Eigen  3.3.3
OrthoMethods.h
00001 // This file is part of Eigen, a lightweight C++ template library
00002 // for linear algebra.
00003 //
00004 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
00005 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
00006 //
00007 // This Source Code Form is subject to the terms of the Mozilla
00008 // Public License v. 2.0. If a copy of the MPL was not distributed
00009 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
00010 
00011 #ifndef EIGEN_ORTHOMETHODS_H
00012 #define EIGEN_ORTHOMETHODS_H
00013 
00014 namespace Eigen { 
00015 
00027 template<typename Derived>
00028 template<typename OtherDerived>
00029 #ifndef EIGEN_PARSED_BY_DOXYGEN
00030 EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type
00031 #else
00032 inline typename MatrixBase<Derived>::PlainObject
00033 #endif
00034 MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const
00035 {
00036   EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,3)
00037   EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
00038 
00039   // Note that there is no need for an expression here since the compiler
00040   // optimize such a small temporary very well (even within a complex expression)
00041   typename internal::nested_eval<Derived,2>::type lhs(derived());
00042   typename internal::nested_eval<OtherDerived,2>::type rhs(other.derived());
00043   return typename cross_product_return_type<OtherDerived>::type(
00044     numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
00045     numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
00046     numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0))
00047   );
00048 }
00049 
00050 namespace internal {
00051 
00052 template< int Arch,typename VectorLhs,typename VectorRhs,
00053           typename Scalar = typename VectorLhs::Scalar,
00054           bool Vectorizable = bool((VectorLhs::Flags&VectorRhs::Flags)&PacketAccessBit)>
00055 struct cross3_impl {
00056   EIGEN_DEVICE_FUNC static inline typename internal::plain_matrix_type<VectorLhs>::type
00057   run(const VectorLhs& lhs, const VectorRhs& rhs)
00058   {
00059     return typename internal::plain_matrix_type<VectorLhs>::type(
00060       numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
00061       numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
00062       numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)),
00063       0
00064     );
00065   }
00066 };
00067 
00068 }
00069 
00079 template<typename Derived>
00080 template<typename OtherDerived>
00081 EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::PlainObject
00082 MatrixBase<Derived>::cross3(const MatrixBase<OtherDerived>& other) const
00083 {
00084   EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,4)
00085   EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,4)
00086 
00087   typedef typename internal::nested_eval<Derived,2>::type DerivedNested;
00088   typedef typename internal::nested_eval<OtherDerived,2>::type OtherDerivedNested;
00089   DerivedNested lhs(derived());
00090   OtherDerivedNested rhs(other.derived());
00091 
00092   return internal::cross3_impl<Architecture::Target,
00093                         typename internal::remove_all<DerivedNested>::type,
00094                         typename internal::remove_all<OtherDerivedNested>::type>::run(lhs,rhs);
00095 }
00096 
00106 template<typename ExpressionType, int Direction>
00107 template<typename OtherDerived>
00108 EIGEN_DEVICE_FUNC 
00109 const typename VectorwiseOp<ExpressionType,Direction>::CrossReturnType
00110 VectorwiseOp<ExpressionType,Direction>::cross(const MatrixBase<OtherDerived>& other) const
00111 {
00112   EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
00113   EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
00114     YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
00115   
00116   typename internal::nested_eval<ExpressionType,2>::type mat(_expression());
00117   typename internal::nested_eval<OtherDerived,2>::type vec(other.derived());
00118 
00119   CrossReturnType res(_expression().rows(),_expression().cols());
00120   if(Direction==Vertical)
00121   {
00122     eigen_assert(CrossReturnType::RowsAtCompileTime==3 && "the matrix must have exactly 3 rows");
