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GCC Code Coverage Report

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File:	include/pinocchio/spatial/skew.hpp	Lines:	58	58	100.0 %
Date:	2024-04-26 13:14:21	Branches:	38	76	50.0 %


//
// Copyright (c) 2015-2018 CNRS INRIA
//

#ifndef __pinocchio_skew_hpp__
#define __pinocchio_skew_hpp__

#include "pinocchio/macros.hpp"

namespace pinocchio
{

  ///
  /// \brief Computes the skew representation of a given 3d vector,
  ///        i.e. the antisymmetric matrix representation of the cross product operator (\f$ [v]_{\times} x = v \times x \f$)
  ///
  /// \param[in]  v a vector of dimension 3.
  /// \param[out] M the skew matrix representation of dimension 3x3.
  ///
  template <typename Vector3, typename Matrix3>
  inline void skew(const Eigen::MatrixBase<Vector3> & v,
                   const Eigen::MatrixBase<Matrix3> & M)
  {
    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Vector3,3);
    EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix3,3,3);

    Matrix3 & M_ = PINOCCHIO_EIGEN_CONST_CAST(Matrix3,M);
    typedef typename Matrix3::RealScalar Scalar;

    M_(0,0) = Scalar(0);  M_(0,1) = -v[2];      M_(0,2) = v[1];
    M_(1,0) = v[2];       M_(1,1) = Scalar(0);  M_(1,2) = -v[0];
    M_(2,0) = -v[1];      M_(2,1) = v[0];       M_(2,2) = Scalar(0);
  }

  ///
  /// \brief Computes the skew representation of a given 3D vector,
  ///        i.e. the antisymmetric matrix representation of the cross product operator.
  ///
  /// \param[in] v a vector of dimension 3.
  ///
  /// \return The skew matrix representation of v.
  ///
  template <typename D>
  inline Eigen::Matrix<typename D::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(D)::Options>
  skew(const Eigen::MatrixBase<D> & v)
  {
    Eigen::Matrix<typename D::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(D)::Options> M;
    skew(v,M);
    return M;
  }

  ///
  /// \brief Add skew matrix represented by a 3d vector to a given matrix,
  ///        i.e. add the antisymmetric matrix representation of the cross product operator (\f$ [v]_{\times} x = v \times x \f$)
  ///
  /// \param[in]  v a vector of dimension 3.
  /// \param[out] M the 3x3 matrix to which the skew matrix is added.
  ///
  template <typename Vector3Like, typename Matrix3Like>
  inline void addSkew(const Eigen::MatrixBase<Vector3Like> & v,
                      const Eigen::MatrixBase<Matrix3Like> & M)
  {
    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Vector3Like,3);
    PINOCCHIO_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix3Like,M,3,3);

    Matrix3Like & M_ = PINOCCHIO_EIGEN_CONST_CAST(Matrix3Like,M);

                          M_(0,1) -= v[2];      M_(0,2) += v[1];
    M_(1,0) += v[2];                            M_(1,2) -= v[0];
    M_(2,0) -= v[1];      M_(2,1) += v[0];                     ;
  }

  ///
  /// \brief Inverse of skew operator. From a given skew-symmetric matrix M
  ///        of dimension 3x3, it extracts the supporting vector, i.e. the entries of M.
  ///        Mathematically speacking, it computes \f$ v \f$ such that \f$ M x = v \times x \f$.
  ///
  /// \param[in]  M a 3x3 skew symmetric matrix.
  /// \param[out] v the 3d vector representation of M.
  ///
  template <typename Matrix3, typename Vector3>
  inline void unSkew(const Eigen::MatrixBase<Matrix3> & M,
                     const Eigen::MatrixBase<Vector3> & v)
  {
    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Vector3,3);
    EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix3,3,3);
    assert((M + M.transpose()).isMuchSmallerThan(M));

