evaluators.cpp

#include "main.h"

namespace Eigen {

template <typename Lhs, typename Rhs>
const Product<Lhs, Rhs> prod(const Lhs& lhs, const Rhs& rhs) {
  return Product<Lhs, Rhs>(lhs, rhs);
}

template <typename Lhs, typename Rhs>
const Product<Lhs, Rhs, LazyProduct> lazyprod(const Lhs& lhs, const Rhs& rhs) {
  return Product<Lhs, Rhs, LazyProduct>(lhs, rhs);
}

template <typename DstXprType, typename SrcXprType>
EIGEN_STRONG_INLINE DstXprType& copy_using_evaluator(
    const EigenBase<DstXprType>& dst, const SrcXprType& src) {
  call_assignment(dst.const_cast_derived(), src.derived(),
                  internal::assign_op<typename DstXprType::Scalar,
                                      typename SrcXprType::Scalar>());
  return dst.const_cast_derived();
}

template <typename DstXprType, template <typename> class StorageBase,
          typename SrcXprType>
EIGEN_STRONG_INLINE const DstXprType& copy_using_evaluator(
    const NoAlias<DstXprType, StorageBase>& dst, const SrcXprType& src) {
  call_assignment(dst, src.derived(),
                  internal::assign_op<typename DstXprType::Scalar,
                                      typename SrcXprType::Scalar>());
  return dst.expression();
}

template <typename DstXprType, typename SrcXprType>
EIGEN_STRONG_INLINE DstXprType& copy_using_evaluator(
    const PlainObjectBase<DstXprType>& dst, const SrcXprType& src) {
#ifdef EIGEN_NO_AUTOMATIC_RESIZING
  eigen_assert((dst.size() == 0 ||
                (IsVectorAtCompileTime ? (dst.size() == src.size())
                                       : (dst.rows() == src.rows() &&
                                          dst.cols() == src.cols()))) &&
               "Size mismatch. Automatic resizing is disabled because "
               "EIGEN_NO_AUTOMATIC_RESIZING is defined");
#else
  dst.const_cast_derived().resizeLike(src.derived());
#endif

  call_assignment(dst.const_cast_derived(), src.derived(),
                  internal::assign_op<typename DstXprType::Scalar,
                                      typename SrcXprType::Scalar>());
  return dst.const_cast_derived();
}

template <typename DstXprType, typename SrcXprType>
void add_assign_using_evaluator(const DstXprType& dst, const SrcXprType& src) {
  typedef typename DstXprType::Scalar Scalar;
  call_assignment(
      const_cast<DstXprType&>(dst), src.derived(),
      internal::add_assign_op<Scalar, typename SrcXprType::Scalar>());
}

template <typename DstXprType, typename SrcXprType>
void subtract_assign_using_evaluator(const DstXprType& dst,
                                     const SrcXprType& src) {
  typedef typename DstXprType::Scalar Scalar;
  call_assignment(
      const_cast<DstXprType&>(dst), src.derived(),
      internal::sub_assign_op<Scalar, typename SrcXprType::Scalar>());
}

template <typename DstXprType, typename SrcXprType>
void multiply_assign_using_evaluator(const DstXprType& dst,
                                     const SrcXprType& src) {
  typedef typename DstXprType::Scalar Scalar;
  call_assignment(
      dst.const_cast_derived(), src.derived(),
      internal::mul_assign_op<Scalar, typename SrcXprType::Scalar>());
}

template <typename DstXprType, typename SrcXprType>
void divide_assign_using_evaluator(const DstXprType& dst,
                                   const SrcXprType& src) {
  typedef typename DstXprType::Scalar Scalar;
  call_assignment(
      dst.const_cast_derived(), src.derived(),
      internal::div_assign_op<Scalar, typename SrcXprType::Scalar>());
}

template <typename DstXprType, typename SrcXprType>
void swap_using_evaluator(const DstXprType& dst, const SrcXprType& src) {
  typedef typename DstXprType::Scalar Scalar;
  call_assignment(dst.const_cast_derived(), src.const_cast_derived(),
                  internal::swap_assign_op<Scalar>());
}

namespace internal {
template <typename Dst, template <typename> class StorageBase, typename Src,
          typename Func>
EIGEN_DEVICE_FUNC void call_assignment(const NoAlias<Dst, StorageBase>& dst,
                                       const Src& src, const Func& func) {
  call_assignment_no_alias(dst.expression(), src, func);
}

template <typename Dst, template <typename> class StorageBase, typename Src,
          typename Func>
EIGEN_DEVICE_FUNC void call_restricted_packet_assignment(
    const NoAlias<Dst, StorageBase>& dst, const Src& src, const Func& func) {
  call_restricted_packet_assignment_no_alias(dst.expression(), src, func);
}
}
}

template <typename XprType>
long get_cost(const XprType&) {
  return Eigen::internal::evaluator<XprType>::CoeffReadCost;
}

using namespace std;

