Eigen  3.3.7
OrthoMethods.h
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
5 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
6 //
7 // This Source Code Form is subject to the terms of the Mozilla
8 // Public License v. 2.0. If a copy of the MPL was not distributed
9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10 
11 #ifndef EIGEN_ORTHOMETHODS_H
12 #define EIGEN_ORTHOMETHODS_H
13 
14 namespace Eigen {
15 
27 template<typename Derived>
28 template<typename OtherDerived>
29 #ifndef EIGEN_PARSED_BY_DOXYGEN
30 EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type
31 #else
32 inline typename MatrixBase<Derived>::PlainObject
33 #endif
35 {
36  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,3)
37  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
38 
39  // Note that there is no need for an expression here since the compiler
40  // optimize such a small temporary very well (even within a complex expression)
41  typename internal::nested_eval<Derived,2>::type lhs(derived());
42  typename internal::nested_eval<OtherDerived,2>::type rhs(other.derived());
43  return typename cross_product_return_type<OtherDerived>::type(
44  numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
45  numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
46  numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0))
47  );
48 }
49 
50 namespace internal {
51 
52 template< int Arch,typename VectorLhs,typename VectorRhs,
53  typename Scalar = typename VectorLhs::Scalar,
54  bool Vectorizable = bool((VectorLhs::Flags&VectorRhs::Flags)&PacketAccessBit)>
55 struct cross3_impl {
56  EIGEN_DEVICE_FUNC static inline typename internal::plain_matrix_type<VectorLhs>::type
57  run(const VectorLhs& lhs, const VectorRhs& rhs)
58  {
59  return typename internal::plain_matrix_type<VectorLhs>::type(
60  numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
61  numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
62  numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)),
63  0
64  );
65  }
66 };
67 
68 }
69 
79 template<typename Derived>
80 template<typename OtherDerived>
81 EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::PlainObject
83 {
84  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,4)
85  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,4)
86 
87  typedef typename internal::nested_eval<Derived,2>::type DerivedNested;
88  typedef typename internal::nested_eval<OtherDerived,2>::type OtherDerivedNested;
89  DerivedNested lhs(derived());
90  OtherDerivedNested rhs(other.derived());
91 
92  return internal::cross3_impl<Architecture::Target,
93  typename internal::remove_all<DerivedNested>::type,
94  typename internal::remove_all<OtherDerivedNested>::type>::run(lhs,rhs);
95 }
96 
106 template<typename ExpressionType, int Direction>
107 template<typename OtherDerived>
108 EIGEN_DEVICE_FUNC
109 const typename VectorwiseOp<ExpressionType,Direction>::CrossReturnType
111 {
112  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
113  EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
114  YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
115 
116  typename internal::nested_eval<ExpressionType,2>::type mat(_expression());
117  typename internal::nested_eval<OtherDerived,2>::type vec(other.derived());
118 
119  CrossReturnType res(_expression().rows(),_expression().cols());
120  if(Direction==Vertical)
121  {
122  eigen_assert(CrossReturnType::RowsAtCompileTime==3 && "the matrix must have exactly 3 rows");
123  res.row(0) = (mat.row(1) * vec.coeff(2) - mat.row(2) * vec.coeff(1)).conjugate();
124  res.row(1) = (mat.row(2) * vec.coeff(0) - mat.row(0) * vec.coeff(2)).conjugate();
125  res.row(2) = (mat.row(0) * vec.coeff(1) - mat.row(1) * vec.coeff(0)).conjugate();
126  }
127  else
128  {
129  eigen_assert(CrossReturnType::ColsAtCompileTime==3 && "the matrix must have exactly 3 columns");
130  res.col(0) = (mat.col(1) * vec.coeff(2) - mat.col(2) * vec.coeff(1)).conjugate();
131  res.col(1) = (mat.col(2) * vec.coeff(0) - mat.col(0) * vec.coeff(2)).conjugate();
