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++ // This file is part of Eigen, a lightweight C++ template library
++ // for linear algebra.
++ //
++ // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
++ // 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/.
++
++ #ifndef EIGEN_ORTHOMETHODS_H
++ #define EIGEN_ORTHOMETHODS_H
++
++ // IWYU pragma: private
++ #include "./InternalHeaderCheck.h"
++
++ namespace Eigen {
++
++ namespace internal {
++
++ // Vector3 version (default)
++ template <typename Derived, typename OtherDerived, int Size>
++ struct cross_impl {
++ typedef typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,
++ typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
++ typedef Matrix<Scalar, MatrixBase<Derived>::RowsAtCompileTime, MatrixBase<Derived>::ColsAtCompileTime> return_type;
++
++ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE return_type run(const MatrixBase<Derived>& first,
++ const MatrixBase<OtherDerived>& second) {
++ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived, 3)
++ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived, 3)
++
++ // Note that there is no need for an expression here since the compiler
++ // optimize such a small temporary very well (even within a complex expression)
++ typename internal::nested_eval<Derived, 2>::type lhs(first.derived());
++ typename internal::nested_eval<OtherDerived, 2>::type rhs(second.derived());
++ return return_type(numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
++ numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
++ numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)));
++ }
++ };
++
++ // Vector2 version
++ template <typename Derived, typename OtherDerived>
++ struct cross_impl<Derived, OtherDerived, 2> {
++ typedef typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,
++ typename internal::traits<OtherDerived>::Scalar>::ReturnType Scalar;
++ typedef Scalar return_type;
++
++ static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE return_type run(const MatrixBase<Derived>& first,
++ const MatrixBase<OtherDerived>& second) {
++ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived, 2);
++ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived, 2);
++ typename internal::nested_eval<Derived, 2>::type lhs(first.derived());
++ typename internal::nested_eval<OtherDerived, 2>::type rhs(second.derived());
++ return numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0));
++ }
++ };
++
++ } // end namespace internal
++
++ /** \geometry_module \ingroup Geometry_Module
++ *
++ * \returns the cross product of \c *this and \a other. This is either a scalar for size-2 vectors or a size-3 vector
++ * for size-3 vectors.
++ *
++ * This method is implemented for two different cases: between vectors of fixed size 2 and between vectors of fixed
++ * size 3.
++ *
++ * For vectors of size 3, the output is simply the traditional cross product.
++ *
++ * For vectors of size 2, the output is a scalar.
++ * Given vectors \f$ v = \begin{bmatrix} v_1 & v_2 \end{bmatrix} \f$ and \f$ w = \begin{bmatrix} w_1 & w_2 \end{bmatrix}
++ * \f$, the result is simply \f$ v\times w = \overline{v_1 w_2 - v_2 w_1} = \text{conj}\left|\begin{smallmatrix} v_1 &
++ * w_1 \\ v_2 & w_2 \end{smallmatrix}\right| \f$; or, to put it differently, it is the third coordinate of the cross
++ * product of \f$ \begin{bmatrix} v_1 & v_2 & v_3 \end{bmatrix} \f$ and \f$ \begin{bmatrix} w_1 & w_2 & w_3
++ * \end{bmatrix} \f$. For real-valued inputs, the result can be interpreted as the signed area of a parallelogram
++ * spanned by the two vectors.
++ *
++ * \note With complex numbers, the cross product is implemented as
++ * \f[ (\mathbf{a}+i\mathbf{b}) \times (\mathbf{c}+i\mathbf{d}) = (\mathbf{a} \times \mathbf{c} - \mathbf{b} \times
++ * \mathbf{d}) - i(\mathbf{a} \times \mathbf{d} + \mathbf{b} \times \mathbf{c}).\f]
++ * This definition preserves the orthogonality condition that \f$\mathbf{u} \cdot (\mathbf{u} \times \mathbf{v}) =
++ * \mathbf{v} \cdot (\mathbf{u} \times \mathbf{v}) = 0\f$.
