* add VERIFY_IS_EQUAL, should compile faster and it's natural when no arithmetic is involved.

* rename 'submatrices' test to 'block'
* add block-inside-of-block tests
* remove old cruft
* split diagonal() tests into separate file

7 files changed, 200 insertions, 68 deletions

diff --git a/Eigen/src/Core/Assign.h b/Eigen/src/Core/Assign.h
index 99d497449..38c68778f 100644
--- a/Eigen/src/Core/Assign.h
+++ b/Eigen/src/Core/Assign.h
@@ -2,7 +2,7 @@
 // for linear algebra.
 //
 // Copyright (C) 2007 Michael Olbrich <michael.olbrich@gmx.net>
-// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2006-2010 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
diff --git a/Eigen/src/Core/Block.h b/Eigen/src/Core/Block.h
index d3c4dfa99..e6cfb0859 100644
--- a/Eigen/src/Core/Block.h
+++ b/Eigen/src/Core/Block.h
@@ -2,7 +2,7 @@
 // for linear algebra.
 //
 // Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
-// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2006-2010 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
diff --git a/Eigen/src/Core/Matrix.h b/Eigen/src/Core/Matrix.h
index eae2711f4..dc1be9ea2 100644
--- a/Eigen/src/Core/Matrix.h
+++ b/Eigen/src/Core/Matrix.h
@@ -1,7 +1,7 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
-// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
 // Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr>
 //
 // Eigen is free software; you can redistribute it and/or
diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
index b0da2a1d8..c6b359ce9 100644
--- a/test/CMakeLists.txt
+++ b/test/CMakeLists.txt
@@ -104,12 +104,13 @@ ei_add_test(cwiseop)
 ei_add_test(unalignedcount)
 ei_add_test(redux)
 ei_add_test(visitor)
+ei_add_test(block)
 ei_add_test(product_small)
 ei_add_test(product_large)
 ei_add_test(product_extra)
 ei_add_test(diagonalmatrices)
 ei_add_test(adjoint)
-ei_add_test(submatrices)
+ei_add_test(diagonal)
 ei_add_test(miscmatrices)
 ei_add_test(commainitializer)
 ei_add_test(smallvectors)
diff --git a/test/submatrices.cpp b/test/block.cpp
index e71c28ceb..c180afb75 100644
--- a/test/submatrices.cpp
+++ b/test/block.cpp
@@ -1,7 +1,7 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
-// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2006-2010 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
@@ -51,16 +51,18 @@ template<typename Scalar> struct CheckMinor<Scalar,1,1>
     CheckMinor(MatrixType&, int, int) {}
 };
 
-template<typename MatrixType> void submatrices(const MatrixType& m)
+template<typename MatrixType> void block(const MatrixType& m)
 {
   /* this test covers the following files:
-     Row.h Column.h Block.h Minor.h DiagonalCoeffs.h
+     Row.h Column.h Block.h Minor.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;
-  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
+  typedef Matrix<Scalar, Dynamic, Dynamic> DynamicMatrixType;
+  typedef Matrix<Scalar, Dynamic, 1> DynamicVectorType;
+  
   int rows = m.rows();
   int cols = m.cols();
 
@@ -69,8 +71,6 @@ template<typename MatrixType> void submatrices(const MatrixType& m)
              m3(rows, cols),
              mzero = MatrixType::Zero(rows, cols),
              ones = MatrixType::Ones(rows, cols);
-  SquareMatrixType identity = SquareMatrixType::Identity(rows, rows),
-                    square = SquareMatrixType::Random(rows, rows);
   VectorType v1 = VectorType::Random(rows),
              v2 = VectorType::Random(rows),
              v3 = VectorType::Random(rows),
@@ -84,9 +84,7 @@ template<typename MatrixType> void submatrices(const MatrixType& m)
   int c2 = ei_random<int>(c1,cols-1);
 
   //check row() and col()
-  VERIFY_IS_APPROX(m1.col(c1).transpose(), m1.transpose().row(c1));
-  // FIXME perhaps we should re-enable that without the .eval()
-  VERIFY_IS_APPROX(m1.col(c1).dot(square.row(r1)), (square * m1.conjugate()).eval()(r1,c1));
+  VERIFY_IS_EQUAL(m1.col(c1).transpose(), m1.transpose().row(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);
@@ -96,9 +94,9 @@ template<typename MatrixType> void submatrices(const MatrixType& m)
 
