix4f>()));
+  CALL_SUBTEST(( inverse_general_4x4<Matrix4f>(200000 * g_repeat) ));
+
+  CALL_SUBTEST((inverse_permutation_4x4<Matrix<double,4,4,RowMajor> >()));
+  CALL_SUBTEST(( inverse_general_4x4<Matrix<double,4,4,RowMajor> >(200000 * g_repeat) ));
+
+  CALL_SUBTEST((inverse_permutation_4x4<Matrix4cf>()));
+  CALL_SUBTEST((inverse_general_4x4<Matrix4cf>(50000 * g_repeat)));
+}

test/eigen2/product.h

@@ -0,0 +1,147 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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/Array>
+#include <Eigen/QR>
+
+template<typename Derived1, typename Derived2>
+bool areNotApprox(const MatrixBase<Derived1>& m1, const MatrixBase<Derived2>& m2, typename Derived1::RealScalar epsilon = precision<typename Derived1::RealScalar>())
+{
+  return !((m1-m2).cwise().abs2().maxCoeff() < epsilon * epsilon
+                          * std::max(m1.cwise().abs2().maxCoeff(), m2.cwise().abs2().maxCoeff()));
+}
+
+template<typename MatrixType> void product(const MatrixType& m)
+{
+  /* this test covers the following files:
+     Identity.h Product.h
+  */
+
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::FloatingPoint FloatingPoint;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> RowVectorType;
+  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> ColVectorType;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> RowSquareMatrixType;
+  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> ColSquareMatrixType;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime,
+                         MatrixType::Options^RowMajor> OtherMajorMatrixType;
+
+  int rows = m.rows();
+  int cols = m.cols();
+
+  // this test relies a lot on Random.h, and there's not much more that we can do
+  // to test it, hence I consider that we will have tested Random.h
+  MatrixType m1 = MatrixType::Random(rows, cols),
+             m2 = MatrixType::Random(rows, cols),
+             m3(rows, cols),
+             mzero = MatrixType::Zero(rows, cols);
+  RowSquareMatrixType
+             identity = RowSquareMatrixType::Identity(rows, rows),
+             square = RowSquareMatrixType::Random(rows, rows),
+             res = RowSquareMatrixType::Random(rows, rows);
+  ColSquareMatrixType
+             square2 = ColSquareMatrixType::Random(cols, cols),
+             res2 = ColSquareMatrixType::Random(cols, cols);
+  RowVectorType v1 = RowVectorType::Random(rows),
+             v2 = RowVectorType::Random(rows),
+             vzero = RowVectorType::Zero(rows);
+  ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);
+  OtherMajorMatrixType tm1 = m1;
+
+  Scalar s1 = ei_random<Scalar>();
+
+  int r = ei_random<int>(0, rows-1),
+      c = ei_random<int>(0, cols-1);
+
+  // begin testing Product.h: only associativity for now
+  // (we use Transpose.h but this doesn't count as a test for it)
+
+  VERIFY_IS_APPROX((m1*m1.transpose())*m2,  m1*(m1.transpose()*m2));
+  m3 = m1;
+  m3 *= m1.transpose() * m2;
+  VERIFY_IS_APPROX(m3,                      m1 * (m1.transpose()*m2));
+  VERIFY_IS_APPROX(m3,                      m1.lazy() * (m1.transpose()*m2));
+
+  // continue testing Product.h: distributivity
+  VERIFY_IS_APPROX(square*(m1 + m2),        square*m1+square*m2);
+  VERIFY_IS_APPROX(square*(m1 - m2),        square*m1-square*m2);
+
+  // continue testing Product.h: compatibility with ScalarMultiple.h
+  VERIFY_IS_APPROX(s1*(square*m1),          (s1*square)*m1);
+  VERIFY_IS_APPROX(s1*(square*m1),          square*(m1*s1));
+
+  // again, test operator() to check const-qualification
+  s1 += (square.lazy() * m1)(r,c);
+
+  // test Product.h together with Identity.h
+  VERIFY_IS_APPROX(v1,                      identity*v1);
+  VERIFY_IS_APPROX(v1.transpose(),          v1.transpose() * identity);
+  // again, test operator() to check const-qualification
+  VERIFY_IS_APPROX(MatrixType::Identity(rows, cols)(r,c), static_cast<Scalar>(r==c));
+
+  if (rows!=cols)
+     VERIFY_RAISES_ASSERT(m3 = m1*m1);
+
+  // test the previous tests were not screwed up because operator* returns 0
+  // (we use the more accurate default epsilon)
+  if (NumTraits<Scalar>::HasFloatingPoint && std::min(rows,cols)>1)
+  {
+    VERIFY(areNotApprox(m1.transpose()*m2,m2.transpose()*m1));
+  }
+
+  // test optimized operator+= path
+  res = square;
+  res += (m1 * m2.transpose()).lazy();
+  VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
+  if (NumTraits<Scalar>::HasFloatingPoint && std::min(rows,cols)>1)
+  {
+    VERIFY(areNotApprox(res,square + m2 * m1.transpose()));
+  }
+  vcres = vc2;
+  vcres += (m1.transpose() * v1).lazy();
+  VERIFY_IS_APPROX(vcres, vc2 + m1.transpose() * v1);
+  tm1 = m1;
+  VERIFY_IS_APPROX(tm1.transpose() * v1, m1.transpose() * v1);
+  VERIFY_IS_APPROX(v1.transpose() * tm1, v1.transpose() * m1);
+
+  // test submatrix and matrix/vector product
+  for (int i=0; i<rows; ++i)
+    res.row(i) = m1.row(i) * m2.transpose();
+  VERIFY_IS_APPROX(res, m1 * m2.transpose());
+  // the other way round:
+  for (int i=0; i<rows; ++i)
+    res.col(i) = m1 * m2.transpose().col(i);
+  VERIFY_IS_APPROX(res, m1 * m2.transpose());
+
+  res2 = square2;
+  res2 += (m1.transpose() * m2).lazy();
+  VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2);
+
+  if (NumTraits<Scalar>::HasFloatingPoint && std::min(rows,cols)>1)
+  {
+    VERIFY(areNotApprox(res2,square2 + m2.transpose() * m1));
+  }
+}
+

test/eigen2/product_large.cpp

@@ -0,0 +1,58 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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 "product.h"
+
+void test_product_large()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( product(MatrixXf(ei_random<int>(1,320), ei_random<int>(1,320))) );
+    CALL_SUBTEST( product(MatrixXd(ei_random<int>(1,320), ei_random<int>(1,320))) );
+    CALL_SUBTEST( product(MatrixXi(ei_random<int>(1,320), ei_random<int>(1,320))) );
+    CALL_SUBTEST( product(MatrixXcf(ei_random<int>(1,50), ei_random<int>(1,50))) );
+    CALL_SUBTEST( product(Matrix<float,Dynamic,Dynamic,RowMajor>(ei_random<int>(1,320), ei_random<int>(1,320))) );
+  }
+
+  {
+    // test a specific issue in DiagonalProduct
+    int N = 1000000;
+    VectorXf v = VectorXf::Ones(N);
+    MatrixXf m = MatrixXf::Ones(N,3);
+    m = (v+v).asDiagonal() * m;
+    VERIFY_IS_APPROX(m, MatrixXf::Constant(N,3,2));
+  }
+
+  {
+    // test deferred resizing in Matrix::operator=
+    MatrixXf a = MatrixXf::Random(10,4), b = MatrixXf::Random(4,10), c = a;
+    VERIFY_IS_APPROX((a = a * b), (c * b).eval());
+  }
+
+  {
+    MatrixXf mat1(10,10); mat1.setRandom();
+    MatrixXf mat2(32,10); mat2.setRandom();
+    MatrixXf result = mat1.row(2)*mat2.transpose();
+    VERIFY_IS_APPROX(result, (mat1.row(2)*mat2.transpose()).eval());
+  }
+}

test/eigen2/product_small.cpp

@@ -0,0 +1,37 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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/>.
+
+#define EIGEN_NO_STATIC_ASSERT
+#include "product.h"
+
+void test_product_small()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( product(Matrix<float, 3, 2>()) );
+    CALL_SUBTEST( product(Matrix<int, 3, 5>()) );
+    CALL_SUBTEST( product(Matrix3d()) );
+    CALL_SUBTEST( product(Matrix4d()) );
+    CALL_SUBTEST( product(Matrix4f()) );
+  }
+}

test/eigen2/qr.cpp

@@ -0,0 +1,85 @@
+// 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>
+//
+// 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/QR>
+
+template<typename MatrixType> void qr(const MatrixType& m)
+{
+  /* this test covers the following files:
+     QR.h
+  */
+  int rows = m.rows();
+  int cols = m.cols();
+
+  typedef typename MatrixType::Scalar Scalar;
+  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> SquareMatrixType;
+  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
+
+  MatrixType a = MatrixType::Random(rows,cols);
+  QR<MatrixType> qrOfA(a);
+  VERIFY_IS_APPROX(a, qrOfA.matrixQ() * qrOfA.matrixR());
+  VERIFY_IS_NOT_APPROX(a+MatrixType::Identity(rows, cols), qrOfA.matrixQ() * qrOfA.matrixR());
+
+  SquareMatrixType b = a.adjoint() * a;
+
+  // check tridiagonalization
+  Tridiagonalization<SquareMatrixType> tridiag(b);
+  VERIFY_IS_APPROX(b, tridiag.matrixQ() * tridiag.matrixT() * tridiag.matrixQ().adjoint());
+
+  // check hessenberg decomposition
+  HessenbergDecomposition<SquareMatrixType> hess(b);
+  VERIFY_IS_APPROX(b, hess.matrixQ() * hess.matrixH() * hess.matrixQ().adjoint());
+  VERIFY_IS_APPROX(tridiag.matrixT(), hess.matrixH());
+  b = SquareMatrixType::Random(cols,cols);
+  hess.compute(b);
+  VERIFY_IS_APPROX(b, hess.matrixQ() * hess.matrixH() * hess.matrixQ().adjoint());
+}
+
+void test_qr()
+{
+  for(int i = 0; i < 1; i++) {
+    CALL_SUBTEST( qr(Matrix2f()) );
+    CALL_SUBTEST( qr(Matrix4d()) );
+    CALL_SUBTEST( qr(MatrixXf(12,8)) );
+    CALL_SUBTEST( qr(MatrixXcd(5,5)) );
+    CALL_SUBTEST( qr(MatrixXcd(7,3)) );
+  }
+
+  // small isFullRank test
+  {
+    Matrix3d mat;
+    mat << 1, 45, 1, 2, 2, 2, 1, 2, 3;
+    VERIFY(mat.qr().isFullRank());
+    mat << 1, 1, 1, 2, 2, 2, 1, 2, 3;
+    VERIFY(!mat.qr().isFullRank());
+  }
+  {
+    MatrixXf m = MatrixXf::Zero(10,10);
+    VectorXf b = VectorXf::Zero(10);
+    VectorXf x = VectorXf::Random(10);
+    VERIFY(m.qr().solve(b,&x));
+    VERIFY(x.isZero());
+  }
+}

test/eigen2/qtvector.cpp

@@ -0,0 +1,173 @@
+// 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>
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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/>.
+
+#define EIGEN_WORK_AROUND_QT_BUG_CALLING_WRONG_OPERATOR_NEW_FIXED_IN_QT_4_5
+
+#include "main.h"
+
+#include <Eigen/Geometry>
+#include <Eigen/QtAlignedMalloc>
+
+#include <QtCore/QVector>
+
+template<typename MatrixType>
+void check_qtvector_matrix(const MatrixType& m)
+{
+  int rows = m.rows();
+  int cols = m.cols();
+  MatrixType x = MatrixType::Random(rows,cols), y = MatrixType::Random(rows,cols);
+  QVector<MatrixType> v(10, MatrixType(rows,cols)), w(20, y);
+  for(int i = 0; i < 20; i++)
+  {
+    VERIFY_IS_APPROX(w[i], y);
+  }
+  v[5] = x;
+  w[6] = v[5];
+  VERIFY_IS_APPROX(w[6], v[5]);
+  v = w;
+  for(int i = 0; i < 20; i++)
+  {
+    VERIFY_IS_APPROX(w[i], v[i]);
+  }
+
+  v.resize(21);
+  v[20] = x;
+  VERIFY_IS_APPROX(v[20], x);
+  v.fill(y,22);
+  VERIFY_IS_APPROX(v[21], y);
+  v.push_back(x);
+  VERIFY_IS_APPROX(v[22], x);
+  VERIFY((size_t)&(v[22]) == (size_t)&(v[21]) + sizeof(MatrixType));
+
+  // do a lot of push_back such that the vector gets internally resized
+  // (with memory reallocation)
+  MatrixType* ref = &w[0];
+  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+    v.push_back(w[i%w.size()]);
+  for(int i=23; i<v.size(); ++i)
+  {
+    VERIFY(v[i]==w[(i-23)%w.size()]);
+  }
+}
+
+template<typename TransformType>
+void check_qtvector_transform(const TransformType&)
+{
+  typedef typename TransformType::MatrixType MatrixType;
+  TransformType x(MatrixType::Random()), y(MatrixType::Random());
+  QVector<TransformType> v(10), w(20, y);
+  v[5] = x;
+  w[6] = v[5];
+  VERIFY_IS_APPROX(w[6], v[5]);
+  v = w;
+  for(int i = 0; i < 20; i++)
+  {
+    VERIFY_IS_APPROX(w[i], v[i]);
+  }
+
+  v.resize(21);
+  v[20] = x;
+  VERIFY_IS_APPROX(v[20], x);
+  v.fill(y,22);
+  VERIFY_IS_APPROX(v[21], y);
+  v.push_back(x);
+  VERIFY_IS_APPROX(v[22], x);
+  VERIFY((size_t)&(v[22]) == (size_t)&(v[21]) + sizeof(TransformType));
+
+  // do a lot of push_back such that the vector gets internally resized
+  // (with memory reallocation)
+  TransformType* ref = &w[0];
+  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+    v.push_back(w[i%w.size()]);
+  for(unsigned int i=23; int(i)<v.size(); ++i)
+  {
+    VERIFY(v[i].matrix()==w[(i-23)%w.size()].matrix());
+  }
+}
+
+template<typename QuaternionType>
+void check_qtvector_quaternion(const QuaternionType&)
+{
+  typedef typename QuaternionType::Coefficients Coefficients;
+  QuaternionType x(Coefficients::Random()), y(Coefficients::Random());
+  QVector<QuaternionType> v(10), w(20, y);
+  v[5] = x;
+  w[6] = v[5];
+  VERIFY_IS_APPROX(w[6], v[5]);
+  v = w;
+  for(int i = 0; i < 20; i++)
+  {
+    VERIFY_IS_APPROX(w[i], v[i]);
+  }
+
+  v.resize(21);
+  v[20] = x;
+  VERIFY_IS_APPROX(v[20], x);
+  v.fill(y,22);
+  VERIFY_IS_APPROX(v[21], y);
+  v.push_back(x);
+  VERIFY_IS_APPROX(v[22], x);
+  VERIFY((size_t)&(v[22]) == (size_t)&(v[21]) + sizeof(QuaternionType));
+
+  // do a lot of push_back such that the vector gets internally resized
+  // (with memory reallocation)
+  QuaternionType* ref = &w[0];
+  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+    v.push_back(w[i%w.size()]);
+  for(unsigned int i=23; int(i)<v.size(); ++i)
+  {
+    VERIFY(v[i].coeffs()==w[(i-23)%w.size()].coeffs());
+  }
+}
+
+void test_qtvector()
+{
+  // some non vectorizable fixed sizes
+  CALL_SUBTEST(check_qtvector_matrix(Vector2f()));
+  CALL_SUBTEST(check_qtvector_matrix(Matrix3f()));
+  CALL_SUBTEST(check_qtvector_matrix(Matrix3d()));
+
+  // some vectorizable fixed sizes
+  CALL_SUBTEST(check_qtvector_matrix(Matrix2f()));
+  CALL_SUBTEST(check_qtvector_matrix(Vector4f()));
+  CALL_SUBTEST(check_qtvector_matrix(Matrix4f()));
+  CALL_SUBTEST(check_qtvector_matrix(Matrix4d()));
+
+  // some dynamic sizes
+  CALL_SUBTEST(check_qtvector_matrix(MatrixXd(1,1)));
+  CALL_SUBTEST(check_qtvector_matrix(VectorXd(20)));
+  CALL_SUBTEST(check_qtvector_matrix(RowVectorXf(20)));
+  CALL_SUBTEST(check_qtvector_matrix(MatrixXcf(10,10)));
+
+  // some Transform
+  CALL_SUBTEST(check_qtvector_transform(Transform2f()));
+  CALL_SUBTEST(check_qtvector_transform(Transform3f()));
+  CALL_SUBTEST(check_qtvector_transform(Transform3d()));
+  //CALL_SUBTEST(check_qtvector_transform(Transform4d()));
+
+  // some Quaternion
+  CALL_SUBTEST(check_qtvector_quaternion(Quaternionf()));
+  CALL_SUBTEST(check_qtvector_quaternion(Quaternionf()));
+}