#define VERIFY_IS_APPROX_EVALUATOR(DEST, EXPR) \
  VERIFY_IS_APPROX(copy_using_evaluator(DEST, (EXPR)), (EXPR).eval());
#define VERIFY_IS_APPROX_EVALUATOR2(DEST, EXPR, REF) \
  VERIFY_IS_APPROX(copy_using_evaluator(DEST, (EXPR)), (REF).eval());

EIGEN_DECLARE_TEST(evaluators) {
  // Testing Matrix evaluator and Transpose
  Vector2d v = Vector2d::Random();
  const Vector2d v_const(v);
  Vector2d v2;
  RowVector2d w;

  VERIFY_IS_APPROX_EVALUATOR(v2, v);
  VERIFY_IS_APPROX_EVALUATOR(v2, v_const);

  // Testing Transpose
  VERIFY_IS_APPROX_EVALUATOR(w, v.transpose());  // Transpose as rvalue
  VERIFY_IS_APPROX_EVALUATOR(w, v_const.transpose());

  copy_using_evaluator(w.transpose(), v);  // Transpose as lvalue
  VERIFY_IS_APPROX(w, v.transpose().eval());

  copy_using_evaluator(w.transpose(), v_const);
  VERIFY_IS_APPROX(w, v_const.transpose().eval());

  // Testing Array evaluator
  {
    ArrayXXf a(2, 3);
    ArrayXXf b(3, 2);
    a << 1, 2, 3, 4, 5, 6;
    const ArrayXXf a_const(a);

    VERIFY_IS_APPROX_EVALUATOR(b, a.transpose());

    VERIFY_IS_APPROX_EVALUATOR(b, a_const.transpose());

    // Testing CwiseNullaryOp evaluator
    copy_using_evaluator(w, RowVector2d::Random());
    VERIFY((w.array() >= -1).all() &&
           (w.array() <= 1).all());  // not easy to test ...

    VERIFY_IS_APPROX_EVALUATOR(w, RowVector2d::Zero());

    VERIFY_IS_APPROX_EVALUATOR(w, RowVector2d::Constant(3));

    // mix CwiseNullaryOp and transpose
    VERIFY_IS_APPROX_EVALUATOR(w, Vector2d::Zero().transpose());
  }

  {
    // test product expressions
    int s = internal::random<int>(1, 100);
    MatrixXf a(s, s), b(s, s), c(s, s), d(s, s);
    a.setRandom();
    b.setRandom();
    c.setRandom();
    d.setRandom();
    VERIFY_IS_APPROX_EVALUATOR(d, (a + b));
    VERIFY_IS_APPROX_EVALUATOR(d, (a + b).transpose());
    VERIFY_IS_APPROX_EVALUATOR2(d, prod(a, b), a * b);
    VERIFY_IS_APPROX_EVALUATOR2(d.noalias(), prod(a, b), a * b);
    VERIFY_IS_APPROX_EVALUATOR2(d, prod(a, b) + c, a * b + c);
    VERIFY_IS_APPROX_EVALUATOR2(d, s * prod(a, b), s * a * b);
    VERIFY_IS_APPROX_EVALUATOR2(d, prod(a, b).transpose(), (a * b).transpose());
    VERIFY_IS_APPROX_EVALUATOR2(d, prod(a, b) + prod(b, c), a * b + b * c);

    // check that prod works even with aliasing present
    c = a * a;
    copy_using_evaluator(a, prod(a, a));
    VERIFY_IS_APPROX(a, c);

    // check compound assignment of products
    d = c;
    add_assign_using_evaluator(c.noalias(), prod(a, b));
    d.noalias() += a * b;
    VERIFY_IS_APPROX(c, d);

    d = c;
    subtract_assign_using_evaluator(c.noalias(), prod(a, b));
    d.noalias() -= a * b;
    VERIFY_IS_APPROX(c, d);
  }