    Vector3 & v_ = PINOCCHIO_EIGEN_CONST_CAST(Vector3,v);
    typedef typename Vector3::RealScalar Scalar;

    v_[0] = Scalar(0.5) * (M(2,1) - M(1,2));
    v_[1] = Scalar(0.5) * (M(0,2) - M(2,0));
    v_[2] = Scalar(0.5) * (M(1,0) - M(0,1));
  }

  ///
  /// \brief Inverse of skew operator. From a given skew-symmetric matrix M
  ///        of dimension 3x3, it extracts the supporting vector, i.e. the entries of M.
  ///        Mathematically speacking, it computes \f$ v \f$ such that \f$ M x = v \times x \f$.
  ///
  /// \param[in] M a 3x3 matrix.
  ///
  /// \return The vector entries of the skew-symmetric matrix.
  ///
  template <typename Matrix3>
  inline Eigen::Matrix<typename PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3)::Scalar,3,1,PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3)::Options>
  unSkew(const Eigen::MatrixBase<Matrix3> & M)
  {
    Eigen::Matrix<typename PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3)::Scalar,3,1,PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3)::Options> v;
    unSkew(M,v);
    return v;
  }

  ///
  /// \brief Computes the skew representation of a given 3d vector multiplied by a given scalar.
  ///        i.e. the antisymmetric matrix representation of the cross product operator (\f$ [\alpha v]_{\times} x = \alpha v \times x \f$)
  ///
  /// \param[in]  alpha a real scalar.
  /// \param[in]  v a vector of dimension 3.
  /// \param[out] M the skew matrix representation of dimension 3x3.
  ///
  template <typename Scalar, typename Vector3, typename Matrix3>
  void alphaSkew(const Scalar alpha,
                 const Eigen::MatrixBase<Vector3> & v,
                 const Eigen::MatrixBase<Matrix3> & M)
  {
    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Vector3,3);
    EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix3,3,3);

    Matrix3 & M_ = PINOCCHIO_EIGEN_CONST_CAST(Matrix3,M);
    typedef typename Matrix3::RealScalar RealScalar;

    M_(0,0) = RealScalar(0);  M_(0,1) = -v[2] * alpha;  M_(0,2) = v[1] * alpha;
    M_(1,0) = -M_(0,1);       M_(1,1) = RealScalar(0);  M_(1,2) = -v[0] * alpha;
    M_(2,0) = -M_(0,2);       M_(2,1) = -M_(1,2);       M_(2,2) = RealScalar(0);
  }

  ///
  /// \brief Computes the skew representation of a given 3d vector multiplied by a given scalar.
  ///        i.e. the antisymmetric matrix representation of the cross product operator (\f$ [\alpha v]_{\times} x = \alpha v \times x \f$)
  ///
  /// \param[in]  alpha a real scalar.
  /// \param[in]  v a vector of dimension 3.
  ///
  /// \returns the skew matrix representation of \f$ \alpha v \f$.
  ///
  template <typename Scalar, typename Vector3>
  inline Eigen::Matrix<typename Vector3::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(Vector3)::Options>
  alphaSkew(const Scalar alpha,
            const Eigen::MatrixBase<Vector3> & v)
  {
    Eigen::Matrix<typename Vector3::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(Vector3)::Options> M;
    alphaSkew(alpha,v,M);
    return M;
  }

  ///
  /// \brief Computes the square cross product linear operator C(u,v) such that for any vector w, \f$ u \times ( v \times w ) = C(u,v) w \f$.
  ///
  /// \param[in]  u a 3 dimensional vector.
  /// \param[in]  v a 3 dimensional vector.
  /// \param[out] C the skew square matrix representation of dimension 3x3.
  ///
  template <typename V1, typename V2, typename Matrix3>
  inline void skewSquare(const Eigen::MatrixBase<V1> & u,
                         const Eigen::MatrixBase<V2> & v,
                         const Eigen::MatrixBase<Matrix3> & C)
  {
    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(V1,3);
    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(V2,3);
    EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix3,3,3);