test/eigen2/regression.cpp

@@ -0,0 +1,145 @@
+// 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 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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/LeastSquares>
+
+template<typename VectorType,
+         typename HyperplaneType>
+void makeNoisyCohyperplanarPoints(int numPoints,
+                                  VectorType **points,
+                                  HyperplaneType *hyperplane,
+                                  typename VectorType::Scalar noiseAmplitude)
+{
+  typedef typename VectorType::Scalar Scalar;
+  const int size = points[0]->size();
+  // pick a random hyperplane, store the coefficients of its equation
+  hyperplane->coeffs().resize(size + 1);
+  for(int j = 0; j < size + 1; j++)
+  {
+    do {
+      hyperplane->coeffs().coeffRef(j) = ei_random<Scalar>();
+    } while(ei_abs(hyperplane->coeffs().coeff(j)) < 0.5);
+  }
+
+  // now pick numPoints random points on this hyperplane
+  for(int i = 0; i < numPoints; i++)
+  {
+    VectorType& cur_point = *(points[i]);
+    do
+    {
+      cur_point = VectorType::Random(size)/*.normalized()*/;
+      // project cur_point onto the hyperplane
+      Scalar x = - (hyperplane->coeffs().start(size).cwise()*cur_point).sum();
+      cur_point *= hyperplane->coeffs().coeff(size) / x;
+    } while( cur_point.norm() < 0.5
+          || cur_point.norm() > 2.0 );
+  }
+
+  // add some noise to these points
+  for(int i = 0; i < numPoints; i++ )
+    *(points[i]) += noiseAmplitude * VectorType::Random(size);
+}
+
+template<typename VectorType>
+void check_linearRegression(int numPoints,
+                            VectorType **points,
+                            const VectorType& original,
+                            typename VectorType::Scalar tolerance)
+{
+  int size = points[0]->size();
+  assert(size==2);
+  VectorType result(size);
+  linearRegression(numPoints, points, &result, 1);
+  typename VectorType::Scalar error = (result - original).norm() / original.norm();
+  VERIFY(ei_abs(error) < ei_abs(tolerance));
+}
+
+template<typename VectorType,
+         typename HyperplaneType>
+void check_fitHyperplane(int numPoints,
+                         VectorType **points,
+                         const HyperplaneType& original,
+                         typename VectorType::Scalar tolerance)
+{
+  int size = points[0]->size();
+  HyperplaneType result(size);
+  fitHyperplane(numPoints, points, &result);
+  result.coeffs() *= original.coeffs().coeff(size)/result.coeffs().coeff(size);
+  typename VectorType::Scalar error = (result.coeffs() - original.coeffs()).norm() / original.coeffs().norm();
+  VERIFY(ei_abs(error) < ei_abs(tolerance));
+}
+
+void test_regression()
+{
+  for(int i = 0; i < g_repeat; i++)
+  {
+    {
+      Vector2f points2f [1000];
+      Vector2f *points2f_ptrs [1000];
+      for(int i = 0; i < 1000; i++) points2f_ptrs[i] = &(points2f[i]);
+      Vector2f coeffs2f;
+      Hyperplane<float,2> coeffs3f;
+      makeNoisyCohyperplanarPoints(1000, points2f_ptrs, &coeffs3f, 0.01f);
+      coeffs2f[0] = -coeffs3f.coeffs()[0]/coeffs3f.coeffs()[1];
+      coeffs2f[1] = -coeffs3f.coeffs()[2]/coeffs3f.coeffs()[1];
+      CALL_SUBTEST(check_linearRegression(10, points2f_ptrs, coeffs2f, 0.05f));
+      CALL_SUBTEST(check_linearRegression(100, points2f_ptrs, coeffs2f, 0.01f));
+      CALL_SUBTEST(check_linearRegression(1000, points2f_ptrs, coeffs2f, 0.002f));
+    }
+    
+    {
+      Vector2f points2f [1000];
+      Vector2f *points2f_ptrs [1000];
+      for(int i = 0; i < 1000; i++) points2f_ptrs[i] = &(points2f[i]);
+      Hyperplane<float,2> coeffs3f;
+      makeNoisyCohyperplanarPoints(1000, points2f_ptrs, &coeffs3f, 0.01f);
+      CALL_SUBTEST(check_fitHyperplane(10, points2f_ptrs, coeffs3f, 0.05f));
+      CALL_SUBTEST(check_fitHyperplane(100, points2f_ptrs, coeffs3f, 0.01f));
+      CALL_SUBTEST(check_fitHyperplane(1000, points2f_ptrs, coeffs3f, 0.002f));
+    }
+
+    {
+      Vector4d points4d [1000];
+      Vector4d *points4d_ptrs [1000];
+      for(int i = 0; i < 1000; i++) points4d_ptrs[i] = &(points4d[i]);
+      Hyperplane<double,4> coeffs5d;
+      makeNoisyCohyperplanarPoints(1000, points4d_ptrs, &coeffs5d, 0.01);
+      CALL_SUBTEST(check_fitHyperplane(10, points4d_ptrs, coeffs5d, 0.05));
+      CALL_SUBTEST(check_fitHyperplane(100, points4d_ptrs, coeffs5d, 0.01));
+      CALL_SUBTEST(check_fitHyperplane(1000, points4d_ptrs, coeffs5d, 0.002));
+    }
+
+    {
+      VectorXcd *points11cd_ptrs[1000];
+      for(int i = 0; i < 1000; i++) points11cd_ptrs[i] = new VectorXcd(11);
+      Hyperplane<std::complex<double>,Dynamic> *coeffs12cd = new Hyperplane<std::complex<double>,Dynamic>(11);
+      makeNoisyCohyperplanarPoints(1000, points11cd_ptrs, coeffs12cd, 0.01);
+      CALL_SUBTEST(check_fitHyperplane(100, points11cd_ptrs, *coeffs12cd, 0.025));
+      CALL_SUBTEST(check_fitHyperplane(1000, points11cd_ptrs, *coeffs12cd, 0.006));
+      delete coeffs12cd;
+      for(int i = 0; i < 1000; i++) delete points11cd_ptrs[i];
+    }
+  }
+}

test/eigen2/runtest.sh

@@ -0,0 +1,28 @@
+#!/bin/bash
+
+black='\E[30m'
+red='\E[31m'
+green='\E[32m'
+yellow='\E[33m'
+blue='\E[34m'
+magenta='\E[35m'
+cyan='\E[36m'
+white='\E[37m'
+
+if make test_$1 > /dev/null  2> .runtest.log ; then
+  if ! ./test_$1 r20 > /dev/null 2> .runtest.log ; then
+    echo -e  $red Test $1 failed: $black
+    echo -e $blue
+    cat .runtest.log
+    echo -e $black
+    exit 1
+  else
+  echo -e $green Test $1 passed$black
+  fi
+else
+  echo -e  $red Build of target $1 failed: $black
+  echo -e $blue
+  cat .runtest.log
+  echo -e $black
+  exit 1
+fi

test/eigen2/sizeof.cpp

@@ -0,0 +1,46 @@
+// 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>
+//
+// 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"
+
+template<typename MatrixType> void verifySizeOf(const MatrixType&)
+{
+  typedef typename MatrixType::Scalar Scalar;
+  if (MatrixType::RowsAtCompileTime!=Dynamic && MatrixType::ColsAtCompileTime!=Dynamic)
+    VERIFY(sizeof(MatrixType)==sizeof(Scalar)*MatrixType::SizeAtCompileTime);
+  else
+    VERIFY(sizeof(MatrixType)==sizeof(Scalar*) + 2 * sizeof(int));
+}
+
+void test_sizeof()
+{
+  CALL_SUBTEST( verifySizeOf(Matrix<float, 1, 1>()) );
+  CALL_SUBTEST( verifySizeOf(Matrix4d()) );
+  CALL_SUBTEST( verifySizeOf(Matrix<double, 4, 2>()) );
+  CALL_SUBTEST( verifySizeOf(Matrix<bool, 7, 5>()) );
+  CALL_SUBTEST( verifySizeOf(MatrixXcf(3, 3)) );
+  CALL_SUBTEST( verifySizeOf(MatrixXi(8, 12)) );
+  CALL_SUBTEST( verifySizeOf(MatrixXcd(20, 20)) );
+  CALL_SUBTEST( verifySizeOf(Matrix<float, 100, 100>()) );
+}

test/eigen2/smallvectors.cpp

@@ -0,0 +1,57 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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"
+
+template<typename Scalar> void smallVectors()
+{
+  typedef Matrix<Scalar, 1, 2> V2;
+  typedef Matrix<Scalar, 3, 1> V3;
+  typedef Matrix<Scalar, 1, 4> V4;
+  Scalar x1 = ei_random<Scalar>(),
+         x2 = ei_random<Scalar>(),
+         x3 = ei_random<Scalar>(),
+         x4 = ei_random<Scalar>();
+  V2 v2(x1, x2);
+  V3 v3(x1, x2, x3);
+  V4 v4(x1, x2, x3, x4);
+  VERIFY_IS_APPROX(x1, v2.x());
+  VERIFY_IS_APPROX(x1, v3.x());
+  VERIFY_IS_APPROX(x1, v4.x());
+  VERIFY_IS_APPROX(x2, v2.y());
+  VERIFY_IS_APPROX(x2, v3.y());
+  VERIFY_IS_APPROX(x2, v4.y());
+  VERIFY_IS_APPROX(x3, v3.z());
+  VERIFY_IS_APPROX(x3, v4.z());
+  VERIFY_IS_APPROX(x4, v4.w());
+}
+
+void test_smallvectors()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( smallVectors<int>() );
+    CALL_SUBTEST( smallVectors<float>() );
+    CALL_SUBTEST( smallVectors<double>() );
+  }
+}