   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);
+  VERIFY_IS_EQUAL(b1, m1.block(r1,c1,1,1));
+  VERIFY_IS_EQUAL(m1.row(r1), br1);
+  VERIFY_IS_EQUAL(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);
@@ -106,11 +104,6 @@ template<typename MatrixType> void submatrices(const MatrixType& m)
   //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;
-
   const int BlockRows = EIGEN_ENUM_MIN(MatrixType::RowsAtCompileTime,2);
   const int BlockCols = EIGEN_ENUM_MIN(MatrixType::ColsAtCompileTime,5);
   if (rows>=5 && cols>=8)
@@ -121,45 +114,23 @@ template<typename MatrixType> void submatrices(const MatrixType& m)
     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));
+    VERIFY_IS_EQUAL(b, m1.block(3,3,BlockRows,BlockCols));
   }
 
   if (rows>2)
   {
     // test sub vectors
-    VERIFY_IS_APPROX(v1.template head<2>(), v1.block(0,0,2,1));
-    VERIFY_IS_APPROX(v1.template head<2>(), v1.head(2));
-    VERIFY_IS_APPROX(v1.template head<2>(), v1.segment(0,2));
-    VERIFY_IS_APPROX(v1.template head<2>(), v1.template segment<2>(0));
+    VERIFY_IS_EQUAL(v1.template head<2>(), v1.block(0,0,2,1));
+    VERIFY_IS_EQUAL(v1.template head<2>(), v1.head(2));
+    VERIFY_IS_EQUAL(v1.template head<2>(), v1.segment(0,2));
+    VERIFY_IS_EQUAL(v1.template head<2>(), v1.template segment<2>(0));
     int i = rows-2;
-    VERIFY_IS_APPROX(v1.template tail<2>(), v1.block(i,0,2,1));
-    VERIFY_IS_APPROX(v1.template tail<2>(), v1.tail(2));
-    VERIFY_IS_APPROX(v1.template tail<2>(), v1.segment(i,2));
-    VERIFY_IS_APPROX(v1.template tail<2>(), v1.template segment<2>(i));
+    VERIFY_IS_EQUAL(v1.template tail<2>(), v1.block(i,0,2,1));
+    VERIFY_IS_EQUAL(v1.template tail<2>(), v1.tail(2));
+    VERIFY_IS_EQUAL(v1.template tail<2>(), v1.segment(i,2));
+    VERIFY_IS_EQUAL(v1.template tail<2>(), v1.template segment<2>(i));
     i = ei_random(0,rows-2);
-    VERIFY_IS_APPROX(v1.segment(i,2), v1.template segment<2>(i));
-
-    enum {
-      N1 = MatrixType::RowsAtCompileTime>1 ?  1 : 0,
-      N2 = MatrixType::RowsAtCompileTime>2 ? -2 : 0
-    };
-
-    // check sub/super diagonal
-    m2.template diagonal<N1>() = 2 * m1.template diagonal<N1>();
-    m2.template diagonal<N1>()[0] *= 3;
-    VERIFY_IS_APPROX(m2.template diagonal<N1>()[0], static_cast<Scalar>(6) * m1.template diagonal<N1>()[0]);
-
-    m2.template diagonal<N2>() = 2 * m1.template diagonal<N2>();
-    m2.template diagonal<N2>()[0] *= 3;
-    VERIFY_IS_APPROX(m2.template diagonal<N2>()[0], static_cast<Scalar>(6) * m1.template diagonal<N2>()[0]);
-
-    m2.diagonal(N1) = 2 * m1.diagonal(N1);
-    m2.diagonal(N1)[0] *= 3;
-    VERIFY_IS_APPROX(m2.diagonal(N1)[0], static_cast<Scalar>(6) * m1.diagonal(N1)[0]);
-
-    m2.diagonal(N2) = 2 * m1.diagonal(N2);
-    m2.diagonal(N2)[0] *= 3;
-    VERIFY_IS_APPROX(m2.diagonal(N2)[0], static_cast<Scalar>(6) * m1.diagonal(N2)[0]);
+    VERIFY_IS_EQUAL(v1.segment(i,2), v1.template segment<2>(i));
   }
 
