diff --git a/test/redux.cpp b/test/redux.cpp
new file mode 100644
index 0000000..0d176e5
--- /dev/null
+++ b/test/redux.cpp
@@ -0,0 +1,159 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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"
+
+template<typename MatrixType> void matrixRedux(const MatrixType& m)
+{
+  typedef typename MatrixType::Index Index;
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename MatrixType::RealScalar RealScalar;
+
+  Index rows = m.rows();
+  Index cols = m.cols();
+
+  MatrixType m1 = MatrixType::Random(rows, cols);
+
+  // The entries of m1 are uniformly distributed in [0,1], so m1.prod() is very small. This may lead to test
+  // failures if we underflow into denormals. Thus, we scale so that entires are close to 1.
+  MatrixType m1_for_prod = MatrixType::Ones(rows, cols) + RealScalar(0.2) * m1;
+
+  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 s(0), p(1), minc(numext::real(m1.coeff(0))), maxc(numext::real(m1.coeff(0)));
+  for(int j = 0; j < cols; j++)
+  for(int i = 0; i < rows; i++)
+  {
+    s += m1(i,j);
+    p *= m1_for_prod(i,j);
+    minc = (std::min)(numext::real(minc), numext::real(m1(i,j)));
+    maxc = (std::max)(numext::real(maxc), numext::real(m1(i,j)));
+  }
+  const Scalar mean = s/Scalar(RealScalar(rows*cols));
+
+  VERIFY_IS_APPROX(m1.sum(), s);
+  VERIFY_IS_APPROX(m1.mean(), mean);
+  VERIFY_IS_APPROX(m1_for_prod.prod(), p);
+  VERIFY_IS_APPROX(m1.real().minCoeff(), numext::real(minc));
+  VERIFY_IS_APPROX(m1.real().maxCoeff(), numext::real(maxc));
+
+  // test slice vectorization assuming assign is ok
+  Index r0 = internal::random<Index>(0,rows-1);
+  Index c0 = internal::random<Index>(0,cols-1);
+  Index r1 = internal::random<Index>(r0+1,rows)-r0;
+  Index c1 = internal::random<Index>(c0+1,cols)-c0;
+  VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).sum(), m1.block(r0,c0,r1,c1).eval().sum());
+  VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).mean(), m1.block(r0,c0,r1,c1).eval().mean());
+  VERIFY_IS_APPROX(m1_for_prod.block(r0,c0,r1,c1).prod(), m1_for_prod.block(r0,c0,r1,c1).eval().prod());
+  VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).real().minCoeff(), m1.block(r0,c0,r1,c1).real().eval().minCoeff());
+  VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).real().maxCoeff(), m1.block(r0,c0,r1,c1).real().eval().maxCoeff());
+  
+  // test empty objects
+  VERIFY_IS_APPROX(m1.block(r0,c0,0,0).sum(),   Scalar(0));
+  VERIFY_IS_APPROX(m1.block(r0,c0,0,0).prod(),  Scalar(1));
+}
+
+template<typename VectorType> void vectorRedux(const VectorType& w)
+{
+  using std::abs;
+  typedef typename VectorType::Index Index;
+  typedef typename VectorType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  Index size = w.size();
+
+  VectorType v = VectorType::Random(size);
+  VectorType v_for_prod = VectorType::Ones(size) + Scalar(0.2) * v; // see comment above declaration of m1_for_prod
+
+  for(int i = 1; i < size; i++)
+  {
+    Scalar s(0), p(1);
+    RealScalar minc(numext::real(v.coeff(0))), maxc(numext::real(v.coeff(0)));
+    for(int j = 0; j < i; j++)
+    {
+      s += v[j];
+      p *= v_for_prod[j];
+      minc = (std::min)(minc, numext::real(v[j]));
+      maxc = (std::max)(maxc, numext::real(v[j]));
+    }
+    VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.head(i).sum()), Scalar(1));
