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Diffstat (limited to 'runtimes/nn/depend/external/eigen/Eigen/src/Geometry/OrthoMethods.h')
| -rw-r--r-- | runtimes/nn/depend/external/eigen/Eigen/src/Geometry/OrthoMethods.h | 234 |
1 files changed, 234 insertions, 0 deletions
diff --git a/runtimes/nn/depend/external/eigen/Eigen/src/Geometry/OrthoMethods.h b/runtimes/nn/depend/external/eigen/Eigen/src/Geometry/OrthoMethods.h new file mode 100644 index 000000000..a035e6310 --- /dev/null +++ b/runtimes/nn/depend/external/eigen/Eigen/src/Geometry/OrthoMethods.h @@ -0,0 +1,234 @@ +// 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 + +namespace Eigen { + +/** \geometry_module \ingroup Geometry_Module + * + * \returns the cross product of \c *this and \a other + * + * Here is a very good explanation of cross-product: http://xkcd.com/199/ + * + * 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$ + * + * \sa MatrixBase::cross3() + */ +template<typename Derived> +template<typename OtherDerived> +#ifndef EIGEN_PARSED_BY_DOXYGEN +EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type +#else +inline typename MatrixBase<Derived>::PlainObject +#endif +MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const +{ + 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(derived()); + typename internal::nested_eval<OtherDerived,2>::type rhs(other.derived()); + return typename cross_product_return_type<OtherDerived>::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)) + ); +} + +namespace internal { + +template< int Arch,typename VectorLhs,typename VectorRhs, + typename Scalar = typename VectorLhs::Scalar, + bool Vectorizable = bool((VectorLhs::Flags&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 + ); + } +}; + +} + +/** \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, + typename internal::remove_all<DerivedNested>::type, + typename internal::remove_all<OtherDerivedNested>::type>::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 |