    Matrix3 & C_ = PINOCCHIO_EIGEN_CONST_CAST(Matrix3,C);
    typedef typename Matrix3::RealScalar Scalar;

    C_.noalias() = v*u.transpose();
    const Scalar udotv(u.dot(v));
    C_.diagonal().array() -= udotv;
  }

  ///
  /// \brief Computes the square cross product linear operator C(u,v) such that for any vector w, \f$ u \times ( v \times w ) = C(u,v) w \f$.
  ///
  /// \param[in] u A 3 dimensional vector.
  /// \param[in] v A 3 dimensional vector.
  ///
  /// \return The square cross product matrix skew[u] * skew[v].
  ///
  template <typename V1, typename V2>
  inline Eigen::Matrix<typename V1::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(V1)::Options>
  skewSquare(const Eigen::MatrixBase<V1> & u,
             const Eigen::MatrixBase<V2> & v)
  {

    Eigen::Matrix<typename V1::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(V1)::Options> M;
    skewSquare(u,v,M);
    return M;
  }

  ///
  /// \brief Applies the cross product onto the columns of M.
  ///
  /// \param[in] v      a vector of dimension 3.
  /// \param[in] Min    a 3 rows matrix.
  /// \param[out] Mout  a 3 rows matrix.
  ///
  /// \return the results of \f$ Mout = [v]_{\times} Min \f$.
  ///
  template <typename Vector3, typename Matrix3xIn, typename Matrix3xOut>
  inline void cross(const Eigen::MatrixBase<Vector3> & v,
                    const Eigen::MatrixBase<Matrix3xIn> & Min,
                    const Eigen::MatrixBase<Matrix3xOut> & Mout)
  {
    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Vector3,3);
    EIGEN_STATIC_ASSERT(Matrix3xIn::RowsAtCompileTime==3,THIS_METHOD_IS_ONLY_FOR_MATRICES_OF_A_SPECIFIC_SIZE);
    EIGEN_STATIC_ASSERT(Matrix3xOut::RowsAtCompileTime==3,THIS_METHOD_IS_ONLY_FOR_MATRICES_OF_A_SPECIFIC_SIZE);

    Matrix3xOut & Mout_ = PINOCCHIO_EIGEN_CONST_CAST(Matrix3xOut,Mout);

    Mout_.row(0) = v[1]*Min.row(2) - v[2]*Min.row(1);
    Mout_.row(1) = v[2]*Min.row(0) - v[0]*Min.row(2);
    Mout_.row(2) = v[0]*Min.row(1) - v[1]*Min.row(0);
  }

  ///
  /// \brief Applies the cross product onto the columns of M.
  ///
  /// \param[in] v a vector of dimension 3.
  /// \param[in] M a 3 rows matrix.
  ///
  /// \return the results of \f$ [v]_{\times} M \f$.
  ///
  template <typename Vector3, typename Matrix3x>
  inline typename PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3x)
  cross(const Eigen::MatrixBase<Vector3> & v,
        const Eigen::MatrixBase<Matrix3x> & M)
  {
    typename PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3x) res(3,M.cols());
    cross(v,M,res);
    return res;
  }

} // namespace pinocchio

#endif // ifndef __pinocchio_skew_hpp__


Generated by: GCOVR (Version 4.2)