00123     res.row(0) = (mat.row(1) * vec.coeff(2) - mat.row(2) * vec.coeff(1)).conjugate();
00124     res.row(1) = (mat.row(2) * vec.coeff(0) - mat.row(0) * vec.coeff(2)).conjugate();
00125     res.row(2) = (mat.row(0) * vec.coeff(1) - mat.row(1) * vec.coeff(0)).conjugate();
00126   }
00127   else
00128   {
00129     eigen_assert(CrossReturnType::ColsAtCompileTime==3 && "the matrix must have exactly 3 columns");
00130     res.col(0) = (mat.col(1) * vec.coeff(2) - mat.col(2) * vec.coeff(1)).conjugate();
00131     res.col(1) = (mat.col(2) * vec.coeff(0) - mat.col(0) * vec.coeff(2)).conjugate();
00132     res.col(2) = (mat.col(0) * vec.coeff(1) - mat.col(1) * vec.coeff(0)).conjugate();
00133   }
00134   return res;
00135 }
00136 
00137 namespace internal {
00138 
00139 template<typename Derived, int Size = Derived::SizeAtCompileTime>
00140 struct unitOrthogonal_selector
00141 {
00142   typedef typename plain_matrix_type<Derived>::type VectorType;
00143   typedef typename traits<Derived>::Scalar Scalar;
00144   typedef typename NumTraits<Scalar>::Real RealScalar;
00145   typedef Matrix<Scalar,2,1> Vector2;
00146   EIGEN_DEVICE_FUNC
00147   static inline VectorType run(const Derived& src)
00148   {
00149     VectorType perp = VectorType::Zero(src.size());
00150     Index maxi = 0;
00151     Index sndi = 0;
00152     src.cwiseAbs().maxCoeff(&maxi);
00153     if (maxi==0)
00154       sndi = 1;
00155     RealScalar invnm = RealScalar(1)/(Vector2() << src.coeff(sndi),src.coeff(maxi)).finished().norm();
00156     perp.coeffRef(maxi) = -numext::conj(src.coeff(sndi)) * invnm;
00157     perp.coeffRef(sndi) =  numext::conj(src.coeff(maxi)) * invnm;
00158 
00159     return perp;
00160    }
00161 };
00162 
00163 template<typename Derived>
00164 struct unitOrthogonal_selector<Derived,3>
00165 {
00166   typedef typename plain_matrix_type<Derived>::type VectorType;
00167   typedef typename traits<Derived>::Scalar Scalar;
00168   typedef typename NumTraits<Scalar>::Real RealScalar;
00169   EIGEN_DEVICE_FUNC
00170   static inline VectorType run(const Derived& src)
00171   {
00172     VectorType perp;
00173     /* Let us compute the crossed product of *this with a vector
00174      * that is not too close to being colinear to *this.
00175      */
00176 
00177     /* unless the x and y coords are both close to zero, we can
00178      * simply take ( -y, x, 0 ) and normalize it.
00179      */
00180     if((!isMuchSmallerThan(src.x(), src.z()))
00181     || (!isMuchSmallerThan(src.y(), src.z())))
00182     {
00183       RealScalar invnm = RealScalar(1)/src.template head<2>().norm();
00184       perp.coeffRef(0) = -numext::conj(src.y())*invnm;
00185       perp.coeffRef(1) = numext::conj(src.x())*invnm;
00186       perp.coeffRef(2) = 0;
00187     }
00188     /* if both x and y are close to zero, then the vector is close
00189      * to the z-axis, so it's far from colinear to the x-axis for instance.
00190      * So we take the crossed product with (1,0,0) and normalize it.
00191      */
00192     else
00193     {
00194       RealScalar invnm = RealScalar(1)/src.template tail<2>().norm();
00195       perp.coeffRef(0) = 0;
00196       perp.coeffRef(1) = -numext::conj(src.z())*invnm;
00197       perp.coeffRef(2) = numext::conj(src.y())*invnm;
00198     }
00199 
00200     return perp;
00201    }
00202 };
00203 
00204 template<typename Derived>
00205 struct unitOrthogonal_selector<Derived,2>
00206 {
00207   typedef typename plain_matrix_type<Derived>::type VectorType;
00208   EIGEN_DEVICE_FUNC
00209   static inline VectorType run(const Derived& src)
00210   { return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized(); }
00211 };
00212 
00213 } // end namespace internal
00214 
00224 template<typename Derived>
00225 EIGEN_DEVICE_FUNC typename MatrixBase<Derived>::PlainObject
00226 MatrixBase<Derived>::unitOrthogonal() const
00227 {
00228   EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
00229   return internal::unitOrthogonal_selector<Derived>::run(derived());
00230 }
00231 
00232 } // end namespace Eigen
00233 
00234 #endif // EIGEN_ORTHOMETHODS_H
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