   // stress some basic stuffs with block matrices
@@ -168,6 +139,49 @@ template<typename MatrixType> void submatrices(const MatrixType& m)
 
   VERIFY(ei_real(ones.col(c1).dot(ones.col(c2))) == RealScalar(rows));
   VERIFY(ei_real(ones.row(r1).dot(ones.row(r2))) == RealScalar(cols));
+
+  // now test some block-inside-of-block.
+  
+  // expressions with direct access
+  VERIFY_IS_EQUAL( (m1.block(r1,c1,rows-r1,cols-c1).block(r2-r1,c2-c1,rows-r2,cols-c2)) , (m1.block(r2,c2,rows-r2,cols-c2)) );
+  VERIFY_IS_EQUAL( (m1.block(r1,c1,r2-r1+1,c2-c1+1).row(0)) , (m1.row(r1).segment(c1,c2-c1+1)) );
+  VERIFY_IS_EQUAL( (m1.block(r1,c1,r2-r1+1,c2-c1+1).col(0)) , (m1.col(c1).segment(r1,r2-r1+1)) );
+  VERIFY_IS_EQUAL( (m1.block(r1,c1,r2-r1+1,c2-c1+1).transpose().col(0)) , (m1.row(r1).segment(c1,c2-c1+1)) );
+  VERIFY_IS_EQUAL( (m1.transpose().block(c1,r1,c2-c1+1,r2-r1+1).col(0)) , (m1.row(r1).segment(c1,c2-c1+1)) );
+
+  // expressions without direct access
+  VERIFY_IS_EQUAL( ((m1+m2).block(r1,c1,rows-r1,cols-c1).block(r2-r1,c2-c1,rows-r2,cols-c2)) , ((m1+m2).block(r2,c2,rows-r2,cols-c2)) );
+  VERIFY_IS_EQUAL( ((m1+m2).block(r1,c1,r2-r1+1,c2-c1+1).row(0)) , ((m1+m2).row(r1).segment(c1,c2-c1+1)) );
+  VERIFY_IS_EQUAL( ((m1+m2).block(r1,c1,r2-r1+1,c2-c1+1).col(0)) , ((m1+m2).col(c1).segment(r1,r2-r1+1)) );
+  VERIFY_IS_EQUAL( ((m1+m2).block(r1,c1,r2-r1+1,c2-c1+1).transpose().col(0)) , ((m1+m2).row(r1).segment(c1,c2-c1+1)) );
+  VERIFY_IS_EQUAL( ((m1+m2).transpose().block(c1,r1,c2-c1+1,r2-r1+1).col(0)) , ((m1+m2).row(r1).segment(c1,c2-c1+1)) );
+
+  // evaluation into plain matrices from expressions with direct access (stress MapBase)
+  DynamicMatrixType dm;
+  DynamicVectorType dv;
+  dm.setZero();
+  dm = m1.block(r1,c1,rows-r1,cols-c1).block(r2-r1,c2-c1,rows-r2,cols-c2);
+  VERIFY_IS_EQUAL(dm, (m1.block(r2,c2,rows-r2,cols-c2)));
+  dm.setZero();
+  dv.setZero();
+  dm = m1.block(r1,c1,r2-r1+1,c2-c1+1).row(0).transpose();
+  dv = m1.row(r1).segment(c1,c2-c1+1);
+  VERIFY_IS_EQUAL(dv, dm);
+  dm.setZero();
+  dv.setZero();
+  dm = m1.col(c1).segment(r1,r2-r1+1);
+  dv = m1.block(r1,c1,r2-r1+1,c2-c1+1).col(0);
+  VERIFY_IS_EQUAL(dv, dm);
+  dm.setZero();
+  dv.setZero();
+  dm = m1.block(r1,c1,r2-r1+1,c2-c1+1).transpose().col(0);
+  dv = m1.row(r1).segment(c1,c2-c1+1);
+  VERIFY_IS_EQUAL(dv, dm);
+  dm.setZero();
+  dv.setZero();
+  dm = m1.row(r1).segment(c1,c2-c1+1).transpose();
+  dv = m1.transpose().block(c1,r1,c2-c1+1,r2-r1+1).col(0);
+  VERIFY_IS_EQUAL(dv, dm);
 }
 