Line	Branch	Exec	Source
1			//
2			// Copyright (c) 2015-2018 CNRS INRIA
3			//
4
5			#ifndef __pinocchio_skew_hpp__
6			#define __pinocchio_skew_hpp__
7
8			#include "pinocchio/macros.hpp"
9
10			namespace pinocchio
11			{
12
13			///
14			/// \brief Computes the skew representation of a given 3d vector,
15			/// i.e. the antisymmetric matrix representation of the cross product operator (\f$ [v]_{\times} x = v \times x \f$)
16			///
17			/// \param[in] v a vector of dimension 3.
18			/// \param[out] M the skew matrix representation of dimension 3x3.
19			///
20			template <typename Vector3, typename Matrix3>
21		34268	inline void skew(const Eigen::MatrixBase<Vector3> & v,
22			const Eigen::MatrixBase<Matrix3> & M)
23			{
24			EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Vector3,3);
25			EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix3,3,3);
26
27		34268	Matrix3 & M_ = PINOCCHIO_EIGEN_CONST_CAST(Matrix3,M);
28			typedef typename Matrix3::RealScalar Scalar;
29
30		34268	M_(0,0) = Scalar(0); M_(0,1) = -v[2]; M_(0,2) = v[1];
31		34268	M_(1,0) = v[2]; M_(1,1) = Scalar(0); M_(1,2) = -v[0];
32		34268	M_(2,0) = -v[1]; M_(2,1) = v[0]; M_(2,2) = Scalar(0);
33		34268	}
34
35			///
36			/// \brief Computes the skew representation of a given 3D vector,
37			/// i.e. the antisymmetric matrix representation of the cross product operator.
38			///
39			/// \param[in] v a vector of dimension 3.
40			///
41			/// \return The skew matrix representation of v.
42			///
43			template <typename D>
44			inline Eigen::Matrix<typename D::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(D)::Options>
45		34120	skew(const Eigen::MatrixBase<D> & v)
46			{
47		34120	Eigen::Matrix<typename D::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(D)::Options> M;
48		34120	skew(v,M);
49		34120	return M;
50			}
51
52			///
53			/// \brief Add skew matrix represented by a 3d vector to a given matrix,
54			/// i.e. add the antisymmetric matrix representation of the cross product operator (\f$ [v]_{\times} x = v \times x \f$)
55			///
56			/// \param[in] v a vector of dimension 3.
57			/// \param[out] M the 3x3 matrix to which the skew matrix is added.
58			///
59			template <typename Vector3Like, typename Matrix3Like>
60		18893	inline void addSkew(const Eigen::MatrixBase<Vector3Like> & v,
61			const Eigen::MatrixBase<Matrix3Like> & M)
62			{
63			EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Vector3Like,3);
64	✓✗✓✗	18893	PINOCCHIO_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix3Like,M,3,3);
65
66		18893	Matrix3Like & M_ = PINOCCHIO_EIGEN_CONST_CAST(Matrix3Like,M);
67
68		18893	M_(0,1) -= v[2]; M_(0,2) += v[1];
69		18893	M_(1,0) += v[2]; M_(1,2) -= v[0];
70		18893	M_(2,0) -= v[1]; M_(2,1) += v[0]; ;
71		18893	}
72
73			///
74			/// \brief Inverse of skew operator. From a given skew-symmetric matrix M
75			/// of dimension 3x3, it extracts the supporting vector, i.e. the entries of M.
76			/// Mathematically speacking, it computes \f$ v \f$ such that \f$ M x = v \times x \f$.
77			///
78			/// \param[in] M a 3x3 skew symmetric matrix.
79			/// \param[out] v the 3d vector representation of M.
80			///
81			template <typename Matrix3, typename Vector3>
82		3	inline void unSkew(const Eigen::MatrixBase<Matrix3> & M,
83			const Eigen::MatrixBase<Vector3> & v)
84			{
85			EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Vector3,3);
86			EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix3,3,3);
87	✓✗✓✗ ✗✓	3	assert((M + M.transpose()).isMuchSmallerThan(M));