test/eigen2/sparse.h

@@ -0,0 +1,169 @@
+// 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 Daniel Gomez Ferro <dgomezferro@gmail.com>
+//
+// 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/>.
+
+#ifndef EIGEN_TESTSPARSE_H
+
+#include "main.h"
+
+#if EIGEN_GNUC_AT_LEAST(4,0) && !defined __ICC
+#include <tr1/unordered_map>
+#define EIGEN_UNORDERED_MAP_SUPPORT
+namespace std {
+  using std::tr1::unordered_map;
+}
+#endif
+
+#ifdef EIGEN_GOOGLEHASH_SUPPORT
+  #include <google/sparse_hash_map>
+#endif
+
+#include <Eigen/Cholesky>
+#include <Eigen/LU>
+#include <Eigen/Sparse>
+
+enum {
+  ForceNonZeroDiag = 1,
+  MakeLowerTriangular = 2,
+  MakeUpperTriangular = 4,
+  ForceRealDiag = 8
+};
+
+/* Initializes both a sparse and dense matrix with same random values,
+ * and a ratio of \a density non zero entries.
+ * \param flags is a union of ForceNonZeroDiag, MakeLowerTriangular and MakeUpperTriangular
+ *        allowing to control the shape of the matrix.
+ * \param zeroCoords and nonzeroCoords allows to get the coordinate lists of the non zero,
+ *        and zero coefficients respectively.
+ */
+template<typename Scalar> void
+initSparse(double density,
+           Matrix<Scalar,Dynamic,Dynamic>& refMat,
+           SparseMatrix<Scalar>& sparseMat,
+           int flags = 0,
+           std::vector<Vector2i>* zeroCoords = 0,
+           std::vector<Vector2i>* nonzeroCoords = 0)
+{
+  sparseMat.startFill(int(refMat.rows()*refMat.cols()*density));
+  for(int j=0; j<refMat.cols(); j++)
+  {
+    for(int i=0; i<refMat.rows(); i++)
+    {
+      Scalar v = (ei_random<double>(0,1) < density) ? ei_random<Scalar>() : Scalar(0);
+      if ((flags&ForceNonZeroDiag) && (i==j))
+      {
+        v = ei_random<Scalar>()*Scalar(3.);
+        v = v*v + Scalar(5.);
+      }
+      if ((flags & MakeLowerTriangular) && j>i)
+        v = Scalar(0);
+      else if ((flags & MakeUpperTriangular) && j<i)
+        v = Scalar(0);
+      
+      if ((flags&ForceRealDiag) && (i==j))
+        v = ei_real(v);
+        
+      if (v!=Scalar(0))
+      {
+        sparseMat.fill(i,j) = v;
+        if (nonzeroCoords)
+          nonzeroCoords->push_back(Vector2i(i,j));
+      }
+      else if (zeroCoords)
+      {
+        zeroCoords->push_back(Vector2i(i,j));
+      }
+      refMat(i,j) = v;
+    }
+  }
+  sparseMat.endFill();
+}
+
+template<typename Scalar> void
+initSparse(double density,
+           Matrix<Scalar,Dynamic,Dynamic>& refMat,
+           DynamicSparseMatrix<Scalar>& sparseMat,
+           int flags = 0,
+           std::vector<Vector2i>* zeroCoords = 0,
+           std::vector<Vector2i>* nonzeroCoords = 0)
+{
+  sparseMat.startFill(int(refMat.rows()*refMat.cols()*density));
+  for(int j=0; j<refMat.cols(); j++)
+  {
+    for(int i=0; i<refMat.rows(); i++)
+    {
+      Scalar v = (ei_random<double>(0,1) < density) ? ei_random<Scalar>() : Scalar(0);
+      if ((flags&ForceNonZeroDiag) && (i==j))
+      {
+        v = ei_random<Scalar>()*Scalar(3.);
+        v = v*v + Scalar(5.);
+      }
+      if ((flags & MakeLowerTriangular) && j>i)
+        v = Scalar(0);
+      else if ((flags & MakeUpperTriangular) && j<i)
+        v = Scalar(0);
+      
+      if ((flags&ForceRealDiag) && (i==j))
+        v = ei_real(v);
+        
+      if (v!=Scalar(0))
+      {
+        sparseMat.fill(i,j) = v;
+        if (nonzeroCoords)
+          nonzeroCoords->push_back(Vector2i(i,j));
+      }
+      else if (zeroCoords)
+      {
+        zeroCoords->push_back(Vector2i(i,j));
+      }
+      refMat(i,j) = v;
+    }
+  }
+  sparseMat.endFill();
+}
+
+template<typename Scalar> void
+initSparse(double density,
+           Matrix<Scalar,Dynamic,1>& refVec,
+           SparseVector<Scalar>& sparseVec,
+           std::vector<int>* zeroCoords = 0,
+           std::vector<int>* nonzeroCoords = 0)
+{
+  sparseVec.reserve(int(refVec.size()*density));
+  sparseVec.setZero();
+  for(int i=0; i<refVec.size(); i++)
+  {
+    Scalar v = (ei_random<double>(0,1) < density) ? ei_random<Scalar>() : Scalar(0);
+    if (v!=Scalar(0))
+    {
+      sparseVec.fill(i) = v;
+      if (nonzeroCoords)
+        nonzeroCoords->push_back(i);
+    }
+    else if (zeroCoords)
+        zeroCoords->push_back(i);
+    refVec[i] = v;
+  }
+}
+
+#endif // EIGEN_TESTSPARSE_H

test/eigen2/sparse_basic.cpp

@@ -0,0 +1,332 @@
+// 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 Daniel Gomez Ferro <dgomezferro@gmail.com>
+//
+// 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 "sparse.h"
+
+template<typename SetterType,typename DenseType, typename Scalar, int Options>
+bool test_random_setter(SparseMatrix<Scalar,Options>& sm, const DenseType& ref, const std::vector<Vector2i>& nonzeroCoords)
+{
+  typedef SparseMatrix<Scalar,Options> SparseType;
+  {
+    sm.setZero();
+    SetterType w(sm);
+    std::vector<Vector2i> remaining = nonzeroCoords;
+    while(!remaining.empty())
+    {
+      int i = ei_random<int>(0,remaining.size()-1);
+      w(remaining[i].x(),remaining[i].y()) = ref.coeff(remaining[i].x(),remaining[i].y());
+      remaining[i] = remaining.back();
+      remaining.pop_back();
+    }
+  }
+  return sm.isApprox(ref);
+}
+
+template<typename SetterType,typename DenseType, typename T>
+bool test_random_setter(DynamicSparseMatrix<T>& sm, const DenseType& ref, const std::vector<Vector2i>& nonzeroCoords)
+{
+  sm.setZero();
+  std::vector<Vector2i> remaining = nonzeroCoords;
+  while(!remaining.empty())
+  {
+    int i = ei_random<int>(0,remaining.size()-1);
+    sm.coeffRef(remaining[i].x(),remaining[i].y()) = ref.coeff(remaining[i].x(),remaining[i].y());
+    remaining[i] = remaining.back();
+    remaining.pop_back();
+  }
+  return sm.isApprox(ref);
+}
+
+template<typename SparseMatrixType> void sparse_basic(const SparseMatrixType& ref)
+{
+  const int rows = ref.rows();
+  const int cols = ref.cols();
+  typedef typename SparseMatrixType::Scalar Scalar;
+  enum { Flags = SparseMatrixType::Flags };
+  
+  double density = std::max(8./(rows*cols), 0.01);
+  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+  typedef Matrix<Scalar,Dynamic,1> DenseVector;
+  Scalar eps = 1e-6;
+
+  SparseMatrixType m(rows, cols);
+  DenseMatrix refMat = DenseMatrix::Zero(rows, cols);
+  DenseVector vec1 = DenseVector::Random(rows);
+  Scalar s1 = ei_random<Scalar>();
+
+  std::vector<Vector2i> zeroCoords;
+  std::vector<Vector2i> nonzeroCoords;
+  initSparse<Scalar>(density, refMat, m, 0, &zeroCoords, &nonzeroCoords);
+  
+  if (zeroCoords.size()==0 || nonzeroCoords.size()==0)
+    return;
+
+  // test coeff and coeffRef
+  for (int i=0; i<(int)zeroCoords.size(); ++i)
+  {
+    VERIFY_IS_MUCH_SMALLER_THAN( m.coeff(zeroCoords[i].x(),zeroCoords[i].y()), eps );
+    if(ei_is_same_type<SparseMatrixType,SparseMatrix<Scalar,Flags> >::ret)
+      VERIFY_RAISES_ASSERT( m.coeffRef(zeroCoords[0].x(),zeroCoords[0].y()) = 5 );
+  }
+  VERIFY_IS_APPROX(m, refMat);
+
+  m.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5);
+  refMat.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5);
+
+  VERIFY_IS_APPROX(m, refMat);
+  /*
+  // test InnerIterators and Block expressions
+  for (int t=0; t<10; ++t)
+  {
+    int j = ei_random<int>(0,cols-1);
+    int i = ei_random<int>(0,rows-1);
+    int w = ei_random<int>(1,cols-j-1);
+    int h = ei_random<int>(1,rows-i-1);
+
+//     VERIFY_IS_APPROX(m.block(i,j,h,w), refMat.block(i,j,h,w));
+    for(int c=0; c<w; c++)
+    {
+      VERIFY_IS_APPROX(m.block(i,j,h,w).col(c), refMat.block(i,j,h,w).col(c));
+      for(int r=0; r<h; r++)
+      {
+//         VERIFY_IS_APPROX(m.block(i,j,h,w).col(c).coeff(r), refMat.block(i,j,h,w).col(c).coeff(r));
+      }
+    }
+//     for(int r=0; r<h; r++)
+//     {
+//       VERIFY_IS_APPROX(m.block(i,j,h,w).row(r), refMat.block(i,j,h,w).row(r));
+//       for(int c=0; c<w; c++)
+//       {
+//         VERIFY_IS_APPROX(m.block(i,j,h,w).row(r).coeff(c), refMat.block(i,j,h,w).row(r).coeff(c));
+//       }
+//     }
+  }
+
+  for(int c=0; c<cols; c++)
+  {
+    VERIFY_IS_APPROX(m.col(c) + m.col(c), (m + m).col(c));
+    VERIFY_IS_APPROX(m.col(c) + m.col(c), refMat.col(c) + refMat.col(c));
+  }
+
+  for(int r=0; r<rows; r++)
+  {
+    VERIFY_IS_APPROX(m.row(r) + m.row(r), (m + m).row(r));
+    VERIFY_IS_APPROX(m.row(r) + m.row(r), refMat.row(r) + refMat.row(r));
+  }
+  */
+
+  // test SparseSetters
+  // coherent setter
+  // TODO extend the MatrixSetter
+//   {
+//     m.setZero();
+//     VERIFY_IS_NOT_APPROX(m, refMat);
+//     SparseSetter<SparseMatrixType, FullyCoherentAccessPattern> w(m);
+//     for (int i=0; i<nonzeroCoords.size(); ++i)
+//     {
+//       w->coeffRef(nonzeroCoords[i].x(),nonzeroCoords[i].y()) = refMat.coeff(nonzeroCoords[i].x(),nonzeroCoords[i].y());
+//     }
+//   }
+//   VERIFY_IS_APPROX(m, refMat);
+
+  // random setter
+//   {
+//     m.setZero();
+//     VERIFY_IS_NOT_APPROX(m, refMat);
+//     SparseSetter<SparseMatrixType, RandomAccessPattern> w(m);
+//     std::vector<Vector2i> remaining = nonzeroCoords;
+//     while(!remaining.empty())
+//     {
+//       int i = ei_random<int>(0,remaining.size()-1);
+//       w->coeffRef(remaining[i].x(),remaining[i].y()) = refMat.coeff(remaining[i].x(),remaining[i].y());
+//       remaining[i] = remaining.back();
+//       remaining.pop_back();
+//     }
+//   }
+//   VERIFY_IS_APPROX(m, refMat);
+
+    VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, StdMapTraits> >(m,refMat,nonzeroCoords) ));
+    #ifdef EIGEN_UNORDERED_MAP_SUPPORT
+    VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, StdUnorderedMapTraits> >(m,refMat,nonzeroCoords) ));
+    #endif
+    #ifdef _DENSE_HASH_MAP_H_
+    VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, GoogleDenseHashMapTraits> >(m,refMat,nonzeroCoords) ));
+    #endif
+    #ifdef _SPARSE_HASH_MAP_H_
+    VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, GoogleSparseHashMapTraits> >(m,refMat,nonzeroCoords) ));
+    #endif
+
+    // test fillrand
+    {
+      DenseMatrix m1(rows,cols);
+      m1.setZero();
+      SparseMatrixType m2(rows,cols);
+      m2.startFill();
+      for (int j=0; j<cols; ++j)
+      {
+        for (int k=0; k<rows/2; ++k)
+        {
+          int i = ei_random<int>(0,rows-1);
+          if (m1.coeff(i,j)==Scalar(0))
+            m2.fillrand(i,j) = m1(i,j) = ei_random<Scalar>();
+        }
+      }
+      m2.endFill();
+      VERIFY_IS_APPROX(m2,m1);
+    }
+  
+  // test RandomSetter
+  /*{
+    SparseMatrixType m1(rows,cols), m2(rows,cols);
+    DenseMatrix refM1 = DenseMatrix::Zero(rows, rows);
+    initSparse<Scalar>(density, refM1, m1);
+    {
+      Eigen::RandomSetter<SparseMatrixType > setter(m2);
+      for (int j=0; j<m1.outerSize(); ++j)
+        for (typename SparseMatrixType::InnerIterator i(m1,j); i; ++i)
+          setter(i.index(), j) = i.value();
+    }
+    VERIFY_IS_APPROX(m1, m2);
+  }*/
+//   std::cerr << m.transpose() << "\n\n"  << refMat.transpose() << "\n\n";
+//   VERIFY_IS_APPROX(m, refMat);
+
+  // test basic computations
+  {
+    DenseMatrix refM1 = DenseMatrix::Zero(rows, rows);
+    DenseMatrix refM2 = DenseMatrix::Zero(rows, rows);
+    DenseMatrix refM3 = DenseMatrix::Zero(rows, rows);
+    DenseMatrix refM4 = DenseMatrix::Zero(rows, rows);
+    SparseMatrixType m1(rows, rows);
+    SparseMatrixType m2(rows, rows);
+    SparseMatrixType m3(rows, rows);
+    SparseMatrixType m4(rows, rows);
+    initSparse<Scalar>(density, refM1, m1);
+    initSparse<Scalar>(density, refM2, m2);
+    initSparse<Scalar>(density, refM3, m3);
+    initSparse<Scalar>(density, refM4, m4);
+
+    VERIFY_IS_APPROX(m1+m2, refM1+refM2);
+    VERIFY_IS_APPROX(m1+m2+m3, refM1+refM2+refM3);
+    VERIFY_IS_APPROX(m3.cwise()*(m1+m2), refM3.cwise()*(refM1+refM2));
+    VERIFY_IS_APPROX(m1*s1-m2, refM1*s1-refM2);
+
+    VERIFY_IS_APPROX(m1*=s1, refM1*=s1);
+    VERIFY_IS_APPROX(m1/=s1, refM1/=s1);
+    
+    VERIFY_IS_APPROX(m1+=m2, refM1+=refM2);
+    VERIFY_IS_APPROX(m1-=m2, refM1-=refM2);
+    
+    VERIFY_IS_APPROX(m1.col(0).dot(refM2.row(0)), refM1.col(0).dot(refM2.row(0)));
+    
+    refM4.setRandom();
+    // sparse cwise* dense
+    VERIFY_IS_APPROX(m3.cwise()*refM4, refM3.cwise()*refM4);
+//     VERIFY_IS_APPROX(m3.cwise()/refM4, refM3.cwise()/refM4);
+  }
+
+  // test innerVector()
+  {
+    DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
+    SparseMatrixType m2(rows, rows);
+    initSparse<Scalar>(density, refMat2, m2);
+    int j0 = ei_random(0,rows-1);
+    int j1 = ei_random(0,rows-1);
+    VERIFY_IS_APPROX(m2.innerVector(j0), refMat2.col(j0));
+    VERIFY_IS_APPROX(m2.innerVector(j0)+m2.innerVector(j1), refMat2.col(j0)+refMat2.col(j1));
+    //m2.innerVector(j0) = 2*m2.innerVector(j1);
+    //refMat2.col(j0) = 2*refMat2.col(j1);
+    //VERIFY_IS_APPROX(m2, refMat2);
+  }
+  
+  // test innerVectors()
+  {
+    DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
+    SparseMatrixType m2(rows, rows);
+    initSparse<Scalar>(density, refMat2, m2);
+    int j0 = ei_random(0,rows-2);
+    int j1 = ei_random(0,rows-2);
+    int n0 = ei_random<int>(1,rows-std::max(j0,j1));
+    VERIFY_IS_APPROX(m2.innerVectors(j0,n0), refMat2.block(0,j0,rows,n0));
+    VERIFY_IS_APPROX(m2.innerVectors(j0,n0)+m2.innerVectors(j1,n0),
+                     refMat2.block(0,j0,rows,n0)+refMat2.block(0,j1,rows,n0));
+    //m2.innerVectors(j0,n0) = m2.innerVectors(j0,n0) + m2.innerVectors(j1,n0);
+    //refMat2.block(0,j0,rows,n0) = refMat2.block(0,j0,rows,n0) + refMat2.block(0,j1,rows,n0);
+  }
+
+  // test transpose
+  {
+    DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
+    SparseMatrixType m2(rows, rows);
+    initSparse<Scalar>(density, refMat2, m2);
+    VERIFY_IS_APPROX(m2.transpose().eval(), refMat2.transpose().eval());
+    VERIFY_IS_APPROX(m2.transpose(), refMat2.transpose());
+  }
+  
+  // test prune
+  {
+    SparseMatrixType m2(rows, rows);
+    DenseMatrix refM2(rows, rows);
+    refM2.setZero();
+    int countFalseNonZero = 0;
+    int countTrueNonZero = 0;
+    m2.startFill();
+    for (int j=0; j<m2.outerSize(); ++j)
+      for (int i=0; i<m2.innerSize(); ++i)
+      {
+        float x = ei_random<float>(0,1);
+        if (x<0.1)
+        {
+          // do nothing
+        }
+        else if (x<0.5)
+        {
+          countFalseNonZero++;
+          m2.fill(i,j) = Scalar(0);
+        }
+        else
+        {
+          countTrueNonZero++;
+          m2.fill(i,j) = refM2(i,j) = Scalar(1);
+        }
+      }
+    m2.endFill();
+    VERIFY(countFalseNonZero+countTrueNonZero == m2.nonZeros());
+    VERIFY_IS_APPROX(m2, refM2);
+    m2.prune(1);
+    VERIFY(countTrueNonZero==m2.nonZeros());
+    VERIFY_IS_APPROX(m2, refM2);
+  }
+}
+
+void test_sparse_basic()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( sparse_basic(SparseMatrix<double>(8, 8)) );
+    CALL_SUBTEST( sparse_basic(SparseMatrix<std::complex<double> >(16, 16)) );
+    CALL_SUBTEST( sparse_basic(SparseMatrix<double>(33, 33)) );
+    
+    CALL_SUBTEST( sparse_basic(DynamicSparseMatrix<double>(8, 8)) );
+  }
+}

