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
19template<typename Scalar> void orthomethods_3()
20{
21  typedef typename NumTraits<Scalar>::Real RealScalar;
22  typedef Matrix<Scalar,3,3> Matrix3;
23  typedef Matrix<Scalar,3,1> Vector3;
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
80template<typename Scalar, int Size> void orthomethods(int size=Size)
81{
82  typedef typename NumTraits<Scalar>::Real RealScalar;
83  typedef Matrix<Scalar,Size,1> VectorType;
84  typedef Matrix<Scalar,3,Size> Matrix3N;
85  typedef Matrix<Scalar,Size,3> MatrixN3;
86  typedef Matrix<Scalar,3,1> Vector3;
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
118void 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}
134