geo_orthomethods.cpp
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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 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9 
10 #include "main.h"
11 #include <Eigen/Geometry>
12 #include <Eigen/LU>
13 #include <Eigen/SVD>
14 
15 /* this test covers the following files:
16  Geometry/OrthoMethods.h
17 */
18 
19 template<typename Scalar> void orthomethods_3()
20 {
21  typedef typename NumTraits<Scalar>::Real RealScalar;
22  typedef Matrix<Scalar,3,3> Matrix3;
24 
25  typedef Matrix<Scalar,4,1> Vector4;
26 
27  Vector3 v0 = Vector3::Random(),
28  v1 = Vector3::Random(),
29  v2 = Vector3::Random();
30 
31  // cross product
32  VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v1), Scalar(1));
33  VERIFY_IS_MUCH_SMALLER_THAN(v1.dot(v1.cross(v2)), Scalar(1));
34  VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v2), Scalar(1));
35  VERIFY_IS_MUCH_SMALLER_THAN(v2.dot(v1.cross(v2)), Scalar(1));
36  VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(Vector3::Random()).dot(v1), Scalar(1));
37  Matrix3 mat3;
38  mat3 << v0.normalized(),
39  (v0.cross(v1)).normalized(),
40  (v0.cross(v1).cross(v0)).normalized();
41  VERIFY(mat3.isUnitary());
42 
43  mat3.setRandom();
44  VERIFY_IS_APPROX(v0.cross(mat3*v1), -(mat3*v1).cross(v0));
45  VERIFY_IS_APPROX(v0.cross(mat3.lazyProduct(v1)), -(mat3.lazyProduct(v1)).cross(v0));
46 
47  // colwise/rowwise cross product
48  mat3.setRandom();
49  Vector3 vec3 = Vector3::Random();
50  Matrix3 mcross;
51  int i = internal::random<int>(0,2);
52  mcross = mat3.colwise().cross(vec3);
53  VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3));
54 
55  VERIFY_IS_MUCH_SMALLER_THAN((mat3.adjoint() * mat3.colwise().cross(vec3)).diagonal().cwiseAbs().sum(), Scalar(1));
56  VERIFY_IS_MUCH_SMALLER_THAN((mat3.adjoint() * mat3.colwise().cross(Vector3::Random())).diagonal().cwiseAbs().sum(), Scalar(1));
57 
58  VERIFY_IS_MUCH_SMALLER_THAN((vec3.adjoint() * mat3.colwise().cross(vec3)).cwiseAbs().sum(), Scalar(1));
59  VERIFY_IS_MUCH_SMALLER_THAN((vec3.adjoint() * Matrix3::Random().colwise().cross(vec3)).cwiseAbs().sum(), Scalar(1));
60 
61  mcross = mat3.rowwise().cross(vec3);
62  VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3));
63 
64  // cross3
65  Vector4 v40 = Vector4::Random(),
66  v41 = Vector4::Random(),
67  v42 = Vector4::Random();
68  v40.w() = v41.w() = v42.w() = 0;
69  v42.template head<3>() = v40.template head<3>().cross(v41.template head<3>());
70  VERIFY_IS_APPROX(v40.cross3(v41), v42);
71  VERIFY_IS_MUCH_SMALLER_THAN(v40.cross3(Vector4::Random()).dot(v40), Scalar(1));
72 
73  // check mixed product
74  typedef Matrix<RealScalar, 3, 1> RealVector3;
75  RealVector3 rv1 = RealVector3::Random();
76  VERIFY_IS_APPROX(v1.cross(rv1.template cast<Scalar>()), v1.cross(rv1));
77  VERIFY_IS_APPROX(rv1.template cast<Scalar>().cross(v1), rv1.cross(v1));
78 }
79 
80 template<typename Scalar, int Size> void orthomethods(int size=Size)
81 {
82  typedef typename NumTraits<Scalar>::Real RealScalar;
84  typedef Matrix<Scalar,3,Size> Matrix3N;
85  typedef Matrix<Scalar,Size,3> MatrixN3;
87 
88  VectorType v0 = VectorType::Random(size);
89 
90  // unitOrthogonal
91  VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1));
92  VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), RealScalar(1));
93 
94  if (size>=3)
95  {
96  v0.template head<2>().setZero();