test/eigen2/sparse_product.cpp

@@ -0,0 +1,130 @@
+// 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 Daniel Gomez Ferro <dgomezferro@gmail.com>
+//
+// 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 "sparse.h"
+
+template<typename SparseMatrixType> void sparse_product(const SparseMatrixType& ref)
+{
+  const int rows = ref.rows();
+  const int cols = ref.cols();
+  typedef typename SparseMatrixType::Scalar Scalar;
+  enum { Flags = SparseMatrixType::Flags };
+
+  double density = std::max(8./(rows*cols), 0.01);
+  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+  typedef Matrix<Scalar,Dynamic,1> DenseVector;
+
+  // test matrix-matrix product
+  {
+    DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
+    DenseMatrix refMat3 = DenseMatrix::Zero(rows, rows);
+    DenseMatrix refMat4 = DenseMatrix::Zero(rows, rows);
+    DenseMatrix dm4 = DenseMatrix::Zero(rows, rows);
+    SparseMatrixType m2(rows, rows);
+    SparseMatrixType m3(rows, rows);
+    SparseMatrixType m4(rows, rows);
+    initSparse<Scalar>(density, refMat2, m2);
+    initSparse<Scalar>(density, refMat3, m3);
+    initSparse<Scalar>(density, refMat4, m4);
+    VERIFY_IS_APPROX(m4=m2*m3, refMat4=refMat2*refMat3);
+    VERIFY_IS_APPROX(m4=m2.transpose()*m3, refMat4=refMat2.transpose()*refMat3);
+    VERIFY_IS_APPROX(m4=m2.transpose()*m3.transpose(), refMat4=refMat2.transpose()*refMat3.transpose());
+    VERIFY_IS_APPROX(m4=m2*m3.transpose(), refMat4=refMat2*refMat3.transpose());
+
+    // sparse * dense
+    VERIFY_IS_APPROX(dm4=m2*refMat3, refMat4=refMat2*refMat3);
+    VERIFY_IS_APPROX(dm4=m2*refMat3.transpose(), refMat4=refMat2*refMat3.transpose());
+    VERIFY_IS_APPROX(dm4=m2.transpose()*refMat3, refMat4=refMat2.transpose()*refMat3);
+    VERIFY_IS_APPROX(dm4=m2.transpose()*refMat3.transpose(), refMat4=refMat2.transpose()*refMat3.transpose());
+
+    // dense * sparse
+    VERIFY_IS_APPROX(dm4=refMat2*m3, refMat4=refMat2*refMat3);
+    VERIFY_IS_APPROX(dm4=refMat2*m3.transpose(), refMat4=refMat2*refMat3.transpose());
+    VERIFY_IS_APPROX(dm4=refMat2.transpose()*m3, refMat4=refMat2.transpose()*refMat3);
+    VERIFY_IS_APPROX(dm4=refMat2.transpose()*m3.transpose(), refMat4=refMat2.transpose()*refMat3.transpose());
+
+    VERIFY_IS_APPROX(m3=m3*m3, refMat3=refMat3*refMat3);
+  }
+
+  // test matrix - diagonal product
+  if(false) // it compiles, but the precision is terrible. probably doesn't matter in this branch....
+  {
+    DenseMatrix refM2 = DenseMatrix::Zero(rows, rows);
+    DenseMatrix refM3 = DenseMatrix::Zero(rows, rows);
+    DiagonalMatrix<DenseVector> d1(DenseVector::Random(rows));
+    SparseMatrixType m2(rows, rows);
+    SparseMatrixType m3(rows, rows);
+    initSparse<Scalar>(density, refM2, m2);
+    initSparse<Scalar>(density, refM3, m3);
+    VERIFY_IS_APPROX(m3=m2*d1, refM3=refM2*d1);
+    VERIFY_IS_APPROX(m3=m2.transpose()*d1, refM3=refM2.transpose()*d1);
+    VERIFY_IS_APPROX(m3=d1*m2, refM3=d1*refM2);
+    VERIFY_IS_APPROX(m3=d1*m2.transpose(), refM3=d1 * refM2.transpose());
+  }
+
+  // test self adjoint products
+  {
+    DenseMatrix b = DenseMatrix::Random(rows, rows);
+    DenseMatrix x = DenseMatrix::Random(rows, rows);
+    DenseMatrix refX = DenseMatrix::Random(rows, rows);
+    DenseMatrix refUp = DenseMatrix::Zero(rows, rows);
+    DenseMatrix refLo = DenseMatrix::Zero(rows, rows);
+    DenseMatrix refS = DenseMatrix::Zero(rows, rows);
+    SparseMatrixType mUp(rows, rows);
+    SparseMatrixType mLo(rows, rows);
+    SparseMatrixType mS(rows, rows);
+    do {
+      initSparse<Scalar>(density, refUp, mUp, ForceRealDiag|/*ForceNonZeroDiag|*/MakeUpperTriangular);
+    } while (refUp.isZero());
+    refLo = refUp.transpose().conjugate();
+    mLo = mUp.transpose().conjugate();
+    refS = refUp + refLo;
+    refS.diagonal() *= 0.5;
+    mS = mUp + mLo;
+    for (int k=0; k<mS.outerSize(); ++k)
+      for (typename SparseMatrixType::InnerIterator it(mS,k); it; ++it)
+        if (it.index() == k)
+          it.valueRef() *= 0.5;
+
+    VERIFY_IS_APPROX(refS.adjoint(), refS);
+    VERIFY_IS_APPROX(mS.transpose().conjugate(), mS);
+    VERIFY_IS_APPROX(mS, refS);
+    VERIFY_IS_APPROX(x=mS*b, refX=refS*b);
+    VERIFY_IS_APPROX(x=mUp.template marked<UpperTriangular|SelfAdjoint>()*b, refX=refS*b);
+    VERIFY_IS_APPROX(x=mLo.template marked<LowerTriangular|SelfAdjoint>()*b, refX=refS*b);
+    VERIFY_IS_APPROX(x=mS.template marked<SelfAdjoint>()*b, refX=refS*b);
+  }
+
+}
+
+void test_sparse_product()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( sparse_product(SparseMatrix<double>(8, 8)) );
+    CALL_SUBTEST( sparse_product(SparseMatrix<std::complex<double> >(16, 16)) );
+    CALL_SUBTEST( sparse_product(SparseMatrix<double>(33, 33)) );
+
+    CALL_SUBTEST( sparse_product(DynamicSparseMatrix<double>(8, 8)) );
+  }
+}

test/eigen2/sparse_solvers.cpp

@@ -0,0 +1,215 @@
+// 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 Daniel Gomez Ferro <dgomezferro@gmail.com>
+//
+// 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 "sparse.h"
+
+template<typename Scalar> void
+initSPD(double density,
+        Matrix<Scalar,Dynamic,Dynamic>& refMat,
+        SparseMatrix<Scalar>& sparseMat)
+{
+  Matrix<Scalar,Dynamic,Dynamic> aux(refMat.rows(),refMat.cols());
+  initSparse(density,refMat,sparseMat);
+  refMat = refMat * refMat.adjoint();
+  for (int k=0; k<2; ++k)
+  {
+    initSparse(density,aux,sparseMat,ForceNonZeroDiag);
+    refMat += aux * aux.adjoint();
+  }
+  sparseMat.startFill();
+  for (int j=0 ; j<sparseMat.cols(); ++j)
+    for (int i=j ; i<sparseMat.rows(); ++i)
+      if (refMat(i,j)!=Scalar(0))
+        sparseMat.fill(i,j) = refMat(i,j);
+  sparseMat.endFill();
+}
+
+template<typename Scalar> void sparse_solvers(int rows, int cols)
+{
+  double density = std::max(8./(rows*cols), 0.01);
+  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+  typedef Matrix<Scalar,Dynamic,1> DenseVector;
+  // Scalar eps = 1e-6;
+
+  DenseVector vec1 = DenseVector::Random(rows);
+
+  std::vector<Vector2i> zeroCoords;
+  std::vector<Vector2i> nonzeroCoords;
+
+  // test triangular solver
+  {
+    DenseVector vec2 = vec1, vec3 = vec1;
+    SparseMatrix<Scalar> m2(rows, cols);
+    DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
+
+    // lower
+    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
+    VERIFY_IS_APPROX(refMat2.template marked<LowerTriangular>().solveTriangular(vec2),
+                     m2.template marked<LowerTriangular>().solveTriangular(vec3));
+
+    // lower - transpose
+    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeLowerTriangular, &zeroCoords, &nonzeroCoords);
+    VERIFY_IS_APPROX(refMat2.template marked<LowerTriangular>().transpose().solveTriangular(vec2),
+                     m2.template marked<LowerTriangular>().transpose().solveTriangular(vec3));
+
+    // upper
+    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
+    VERIFY_IS_APPROX(refMat2.template marked<UpperTriangular>().solveTriangular(vec2),
+                     m2.template marked<UpperTriangular>().solveTriangular(vec3));
+
+    // upper - transpose
+    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, &zeroCoords, &nonzeroCoords);
+    VERIFY_IS_APPROX(refMat2.template marked<UpperTriangular>().transpose().solveTriangular(vec2),
+                     m2.template marked<UpperTriangular>().transpose().solveTriangular(vec3));
+  }
+
+  // test LLT
+  {
+    // TODO fix the issue with complex (see SparseLLT::solveInPlace)
+    SparseMatrix<Scalar> m2(rows, cols);
+    DenseMatrix refMat2(rows, cols);
+
+    DenseVector b = DenseVector::Random(cols);
+    DenseVector refX(cols), x(cols);
+
+    initSPD(density, refMat2, m2);
+
+    refMat2.llt().solve(b, &refX);
+    typedef SparseMatrix<Scalar,LowerTriangular|SelfAdjoint> SparseSelfAdjointMatrix;
+    if (!NumTraits<Scalar>::IsComplex)
+    {
+      x = b;
+      SparseLLT<SparseSelfAdjointMatrix> (m2).solveInPlace(x);
+      VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: default");
+    }
+    #ifdef EIGEN_CHOLMOD_SUPPORT
+    x = b;
+    SparseLLT<SparseSelfAdjointMatrix,Cholmod>(m2).solveInPlace(x);
+    VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: cholmod");
+    #endif
+    if (!NumTraits<Scalar>::IsComplex)
+    {
+      #ifdef EIGEN_TAUCS_SUPPORT
+      x = b;
+      SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,IncompleteFactorization).solveInPlace(x);
+      VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (IncompleteFactorization)");
+      x = b;
+      SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,SupernodalMultifrontal).solveInPlace(x);
+      VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (SupernodalMultifrontal)");
+      x = b;
+      SparseLLT<SparseSelfAdjointMatrix,Taucs>(m2,SupernodalLeftLooking).solveInPlace(x);
+      VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LLT: taucs (SupernodalLeftLooking)");
+      #endif
+    }
+  }
+
+  // test LDLT
+  if (!NumTraits<Scalar>::IsComplex)
+  {
+    // TODO fix the issue with complex (see SparseLDLT::solveInPlace)
+    SparseMatrix<Scalar> m2(rows, cols);
+    DenseMatrix refMat2(rows, cols);
+
+    DenseVector b = DenseVector::Random(cols);
+    DenseVector refX(cols), x(cols);
+
+    //initSPD(density, refMat2, m2);
+    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag|MakeUpperTriangular, 0, 0);
+    refMat2 += refMat2.adjoint();
+    refMat2.diagonal() *= 0.5;
+
+    refMat2.ldlt().solve(b, &refX);
+    typedef SparseMatrix<Scalar,UpperTriangular|SelfAdjoint> SparseSelfAdjointMatrix;
+    x = b;
+    SparseLDLT<SparseSelfAdjointMatrix> ldlt(m2);
+    if (ldlt.succeeded())
+      ldlt.solveInPlace(x);
+    VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LDLT: default");
+  }
+
+  // test LU
+  {
+    static int count = 0;
+    SparseMatrix<Scalar> m2(rows, cols);
+    DenseMatrix refMat2(rows, cols);
+
+    DenseVector b = DenseVector::Random(cols);
+    DenseVector refX(cols), x(cols);
+
+    initSparse<Scalar>(density, refMat2, m2, ForceNonZeroDiag, &zeroCoords, &nonzeroCoords);
+
+    LU<DenseMatrix> refLu(refMat2);
+    refLu.solve(b, &refX);
+    #if defined(EIGEN_SUPERLU_SUPPORT) || defined(EIGEN_UMFPACK_SUPPORT)
+    Scalar refDet = refLu.determinant();
+    #endif
+    x.setZero();
+    // // SparseLU<SparseMatrix<Scalar> > (m2).solve(b,&x);
+    // // VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: default");
+    #ifdef EIGEN_SUPERLU_SUPPORT
+    {
+      x.setZero();
+      SparseLU<SparseMatrix<Scalar>,SuperLU> slu(m2);
+      if (slu.succeeded())
+      {
+        if (slu.solve(b,&x)) {
+          VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: SuperLU");
+        }
+        // std::cerr << refDet << " == " << slu.determinant() << "\n";
+        if (count==0) {
+          VERIFY_IS_APPROX(refDet,slu.determinant()); // FIXME det is not very stable for complex
+        }
+      }
+    }
+    #endif
+    #ifdef EIGEN_UMFPACK_SUPPORT
+    {
+      // check solve
+      x.setZero();
+      SparseLU<SparseMatrix<Scalar>,UmfPack> slu(m2);
+      if (slu.succeeded()) {
+        if (slu.solve(b,&x)) {
+          if (count==0) {
+            VERIFY(refX.isApprox(x,test_precision<Scalar>()) && "LU: umfpack");  // FIXME solve is not very stable for complex
+          }
+        }
+        VERIFY_IS_APPROX(refDet,slu.determinant());
+        // TODO check the extracted data
+        //std::cerr << slu.matrixL() << "\n";
+      }
+    }
+    #endif
+    count++;
+  }
+
+}
+
+void test_sparse_solvers()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( sparse_solvers<double>(8, 8) );
+    CALL_SUBTEST( sparse_solvers<std::complex<double> >(16, 16) );
+    CALL_SUBTEST( sparse_solvers<double>(101, 101) );
+  }
+}