 
@@ -185,22 +199,22 @@ void compare_using_data_and_stride(const MatrixType& m)
 
   for(int j=0;j<cols;++j)
     for(int i=0;i<rows;++i)
-      VERIFY_IS_APPROX(m.coeff(i,j), data[i*rowStride + j*colStride]);
+      VERIFY(m.coeff(i,j) == data[i*rowStride + j*colStride]);
 
   if(!MatrixType::IsVectorAtCompileTime)
   {
     for(int j=0;j<cols;++j)
       for(int i=0;i<rows;++i)
-        VERIFY_IS_APPROX(m.coeff(i,j), data[(MatrixType::Flags&RowMajorBit)
-                                            ? i*outerStride + j*innerStride
-                                            : j*outerStride + i*innerStride]);
+        VERIFY(m.coeff(i,j) == data[(MatrixType::Flags&RowMajorBit)
+                                     ? i*outerStride + j*innerStride
+                                     : j*outerStride + i*innerStride]);
   }
 
   if(MatrixType::IsVectorAtCompileTime)
   {
-    VERIFY_IS_APPROX(innerStride, int((&m.coeff(1))-(&m.coeff(0))));
+    VERIFY(innerStride == int((&m.coeff(1))-(&m.coeff(0))));
     for (int i=0;i<size;++i)
-      VERIFY_IS_APPROX(m.coeff(i), data[i*innerStride]);
+      VERIFY(m.coeff(i) == data[i*innerStride]);
   }
 }
 
@@ -224,17 +238,17 @@ void data_and_stride(const MatrixType& m)
   compare_using_data_and_stride(m1.col(c1).transpose());
 }
 
-void test_submatrices()
+void test_block()
 {
   for(int i = 0; i < g_repeat; i++) {
-    CALL_SUBTEST_1( submatrices(Matrix<float, 1, 1>()) );
-    CALL_SUBTEST_2( submatrices(Matrix4d()) );
-    CALL_SUBTEST_3( submatrices(MatrixXcf(3, 3)) );
-    CALL_SUBTEST_4( submatrices(MatrixXi(8, 12)) );
-    CALL_SUBTEST_5( submatrices(MatrixXcd(20, 20)) );
-    CALL_SUBTEST_6( submatrices(MatrixXf(20, 20)) );
-
-    CALL_SUBTEST_8( submatrices(Matrix<float,Dynamic,4>(3, 4)) );
+    CALL_SUBTEST_1( block(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST_2( block(Matrix4d()) );
+    CALL_SUBTEST_3( block(MatrixXcf(3, 3)) );
+    CALL_SUBTEST_4( block(MatrixXi(8, 12)) );
+    CALL_SUBTEST_5( block(MatrixXcd(20, 20)) );
+    CALL_SUBTEST_6( block(MatrixXf(20, 20)) );
+
+    CALL_SUBTEST_8( block(Matrix<float,Dynamic,4>(3, 4)) );
 