++ *
++ * \sa MatrixBase::cross3()
++ */
++ template <typename Derived>
++ template <typename OtherDerived>
++ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::cross_impl<Derived, OtherDerived>::return_type
++ MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const {
++ return internal::cross_impl<Derived, OtherDerived>::run(*this, other);
++ }
++
++ namespace internal {
++
++ template <int Arch, typename VectorLhs, typename VectorRhs, typename Scalar = typename VectorLhs::Scalar,
++ bool Vectorizable =
++ bool((int(evaluator<VectorLhs>::Flags) & int(evaluator<VectorRhs>::Flags)) & PacketAccessBit)>
++ struct cross3_impl {
++ EIGEN_DEVICE_FUNC static inline typename internal::plain_matrix_type<VectorLhs>::type run(const VectorLhs& lhs,
++ const VectorRhs& rhs) {
++ return typename internal::plain_matrix_type<VectorLhs>::type(
++ numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
++ numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
++ numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)), 0);
++ }
++ };
++
++ } // namespace internal
++
++ /** \geometry_module \ingroup Geometry_Module
++ *
++ * \returns the cross product of \c *this and \a other using only the x, y, and z coefficients
++ *
++ * The size of \c *this and \a other must be four. This function is especially useful
++ * when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
++ *
++ * \sa MatrixBase::cross()
++ */
++ template <typename Derived>
++ template <typename OtherDerived>
++ EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::PlainObject MatrixBase<Derived>::cross3(
++ const MatrixBase<OtherDerived>& other) const {
++ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived, 4)
++ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived, 4)
++
++ typedef typename internal::nested_eval<Derived, 2>::type DerivedNested;
++ typedef typename internal::nested_eval<OtherDerived, 2>::type OtherDerivedNested;
++ DerivedNested lhs(derived());
++ OtherDerivedNested rhs(other.derived());
++
++ return internal::cross3_impl<Architecture::Target, internal::remove_all_t<DerivedNested>,
++ internal::remove_all_t<OtherDerivedNested>>::run(lhs, rhs);
++ }
++
++ /** \geometry_module \ingroup Geometry_Module
++ *
++ * \returns a matrix expression of the cross product of each column or row
++ * of the referenced expression with the \a other vector.
++ *
++ * The referenced matrix must have one dimension equal to 3.
++ * The result matrix has the same dimensions than the referenced one.
++ *
++ * \sa MatrixBase::cross() */
++ template <typename ExpressionType, int Direction>
++ template <typename OtherDerived>
++ EIGEN_DEVICE_FUNC const typename VectorwiseOp<ExpressionType, Direction>::CrossReturnType
++ VectorwiseOp<ExpressionType, Direction>::cross(const MatrixBase<OtherDerived>& other) const {
++ EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived, 3)
++ EIGEN_STATIC_ASSERT(
++ (internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
++ YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
++
++ typename internal::nested_eval<ExpressionType, 2>::type mat(_expression());
++ typename internal::nested_eval<OtherDerived, 2>::type vec(other.derived());
++
++ CrossReturnType res(_expression().rows(), _expression().cols());
++ if (Direction == Vertical) {
++ eigen_assert(CrossReturnType::RowsAtCompileTime == 3 && "the matrix must have exactly 3 rows");
++ res.row(0) = (mat.row(1) * vec.coeff(2) - mat.row(2) * vec.coeff(1)).conjugate();
++ res.row(1) = (mat.row(2) * vec.coeff(0) - mat.row(0) * vec.coeff(2)).conjugate();
++ res.row(2) = (mat.row(0) * vec.coeff(1) - mat.row(1) * vec.coeff(0)).conjugate();