test/eigen2/sparse_vector.cpp

@@ -0,0 +1,99 @@
+// 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 Daniel Gomez Ferro <dgomezferro@gmail.com>
+//
+// 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 "sparse.h"
+
+template<typename Scalar> void sparse_vector(int rows, int cols)
+{
+  double densityMat = std::max(8./(rows*cols), 0.01);
+  double densityVec = std::max(8./float(rows), 0.1);
+  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+  typedef Matrix<Scalar,Dynamic,1> DenseVector;
+  typedef SparseVector<Scalar> SparseVectorType;
+  typedef SparseMatrix<Scalar> SparseMatrixType;
+  Scalar eps = 1e-6;
+
+  SparseMatrixType m1(rows,cols);
+  SparseVectorType v1(rows), v2(rows), v3(rows);
+  DenseMatrix refM1 = DenseMatrix::Zero(rows, cols);
+  DenseVector refV1 = DenseVector::Random(rows),
+    refV2 = DenseVector::Random(rows),
+    refV3 = DenseVector::Random(rows);
+
+  std::vector<int> zerocoords, nonzerocoords;
+  initSparse<Scalar>(densityVec, refV1, v1, &zerocoords, &nonzerocoords);
+  initSparse<Scalar>(densityMat, refM1, m1);
+
+  initSparse<Scalar>(densityVec, refV2, v2);
+  initSparse<Scalar>(densityVec, refV3, v3);
+
+  Scalar s1 = ei_random<Scalar>();
+
+  // test coeff and coeffRef
+  for (unsigned int i=0; i<zerocoords.size(); ++i)
+  {
+    VERIFY_IS_MUCH_SMALLER_THAN( v1.coeff(zerocoords[i]), eps );
+    //VERIFY_RAISES_ASSERT( v1.coeffRef(zerocoords[i]) = 5 );
+  }
+  {
+    VERIFY(int(nonzerocoords.size()) == v1.nonZeros());
+    int j=0;
+    for (typename SparseVectorType::InnerIterator it(v1); it; ++it,++j)
+    {
+      VERIFY(nonzerocoords[j]==it.index());
+      VERIFY(it.value()==v1.coeff(it.index()));
+      VERIFY(it.value()==refV1.coeff(it.index()));
+    }
+  }
+  VERIFY_IS_APPROX(v1, refV1);
+
+  v1.coeffRef(nonzerocoords[0]) = Scalar(5);
+  refV1.coeffRef(nonzerocoords[0]) = Scalar(5);
+  VERIFY_IS_APPROX(v1, refV1);
+
+  VERIFY_IS_APPROX(v1+v2, refV1+refV2);
+  VERIFY_IS_APPROX(v1+v2+v3, refV1+refV2+refV3);
+
+  VERIFY_IS_APPROX(v1*s1-v2, refV1*s1-refV2);
+
+  VERIFY_IS_APPROX(v1*=s1, refV1*=s1);
+  VERIFY_IS_APPROX(v1/=s1, refV1/=s1);
+  
+  VERIFY_IS_APPROX(v1+=v2, refV1+=refV2);
+  VERIFY_IS_APPROX(v1-=v2, refV1-=refV2);
+
+  VERIFY_IS_APPROX(v1.dot(v2), refV1.dot(refV2));
+  VERIFY_IS_APPROX(v1.dot(refV2), refV1.dot(refV2));
+
+}
+
+void test_sparse_vector()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( sparse_vector<double>(8, 8) );
+    CALL_SUBTEST( sparse_vector<std::complex<double> >(16, 16) );
+    CALL_SUBTEST( sparse_vector<double>(299, 535) );
+  }
+}
+

test/eigen2/stdvector.cpp

@@ -0,0 +1,163 @@
+// 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 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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 <Eigen/StdVector>
+#include "main.h"
+#include <Eigen/Geometry>
+
+template<typename MatrixType>
+void check_stdvector_matrix(const MatrixType& m)
+{
+  int rows = m.rows();
+  int cols = m.cols();
+  MatrixType x = MatrixType::Random(rows,cols), y = MatrixType::Random(rows,cols);
+  std::vector<MatrixType> v(10, MatrixType(rows,cols)), w(20, y);
+  v[5] = x;
+  w[6] = v[5];
+  VERIFY_IS_APPROX(w[6], v[5]);
+  v = w;
+  for(int i = 0; i < 20; i++)
+  {
+    VERIFY_IS_APPROX(w[i], v[i]);
+  }
+
+  v.resize(21);
+  v[20] = x;
+  VERIFY_IS_APPROX(v[20], x);
+  v.resize(22,y);
+  VERIFY_IS_APPROX(v[21], y);
+  v.push_back(x);
+  VERIFY_IS_APPROX(v[22], x);
+  VERIFY((std::size_t)&(v[22]) == (std::size_t)&(v[21]) + sizeof(MatrixType));
+
+  // do a lot of push_back such that the vector gets internally resized
+  // (with memory reallocation)
+  MatrixType* ref = &w[0];
+  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+    v.push_back(w[i%w.size()]);
+  for(unsigned int i=23; i<v.size(); ++i)
+  {
+    VERIFY(v[i]==w[(i-23)%w.size()]);
+  }
+}
+
+template<typename TransformType>
+void check_stdvector_transform(const TransformType&)
+{
+  typedef typename TransformType::MatrixType MatrixType;
+  TransformType x(MatrixType::Random()), y(MatrixType::Random());
+  std::vector<TransformType> v(10), w(20, y);
+  v[5] = x;
+  w[6] = v[5];
+  VERIFY_IS_APPROX(w[6], v[5]);
+  v = w;
+  for(int i = 0; i < 20; i++)
+  {
+    VERIFY_IS_APPROX(w[i], v[i]);
+  }
+
+  v.resize(21);
+  v[20] = x;
+  VERIFY_IS_APPROX(v[20], x);
+  v.resize(22,y);
+  VERIFY_IS_APPROX(v[21], y);
+  v.push_back(x);
+  VERIFY_IS_APPROX(v[22], x);
+  VERIFY((std::size_t)&(v[22]) == (std::size_t)&(v[21]) + sizeof(TransformType));
+
+  // do a lot of push_back such that the vector gets internally resized
+  // (with memory reallocation)
+  TransformType* ref = &w[0];
+  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+    v.push_back(w[i%w.size()]);
+  for(unsigned int i=23; i<v.size(); ++i)
+  {
+    VERIFY(v[i].matrix()==w[(i-23)%w.size()].matrix());
+  }
+}
+
+template<typename QuaternionType>
+void check_stdvector_quaternion(const QuaternionType&)
+{
+  typedef typename QuaternionType::Coefficients Coefficients;
+  QuaternionType x(Coefficients::Random()), y(Coefficients::Random());
+  std::vector<QuaternionType> v(10), w(20, y);
+  v[5] = x;
+  w[6] = v[5];
+  VERIFY_IS_APPROX(w[6], v[5]);
+  v = w;
+  for(int i = 0; i < 20; i++)
+  {
+    VERIFY_IS_APPROX(w[i], v[i]);
+  }
+
+  v.resize(21);
+  v[20] = x;
+  VERIFY_IS_APPROX(v[20], x);
+  v.resize(22,y);
+  VERIFY_IS_APPROX(v[21], y);
+  v.push_back(x);
+  VERIFY_IS_APPROX(v[22], x);
+  VERIFY((std::size_t)&(v[22]) == (std::size_t)&(v[21]) + sizeof(QuaternionType));
+
+  // do a lot of push_back such that the vector gets internally resized
+  // (with memory reallocation)
+  QuaternionType* ref = &w[0];
+  for(int i=0; i<30 || ((ref==&w[0]) && i<300); ++i)
+    v.push_back(w[i%w.size()]);
+  for(unsigned int i=23; i<v.size(); ++i)
+  {
+    VERIFY(v[i].coeffs()==w[(i-23)%w.size()].coeffs());
+  }
+}
+
+void test_stdvector()
+{
+  // some non vectorizable fixed sizes
+  CALL_SUBTEST(check_stdvector_matrix(Vector2f()));
+  CALL_SUBTEST(check_stdvector_matrix(Matrix3f()));
+  CALL_SUBTEST(check_stdvector_matrix(Matrix3d()));
+
+  // some vectorizable fixed sizes
+  CALL_SUBTEST(check_stdvector_matrix(Matrix2f()));
+  CALL_SUBTEST(check_stdvector_matrix(Vector4f()));
+  CALL_SUBTEST(check_stdvector_matrix(Matrix4f()));
+  CALL_SUBTEST(check_stdvector_matrix(Matrix4d()));
+
+  // some dynamic sizes
+  CALL_SUBTEST(check_stdvector_matrix(MatrixXd(1,1)));
+  CALL_SUBTEST(check_stdvector_matrix(VectorXd(20)));
+  CALL_SUBTEST(check_stdvector_matrix(RowVectorXf(20)));
+  CALL_SUBTEST(check_stdvector_matrix(MatrixXcf(10,10)));
+
+  // some Transform
+  CALL_SUBTEST(check_stdvector_transform(Transform2f()));
+  CALL_SUBTEST(check_stdvector_transform(Transform3f()));
+  CALL_SUBTEST(check_stdvector_transform(Transform3d()));
+  //CALL_SUBTEST(check_stdvector_transform(Transform4d()));
+
+  // some Quaternion
+  CALL_SUBTEST(check_stdvector_quaternion(Quaternionf()));
+  CALL_SUBTEST(check_stdvector_quaternion(Quaternionf()));
+}

