/usr/include/eigen3/Eigen/src/Geometry/OrthoMethods.h is in libeigen3-dev 3.2.2-3.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 | // 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
*
* \returns the cross product of \c *this and \a other
*
* Here is a very good explanation of cross-product: http://xkcd.com/199/
* \sa MatrixBase::cross3()
*/
template<typename Derived>
template<typename OtherDerived>
inline typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type
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<Derived,2>::type lhs(derived());
typename internal::nested<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 {
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
*
* \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>
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<Derived,2>::type DerivedNested;
typedef typename internal::nested<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);
}
/** \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.
*
* \geometry_module
*
* \sa MatrixBase::cross() */
template<typename ExpressionType, int Direction>
template<typename OtherDerived>
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)
CrossReturnType res(_expression().rows(),_expression().cols());
if(Direction==Vertical)
{
eigen_assert(CrossReturnType::RowsAtCompileTime==3 && "the matrix must have exactly 3 rows");
res.row(0) = (_expression().row(1) * other.coeff(2) - _expression().row(2) * other.coeff(1)).conjugate();
res.row(1) = (_expression().row(2) * other.coeff(0) - _expression().row(0) * other.coeff(2)).conjugate();
res.row(2) = (_expression().row(0) * other.coeff(1) - _expression().row(1) * other.coeff(0)).conjugate();
}
else
{
eigen_assert(CrossReturnType::ColsAtCompileTime==3 && "the matrix must have exactly 3 columns");
res.col(0) = (_expression().col(1) * other.coeff(2) - _expression().col(2) * other.coeff(1)).conjugate();
res.col(1) = (_expression().col(2) * other.coeff(0) - _expression().col(0) * other.coeff(2)).conjugate();
res.col(2) = (_expression().col(0) * other.coeff(1) - _expression().col(1) * other.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 typename Derived::Index Index;
typedef Matrix<Scalar,2,1> Vector2;
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;
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;
static inline VectorType run(const Derived& src)
{ return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized(); }
};
} // end namespace internal
/** \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>
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
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