- eigen2 now fully enforces constness! found a way to achieve that

with minimal code duplication. There now are only two (2)
  const_cast remaining in the whole source code.
- eigen2 now fully allows copying a row-vector into a column-vector.
  added a unit-test for that.
- split unit tests, improve docs, various improvements.

test/linearstructure.cpp

@@ -0,0 +1,106 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2007 Benoit Jacob <jacob@math.jussieu.fr>
+//
+// Eigen is free software; 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 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 General Public License for more
+// details.
+//
+// You should have received a copy of the GNU General Public License along
+// with Eigen; if not, write to the Free Software Foundation, Inc., 51
+// Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
+//
+// As a special exception, if other files instantiate templates or use macros
+// or functions from this file, or you compile this file and link it
+// with other works to produce a work based on this file, this file does not
+// by itself cause the resulting work to be covered by the GNU General Public
+// License. This exception does not invalidate any other reasons why a work
+// based on this file might be covered by the GNU General Public License.
+
+#include "main.h"
+
+namespace Eigen {
+
+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),
+             identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+                              ::identity(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 = random<Scalar>(),
+         s2 = random<Scalar>();
+  
+  int r = random<int>(0, rows-1),
+      c = 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((s1+s2)*m1,              m1*s1+m1*s2);
+  VERIFY_IS_APPROX((m1-m2)*s1,              s1*m1-s1*m2);
+  VERIFY_IS_APPROX((s1-s2)*m1,              m1*s1-m1*s2);
+  VERIFY_IS_APPROX((-m1+m2)*s1,             -s1*m1+s1*m2);
+  VERIFY_IS_APPROX((-s1+s2)*m1,             -m1*s1+m1*s2);
+  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);
+}
+
+void EigenTest::testLinearStructure()
+{
+  for(int i = 0; i < m_repeat; i++) {
+    linearStructure(Matrix<float, 1, 1>());
+    linearStructure(Matrix4d());
+    linearStructure(MatrixXcf(3, 3));
+    linearStructure(MatrixXi(8, 12));
+    linearStructure(MatrixXcd(20, 20));
+  }
+}
+
+} // namespace Eigen