test/eigen2/submatrices.cpp

@@ -0,0 +1,161 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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"
+
+// check minor separately in order to avoid the possible creation of a zero-sized
+// array. Comes from a compilation error with gcc-3.4 or gcc-4 with -ansi -pedantic.
+// Another solution would be to declare the array like this: T m_data[Size==0?1:Size]; in ei_matrix_storage
+// but this is probably not bad to raise such an error at compile time...
+template<typename Scalar, int _Rows, int _Cols> struct CheckMinor
+{
+    typedef Matrix<Scalar, _Rows, _Cols> MatrixType;
+    CheckMinor(MatrixType& m1, int r1, int c1)
+    {
+        int rows = m1.rows();
+        int cols = m1.cols();
+
+        Matrix<Scalar, Dynamic, Dynamic> mi = m1.minor(0,0).eval();
+        VERIFY_IS_APPROX(mi, m1.block(1,1,rows-1,cols-1));
+        mi = m1.minor(r1,c1);
+        VERIFY_IS_APPROX(mi.transpose(), m1.transpose().minor(c1,r1));
+        //check operator(), both constant and non-constant, on minor()
+        m1.minor(r1,c1)(0,0) = m1.minor(0,0)(0,0);
+    }
+};
+
+template<typename Scalar> struct CheckMinor<Scalar,1,1>
+{
+    typedef Matrix<Scalar, 1, 1> MatrixType;
+    CheckMinor(MatrixType&, int, int) {}
+};
+
+template<typename MatrixType> void submatrices(const MatrixType& m)
+{
+  /* this test covers the following files:
+     Row.h Column.h Block.h Minor.h DiagonalCoeffs.h
+  */
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename MatrixType::RealScalar RealScalar;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+  typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType;
+  int rows = m.rows();
+  int cols = m.cols();
+
+  MatrixType m1 = MatrixType::Random(rows, cols),
+             m2 = MatrixType::Random(rows, cols),
+             m3(rows, cols),
+             mzero = MatrixType::Zero(rows, cols),
+             ones = MatrixType::Ones(rows, cols),
+             identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+                              ::Identity(rows, rows),
+             square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+                              ::Random(rows, rows);
+  VectorType v1 = VectorType::Random(rows),
+             v2 = VectorType::Random(rows),
+             v3 = VectorType::Random(rows),
+             vzero = VectorType::Zero(rows);
+
+  Scalar s1 = ei_random<Scalar>();
+
+  int r1 = ei_random<int>(0,rows-1);
+  int r2 = ei_random<int>(r1,rows-1);
+  int c1 = ei_random<int>(0,cols-1);
+  int c2 = ei_random<int>(c1,cols-1);
+
+  //check row() and col()
+  VERIFY_IS_APPROX(m1.col(c1).transpose(), m1.transpose().row(c1));
+  VERIFY_IS_APPROX(square.row(r1).dot(m1.col(c1)), (square.lazy() * m1.conjugate())(r1,c1));
+  //check operator(), both constant and non-constant, on row() and col()
+  m1.row(r1) += s1 * m1.row(r2);
+  m1.col(c1) += s1 * m1.col(c2);
+
+  //check block()
+  Matrix<Scalar,Dynamic,Dynamic> b1(1,1); b1(0,0) = m1(r1,c1);
+  RowVectorType br1(m1.block(r1,0,1,cols));
+  VectorType bc1(m1.block(0,c1,rows,1));
+  VERIFY_IS_APPROX(b1, m1.block(r1,c1,1,1));
+  VERIFY_IS_APPROX(m1.row(r1), br1);
+  VERIFY_IS_APPROX(m1.col(c1), bc1);
+  //check operator(), both constant and non-constant, on block()
+  m1.block(r1,c1,r2-r1+1,c2-c1+1) = s1 * m2.block(0, 0, r2-r1+1,c2-c1+1);
+  m1.block(r1,c1,r2-r1+1,c2-c1+1)(r2-r1,c2-c1) = m2.block(0, 0, r2-r1+1,c2-c1+1)(0,0);
+
+  //check minor()
+  CheckMinor<Scalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime> checkminor(m1,r1,c1);
+
+  //check diagonal()
+  VERIFY_IS_APPROX(m1.diagonal(), m1.transpose().diagonal());
+  m2.diagonal() = 2 * m1.diagonal();
+  m2.diagonal()[0] *= 3;
+  VERIFY_IS_APPROX(m2.diagonal()[0], static_cast<Scalar>(6) * m1.diagonal()[0]);
+
+  const int BlockRows = EIGEN_ENUM_MIN(MatrixType::RowsAtCompileTime,2);
+  const int BlockCols = EIGEN_ENUM_MIN(MatrixType::ColsAtCompileTime,5);
+  if (rows>=5 && cols>=8)
+  {
+    // test fixed block() as lvalue
+    m1.template block<BlockRows,BlockCols>(1,1) *= s1;
+    // test operator() on fixed block() both as constant and non-constant
+    m1.template block<BlockRows,BlockCols>(1,1)(0, 3) = m1.template block<2,5>(1,1)(1,2);
+    // check that fixed block() and block() agree
+    Matrix<Scalar,Dynamic,Dynamic> b = m1.template block<BlockRows,BlockCols>(3,3);
+    VERIFY_IS_APPROX(b, m1.block(3,3,BlockRows,BlockCols));
+  }
+
+  if (rows>2)
+  {
+    // test sub vectors
+    VERIFY_IS_APPROX(v1.template start<2>(), v1.block(0,0,2,1));
+    VERIFY_IS_APPROX(v1.template start<2>(), v1.start(2));
+    VERIFY_IS_APPROX(v1.template start<2>(), v1.segment(0,2));
+    VERIFY_IS_APPROX(v1.template start<2>(), v1.template segment<2>(0));
+    int i = rows-2;
+    VERIFY_IS_APPROX(v1.template end<2>(), v1.block(i,0,2,1));
+    VERIFY_IS_APPROX(v1.template end<2>(), v1.end(2));
+    VERIFY_IS_APPROX(v1.template end<2>(), v1.segment(i,2));
+    VERIFY_IS_APPROX(v1.template end<2>(), v1.template segment<2>(i));
+    i = ei_random(0,rows-2);
+    VERIFY_IS_APPROX(v1.segment(i,2), v1.template segment<2>(i));
+  }
+
+  // stress some basic stuffs with block matrices
+  VERIFY(ei_real(ones.col(c1).sum()) == RealScalar(rows));
+  VERIFY(ei_real(ones.row(r1).sum()) == RealScalar(cols));
+
+  VERIFY(ei_real(ones.col(c1).dot(ones.col(c2))) == RealScalar(rows));
+  VERIFY(ei_real(ones.row(r1).dot(ones.row(r2))) == RealScalar(cols));
+}
+
+void test_submatrices()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( submatrices(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST( submatrices(Matrix4d()) );
+    CALL_SUBTEST( submatrices(MatrixXcf(3, 3)) );
+    CALL_SUBTEST( submatrices(MatrixXi(8, 12)) );
+    CALL_SUBTEST( submatrices(MatrixXcd(20, 20)) );
+    CALL_SUBTEST( submatrices(MatrixXf(20, 20)) );
+  }
+}

test/eigen2/sum.cpp

@@ -0,0 +1,86 @@
+// 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 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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"
+
+template<typename MatrixType> void matrixSum(const MatrixType& m)
+{
+  typedef typename MatrixType::Scalar Scalar;
+
+  int rows = m.rows();
+  int cols = m.cols();
+
+  MatrixType m1 = MatrixType::Random(rows, cols);
+
+  VERIFY_IS_MUCH_SMALLER_THAN(MatrixType::Zero(rows, cols).sum(), Scalar(1));
+  VERIFY_IS_APPROX(MatrixType::Ones(rows, cols).sum(), Scalar(float(rows*cols))); // the float() here to shut up excessive MSVC warning about int->complex conversion being lossy
+  Scalar x = Scalar(0);
+  for(int i = 0; i < rows; i++) for(int j = 0; j < cols; j++) x += m1(i,j);
+  VERIFY_IS_APPROX(m1.sum(), x);
+}
+
+template<typename VectorType> void vectorSum(const VectorType& w)
+{
+  typedef typename VectorType::Scalar Scalar;
+  int size = w.size();
+
+  VectorType v = VectorType::Random(size);
+  for(int i = 1; i < size; i++)
+  {
+    Scalar s = Scalar(0);
+    for(int j = 0; j < i; j++) s += v[j];
+    VERIFY_IS_APPROX(s, v.start(i).sum());
+  }
+
+  for(int i = 0; i < size-1; i++)
+  {
+    Scalar s = Scalar(0);
+    for(int j = i; j < size; j++) s += v[j];
+    VERIFY_IS_APPROX(s, v.end(size-i).sum());
+  }
+
+  for(int i = 0; i < size/2; i++)
+  {
+    Scalar s = Scalar(0);
+    for(int j = i; j < size-i; j++) s += v[j];
+    VERIFY_IS_APPROX(s, v.segment(i, size-2*i).sum());
+  }
+}
+
+void test_sum()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( matrixSum(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST( matrixSum(Matrix2f()) );
+    CALL_SUBTEST( matrixSum(Matrix4d()) );
+    CALL_SUBTEST( matrixSum(MatrixXcf(3, 3)) );
+    CALL_SUBTEST( matrixSum(MatrixXf(8, 12)) );
+    CALL_SUBTEST( matrixSum(MatrixXi(8, 12)) );
+  }
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( vectorSum(VectorXf(5)) );
+    CALL_SUBTEST( vectorSum(VectorXd(10)) );
+    CALL_SUBTEST( vectorSum(VectorXf(33)) );
+  }
+}

test/eigen2/svd.cpp

@@ -0,0 +1,102 @@
+// 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>
+//
+// 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/SVD>
+
+template<typename MatrixType> void svd(const MatrixType& m)
+{
+  /* this test covers the following files:
+     SVD.h
+  */
+  int rows = m.rows();
+  int cols = m.cols();
+
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  MatrixType a = MatrixType::Random(rows,cols);
+  Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> b =
+    Matrix<Scalar, MatrixType::RowsAtCompileTime, 1>::Random(rows,1);
+  Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> x(cols,1), x2(cols,1);
+
+  RealScalar largerEps = test_precision<RealScalar>();
+  if (ei_is_same_type<RealScalar,float>::ret)
+    largerEps = 1e-3f;
+
+  {
+    SVD<MatrixType> svd(a);
+    MatrixType sigma = MatrixType::Zero(rows,cols);
+    MatrixType matU  = MatrixType::Zero(rows,rows);
+    sigma.block(0,0,cols,cols) = svd.singularValues().asDiagonal();
+    matU.block(0,0,rows,cols) = svd.matrixU();
+    VERIFY_IS_APPROX(a, matU * sigma * svd.matrixV().transpose());
+  }
+
+
+  if (rows==cols)
+  {
+    if (ei_is_same_type<RealScalar,float>::ret)
+    {
+      MatrixType a1 = MatrixType::Random(rows,cols);
+      a += a * a.adjoint() + a1 * a1.adjoint();
+    }
+    SVD<MatrixType> svd(a);
+    svd.solve(b, &x);
+    VERIFY_IS_APPROX(a * x,b);
+  }
+
+
+  if(rows==cols)
+  {
+    SVD<MatrixType> svd(a);
+    MatrixType unitary, positive;
+    svd.computeUnitaryPositive(&unitary, &positive);
+    VERIFY_IS_APPROX(unitary * unitary.adjoint(), MatrixType::Identity(unitary.rows(),unitary.rows()));
+    VERIFY_IS_APPROX(positive, positive.adjoint());
+    for(int i = 0; i < rows; i++) VERIFY(positive.diagonal()[i] >= 0); // cheap necessary (not sufficient) condition for positivity
+    VERIFY_IS_APPROX(unitary*positive, a);
+
+    svd.computePositiveUnitary(&positive, &unitary);
+    VERIFY_IS_APPROX(unitary * unitary.adjoint(), MatrixType::Identity(unitary.rows(),unitary.rows()));
+    VERIFY_IS_APPROX(positive, positive.adjoint());
+    for(int i = 0; i < rows; i++) VERIFY(positive.diagonal()[i] >= 0); // cheap necessary (not sufficient) condition for positivity
+    VERIFY_IS_APPROX(positive*unitary, a);
+  }
+}
+
+void test_svd()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( svd(Matrix3f()) );
+    CALL_SUBTEST( svd(Matrix4d()) );
+    CALL_SUBTEST( svd(MatrixXf(7,7)) );
+    CALL_SUBTEST( svd(MatrixXd(14,7)) );
+    // complex are not implemented yet
+//     CALL_SUBTEST( svd(MatrixXcd(6,6)) );
+//     CALL_SUBTEST( svd(MatrixXcf(3,3)) );
+    SVD<MatrixXf> s;
+    MatrixXf m = MatrixXf::Random(10,1);
+    s.compute(m);
+  }
+}

test/eigen2/swap.cpp

@@ -0,0 +1,98 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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/>.
+
+#define EIGEN_NO_STATIC_ASSERT
+#include "main.h"
+
+template<typename T>
+struct other_matrix_type
+{
+  typedef int type;
+};
+
+template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
+struct other_matrix_type<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
+{
+  typedef Matrix<_Scalar, _Rows, _Cols, _Options^RowMajor, _MaxRows, _MaxCols> type;
+};
+
+template<typename MatrixType> void swap(const MatrixType& m)
+{
+  typedef typename other_matrix_type<MatrixType>::type OtherMatrixType;
+  typedef typename MatrixType::Scalar Scalar;
+
+  ei_assert((!ei_is_same_type<MatrixType,OtherMatrixType>::ret));
+  int rows = m.rows();
+  int cols = m.cols();
+  
+  // construct 3 matrix guaranteed to be distinct
+  MatrixType m1 = MatrixType::Random(rows,cols);
+  MatrixType m2 = MatrixType::Random(rows,cols) + Scalar(100) * MatrixType::Identity(rows,cols);
+  OtherMatrixType m3 = OtherMatrixType::Random(rows,cols) + Scalar(200) * OtherMatrixType::Identity(rows,cols);
+  
+  MatrixType m1_copy = m1;
+  MatrixType m2_copy = m2;
+  OtherMatrixType m3_copy = m3;
+  
+  // test swapping 2 matrices of same type
+  m1.swap(m2);
+  VERIFY_IS_APPROX(m1,m2_copy);
+  VERIFY_IS_APPROX(m2,m1_copy);
+  m1 = m1_copy;
+  m2 = m2_copy;
+  
+  // test swapping 2 matrices of different types
+  m1.swap(m3);
+  VERIFY_IS_APPROX(m1,m3_copy);
+  VERIFY_IS_APPROX(m3,m1_copy);
+  m1 = m1_copy;
+  m3 = m3_copy;
+  
+  // test swapping matrix with expression
+  m1.swap(m2.block(0,0,rows,cols));
+  VERIFY_IS_APPROX(m1,m2_copy);
+  VERIFY_IS_APPROX(m2,m1_copy);
+  m1 = m1_copy;
+  m2 = m2_copy;
+
+  // test swapping two expressions of different types
+  m1.transpose().swap(m3.transpose());
+  VERIFY_IS_APPROX(m1,m3_copy);
+  VERIFY_IS_APPROX(m3,m1_copy);
+  m1 = m1_copy;
+  m3 = m3_copy;
+  
+  // test assertion on mismatching size -- matrix case
+  VERIFY_RAISES_ASSERT(m1.swap(m1.row(0)));
+  // test assertion on mismatching size -- xpr case
+  VERIFY_RAISES_ASSERT(m1.row(0).swap(m1));
+}
+
+void test_swap()
+{
+  CALL_SUBTEST( swap(Matrix3f()) ); // fixed size, no vectorization 
+  CALL_SUBTEST( swap(Matrix4d()) ); // fixed size, possible vectorization 
+  CALL_SUBTEST( swap(MatrixXd(3,3)) ); // dyn size, no vectorization 
+  CALL_SUBTEST( swap(MatrixXf(30,30)) ); // dyn size, possible vectorization 
+}