88
89		3	Vector3 & v_ = PINOCCHIO_EIGEN_CONST_CAST(Vector3,v);
90			typedef typename Vector3::RealScalar Scalar;
91
92		3	v_[0] = Scalar(0.5) * (M(2,1) - M(1,2));
93		3	v_[1] = Scalar(0.5) * (M(0,2) - M(2,0));
94		3	v_[2] = Scalar(0.5) * (M(1,0) - M(0,1));
95		3	}
96
97			///
98			/// \brief Inverse of skew operator. From a given skew-symmetric matrix M
99			/// of dimension 3x3, it extracts the supporting vector, i.e. the entries of M.
100			/// Mathematically speacking, it computes \f$ v \f$ such that \f$ M x = v \times x \f$.
101			///
102			/// \param[in] M a 3x3 matrix.
103			///
104			/// \return The vector entries of the skew-symmetric matrix.
105			///
106			template <typename Matrix3>
107			inline Eigen::Matrix<typename PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3)::Scalar,3,1,PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3)::Options>
108		3	unSkew(const Eigen::MatrixBase<Matrix3> & M)
109			{
110		3	Eigen::Matrix<typename PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3)::Scalar,3,1,PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3)::Options> v;
111		3	unSkew(M,v);
112		3	return v;
113			}
114
115			///
116			/// \brief Computes the skew representation of a given 3d vector multiplied by a given scalar.
117			/// i.e. the antisymmetric matrix representation of the cross product operator (\f$ [\alpha v]_{\times} x = \alpha v \times x \f$)
118			///
119			/// \param[in] alpha a real scalar.
120			/// \param[in] v a vector of dimension 3.
121			/// \param[out] M the skew matrix representation of dimension 3x3.
122			///
123			template <typename Scalar, typename Vector3, typename Matrix3>
124		9380	void alphaSkew(const Scalar alpha,
125			const Eigen::MatrixBase<Vector3> & v,
126			const Eigen::MatrixBase<Matrix3> & M)
127			{
128			EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Vector3,3);
129			EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix3,3,3);
130
131		9380	Matrix3 & M_ = PINOCCHIO_EIGEN_CONST_CAST(Matrix3,M);
132			typedef typename Matrix3::RealScalar RealScalar;
133
134		9380	M_(0,0) = RealScalar(0); M_(0,1) = -v[2] * alpha; M_(0,2) = v[1] * alpha;
135		9380	M_(1,0) = -M_(0,1); M_(1,1) = RealScalar(0); M_(1,2) = -v[0] * alpha;
136		9380	M_(2,0) = -M_(0,2); M_(2,1) = -M_(1,2); M_(2,2) = RealScalar(0);
137		9380	}
138
139			///
140			/// \brief Computes the skew representation of a given 3d vector multiplied by a given scalar.
141			/// i.e. the antisymmetric matrix representation of the cross product operator (\f$ [\alpha v]_{\times} x = \alpha v \times x \f$)
142			///
143			/// \param[in] alpha a real scalar.
144			/// \param[in] v a vector of dimension 3.
145			///
146			/// \returns the skew matrix representation of \f$ \alpha v \f$.
147			///
148			template <typename Scalar, typename Vector3>
149			inline Eigen::Matrix<typename Vector3::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(Vector3)::Options>
150		7672	alphaSkew(const Scalar alpha,
151			const Eigen::MatrixBase<Vector3> & v)
152			{
153		7672	Eigen::Matrix<typename Vector3::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(Vector3)::Options> M;
154		7672	alphaSkew(alpha,v,M);
155		7672	return M;
156			}
157
158			///
159			/// \brief Computes the square cross product linear operator C(u,v) such that for any vector w, \f$ u \times ( v \times w ) = C(u,v) w \f$.
160			///
161			/// \param[in] u a 3 dimensional vector.
162			/// \param[in] v a 3 dimensional vector.