  {
    // test product with all possible sizes
    int s = internal::random<int>(1, 100);
    Matrix<float, 1, 1> m11, res11;
    m11.setRandom(1, 1);
    Matrix<float, 1, 4> m14, res14;
    m14.setRandom(1, 4);
    Matrix<float, 1, Dynamic> m1X, res1X;
    m1X.setRandom(1, s);
    Matrix<float, 4, 1> m41, res41;
    m41.setRandom(4, 1);
    Matrix<float, 4, 4> m44, res44;
    m44.setRandom(4, 4);
    Matrix<float, 4, Dynamic> m4X, res4X;
    m4X.setRandom(4, s);
    Matrix<float, Dynamic, 1> mX1, resX1;
    mX1.setRandom(s, 1);
    Matrix<float, Dynamic, 4> mX4, resX4;
    mX4.setRandom(s, 4);
    Matrix<float, Dynamic, Dynamic> mXX, resXX;
    mXX.setRandom(s, s);

    VERIFY_IS_APPROX_EVALUATOR2(res11, prod(m11, m11), m11 * m11);
    VERIFY_IS_APPROX_EVALUATOR2(res11, prod(m14, m41), m14 * m41);
    VERIFY_IS_APPROX_EVALUATOR2(res11, prod(m1X, mX1), m1X * mX1);
    VERIFY_IS_APPROX_EVALUATOR2(res14, prod(m11, m14), m11 * m14);
    VERIFY_IS_APPROX_EVALUATOR2(res14, prod(m14, m44), m14 * m44);
    VERIFY_IS_APPROX_EVALUATOR2(res14, prod(m1X, mX4), m1X * mX4);
    VERIFY_IS_APPROX_EVALUATOR2(res1X, prod(m11, m1X), m11 * m1X);
    VERIFY_IS_APPROX_EVALUATOR2(res1X, prod(m14, m4X), m14 * m4X);
    VERIFY_IS_APPROX_EVALUATOR2(res1X, prod(m1X, mXX), m1X * mXX);
    VERIFY_IS_APPROX_EVALUATOR2(res41, prod(m41, m11), m41 * m11);
    VERIFY_IS_APPROX_EVALUATOR2(res41, prod(m44, m41), m44 * m41);
    VERIFY_IS_APPROX_EVALUATOR2(res41, prod(m4X, mX1), m4X * mX1);
    VERIFY_IS_APPROX_EVALUATOR2(res44, prod(m41, m14), m41 * m14);
    VERIFY_IS_APPROX_EVALUATOR2(res44, prod(m44, m44), m44 * m44);
    VERIFY_IS_APPROX_EVALUATOR2(res44, prod(m4X, mX4), m4X * mX4);
    VERIFY_IS_APPROX_EVALUATOR2(res4X, prod(m41, m1X), m41 * m1X);
    VERIFY_IS_APPROX_EVALUATOR2(res4X, prod(m44, m4X), m44 * m4X);
    VERIFY_IS_APPROX_EVALUATOR2(res4X, prod(m4X, mXX), m4X * mXX);
    VERIFY_IS_APPROX_EVALUATOR2(resX1, prod(mX1, m11), mX1 * m11);
    VERIFY_IS_APPROX_EVALUATOR2(resX1, prod(mX4, m41), mX4 * m41);
    VERIFY_IS_APPROX_EVALUATOR2(resX1, prod(mXX, mX1), mXX * mX1);
    VERIFY_IS_APPROX_EVALUATOR2(resX4, prod(mX1, m14), mX1 * m14);
    VERIFY_IS_APPROX_EVALUATOR2(resX4, prod(mX4, m44), mX4 * m44);
    VERIFY_IS_APPROX_EVALUATOR2(resX4, prod(mXX, mX4), mXX * mX4);
    VERIFY_IS_APPROX_EVALUATOR2(resXX, prod(mX1, m1X), mX1 * m1X);
    VERIFY_IS_APPROX_EVALUATOR2(resXX, prod(mX4, m4X), mX4 * m4X);
    VERIFY_IS_APPROX_EVALUATOR2(resXX, prod(mXX, mXX), mXX * mXX);
  }