test/eigen2/testsuite.cmake

@@ -0,0 +1,197 @@
+
+####################################################################
+#
+# Usage:
+#  - create a new folder, let's call it cdash
+#  - in that folder, do:
+#    ctest -S path/to/eigen2/test/testsuite.cmake[,option1=value1[,option2=value2]]
+#
+# Options:
+#  - EIGEN_CXX: compiler, eg.: g++-4.2
+#      default: default c++ compiler
+#  - EIGEN_SITE: eg, INRIA-Bdx_pc-gael, or the name of the contributor, etc.
+#      default: hostname
+#  - EIGEN_BUILD_STRING: a string which identify the system/compiler. It should be formed like that:
+#        <OS_name>-<OS_version>-<arch>-<compiler-version>
+#      with:
+#        <OS_name> = opensuse, debian, osx, windows, cygwin, freebsd, solaris, etc.
+#        <OS_version> = 11.1, XP, vista, leopard, etc.
+#        <arch> = i386, x86_64, ia64, powerpc, etc.
+#        <compiler-version> = gcc-4.3.2, icc-11.0, MSVC-2008, etc.
+#  - EIGEN_EXPLICIT_VECTORIZATION: novec, SSE2, Altivec
+#       default: SSE2 for x86_64 systems, novec otherwise
+#       Its value is automatically appended to EIGEN_BUILD_STRING
+#  - EIGEN_CMAKE_DIR: path to cmake executable
+#  - EIGEN_MODE: dashboard model, can be Experimental, Nightly, or Continuous
+#      default: Nightly
+#  - EIGEN_WORK_DIR: directory used to download the source files and make the builds
+#      default: folder which contains this script
+#  - EIGEN_CMAKE_ARGS: additional arguments passed to cmake
+#  - CTEST_SOURCE_DIRECTORY: path to eigen's src (use a new and empty folder, not the one you are working on)
+#      default: <EIGEN_WORK_DIR>/src
+#  - CTEST_BINARY_DIRECTORY: build directory
+#      default: <EIGEN_WORK_DIR>/nightly-<EIGEN_CXX>
+#
+# Here is an example running several compilers on a linux system:
+# #!/bin/bash
+# ARCH=`uname -m`
+# SITE=`hostname`
+# VERSION=opensuse-11.1
+# WORK_DIR=/home/gael/Coding/eigen2/cdash
+# # get the last version of the script
+# wget http://bitbucket.org/eigen/eigen/raw/tip/test/testsuite.cmake -o $WORK_DIR/testsuite.cmake
+# COMMON="ctest -S $WORK_DIR/testsuite.cmake,EIGEN_WORK_DIR=$WORK_DIR,EIGEN_SITE=$SITE,EIGEN_MODE=$1,EIGEN_BUILD_STRING=$OS_VERSION-$ARCH"
+# $COMMON-gcc-3.4.6,EIGEN_CXX=g++-3.4
+# $COMMON-gcc-4.0.1,EIGEN_CXX=g++-4.0.1
+# $COMMON-gcc-4.3.2,EIGEN_CXX=g++-4.3,EIGEN_EXPLICIT_VECTORIZATION=novec
+# $COMMON-gcc-4.3.2,EIGEN_CXX=g++-4.3,EIGEN_EXPLICIT_VECTORIZATION=SSE2
+# $COMMON-icc-11.0,EIGEN_CXX=icpc
+#
+####################################################################
+
+# process the arguments
+
+set(ARGLIST ${CTEST_SCRIPT_ARG})
+while(${ARGLIST} MATCHES  ".+.*")
+
+  # pick first
+  string(REGEX MATCH "([^,]*)(,.*)?" DUMMY ${ARGLIST})
+  SET(TOP ${CMAKE_MATCH_1})
+
+  # remove first
+  string(REGEX MATCHALL "[^,]*,(.*)" DUMMY ${ARGLIST})
+  SET(ARGLIST ${CMAKE_MATCH_1})
+
+  # decompose as a pair key=value
+  string(REGEX MATCH "([^=]*)(=.*)?" DUMMY ${TOP})
+  SET(KEY ${CMAKE_MATCH_1})
+
+  string(REGEX MATCH "[^=]*=(.*)" DUMMY ${TOP})
+  SET(VALUE ${CMAKE_MATCH_1})
+
+  # set the variable to the specified value
+  if(VALUE)
+    SET(${KEY} ${VALUE})
+  else(VALUE)
+    SET(${KEY} ON)
+  endif(VALUE)
+
+endwhile(${ARGLIST} MATCHES ".+.*")
+
+####################################################################
+# Automatically set some user variables if they have not been defined manually
+####################################################################
+cmake_minimum_required(VERSION 2.6 FATAL_ERROR)
+
+if(NOT EIGEN_SITE)
+  site_name(EIGEN_SITE)
+endif(NOT EIGEN_SITE)
+
+if(NOT EIGEN_CMAKE_DIR)
+  SET(EIGEN_CMAKE_DIR "")
+endif(NOT EIGEN_CMAKE_DIR)
+
+if(NOT EIGEN_BUILD_STRING)
+
+  # let's try to find all information we need to make the build string ourself
+
+  # OS
+  build_name(EIGEN_OS_VERSION)
+
+  # arch
+  set(EIGEN_ARCH ${CMAKE_SYSTEM_PROCESSOR})
+  if(WIN32)
+    set(EIGEN_ARCH $ENV{PROCESSOR_ARCHITECTURE})
+  else(WIN32)
+    execute_process(COMMAND uname -m OUTPUT_VARIABLE EIGEN_ARCH OUTPUT_STRIP_TRAILING_WHITESPACE)
+  endif(WIN32)
+
+  set(EIGEN_BUILD_STRING ${EIGEN_OS_VERSION}${EIGEN_ARCH}-${EIGEN_CXX})
+
+endif(NOT EIGEN_BUILD_STRING)
+
+if(DEFINED EIGEN_EXPLICIT_VECTORIZATION)
+  set(EIGEN_BUILD_STRING ${EIGEN_BUILD_STRING}-${EIGEN_EXPLICIT_VECTORIZATION})
+endif(DEFINED EIGEN_EXPLICIT_VECTORIZATION)
+
+if(NOT EIGEN_WORK_DIR)
+  set(EIGEN_WORK_DIR ${CTEST_SCRIPT_DIRECTORY})
+endif(NOT EIGEN_WORK_DIR)
+
+if(NOT CTEST_SOURCE_DIRECTORY)
+  SET (CTEST_SOURCE_DIRECTORY "${EIGEN_WORK_DIR}/src")
+endif(NOT CTEST_SOURCE_DIRECTORY)
+
+if(NOT CTEST_BINARY_DIRECTORY)
+  SET (CTEST_BINARY_DIRECTORY "${EIGEN_WORK_DIR}/nightly_${EIGEN_CXX}")
+endif(NOT CTEST_BINARY_DIRECTORY)
+
+if(NOT EIGEN_MODE)
+  set(EIGEN_MODE Nightly)
+endif(NOT EIGEN_MODE)
+
+## mandatory variables (the default should be ok in most cases):
+
+SET (CTEST_CVS_COMMAND "hg")
+SET (CTEST_CVS_CHECKOUT "${CTEST_CVS_COMMAND} clone -r 2.0 http://bitbucket.org/eigen/eigen \"${CTEST_SOURCE_DIRECTORY}\"")
+
+# which ctest command to use for running the dashboard
+SET (CTEST_COMMAND "${EIGEN_CMAKE_DIR}ctest -D ${EIGEN_MODE}")
+
+# what cmake command to use for configuring this dashboard
+SET (CTEST_CMAKE_COMMAND "${EIGEN_CMAKE_DIR}cmake -DEIGEN_BUILD_TESTS=on ")
+
+####################################################################
+# The values in this section are optional you can either
+# have them or leave them commented out
+####################################################################
+
+# this make sure we get consistent outputs
+SET($ENV{LC_MESSAGES} "en_EN")
+
+# should ctest wipe the binary tree before running
+SET(CTEST_START_WITH_EMPTY_BINARY_DIRECTORY TRUE)
+SET(CTEST_BACKUP_AND_RESTORE TRUE)
+
+# this is the initial cache to use for the binary tree, be careful to escape
+# any quotes inside of this string if you use it
+if(WIN32 AND NOT UNIX)
+  #message(SEND_ERROR "win32")
+  set(CTEST_CMAKE_COMMAND "${CTEST_CMAKE_COMMAND} -G \"NMake Makefiles\" -DCMAKE_MAKE_PROGRAM=nmake")
+  SET (CTEST_INITIAL_CACHE "
+    MAKECOMMAND:STRING=nmake -i
+    CMAKE_MAKE_PROGRAM:FILEPATH=nmake
+    CMAKE_GENERATOR:INTERNAL=NMake Makefiles
+    BUILDNAME:STRING=${EIGEN_BUILD_STRING}
+    SITE:STRING=${EIGEN_SITE}
+  ")
+else(WIN32 AND NOT UNIX)
+  SET (CTEST_INITIAL_CACHE "
+    BUILDNAME:STRING=${EIGEN_BUILD_STRING}
+    SITE:STRING=${EIGEN_SITE}
+  ")
+endif(WIN32 AND NOT UNIX)
+
+# set any extra environment variables to use during the execution of the script here:
+
+if(EIGEN_CXX)
+  set(CTEST_ENVIRONMENT "CXX=${EIGEN_CXX}")
+endif(EIGEN_CXX)
+
+if(DEFINED EIGEN_EXPLICIT_VECTORIZATION)
+  if(EIGEN_EXPLICIT_VECTORIZATION MATCHES SSE2)
+    set(CTEST_CMAKE_COMMAND "${CTEST_CMAKE_COMMAND} -DEIGEN_TEST_SSE2=ON")
+  elseif(EIGEN_EXPLICIT_VECTORIZATION MATCHES SSE3)
+    set(CTEST_CMAKE_COMMAND "${CTEST_CMAKE_COMMAND} -DEIGEN_TEST_SSE2=ON -DEIGEN_TEST_SSE3=ON")
+  elseif(EIGEN_EXPLICIT_VECTORIZATION MATCHES Altivec)
+    set(CTEST_CMAKE_COMMAND "${CTEST_CMAKE_COMMAND} -DEIGEN_TEST_ALTIVEC=ON")
+  elseif(EIGEN_EXPLICIT_VECTORIZATION MATCHES novec)
+    set(CTEST_CMAKE_COMMAND "${CTEST_CMAKE_COMMAND} -DEIGEN_TEST_NO_EXPLICIT_VECTORIZATION=ON")
+  else(EIGEN_EXPLICIT_VECTORIZATION MATCHES SSE2)
+    message(FATAL_ERROR "Invalid value for EIGEN_EXPLICIT_VECTORIZATION (${EIGEN_EXPLICIT_VECTORIZATION}), must be: novec, SSE2, SSE3, Altivec")
+  endif(EIGEN_EXPLICIT_VECTORIZATION MATCHES SSE2)
+endif(DEFINED EIGEN_EXPLICIT_VECTORIZATION)
+
+if(DEFINED EIGEN_CMAKE_ARGS)
+  set(CTEST_CMAKE_COMMAND "${CTEST_CMAKE_COMMAND} ${EIGEN_CMAKE_ARGS}")
+endif(DEFINED EIGEN_CMAKE_ARGS)

test/eigen2/triangular.cpp

@@ -0,0 +1,138 @@
+// 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 <gael.guennebaud@gmail.com>
+//
+// 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"
+
+template<typename MatrixType> void triangular(const MatrixType& m)
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+
+  RealScalar largerEps = 10*test_precision<RealScalar>();
+
+  int rows = m.rows();
+  int cols = m.cols();
+
+  MatrixType m1 = MatrixType::Random(rows, cols),
+             m2 = MatrixType::Random(rows, cols),
+             m3(rows, cols),
+             m4(rows, cols),
+             r1(rows, cols),
+             r2(rows, cols),
+             mzero = MatrixType::Zero(rows, cols),
+             mones = MatrixType::Ones(rows, cols),
+             identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+                              ::Identity(rows, rows),
+             square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+                              ::Random(rows, rows);
+  VectorType v1 = VectorType::Random(rows),
+             v2 = VectorType::Random(rows),
+             vzero = VectorType::Zero(rows);
+
+  MatrixType m1up = m1.template part<Eigen::UpperTriangular>();
+  MatrixType m2up = m2.template part<Eigen::UpperTriangular>();
+
+  if (rows*cols>1)
+  {
+    VERIFY(m1up.isUpperTriangular());
+    VERIFY(m2up.transpose().isLowerTriangular());
+    VERIFY(!m2.isLowerTriangular());
+  }
+
+//   VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2);
+
+  // test overloaded operator+=
+  r1.setZero();
+  r2.setZero();
+  r1.template part<Eigen::UpperTriangular>() +=  m1;
+  r2 += m1up;
+  VERIFY_IS_APPROX(r1,r2);
+
+  // test overloaded operator=
+  m1.setZero();
+  m1.template part<Eigen::UpperTriangular>() = (m2.transpose() * m2).lazy();
+  m3 = m2.transpose() * m2;
+  VERIFY_IS_APPROX(m3.template part<Eigen::LowerTriangular>().transpose(), m1);
+
+  // test overloaded operator=
+  m1.setZero();
+  m1.template part<Eigen::LowerTriangular>() = (m2.transpose() * m2).lazy();
+  VERIFY_IS_APPROX(m3.template part<Eigen::LowerTriangular>(), m1);
+
+  VERIFY_IS_APPROX(m3.template part<Diagonal>(), m3.diagonal().asDiagonal());
+
+  m1 = MatrixType::Random(rows, cols);
+  for (int i=0; i<rows; ++i)
+    while (ei_abs2(m1(i,i))<1e-3) m1(i,i) = ei_random<Scalar>();
+
+  Transpose<MatrixType> trm4(m4);
+  // test back and forward subsitution
+  m3 = m1.template part<Eigen::LowerTriangular>();
+  VERIFY(m3.template marked<Eigen::LowerTriangular>().solveTriangular(m3).cwise().abs().isIdentity(test_precision<RealScalar>()));
+  VERIFY(m3.transpose().template marked<Eigen::UpperTriangular>()
+    .solveTriangular(m3.transpose()).cwise().abs().isIdentity(test_precision<RealScalar>()));
+  // check M * inv(L) using in place API
+  m4 = m3;
+  m3.transpose().template marked<Eigen::UpperTriangular>().solveTriangularInPlace(trm4);
+  VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
+
+  m3 = m1.template part<Eigen::UpperTriangular>();
+  VERIFY(m3.template marked<Eigen::UpperTriangular>().solveTriangular(m3).cwise().abs().isIdentity(test_precision<RealScalar>()));
+  VERIFY(m3.transpose().template marked<Eigen::LowerTriangular>()
+    .solveTriangular(m3.transpose()).cwise().abs().isIdentity(test_precision<RealScalar>()));
+  // check M * inv(U) using in place API
+  m4 = m3;
+  m3.transpose().template marked<Eigen::LowerTriangular>().solveTriangularInPlace(trm4);
+  VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
+
+  m3 = m1.template part<Eigen::UpperTriangular>();
+  VERIFY(m2.isApprox(m3 * (m3.template marked<Eigen::UpperTriangular>().solveTriangular(m2)), largerEps));
+  m3 = m1.template part<Eigen::LowerTriangular>();
+  VERIFY(m2.isApprox(m3 * (m3.template marked<Eigen::LowerTriangular>().solveTriangular(m2)), largerEps));
+
+  VERIFY((m1.template part<Eigen::UpperTriangular>() * m2.template part<Eigen::UpperTriangular>()).isUpperTriangular());
+
+  // test swap
+  m1.setOnes();
+  m2.setZero();
+  m2.template part<Eigen::UpperTriangular>().swap(m1);
+  m3.setZero();
+  m3.template part<Eigen::UpperTriangular>().setOnes();
+  VERIFY_IS_APPROX(m2,m3);
+
+}
+
+void test_triangular()
+{
+  for(int i = 0; i < g_repeat ; i++) {
+    CALL_SUBTEST( triangular(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST( triangular(Matrix<float, 2, 2>()) );
+    CALL_SUBTEST( triangular(Matrix3d()) );
+    CALL_SUBTEST( triangular(MatrixXcf(4, 4)) );
+    CALL_SUBTEST( triangular(Matrix<std::complex<float>,8, 8>()) );
+    CALL_SUBTEST( triangular(MatrixXd(17,17)) );
+    CALL_SUBTEST( triangular(Matrix<float,Dynamic,Dynamic,RowMajor>(5, 5)) );
+  }
+}