163			/// \param[out] C the skew square matrix representation of dimension 3x3.
164			///
165			template <typename V1, typename V2, typename Matrix3>
166		94804	inline void skewSquare(const Eigen::MatrixBase<V1> & u,
167			const Eigen::MatrixBase<V2> & v,
168			const Eigen::MatrixBase<Matrix3> & C)
169			{
170			EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(V1,3);
171			EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(V2,3);
172			EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix3,3,3);
173
174		94804	Matrix3 & C_ = PINOCCHIO_EIGEN_CONST_CAST(Matrix3,C);
175			typedef typename Matrix3::RealScalar Scalar;
176
177	✓✗✓✗ ✓✗✓✗	94804	C_.noalias() = v*u.transpose();
178	✓✗	94804	const Scalar udotv(u.dot(v));
179	✓✗✓✗ ✓✗	94804	C_.diagonal().array() -= udotv;
180		94804	}
181
182			///
183			/// \brief Computes the square cross product linear operator C(u,v) such that for any vector w, \f$ u \times ( v \times w ) = C(u,v) w \f$.
184			///
185			/// \param[in] u A 3 dimensional vector.
186			/// \param[in] v A 3 dimensional vector.
187			///
188			/// \return The square cross product matrix skew[u] * skew[v].
189			///
190			template <typename V1, typename V2>
191			inline Eigen::Matrix<typename V1::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(V1)::Options>
192		94274	skewSquare(const Eigen::MatrixBase<V1> & u,
193			const Eigen::MatrixBase<V2> & v)
194			{
195
196		94274	Eigen::Matrix<typename V1::Scalar,3,3,PINOCCHIO_EIGEN_PLAIN_TYPE(V1)::Options> M;
197		94274	skewSquare(u,v,M);
198		94274	return M;
199			}
200
201			///
202			/// \brief Applies the cross product onto the columns of M.
203			///
204			/// \param[in] v a vector of dimension 3.
205			/// \param[in] Min a 3 rows matrix.
206			/// \param[out] Mout a 3 rows matrix.
207			///
208			/// \return the results of \f$ Mout = [v]_{\times} Min \f$.
209			///
210			template <typename Vector3, typename Matrix3xIn, typename Matrix3xOut>
211		23824	inline void cross(const Eigen::MatrixBase<Vector3> & v,
212			const Eigen::MatrixBase<Matrix3xIn> & Min,
213			const Eigen::MatrixBase<Matrix3xOut> & Mout)
214			{
215			EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Vector3,3);
216			EIGEN_STATIC_ASSERT(Matrix3xIn::RowsAtCompileTime==3,THIS_METHOD_IS_ONLY_FOR_MATRICES_OF_A_SPECIFIC_SIZE);
217			EIGEN_STATIC_ASSERT(Matrix3xOut::RowsAtCompileTime==3,THIS_METHOD_IS_ONLY_FOR_MATRICES_OF_A_SPECIFIC_SIZE);
218
219		23824	Matrix3xOut & Mout_ = PINOCCHIO_EIGEN_CONST_CAST(Matrix3xOut,Mout);
220
221	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗	23824	Mout_.row(0) = v[1]Min.row(2) - v[2]Min.row(1);
222	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗	23824	Mout_.row(1) = v[2]Min.row(0) - v[0]Min.row(2);
223	✓✗✓✗ ✓✗✓✗ ✓✗✓✗ ✓✗✓✗	23824	Mout_.row(2) = v[0]Min.row(1) - v[1]Min.row(0);
224		23824	}
225
226			///
227			/// \brief Applies the cross product onto the columns of M.
228			///
229			/// \param[in] v a vector of dimension 3.
230			/// \param[in] M a 3 rows matrix.
231			///
232			/// \return the results of \f$ [v]_{\times} M \f$.
233			///
234			template <typename Vector3, typename Matrix3x>
235			inline typename PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3x)
236		11842	cross(const Eigen::MatrixBase<Vector3> & v,
237			const Eigen::MatrixBase<Matrix3x> & M)
238			{
239	✓✗	11842	typename PINOCCHIO_EIGEN_PLAIN_TYPE(Matrix3x) res(3,M.cols());
240		11842	cross(v,M,res);
241		11842	return res;
242			}
243
244			} // namespace pinocchio
245
246			#endif // ifndef __pinocchio_skew_hpp__