+    VERIFY_IS_APPROX(p, v_for_prod.head(i).prod());
+    VERIFY_IS_APPROX(minc, v.real().head(i).minCoeff());
+    VERIFY_IS_APPROX(maxc, v.real().head(i).maxCoeff());
+  }
+
+  for(int i = 0; i < size-1; i++)
+  {
+    Scalar s(0), p(1);
+    RealScalar minc(numext::real(v.coeff(i))), maxc(numext::real(v.coeff(i)));
+    for(int j = i; j < size; j++)
+    {
+      s += v[j];
+      p *= v_for_prod[j];
+      minc = (std::min)(minc, numext::real(v[j]));
+      maxc = (std::max)(maxc, numext::real(v[j]));
+    }
+    VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.tail(size-i).sum()), Scalar(1));
+    VERIFY_IS_APPROX(p, v_for_prod.tail(size-i).prod());
+    VERIFY_IS_APPROX(minc, v.real().tail(size-i).minCoeff());
+    VERIFY_IS_APPROX(maxc, v.real().tail(size-i).maxCoeff());
+  }
+
+  for(int i = 0; i < size/2; i++)
+  {
+    Scalar s(0), p(1);
+    RealScalar minc(numext::real(v.coeff(i))), maxc(numext::real(v.coeff(i)));
+    for(int j = i; j < size-i; j++)
+    {
+      s += v[j];
+      p *= v_for_prod[j];
+      minc = (std::min)(minc, numext::real(v[j]));
+      maxc = (std::max)(maxc, numext::real(v[j]));
+    }
+    VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.segment(i, size-2*i).sum()), Scalar(1));
+    VERIFY_IS_APPROX(p, v_for_prod.segment(i, size-2*i).prod());
+    VERIFY_IS_APPROX(minc, v.real().segment(i, size-2*i).minCoeff());
+    VERIFY_IS_APPROX(maxc, v.real().segment(i, size-2*i).maxCoeff());
+  }
+  
+  // test empty objects
+  VERIFY_IS_APPROX(v.head(0).sum(),   Scalar(0));
+  VERIFY_IS_APPROX(v.tail(0).prod(),  Scalar(1));
+  VERIFY_RAISES_ASSERT(v.head(0).mean());
+  VERIFY_RAISES_ASSERT(v.head(0).minCoeff());
+  VERIFY_RAISES_ASSERT(v.head(0).maxCoeff());
+}
+
+void test_redux()
+{
+  // the max size cannot be too large, otherwise reduxion operations obviously generate large errors.
+  int maxsize = (std::min)(100,EIGEN_TEST_MAX_SIZE);
+  TEST_SET_BUT_UNUSED_VARIABLE(maxsize);
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST_1( matrixRedux(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST_1( matrixRedux(Array<float, 1, 1>()) );
+    CALL_SUBTEST_2( matrixRedux(Matrix2f()) );
+    CALL_SUBTEST_2( matrixRedux(Array2f()) );
+    CALL_SUBTEST_3( matrixRedux(Matrix4d()) );
+    CALL_SUBTEST_3( matrixRedux(Array4d()) );
+    CALL_SUBTEST_4( matrixRedux(MatrixXcf(internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
+    CALL_SUBTEST_4( matrixRedux(ArrayXXcf(internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
+    CALL_SUBTEST_5( matrixRedux(MatrixXd (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
+    CALL_SUBTEST_5( matrixRedux(ArrayXXd (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
+    CALL_SUBTEST_6( matrixRedux(MatrixXi (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
+    CALL_SUBTEST_6( matrixRedux(ArrayXXi (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
+  }
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST_7( vectorRedux(Vector4f()) );
+    CALL_SUBTEST_7( vectorRedux(Array4f()) );
+    CALL_SUBTEST_5( vectorRedux(VectorXd(internal::random<int>(1,maxsize))) );
+    CALL_SUBTEST_5( vectorRedux(ArrayXd(internal::random<int>(1,maxsize))) );
+    CALL_SUBTEST_8( vectorRedux(VectorXf(internal::random<int>(1,maxsize))) );
+    CALL_SUBTEST_8( vectorRedux(ArrayXf(internal::random<int>(1,maxsize))) );
+  }
+}