test/eigen2/unalignedassert.cpp

@@ -0,0 +1,131 @@
+// 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 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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"
+
+struct Good1
+{
+  MatrixXd m; // good: m will allocate its own array, taking care of alignment.
+  Good1() : m(20,20) {}
+};
+
+struct Good2
+{
+  Matrix3d m; // good: m's size isn't a multiple of 16 bytes, so m doesn't have to be aligned
+};
+
+struct Good3
+{
+  Vector2f m; // good: same reason
+};
+
+struct Bad4
+{
+  Vector2d m; // bad: sizeof(m)%16==0 so alignment is required
+};
+
+struct Bad5
+{
+  Matrix<float, 2, 6> m; // bad: same reason
+};
+
+struct Bad6
+{
+  Matrix<double, 3, 4> m; // bad: same reason
+};
+
+struct Good7
+{
+  EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+  Vector2d m;
+  float f; // make the struct have sizeof%16!=0 to make it a little more tricky when we allow an array of 2 such objects
+};
+
+struct Good8
+{
+  EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+  float f; // try the f at first -- the EIGEN_ALIGN_128 attribute of m should make that still work
+  Matrix4f m;
+};
+
+struct Good9
+{
+  Matrix<float,2,2,DontAlign> m; // good: no alignment requested
+  float f;
+};
+
+template<bool Align> struct Depends
+{
+  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(Align)
+  Vector2d m;
+  float f;
+};
+
+template<typename T>
+void check_unalignedassert_good()
+{
+  T *x, *y;
+  x = new T;
+  delete x;
+  y = new T[2];
+  delete[] y;
+}
+
+#if EIGEN_ARCH_WANTS_ALIGNMENT
+template<typename T>
+void check_unalignedassert_bad()
+{
+  float buf[sizeof(T)+16];
+  float *unaligned = buf;
+  while((reinterpret_cast<std::size_t>(unaligned)&0xf)==0) ++unaligned; // make sure unaligned is really unaligned
+  T *x = ::new(static_cast<void*>(unaligned)) T;
+  x->~T();
+}
+#endif
+
+void unalignedassert()
+{
+  check_unalignedassert_good<Good1>();
+  check_unalignedassert_good<Good2>();
+  check_unalignedassert_good<Good3>();
+#if EIGEN_ARCH_WANTS_ALIGNMENT
+  VERIFY_RAISES_ASSERT(check_unalignedassert_bad<Bad4>());
+  VERIFY_RAISES_ASSERT(check_unalignedassert_bad<Bad5>());
+  VERIFY_RAISES_ASSERT(check_unalignedassert_bad<Bad6>());
+#endif
+
+  check_unalignedassert_good<Good7>();
+  check_unalignedassert_good<Good8>();
+  check_unalignedassert_good<Good9>();
+  check_unalignedassert_good<Depends<true> >();
+
+#if EIGEN_ARCH_WANTS_ALIGNMENT
+  VERIFY_RAISES_ASSERT(check_unalignedassert_bad<Depends<false> >());
+#endif
+}
+
+void test_unalignedassert()
+{
+  CALL_SUBTEST(unalignedassert());
+}

test/eigen2/vectorization_logic.cpp

@@ -0,0 +1,116 @@
+// 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>
+//
+// 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 <typeinfo>
+
+template<typename Dst, typename Src>
+bool test_assign(const Dst&, const Src&, int vectorization, int unrolling)
+{
+  return ei_assign_traits<Dst,Src>::Vectorization==vectorization
+    && ei_assign_traits<Dst,Src>::Unrolling==unrolling;
+}
+
+template<typename Xpr>
+bool test_sum(const Xpr&, int vectorization, int unrolling)
+{
+  return ei_sum_traits<Xpr>::Vectorization==vectorization
+    && ei_sum_traits<Xpr>::Unrolling==unrolling;
+}
+
+void test_vectorization_logic()
+{
+
+#ifdef EIGEN_VECTORIZE
+
+#ifdef  EIGEN_DEFAULT_TO_ROW_MAJOR
+  VERIFY(test_assign(Vector4f(),Vector4f(),
+    LinearVectorization,CompleteUnrolling));
+  VERIFY(test_assign(Vector4f(),Vector4f()+Vector4f(),
+    LinearVectorization,CompleteUnrolling));
+  VERIFY(test_assign(Vector4f(),Vector4f().cwise() * Vector4f(),
+    LinearVectorization,CompleteUnrolling));
+#else
+  VERIFY(test_assign(Vector4f(),Vector4f(),
+    InnerVectorization,CompleteUnrolling));
+  VERIFY(test_assign(Vector4f(),Vector4f()+Vector4f(),
+    InnerVectorization,CompleteUnrolling));
+  VERIFY(test_assign(Vector4f(),Vector4f().cwise() * Vector4f(),
+    InnerVectorization,CompleteUnrolling));
+#endif
+
+  VERIFY(test_assign(Matrix4f(),Matrix4f(),
+    InnerVectorization,CompleteUnrolling));
+  VERIFY(test_assign(Matrix4f(),Matrix4f()+Matrix4f(),
+    InnerVectorization,CompleteUnrolling));
+  VERIFY(test_assign(Matrix4f(),Matrix4f().cwise() * Matrix4f(),
+    InnerVectorization,CompleteUnrolling));
+
+  VERIFY(test_assign(Matrix<float,16,16>(),Matrix<float,16,16>()+Matrix<float,16,16>(),
+    InnerVectorization,InnerUnrolling));
+
+  VERIFY(test_assign(Matrix<float,16,16,DontAlign>(),Matrix<float,16,16>()+Matrix<float,16,16>(),
+    NoVectorization,InnerUnrolling));
+
+  VERIFY(test_assign(Matrix<float,6,2>(),Matrix<float,6,2>().cwise() / Matrix<float,6,2>(),
+    LinearVectorization,CompleteUnrolling));
+
+  VERIFY(test_assign(Matrix<float,17,17>(),Matrix<float,17,17>()+Matrix<float,17,17>(),
+    NoVectorization,InnerUnrolling));
+
+  VERIFY(test_assign(Matrix<float,4,4>(),Matrix<float,17,17>().block<4,4>(2,3)+Matrix<float,17,17>().block<4,4>(10,4),
+    NoVectorization,CompleteUnrolling));
+
+  VERIFY(test_assign(MatrixXf(10,10),MatrixXf(20,20).block(10,10,2,3),
+    SliceVectorization,NoUnrolling));
+
+  VERIFY(test_assign(VectorXf(10),VectorXf(10)+VectorXf(10),
+    LinearVectorization,NoUnrolling));
+
+  VERIFY(test_sum(VectorXf(10),
+    LinearVectorization,NoUnrolling));
+
+  VERIFY(test_sum(Matrix<float,5,2>(),
+    NoVectorization,CompleteUnrolling));
+  
+  VERIFY(test_sum(Matrix<float,6,2>(),
+    LinearVectorization,CompleteUnrolling));
+
+  VERIFY(test_sum(Matrix<float,16,16>(),
+    LinearVectorization,NoUnrolling));
+
+  VERIFY(test_sum(Matrix<float,16,16>().block<4,4>(1,2),
+    NoVectorization,CompleteUnrolling));
+
+#ifndef EIGEN_DEFAULT_TO_ROW_MAJOR
+  VERIFY(test_sum(Matrix<float,16,16>().block<8,1>(1,2),
+    LinearVectorization,CompleteUnrolling));
+#endif
+
+  VERIFY(test_sum(Matrix<double,7,3>(),
+    NoVectorization,CompleteUnrolling));
+
+#endif // EIGEN_VECTORIZE
+
+}

test/eigen2/visitor.cpp

@@ -0,0 +1,131 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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"
+
+template<typename MatrixType> void matrixVisitor(const MatrixType& p)
+{
+  typedef typename MatrixType::Scalar Scalar;
+
+  int rows = p.rows();
+  int cols = p.cols();
+
+  // construct a random matrix where all coefficients are different
+  MatrixType m;
+  m = MatrixType::Random(rows, cols);
+  for(int i = 0; i < m.size(); i++)
+    for(int i2 = 0; i2 < i; i2++)
+      while(m(i) == m(i2)) // yes, ==
+        m(i) = ei_random<Scalar>();
+  
+  Scalar minc = Scalar(1000), maxc = Scalar(-1000);
+  int minrow=0,mincol=0,maxrow=0,maxcol=0;
+  for(int j = 0; j < cols; j++)
+  for(int i = 0; i < rows; i++)
+  {
+    if(m(i,j) < minc)
+    {
+      minc = m(i,j);
+      minrow = i;
+      mincol = j;
+    }
+    if(m(i,j) > maxc)
+    {
+      maxc = m(i,j);
+      maxrow = i;
+      maxcol = j;
+    }
+  }
+  int eigen_minrow, eigen_mincol, eigen_maxrow, eigen_maxcol;
+  Scalar eigen_minc, eigen_maxc;
+  eigen_minc = m.minCoeff(&eigen_minrow,&eigen_mincol);
+  eigen_maxc = m.maxCoeff(&eigen_maxrow,&eigen_maxcol);
+  VERIFY(minrow == eigen_minrow);
+  VERIFY(maxrow == eigen_maxrow);
+  VERIFY(mincol == eigen_mincol);
+  VERIFY(maxcol == eigen_maxcol);
+  VERIFY_IS_APPROX(minc, eigen_minc);
+  VERIFY_IS_APPROX(maxc, eigen_maxc);
+  VERIFY_IS_APPROX(minc, m.minCoeff());
+  VERIFY_IS_APPROX(maxc, m.maxCoeff());
+}
+
+template<typename VectorType> void vectorVisitor(const VectorType& w)
+{
+  typedef typename VectorType::Scalar Scalar;
+
+  int size = w.size();
+
+  // construct a random vector where all coefficients are different
+  VectorType v;
+  v = VectorType::Random(size);
+  for(int i = 0; i < size; i++)
+    for(int i2 = 0; i2 < i; i2++)
+      while(v(i) == v(i2)) // yes, ==
+        v(i) = ei_random<Scalar>();
+  
+  Scalar minc = Scalar(1000), maxc = Scalar(-1000);
+  int minidx=0,maxidx=0;
+  for(int i = 0; i < size; i++)
+  {
+    if(v(i) < minc)
+    {
+      minc = v(i);
+      minidx = i;
+    }
+    if(v(i) > maxc)
+    {
+      maxc = v(i);
+      maxidx = i;
+    }
+  }
+  int eigen_minidx, eigen_maxidx;
+  Scalar eigen_minc, eigen_maxc;
+  eigen_minc = v.minCoeff(&eigen_minidx);
+  eigen_maxc = v.maxCoeff(&eigen_maxidx);
+  VERIFY(minidx == eigen_minidx);
+  VERIFY(maxidx == eigen_maxidx);
+  VERIFY_IS_APPROX(minc, eigen_minc);
+  VERIFY_IS_APPROX(maxc, eigen_maxc);
+  VERIFY_IS_APPROX(minc, v.minCoeff());
+  VERIFY_IS_APPROX(maxc, v.maxCoeff());
+}
+
+void test_visitor()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( matrixVisitor(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST( matrixVisitor(Matrix2f()) );
+    CALL_SUBTEST( matrixVisitor(Matrix4d()) );
+    CALL_SUBTEST( matrixVisitor(MatrixXd(8, 12)) );
+    CALL_SUBTEST( matrixVisitor(Matrix<double,Dynamic,Dynamic,RowMajor>(20, 20)) );
+    CALL_SUBTEST( matrixVisitor(MatrixXi(8, 12)) );
+  }
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( vectorVisitor(Vector4f()) );
+    CALL_SUBTEST( vectorVisitor(VectorXd(10)) );
+    CALL_SUBTEST( vectorVisitor(RowVectorXd(10)) );
+    CALL_SUBTEST( vectorVisitor(VectorXf(33)) );
+  }
+}