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diff --git a/eigen/test/product.h b/eigen/test/product.h
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+// 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>
+//
+// 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/QR>
+
+template<typename Derived1, typename Derived2>
+bool areNotApprox(const MatrixBase<Derived1>& m1, const MatrixBase<Derived2>& m2, typename Derived1::RealScalar epsilon = NumTraits<typename Derived1::RealScalar>::dummy_precision())
+{
+  return !((m1-m2).cwiseAbs2().maxCoeff() < epsilon * epsilon
+                          * (std::max)(m1.cwiseAbs2().maxCoeff(), m2.cwiseAbs2().maxCoeff()));
+}
+
+template<typename MatrixType> void product(const MatrixType& m)
+{
+  /* this test covers the following files:
+     Identity.h Product.h
+  */
+  typedef typename MatrixType::Index Index;
+  typedef typename MatrixType::Scalar Scalar;
+  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::Flags&RowMajorBit?ColMajor:RowMajor> OtherMajorMatrixType;
+
+  Index rows = m.rows();
+  Index 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);
+  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);
+  ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);
+  OtherMajorMatrixType tm1 = m1;
+
+  Scalar s1 = internal::random<Scalar>();
+
+  Index r  = internal::random<Index>(0, rows-1),
+        c  = internal::random<Index>(0, cols-1),
+        c2 = internal::random<Index>(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 * (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));
+
+  // 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>::IsInteger && (std::min)(rows,cols)>1)
+  {
+    VERIFY(areNotApprox(m1.transpose()*m2,m2.transpose()*m1));
+  }
+
+  // test optimized operator+= path
+  res = square;
+  res.noalias() += m1 * m2.transpose();
+  VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
+  if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
+  {
+    VERIFY(areNotApprox(res,square + m2 * m1.transpose()));
+  }
+  vcres = vc2;
+  vcres.noalias() += m1.transpose() * v1;
+  VERIFY_IS_APPROX(vcres, vc2 + m1.transpose() * v1);
+
+  // test optimized operator-= path
+  res = square;
+  res.noalias() -= m1 * m2.transpose();
+  VERIFY_IS_APPROX(res, square - (m1 * m2.transpose()));
+  if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
+  {
+    VERIFY(areNotApprox(res,square - m2 * m1.transpose()));
+  }
+  vcres = vc2;
+  vcres.noalias() -= m1.transpose() * v1;
+  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.noalias() += m1.transpose() * m2;
+  VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2);
+  if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1)
+  {
+    VERIFY(areNotApprox(res2,square2 + m2.transpose() * m1));
+  }
+
+  VERIFY_IS_APPROX(res.col(r).noalias() = square.adjoint() * square.col(r), (square.adjoint() * square.col(r)).eval());
+  VERIFY_IS_APPROX(res.col(r).noalias() = square * square.col(r), (square * square.col(r)).eval());
+
+  // vector at runtime (see bug 1166)
+  {
+    RowSquareMatrixType ref(square);
+    ColSquareMatrixType ref2(square2);
+    ref = res = square;
+    VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.col(0).transpose() * square.transpose(),            (ref.row(0) = m1.col(0).transpose() * square.transpose()));
+    VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.block(0,0,rows,1).transpose() * square.transpose(), (ref.row(0) = m1.col(0).transpose() * square.transpose()));
+    VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.col(0).transpose() * square,                        (ref.row(0) = m1.col(0).transpose() * square));
+    VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.block(0,0,rows,1).transpose() * square,             (ref.row(0) = m1.col(0).transpose() * square));
+    ref2 = res2 = square2;
+    VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2.transpose(),                      (ref2.row(0) = m1.row(0) * square2.transpose()));
+    VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.block(0,0,1,cols) * square2.transpose(),           (ref2.row(0) = m1.row(0) * square2.transpose()));
+    VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2,                                  (ref2.row(0) = m1.row(0) * square2));
+    VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.block(0,0,1,cols) * square2,                       (ref2.row(0) = m1.row(0) * square2));
+  }
+
+  // inner product
+  {
+    Scalar x = square2.row(c) * square2.col(c2);
+    VERIFY_IS_APPROX(x, square2.row(c).transpose().cwiseProduct(square2.col(c2)).sum());
+  }
+  
+  // outer product
+  VERIFY_IS_APPROX(m1.col(c) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
+  VERIFY_IS_APPROX(m1.row(r).transpose() * m1.col(c).transpose(), m1.block(r,0,1,cols).transpose() * m1.block(0,c,rows,1).transpose());
+  VERIFY_IS_APPROX(m1.block(0,c,rows,1) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
+  VERIFY_IS_APPROX(m1.col(c) * m1.block(r,0,1,cols), m1.block(0,c,rows,1) * m1.block(r,0,1,cols));
+  VERIFY_IS_APPROX(m1.leftCols(1) * m1.row(r), m1.block(0,0,rows,1) * m1.block(r,0,1,cols));
+  VERIFY_IS_APPROX(m1.col(c) * m1.topRows(1), m1.block(0,c,rows,1) * m1.block(0,0,1,cols));
+
+  // Aliasing
+  {
+    ColVectorType x(cols); x.setRandom();
+    ColVectorType z(x);
+    ColVectorType y(cols); y.setZero();
+    ColSquareMatrixType A(cols,cols); A.setRandom();
+    // CwiseBinaryOp
+    VERIFY_IS_APPROX(x = y + A*x, A*z);
+    x = z;
+    // CwiseUnaryOp
+    VERIFY_IS_APPROX(x = Scalar(1.)*(A*x), A*z);
+  }
+
+  // regression for blas_trais
+  {
+    VERIFY_IS_APPROX(square * (square*square).transpose(), square * square.transpose() * square.transpose());
+    VERIFY_IS_APPROX(square * (-(square*square)), -square * square * square);
+    VERIFY_IS_APPROX(square * (s1*(square*square)), s1 * square * square * square);
+    VERIFY_IS_APPROX(square * (square*square).conjugate(), square * square.conjugate() * square.conjugate());
+  }
+}