97  v0.tail(size-2).setRandom();
98 
99  VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1));
100  VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), RealScalar(1));
101  }
102 
103  // colwise/rowwise cross product
104  Vector3 vec3 = Vector3::Random();
105  int i = internal::random<int>(0,size-1);
106 
107  Matrix3N mat3N(3,size), mcross3N(3,size);
108  mat3N.setRandom();
109  mcross3N = mat3N.colwise().cross(vec3);
110  VERIFY_IS_APPROX(mcross3N.col(i), mat3N.col(i).cross(vec3));
111 
112  MatrixN3 matN3(size,3), mcrossN3(size,3);
113  matN3.setRandom();
114  mcrossN3 = matN3.rowwise().cross(vec3);
115  VERIFY_IS_APPROX(mcrossN3.row(i), matN3.row(i).cross(vec3));
116 }
117 
118 EIGEN_DECLARE_TEST(geo_orthomethods)
119 {
120  for(int i = 0; i < g_repeat; i++) {
121  CALL_SUBTEST_1( orthomethods_3<float>() );
122  CALL_SUBTEST_2( orthomethods_3<double>() );
123  CALL_SUBTEST_4( orthomethods_3<std::complex<double> >() );
124  CALL_SUBTEST_1( (orthomethods<float,2>()) );
125  CALL_SUBTEST_2( (orthomethods<double,2>()) );
126  CALL_SUBTEST_1( (orthomethods<float,3>()) );
127  CALL_SUBTEST_2( (orthomethods<double,3>()) );
128  CALL_SUBTEST_3( (orthomethods<float,7>()) );
129  CALL_SUBTEST_4( (orthomethods<std::complex<double>,8>()) );
130  CALL_SUBTEST_5( (orthomethods<float,Dynamic>(36)) );
131  CALL_SUBTEST_6( (orthomethods<double,Dynamic>(35)) );
132  }
133 }
VERIFY_IS_MUCH_SMALLER_THAN
#define VERIFY_IS_MUCH_SMALLER_THAN(a, b)
Definition: main.h:390
v0
static const double v0
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static Vector9 vec3(const Matrix3 &R)
Definition: SO3.cpp:342
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Definition: Vector.h:43
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#define CALL_SUBTEST_4(FUNC)
Definition: split_test_helper.h:22
CALL_SUBTEST_3
#define CALL_SUBTEST_3(FUNC)
Definition: split_test_helper.h:16
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void orthomethods_3()
Definition: geo_orthomethods.cpp:19
CALL_SUBTEST_1
#define CALL_SUBTEST_1(FUNC)
Definition: split_test_helper.h:4
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CALL_SUBTEST_5
#define CALL_SUBTEST_5(FUNC)
Definition: split_test_helper.h:28
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static int g_repeat
Definition: main.h:169
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Definition: geo_orthomethods.cpp:118
CALL_SUBTEST_6
#define CALL_SUBTEST_6(FUNC)
Definition: split_test_helper.h:34
CALL_SUBTEST_2
#define CALL_SUBTEST_2(FUNC)
Definition: split_test_helper.h:10
VERIFY_IS_APPROX
#define VERIFY_IS_APPROX(a, b)
Definition: integer_types.cpp:15
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Definition: bench_gemm.cpp:47
main.h
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void orthomethods(int size=Size)
Definition: geo_orthomethods.cpp:80
v2
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Definition: testSerializationBase.cpp:39
Eigen::Matrix
The matrix class, also used for vectors and row-vectors.
Definition: 3rdparty/Eigen/Eigen/src/Core/Matrix.h:178
VectorType
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Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Definition: NumTraits.h:232
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Definition: main.h:380


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autogenerated on Fri Nov 1 2024 03:32:37