++ } else {
++ eigen_assert(CrossReturnType::ColsAtCompileTime == 3 && "the matrix must have exactly 3 columns");
++ res.col(0) = (mat.col(1) * vec.coeff(2) - mat.col(2) * vec.coeff(1)).conjugate();
++ res.col(1) = (mat.col(2) * vec.coeff(0) - mat.col(0) * vec.coeff(2)).conjugate();
++ res.col(2) = (mat.col(0) * vec.coeff(1) - mat.col(1) * vec.coeff(0)).conjugate();
++ }
++ return res;
++ }
++
++ namespace internal {
++
++ template <typename Derived, int Size = Derived::SizeAtCompileTime>
++ struct unitOrthogonal_selector {
++ typedef typename plain_matrix_type<Derived>::type VectorType;
++ typedef typename traits<Derived>::Scalar Scalar;
++ typedef typename NumTraits<Scalar>::Real RealScalar;
++ typedef Matrix<Scalar, 2, 1> Vector2;
++ EIGEN_DEVICE_FUNC static inline VectorType run(const Derived& src) {
++ VectorType perp = VectorType::Zero(src.size());
++ Index maxi = 0;
++ Index sndi = 0;
++ src.cwiseAbs().maxCoeff(&maxi);
++ if (maxi == 0) sndi = 1;
++ RealScalar invnm = RealScalar(1) / (Vector2() << src.coeff(sndi), src.coeff(maxi)).finished().norm();
++ perp.coeffRef(maxi) = -numext::conj(src.coeff(sndi)) * invnm;
++ perp.coeffRef(sndi) = numext::conj(src.coeff(maxi)) * invnm;
++
++ return perp;
++ }
++ };
++
++ template <typename Derived>
++ struct unitOrthogonal_selector<Derived, 3> {
++ typedef typename plain_matrix_type<Derived>::type VectorType;
++ typedef typename traits<Derived>::Scalar Scalar;
++ typedef typename NumTraits<Scalar>::Real RealScalar;
++ EIGEN_DEVICE_FUNC static inline VectorType run(const Derived& src) {
++ VectorType perp;
++ /* Let us compute the crossed product of *this with a vector
++ * that is not too close to being colinear to *this.
++ */
++
++ /* unless the x and y coords are both close to zero, we can
++ * simply take ( -y, x, 0 ) and normalize it.
++ */
++ if ((!isMuchSmallerThan(src.x(), src.z())) || (!isMuchSmallerThan(src.y(), src.z()))) {
++ RealScalar invnm = RealScalar(1) / src.template head<2>().norm();
++ perp.coeffRef(0) = -numext::conj(src.y()) * invnm;
++ perp.coeffRef(1) = numext::conj(src.x()) * invnm;
++ perp.coeffRef(2) = 0;
++ }
++ /* if both x and y are close to zero, then the vector is close
++ * to the z-axis, so it's far from colinear to the x-axis for instance.
++ * So we take the crossed product with (1,0,0) and normalize it.
++ */
++ else {
++ RealScalar invnm = RealScalar(1) / src.template tail<2>().norm();
++ perp.coeffRef(0) = 0;
++ perp.coeffRef(1) = -numext::conj(src.z()) * invnm;
++ perp.coeffRef(2) = numext::conj(src.y()) * invnm;
++ }
++
++ return perp;
++ }
++ };
++
++ template <typename Derived>
++ struct unitOrthogonal_selector<Derived, 2> {
++ typedef typename plain_matrix_type<Derived>::type VectorType;
++ EIGEN_DEVICE_FUNC static inline VectorType run(const Derived& src) {
++ return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized();
++ }
++ };
++
++ } // end namespace internal
++
++ /** \geometry_module \ingroup Geometry_Module
++ *
++ * \returns a unit vector which is orthogonal to \c *this
++ *
++ * The size of \c *this must be at least 2. If the size is exactly 2,
++ * then the returned vector is a counter clock wise rotation of \c *this, i.e., (-y,x).normalized().
++ *
++ * \sa cross()
++ */
++ template <typename Derived>
++ EIGEN_DEVICE_FUNC typename MatrixBase<Derived>::PlainObject MatrixBase<Derived>::unitOrthogonal() const {
++ EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
++ return internal::unitOrthogonal_selector<Derived>::run(derived());
++ }
++
++ } // end namespace Eigen
++
++ #endif // EIGEN_ORTHOMETHODS_H