Initial import of eigen 3.1.1

Added a README.android and a MODULE_LICENSE_MPL2 file.
Added empty Android.mk and CleanSpec.mk to optimize Android build.
Non MPL2 license code is disabled in ./Eigen/src/Core/util/NonMPL2.h.
Trying to include such files will lead to an error.

Change-Id: I0e148b7c3e83999bcc4dfaa5809d33bfac2aac32
diff --git a/test/eigen2/eigen2_array.cpp b/test/eigen2/eigen2_array.cpp
new file mode 100644
index 0000000..c1ff40c
--- /dev/null
+++ b/test/eigen2/eigen2_array.cpp
@@ -0,0 +1,142 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/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(internal::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().template cast<int>(), RowVectorXi::Constant(cols,rows));
+  VERIFY_IS_APPROX(((m1.cwise().abs().cwise()+1).cwise()>RealScalar(0.1)).rowwise().count().template cast<int>(), 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_eigen2_array()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST_1( array(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST_2( array(Matrix2f()) );
+    CALL_SUBTEST_3( array(Matrix4d()) );
+    CALL_SUBTEST_4( array(MatrixXcf(3, 3)) );
+    CALL_SUBTEST_5( array(MatrixXf(8, 12)) );
+    CALL_SUBTEST_6( array(MatrixXi(8, 12)) );
+  }
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST_1( comparisons(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST_2( comparisons(Matrix2f()) );
+    CALL_SUBTEST_3( comparisons(Matrix4d()) );
+    CALL_SUBTEST_5( comparisons(MatrixXf(8, 12)) );
+    CALL_SUBTEST_6( comparisons(MatrixXi(8, 12)) );
+  }
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST_1( lpNorm(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST_2( lpNorm(Vector2f()) );
+    CALL_SUBTEST_3( lpNorm(Vector3d()) );
+    CALL_SUBTEST_4( lpNorm(Vector4f()) );
+    CALL_SUBTEST_5( lpNorm(VectorXf(16)) );
+    CALL_SUBTEST_7( lpNorm(VectorXcd(10)) );
+  }
+}