132  res.col(2) = (mat.col(0) * vec.coeff(1) - mat.col(1) * vec.coeff(0)).conjugate();
133  }
134  return res;
135 }
136 
137 namespace internal {
138 
139 template<typename Derived, int Size = Derived::SizeAtCompileTime>
140 struct unitOrthogonal_selector
141 {
142  typedef typename plain_matrix_type<Derived>::type VectorType;
143  typedef typename traits<Derived>::Scalar Scalar;
144  typedef typename NumTraits<Scalar>::Real RealScalar;
145  typedef Matrix<Scalar,2,1> Vector2;
146  EIGEN_DEVICE_FUNC
147  static inline VectorType run(const Derived& src)
148  {
149  VectorType perp = VectorType::Zero(src.size());
150  Index maxi = 0;
151  Index sndi = 0;
152  src.cwiseAbs().maxCoeff(&maxi);
153  if (maxi==0)
154  sndi = 1;
155  RealScalar invnm = RealScalar(1)/(Vector2() << src.coeff(sndi),src.coeff(maxi)).finished().norm();
156  perp.coeffRef(maxi) = -numext::conj(src.coeff(sndi)) * invnm;
157  perp.coeffRef(sndi) = numext::conj(src.coeff(maxi)) * invnm;
158 
159  return perp;
160  }
161 };
162 
163 template<typename Derived>
164 struct unitOrthogonal_selector<Derived,3>
165 {
166  typedef typename plain_matrix_type<Derived>::type VectorType;
167  typedef typename traits<Derived>::Scalar Scalar;
168  typedef typename NumTraits<Scalar>::Real RealScalar;
169  EIGEN_DEVICE_FUNC
170  static inline VectorType run(const Derived& src)
171  {
172  VectorType perp;
173  /* Let us compute the crossed product of *this with a vector
174  * that is not too close to being colinear to *this.
175  */
176 
177  /* unless the x and y coords are both close to zero, we can
178  * simply take ( -y, x, 0 ) and normalize it.
179  */
180  if((!isMuchSmallerThan(src.x(), src.z()))
181  || (!isMuchSmallerThan(src.y(), src.z())))
182  {
183  RealScalar invnm = RealScalar(1)/src.template head<2>().norm();
184  perp.coeffRef(0) = -numext::conj(src.y())*invnm;
185  perp.coeffRef(1) = numext::conj(src.x())*invnm;
186  perp.coeffRef(2) = 0;
187  }
188  /* if both x and y are close to zero, then the vector is close
189  * to the z-axis, so it's far from colinear to the x-axis for instance.
190  * So we take the crossed product with (1,0,0) and normalize it.
191  */
192  else
193  {
194  RealScalar invnm = RealScalar(1)/src.template tail<2>().norm();
195  perp.coeffRef(0) = 0;
196  perp.coeffRef(1) = -numext::conj(src.z())*invnm;
197  perp.coeffRef(2) = numext::conj(src.y())*invnm;
198  }
199 
200  return perp;
201  }
202 };
203 
204 template<typename Derived>
205 struct unitOrthogonal_selector<Derived,2>
206 {
207  typedef typename plain_matrix_type<Derived>::type VectorType;
208  EIGEN_DEVICE_FUNC
209  static inline VectorType run(const Derived& src)
210  { return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized(); }
211 };
212 
213 } // end namespace internal
214 
224 template<typename Derived>
225 EIGEN_DEVICE_FUNC typename MatrixBase<Derived>::PlainObject
227 {
228  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
229  return internal::unitOrthogonal_selector<Derived>::run(derived());
230 }
231 
232 } // end namespace Eigen
233 
234 #endif // EIGEN_ORTHOMETHODS_H
Definition: Constants.h:265
const CrossReturnType cross(const MatrixBase< OtherDerived > &other) const
Definition: OrthoMethods.h:110
Namespace containing all symbols from the Eigen library.
Definition: Core:306
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
Definition: NumTraits.h:150
const unsigned int PacketAccessBit
Definition: Constants.h:89
PlainObject cross3(const MatrixBase< OtherDerived > &other) const
Definition: OrthoMethods.h:82
PlainObject unitOrthogonal(void) const
Definition: OrthoMethods.h:226
PlainObject cross(const MatrixBase< OtherDerived > &other) const
Definition: OrthoMethods.h:34
Derived & derived()
Definition: EigenBase.h:45
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33
Definition: Eigen_Colamd.h:50
The matrix class, also used for vectors and row-vectors.
Definition: Matrix.h:178
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:48