  {
    ArrayXXf a(2, 3);
    ArrayXXf b(3, 2);
    a << 1, 2, 3, 4, 5, 6;
    const ArrayXXf a_const(a);

    // this does not work because Random is eval-before-nested:
    // copy_using_evaluator(w, Vector2d::Random().transpose());

    // test CwiseUnaryOp
    VERIFY_IS_APPROX_EVALUATOR(v2, 3 * v);
    VERIFY_IS_APPROX_EVALUATOR(w, (3 * v).transpose());
    VERIFY_IS_APPROX_EVALUATOR(b, (a + 3).transpose());
    VERIFY_IS_APPROX_EVALUATOR(b, (2 * a_const + 3).transpose());

    // test CwiseBinaryOp
    VERIFY_IS_APPROX_EVALUATOR(v2, v + Vector2d::Ones());
    VERIFY_IS_APPROX_EVALUATOR(w, (v + Vector2d::Ones())
                                      .transpose()
                                      .cwiseProduct(RowVector2d::Constant(3)));

    // dynamic matrices and arrays
    MatrixXd mat1(6, 6), mat2(6, 6);
    VERIFY_IS_APPROX_EVALUATOR(mat1, MatrixXd::Identity(6, 6));
    VERIFY_IS_APPROX_EVALUATOR(mat2, mat1);
    copy_using_evaluator(mat2.transpose(), mat1);
    VERIFY_IS_APPROX(mat2.transpose(), mat1);

    ArrayXXd arr1(6, 6), arr2(6, 6);
    VERIFY_IS_APPROX_EVALUATOR(arr1, ArrayXXd::Constant(6, 6, 3.0));
    VERIFY_IS_APPROX_EVALUATOR(arr2, arr1);

    // test automatic resizing
    mat2.resize(3, 3);
    VERIFY_IS_APPROX_EVALUATOR(mat2, mat1);
    arr2.resize(9, 9);
    VERIFY_IS_APPROX_EVALUATOR(arr2, arr1);

    // test direct traversal
    Matrix3f m3;
    Array33f a3;
    VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Identity());  // matrix, nullary
    // TODO: find a way to test direct traversal with array
    VERIFY_IS_APPROX_EVALUATOR(m3.transpose(),
                               Matrix3f::Identity().transpose());  // transpose
    VERIFY_IS_APPROX_EVALUATOR(m3, 2 * Matrix3f::Identity());      // unary
    VERIFY_IS_APPROX_EVALUATOR(
        m3, Matrix3f::Identity() + Matrix3f::Zero());  // binary
    VERIFY_IS_APPROX_EVALUATOR(
        m3.block(0, 0, 2, 2), Matrix3f::Identity().block(1, 1, 2, 2));  // block

    // test linear traversal
    VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Zero());  // matrix, nullary
    VERIFY_IS_APPROX_EVALUATOR(a3, Array33f::Zero());  // array
    VERIFY_IS_APPROX_EVALUATOR(m3.transpose(),
                               Matrix3f::Zero().transpose());  // transpose
    VERIFY_IS_APPROX_EVALUATOR(m3, 2 * Matrix3f::Zero());      // unary
    VERIFY_IS_APPROX_EVALUATOR(m3, Matrix3f::Zero() + m3);     // binary

    // test inner vectorization
    Matrix4f m4, m4src = Matrix4f::Random();
    Array44f a4, a4src = Matrix4f::Random();
    VERIFY_IS_APPROX_EVALUATOR(m4, m4src);                          // matrix
    VERIFY_IS_APPROX_EVALUATOR(a4, a4src);                          // array
    VERIFY_IS_APPROX_EVALUATOR(m4.transpose(), m4src.transpose());  // transpose
    // TODO: find out why Matrix4f::Zero() does not allow inner vectorization
    VERIFY_IS_APPROX_EVALUATOR(m4, 2 * m4src);      // unary
    VERIFY_IS_APPROX_EVALUATOR(m4, m4src + m4src);  // binary

