add Eigen as a dependency
This commit is contained in:
Sven Czarnian
234
external/include/eigen3/Eigen/src/Geometry/OrthoMethods.h
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234
external/include/eigen3/Eigen/src/Geometry/OrthoMethods.h
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_ORTHOMETHODS_H
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#define EIGEN_ORTHOMETHODS_H
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namespace Eigen {
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/** \geometry_module \ingroup Geometry_Module
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*
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* \returns the cross product of \c *this and \a other
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*
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* Here is a very good explanation of cross-product: http://xkcd.com/199/
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*
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* With complex numbers, the cross product is implemented as
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* \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$
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*
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* \sa MatrixBase::cross3()
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*/
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template<typename Derived>
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template<typename OtherDerived>
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#ifndef EIGEN_PARSED_BY_DOXYGEN
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EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type
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#else
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inline typename MatrixBase<Derived>::PlainObject
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#endif
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MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const
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{
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,3)
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
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// Note that there is no need for an expression here since the compiler
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// optimize such a small temporary very well (even within a complex expression)
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typename internal::nested_eval<Derived,2>::type lhs(derived());
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typename internal::nested_eval<OtherDerived,2>::type rhs(other.derived());
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return typename cross_product_return_type<OtherDerived>::type(
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numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
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numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
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numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0))
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);
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}
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namespace internal {
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template< int Arch,typename VectorLhs,typename VectorRhs,
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typename Scalar = typename VectorLhs::Scalar,
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bool Vectorizable = bool((VectorLhs::Flags&VectorRhs::Flags)&PacketAccessBit)>
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struct cross3_impl {
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EIGEN_DEVICE_FUNC static inline typename internal::plain_matrix_type<VectorLhs>::type
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run(const VectorLhs& lhs, const VectorRhs& rhs)
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{
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return typename internal::plain_matrix_type<VectorLhs>::type(
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numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
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numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
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numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)),
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0
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);
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}
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};
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}
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/** \geometry_module \ingroup Geometry_Module
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*
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* \returns the cross product of \c *this and \a other using only the x, y, and z coefficients
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*
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* The size of \c *this and \a other must be four. This function is especially useful
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* when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
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*
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* \sa MatrixBase::cross()
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*/
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template<typename Derived>
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template<typename OtherDerived>
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EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::PlainObject
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MatrixBase<Derived>::cross3(const MatrixBase<OtherDerived>& other) const
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{
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,4)
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,4)
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typedef typename internal::nested_eval<Derived,2>::type DerivedNested;
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typedef typename internal::nested_eval<OtherDerived,2>::type OtherDerivedNested;
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DerivedNested lhs(derived());
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OtherDerivedNested rhs(other.derived());
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return internal::cross3_impl<Architecture::Target,
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typename internal::remove_all<DerivedNested>::type,
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typename internal::remove_all<OtherDerivedNested>::type>::run(lhs,rhs);
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}
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/** \geometry_module \ingroup Geometry_Module
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*
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* \returns a matrix expression of the cross product of each column or row
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* of the referenced expression with the \a other vector.
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*
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* The referenced matrix must have one dimension equal to 3.
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* The result matrix has the same dimensions than the referenced one.