 #ifndef EIGEN_DEFAULT_TO_ROW_MAJOR
     CALL_SUBTEST_6( data_and_stride(MatrixXf(ei_random(5,50), ei_random(5,50))) );
diff --git a/test/diagonal.cpp b/test/diagonal.cpp
new file mode 100644
index 000000000..288d58c6e
--- /dev/null
+++ b/test/diagonal.cpp
@@ -0,0 +1,81 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2010 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 MatrixType> void diagonal(const MatrixType& m)
+{
+  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);
+
+  //check diagonal()
+  VERIFY_IS_APPROX(m1.diagonal(), m1.transpose().diagonal());
+  m2.diagonal() = 2 * m1.diagonal();
+  m2.diagonal()[0] *= 3;
+
+  if (rows>2)
+  {
+    enum {
+      N1 = MatrixType::RowsAtCompileTime>1 ?  1 : 0,
+      N2 = MatrixType::RowsAtCompileTime>2 ? -2 : 0
+    };
+
+    // check sub/super diagonal
+    m2.template diagonal<N1>() = 2 * m1.template diagonal<N1>();
+    m2.template diagonal<N1>()[0] *= 3;
+    VERIFY_IS_APPROX(m2.template diagonal<N1>()[0], static_cast<Scalar>(6) * m1.template diagonal<N1>()[0]);
+
+    m2.template diagonal<N2>() = 2 * m1.template diagonal<N2>();
+    m2.template diagonal<N2>()[0] *= 3;
+    VERIFY_IS_APPROX(m2.template diagonal<N2>()[0], static_cast<Scalar>(6) * m1.template diagonal<N2>()[0]);
+
+    m2.diagonal(N1) = 2 * m1.diagonal(N1);
+    m2.diagonal(N1)[0] *= 3;
+    VERIFY_IS_APPROX(m2.diagonal(N1)[0], static_cast<Scalar>(6) * m1.diagonal(N1)[0]);
+
+    m2.diagonal(N2) = 2 * m1.diagonal(N2);
+    m2.diagonal(N2)[0] *= 3;
+    VERIFY_IS_APPROX(m2.diagonal(N2)[0], static_cast<Scalar>(6) * m1.diagonal(N2)[0]);
+  }
+}
+
+void test_diagonal()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST_1( diagonal(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST_2( diagonal(Matrix4d()) );
+    CALL_SUBTEST_2( diagonal(MatrixXcf(3, 3)) );
+    CALL_SUBTEST_2( diagonal(MatrixXi(8, 12)) );
+    CALL_SUBTEST_2( diagonal(MatrixXcd(20, 20)) );
+    CALL_SUBTEST_1( diagonal(MatrixXf(21, 19)) );
+    CALL_SUBTEST_1( diagonal(Matrix<float,Dynamic,4>(3, 4)) );
+  }
+}
diff --git a/test/main.h b/test/main.h
index 96324de33..5ca9395c2 100644
--- a/test/main.h
+++ b/test/main.h
@@ -157,6 +157,7 @@ namespace Eigen
     exit(2); \
   } } while (0)
 
+#define VERIFY_IS_EQUAL(a, b) VERIFY(test_is_equal(a, b))
 #define VERIFY_IS_APPROX(a, b) VERIFY(test_ei_isApprox(a, b))
 #define VERIFY_IS_NOT_APPROX(a, b) VERIFY(!test_ei_isApprox(a, b))
 #define VERIFY_IS_MUCH_SMALLER_THAN(a, b) VERIFY(test_ei_isMuchSmallerThan(a, b))
@@ -342,6 +343,41 @@ inline bool test_isUnitary(const MatrixBase<Derived>& m)
   return m.isUnitary(test_precision<typename ei_traits<Derived>::Scalar>());
 }
 
+template<typename Derived1, typename Derived2,
+         bool IsVector = bool(Derived1::IsVectorAtCompileTime) && bool(Derived2::IsVectorAtCompileTime) >
+struct test_is_equal_impl
+{
+  static bool run(const Derived1& a1, const Derived2& a2)
+  {
+    if(a1.size() != a2.size()) return false;
+    // we evaluate a2 into a temporary of the shape of a1. this allows to let Assign.h handle the transposing if needed.
+    typename Derived1::PlainObject a2_evaluated(a2);
+    for(int i = 0; i < a1.size(); ++i)
+      if(a1.coeff(i) != a2_evaluated.coeff(i)) return false;
+    return true;
+  }
+};
+
+template<typename Derived1, typename Derived2>
+struct test_is_equal_impl<Derived1, Derived2, false>
+{
+  static bool run(const Derived1& a1, const Derived2& a2)
+  {
+    if(a1.rows() != a2.rows()) return false;
+    if(a1.cols() != a2.cols()) return false;
+    for(int j = 0; j < a1.cols(); ++j)
+      for(int i = 0; i < a1.rows(); ++i)
+        if(a1.coeff(i,j) != a2.coeff(i,j)) return false;
+    return true;
+  }
+};
+
+template<typename Derived1, typename Derived2>
+bool test_is_equal(const Derived1& a1, const Derived2& a2)
+{
+  return test_is_equal_impl<Derived1, Derived2>::run(a1, a2);
+}
+
 /** Creates a random Partial Isometry matrix of given rank.
   *
   * A partial isometry is a matrix all of whose singular values are either 0 or 1.