    // test linear vectorization
    MatrixXf mX(6, 6), mXsrc = MatrixXf::Random(6, 6);
    ArrayXXf aX(6, 6), aXsrc = ArrayXXf::Random(6, 6);
    VERIFY_IS_APPROX_EVALUATOR(mX, mXsrc);                          // matrix
    VERIFY_IS_APPROX_EVALUATOR(aX, aXsrc);                          // array
    VERIFY_IS_APPROX_EVALUATOR(mX.transpose(), mXsrc.transpose());  // transpose
    VERIFY_IS_APPROX_EVALUATOR(mX, MatrixXf::Zero(6, 6));           // nullary
    VERIFY_IS_APPROX_EVALUATOR(mX, 2 * mXsrc);                      // unary
    VERIFY_IS_APPROX_EVALUATOR(mX, mXsrc + mXsrc);                  // binary

    // test blocks and slice vectorization
    VERIFY_IS_APPROX_EVALUATOR(m4, (mXsrc.block<4, 4>(1, 0)));
    VERIFY_IS_APPROX_EVALUATOR(
        aX, ArrayXXf::Constant(10, 10, 3.0).block(2, 3, 6, 6));

    Matrix4f m4ref = m4;
    copy_using_evaluator(m4.block(1, 1, 2, 3), m3.bottomRows(2));
    m4ref.block(1, 1, 2, 3) = m3.bottomRows(2);
    VERIFY_IS_APPROX(m4, m4ref);

    mX.setIdentity(20, 20);
    MatrixXf mXref = MatrixXf::Identity(20, 20);
    mXsrc = MatrixXf::Random(9, 12);
    copy_using_evaluator(mX.block(4, 4, 9, 12), mXsrc);
    mXref.block(4, 4, 9, 12) = mXsrc;
    VERIFY_IS_APPROX(mX, mXref);

    // test Map
    const float raw[3] = {1, 2, 3};
    float buffer[3] = {0, 0, 0};
    Vector3f v3;
    Array3f a3f;
    VERIFY_IS_APPROX_EVALUATOR(v3, Map<const Vector3f>(raw));
    VERIFY_IS_APPROX_EVALUATOR(a3f, Map<const Array3f>(raw));
    Vector3f::Map(buffer) = 2 * v3;
    VERIFY(buffer[0] == 2);
    VERIFY(buffer[1] == 4);
    VERIFY(buffer[2] == 6);

    // test CwiseUnaryView
    mat1.setRandom();
    mat2.setIdentity();
    MatrixXcd matXcd(6, 6), matXcd_ref(6, 6);
    copy_using_evaluator(matXcd.real(), mat1);
    copy_using_evaluator(matXcd.imag(), mat2);
    matXcd_ref.real() = mat1;
    matXcd_ref.imag() = mat2;
    VERIFY_IS_APPROX(matXcd, matXcd_ref);

    // test Select
    VERIFY_IS_APPROX_EVALUATOR(aX, (aXsrc > 0).select(aXsrc, -aXsrc));

    // test Replicate
    mXsrc = MatrixXf::Random(6, 6);
    VectorXf vX = VectorXf::Random(6);
    mX.resize(6, 6);
    VERIFY_IS_APPROX_EVALUATOR(mX, mXsrc.colwise() + vX);
    matXcd.resize(12, 12);
    VERIFY_IS_APPROX_EVALUATOR(matXcd, matXcd_ref.replicate(2, 2));
    VERIFY_IS_APPROX_EVALUATOR(matXcd, (matXcd_ref.replicate<2, 2>()));

    // test partial reductions
    VectorXd vec1(6);
    VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.rowwise().sum());
    VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.colwise().sum().transpose());

    // test MatrixWrapper and ArrayWrapper
    mat1.setRandom(6, 6);
    arr1.setRandom(6, 6);
    VERIFY_IS_APPROX_EVALUATOR(mat2, arr1.matrix());
    VERIFY_IS_APPROX_EVALUATOR(arr2, mat1.array());
    VERIFY_IS_APPROX_EVALUATOR(mat2, (arr1 + 2).matrix());
    VERIFY_IS_APPROX_EVALUATOR(arr2, mat1.array() + 2);
    mat2.array() = arr1 * arr1;
    VERIFY_IS_APPROX(mat2, (arr1 * arr1).matrix());
    arr2.matrix() = MatrixXd::Identity(6, 6);
    VERIFY_IS_APPROX(arr2, MatrixXd::Identity(6, 6).array());