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*
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* \sa MatrixBase::cross() */
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template<typename ExpressionType, int Direction>
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template<typename OtherDerived>
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EIGEN_DEVICE_FUNC
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const typename VectorwiseOp<ExpressionType,Direction>::CrossReturnType
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VectorwiseOp<ExpressionType,Direction>::cross(const MatrixBase<OtherDerived>& other) const
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{
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EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
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EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
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YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
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typename internal::nested_eval<ExpressionType,2>::type mat(_expression());
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typename internal::nested_eval<OtherDerived,2>::type vec(other.derived());
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CrossReturnType res(_expression().rows(),_expression().cols());
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if(Direction==Vertical)
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{
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eigen_assert(CrossReturnType::RowsAtCompileTime==3 && "the matrix must have exactly 3 rows");
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res.row(0) = (mat.row(1) * vec.coeff(2) - mat.row(2) * vec.coeff(1)).conjugate();
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res.row(1) = (mat.row(2) * vec.coeff(0) - mat.row(0) * vec.coeff(2)).conjugate();
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res.row(2) = (mat.row(0) * vec.coeff(1) - mat.row(1) * vec.coeff(0)).conjugate();
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}
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else
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{
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eigen_assert(CrossReturnType::ColsAtCompileTime==3 && "the matrix must have exactly 3 columns");
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res.col(0) = (mat.col(1) * vec.coeff(2) - mat.col(2) * vec.coeff(1)).conjugate();
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res.col(1) = (mat.col(2) * vec.coeff(0) - mat.col(0) * vec.coeff(2)).conjugate();
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res.col(2) = (mat.col(0) * vec.coeff(1) - mat.col(1) * vec.coeff(0)).conjugate();
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}
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return res;
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}
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namespace internal {
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template<typename Derived, int Size = Derived::SizeAtCompileTime>
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struct unitOrthogonal_selector
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{
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typedef typename plain_matrix_type<Derived>::type VectorType;
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typedef typename traits<Derived>::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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typedef Matrix<Scalar,2,1> Vector2;
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EIGEN_DEVICE_FUNC
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static inline VectorType run(const Derived& src)
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{
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VectorType perp = VectorType::Zero(src.size());
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Index maxi = 0;
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Index sndi = 0;
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src.cwiseAbs().maxCoeff(&maxi);
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if (maxi==0)
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sndi = 1;
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RealScalar invnm = RealScalar(1)/(Vector2() << src.coeff(sndi),src.coeff(maxi)).finished().norm();
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perp.coeffRef(maxi) = -numext::conj(src.coeff(sndi)) * invnm;
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perp.coeffRef(sndi) = numext::conj(src.coeff(maxi)) * invnm;
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return perp;
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}
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};
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template<typename Derived>
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struct unitOrthogonal_selector<Derived,3>
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{
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typedef typename plain_matrix_type<Derived>::type VectorType;
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typedef typename traits<Derived>::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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EIGEN_DEVICE_FUNC
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static inline VectorType run(const Derived& src)
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{
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VectorType perp;
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/* Let us compute the crossed product of *this with a vector
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* that is not too close to being colinear to *this.
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*/
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/* unless the x and y coords are both close to zero, we can
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* simply take ( -y, x, 0 ) and normalize it.
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*/
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if((!isMuchSmallerThan(src.x(), src.z()))
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|| (!isMuchSmallerThan(src.y(), src.z())))
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{
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RealScalar invnm = RealScalar(1)/src.template head<2>().norm();
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perp.coeffRef(0) = -numext::conj(src.y())*invnm;
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perp.coeffRef(1) = numext::conj(src.x())*invnm;
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perp.coeffRef(2) = 0;
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}
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/* if both x and y are close to zero, then the vector is close
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* to the z-axis, so it's far from colinear to the x-axis for instance.
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* So we take the crossed product with (1,0,0) and normalize it.
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*/
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else
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{
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RealScalar invnm = RealScalar(1)/src.template tail<2>().norm();
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perp.coeffRef(0) = 0;
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perp.coeffRef(1) = -numext::conj(src.z())*invnm;
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perp.coeffRef(2) = numext::conj(src.y())*invnm;
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}
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return perp;
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}
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};
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template<typename Derived>
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struct unitOrthogonal_selector<Derived,2>
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{
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typedef typename plain_matrix_type<Derived>::type VectorType;
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EIGEN_DEVICE_FUNC
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static inline VectorType run(const Derived& src)
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{ return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized(); }
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};
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} // end namespace internal
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/** \geometry_module \ingroup Geometry_Module
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*
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* \returns a unit vector which is orthogonal to \c *this
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*
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* The size of \c *this must be at least 2. If the size is exactly 2,
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* then the returned vector is a counter clock wise rotation of \c *this, i.e., (-y,x).normalized().
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*
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* \sa cross()
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*/
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template<typename Derived>
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EIGEN_DEVICE_FUNC typename MatrixBase<Derived>::PlainObject
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MatrixBase<Derived>::unitOrthogonal() const
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{
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EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
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return internal::unitOrthogonal_selector<Derived>::run(derived());
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}
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} // end namespace Eigen
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#endif // EIGEN_ORTHOMETHODS_H
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