    // test Reverse
    VERIFY_IS_APPROX_EVALUATOR(arr2, arr1.reverse());
    VERIFY_IS_APPROX_EVALUATOR(arr2, arr1.colwise().reverse());
    VERIFY_IS_APPROX_EVALUATOR(arr2, arr1.rowwise().reverse());
    arr2.reverse() = arr1;
    VERIFY_IS_APPROX(arr2, arr1.reverse());
    mat2.array() = mat1.array().reverse();
    VERIFY_IS_APPROX(mat2.array(), mat1.array().reverse());

    // test Diagonal
    VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.diagonal());
    vec1.resize(5);
    VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.diagonal(1));
    VERIFY_IS_APPROX_EVALUATOR(vec1, mat1.diagonal<-1>());
    vec1.setRandom();

    mat2 = mat1;
    copy_using_evaluator(mat1.diagonal(1), vec1);
    mat2.diagonal(1) = vec1;
    VERIFY_IS_APPROX(mat1, mat2);

    copy_using_evaluator(mat1.diagonal<-1>(), mat1.diagonal(1));
    mat2.diagonal<-1>() = mat2.diagonal(1);
    VERIFY_IS_APPROX(mat1, mat2);
  }

  {
    // test swapping
    MatrixXd mat1, mat2, mat1ref, mat2ref;
    mat1ref = mat1 = MatrixXd::Random(6, 6);
    mat2ref = mat2 = 2 * mat1 + MatrixXd::Identity(6, 6);
    swap_using_evaluator(mat1, mat2);
    mat1ref.swap(mat2ref);
    VERIFY_IS_APPROX(mat1, mat1ref);
    VERIFY_IS_APPROX(mat2, mat2ref);

    swap_using_evaluator(mat1.block(0, 0, 3, 3), mat2.block(3, 3, 3, 3));
    mat1ref.block(0, 0, 3, 3).swap(mat2ref.block(3, 3, 3, 3));
    VERIFY_IS_APPROX(mat1, mat1ref);
    VERIFY_IS_APPROX(mat2, mat2ref);

    swap_using_evaluator(mat1.row(2), mat2.col(3).transpose());
    mat1.row(2).swap(mat2.col(3).transpose());
    VERIFY_IS_APPROX(mat1, mat1ref);
    VERIFY_IS_APPROX(mat2, mat2ref);
  }

  {
    // test compound assignment
    const Matrix4d mat_const = Matrix4d::Random();
    Matrix4d mat, mat_ref;
    mat = mat_ref = Matrix4d::Identity();
    add_assign_using_evaluator(mat, mat_const);
    mat_ref += mat_const;
    VERIFY_IS_APPROX(mat, mat_ref);

    subtract_assign_using_evaluator(mat.row(1), 2 * mat.row(2));
    mat_ref.row(1) -= 2 * mat_ref.row(2);
    VERIFY_IS_APPROX(mat, mat_ref);

    const ArrayXXf arr_const = ArrayXXf::Random(5, 3);
    ArrayXXf arr, arr_ref;
    arr = arr_ref = ArrayXXf::Constant(5, 3, 0.5);
    multiply_assign_using_evaluator(arr, arr_const);
    arr_ref *= arr_const;
    VERIFY_IS_APPROX(arr, arr_ref);

    divide_assign_using_evaluator(arr.row(1), arr.row(2) + 1);
    arr_ref.row(1) /= (arr_ref.row(2) + 1);
    VERIFY_IS_APPROX(arr, arr_ref);
  }

  {
    // test triangular shapes
    MatrixXd A = MatrixXd::Random(6, 6), B(6, 6), C(6, 6), D(6, 6);
    A.setRandom();
    B.setRandom();
    VERIFY_IS_APPROX_EVALUATOR2(B, A.triangularView<Upper>(),
                                MatrixXd(A.triangularView<Upper>()));

    A.setRandom();
    B.setRandom();
    VERIFY_IS_APPROX_EVALUATOR2(B, A.triangularView<UnitLower>(),
                                MatrixXd(A.triangularView<UnitLower>()));

    A.setRandom();
    B.setRandom();
    VERIFY_IS_APPROX_EVALUATOR2(B, A.triangularView<UnitUpper>(),
                                MatrixXd(A.triangularView<UnitUpper>()));

    A.setRandom();
    B.setRandom();
    C = B;
    C.triangularView<Upper>() = A;
    copy_using_evaluator(B.triangularView<Upper>(), A);
    VERIFY(B.isApprox(C) &&
           "copy_using_evaluator(B.triangularView<Upper>(), A)");

    A.setRandom();
    B.setRandom();
    C = B;
    C.triangularView<Lower>() = A.triangularView<Lower>();
    copy_using_evaluator(B.triangularView<Lower>(), A.triangularView<Lower>());
    VERIFY(B.isApprox(C) &&
           "copy_using_evaluator(B.triangularView<Lower>(), "
           "A.triangularView<Lower>())");

    A.setRandom();
    B.setRandom();
    C = B;
    C.triangularView<Lower>() = A.triangularView<Upper>().transpose();
    copy_using_evaluator(B.triangularView<Lower>(),
                         A.triangularView<Upper>().transpose());
    VERIFY(B.isApprox(C) &&
           "copy_using_evaluator(B.triangularView<Lower>(), "
           "A.triangularView<Lower>().transpose())");

    A.setRandom();
    B.setRandom();
    C = B;
    D = A;
    C.triangularView<Upper>().swap(D.triangularView<Upper>());
    swap_using_evaluator(B.triangularView<Upper>(), A.triangularView<Upper>());
    VERIFY(B.isApprox(C) &&
           "swap_using_evaluator(B.triangularView<Upper>(), "
           "A.triangularView<Upper>())");

    VERIFY_IS_APPROX_EVALUATOR2(B, prod(A.triangularView<Upper>(), A),
                                MatrixXd(A.triangularView<Upper>() * A));

    VERIFY_IS_APPROX_EVALUATOR2(B, prod(A.selfadjointView<Upper>(), A),
                                MatrixXd(A.selfadjointView<Upper>() * A));
  }

  {
    // test diagonal shapes
    VectorXd d = VectorXd::Random(6);
    MatrixXd A = MatrixXd::Random(6, 6), B(6, 6);
    A.setRandom();
    B.setRandom();

    VERIFY_IS_APPROX_EVALUATOR2(B, lazyprod(d.asDiagonal(), A),
                                MatrixXd(d.asDiagonal() * A));
    VERIFY_IS_APPROX_EVALUATOR2(B, lazyprod(A, d.asDiagonal()),
                                MatrixXd(A * d.asDiagonal()));
  }

  {
    // test CoeffReadCost
    Matrix4d a, b;
    VERIFY_IS_EQUAL(get_cost(a), 1);
    VERIFY_IS_EQUAL(get_cost(a + b), 3);
    VERIFY_IS_EQUAL(get_cost(2 * a + b), 4);
    VERIFY_IS_EQUAL(get_cost(a * b), 1);
    VERIFY_IS_EQUAL(get_cost(a.lazyProduct(b)), 15);
    VERIFY_IS_EQUAL(get_cost(a * (a * b)), 1);
    VERIFY_IS_EQUAL(get_cost(a.lazyProduct(a * b)), 15);
    VERIFY_IS_EQUAL(get_cost(a * (a + b)), 1);
    VERIFY_IS_EQUAL(get_cost(a.lazyProduct(a + b)), 15);
  }

  // regression test for PR 544 and bug 1622 (introduced in #71609c4)
  {
    // test restricted_packet_assignment with an unaligned destination
    const size_t M = 2;
    const size_t K = 2;
    const size_t N = 5;
    float* destMem = new float[(M * N) + 1];
    float* dest = (internal::UIntPtr(destMem) % EIGEN_MAX_ALIGN_BYTES) == 0
                      ? destMem + 1
                      : destMem;

    const Matrix<float, Dynamic, Dynamic, RowMajor> a =
        Matrix<float, Dynamic, Dynamic, RowMajor>::Random(M, K);
    const Matrix<float, Dynamic, Dynamic, RowMajor> b =
        Matrix<float, Dynamic, Dynamic, RowMajor>::Random(K, N);

    Map<Matrix<float, Dynamic, Dynamic, RowMajor> > z(dest, M, N);
    ;
    Product<Matrix<float, Dynamic, Dynamic, RowMajor>,
            Matrix<float, Dynamic, Dynamic, RowMajor>, LazyProduct>
        tmp(a, b);
    internal::call_restricted_packet_assignment(
        z.noalias(), tmp.derived(), internal::assign_op<float, float>());

    VERIFY_IS_APPROX(z, a * b);
    delete[] destMem;
  }
}