| // This file is part of Eigen, a lightweight C++ template library |
| // for linear algebra. |
| // |
| // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr> |
| // |
| // 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/. |
| |
| #include "main.h" |
| #include <Eigen/Geometry> |
| #include <Eigen/LU> |
| #include <Eigen/SVD> |
| |
| /* this test covers the following files: |
| Geometry/OrthoMethods.h |
| */ |
| |
| template<typename Scalar> void orthomethods_3() |
| { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| typedef Matrix<Scalar,3,3> Matrix3; |
| typedef Matrix<Scalar,3,1> Vector3; |
| |
| typedef Matrix<Scalar,4,1> Vector4; |
| |
| Vector3 v0 = Vector3::Random(), |
| v1 = Vector3::Random(), |
| v2 = Vector3::Random(); |
| |
| // cross product |
| VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v1), Scalar(1)); |
| VERIFY_IS_MUCH_SMALLER_THAN(v1.dot(v1.cross(v2)), Scalar(1)); |
| VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v2), Scalar(1)); |
| VERIFY_IS_MUCH_SMALLER_THAN(v2.dot(v1.cross(v2)), Scalar(1)); |
| VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(Vector3::Random()).dot(v1), Scalar(1)); |
| Matrix3 mat3; |
| mat3 << v0.normalized(), |
| (v0.cross(v1)).normalized(), |
| (v0.cross(v1).cross(v0)).normalized(); |
| VERIFY(mat3.isUnitary()); |
| |
| mat3.setRandom(); |
| VERIFY_IS_APPROX(v0.cross(mat3*v1), -(mat3*v1).cross(v0)); |
| VERIFY_IS_APPROX(v0.cross(mat3.lazyProduct(v1)), -(mat3.lazyProduct(v1)).cross(v0)); |
| |
| // colwise/rowwise cross product |
| mat3.setRandom(); |
| Vector3 vec3 = Vector3::Random(); |
| Matrix3 mcross; |
| int i = internal::random<int>(0,2); |
| mcross = mat3.colwise().cross(vec3); |
| VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3)); |
| |
| VERIFY_IS_MUCH_SMALLER_THAN((mat3.adjoint() * mat3.colwise().cross(vec3)).diagonal().cwiseAbs().sum(), Scalar(1)); |
| VERIFY_IS_MUCH_SMALLER_THAN((mat3.adjoint() * mat3.colwise().cross(Vector3::Random())).diagonal().cwiseAbs().sum(), Scalar(1)); |
| |
| VERIFY_IS_MUCH_SMALLER_THAN((vec3.adjoint() * mat3.colwise().cross(vec3)).cwiseAbs().sum(), Scalar(1)); |
| VERIFY_IS_MUCH_SMALLER_THAN((vec3.adjoint() * Matrix3::Random().colwise().cross(vec3)).cwiseAbs().sum(), Scalar(1)); |
| |
| mcross = mat3.rowwise().cross(vec3); |
| VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3)); |
| |
| // cross3 |
| Vector4 v40 = Vector4::Random(), |
| v41 = Vector4::Random(), |
| v42 = Vector4::Random(); |
| v40.w() = v41.w() = v42.w() = 0; |
| v42.template head<3>() = v40.template head<3>().cross(v41.template head<3>()); |
| VERIFY_IS_APPROX(v40.cross3(v41), v42); |
| VERIFY_IS_MUCH_SMALLER_THAN(v40.cross3(Vector4::Random()).dot(v40), Scalar(1)); |
| |
| // check mixed product |
| typedef Matrix<RealScalar, 3, 1> RealVector3; |
| RealVector3 rv1 = RealVector3::Random(); |
| VERIFY_IS_APPROX(v1.cross(rv1.template cast<Scalar>()), v1.cross(rv1)); |
| VERIFY_IS_APPROX(rv1.template cast<Scalar>().cross(v1), rv1.cross(v1)); |
| } |
| |
| template<typename Scalar, int Size> void orthomethods(int size=Size) |
| { |
| typedef typename NumTraits<Scalar>::Real RealScalar; |
| typedef Matrix<Scalar,Size,1> VectorType; |
| typedef Matrix<Scalar,3,Size> Matrix3N; |
| typedef Matrix<Scalar,Size,3> MatrixN3; |
| typedef Matrix<Scalar,3,1> Vector3; |
| |
| VectorType v0 = VectorType::Random(size); |
| |
| // unitOrthogonal |
| VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1)); |
| VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), RealScalar(1)); |
| |
| if (size>=3) |
| { |
| v0.template head<2>().setZero(); |
| v0.tail(size-2).setRandom(); |
| |
| VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1)); |
| VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), RealScalar(1)); |
| } |
| |
| // colwise/rowwise cross product |
| Vector3 vec3 = Vector3::Random(); |
| int i = internal::random<int>(0,size-1); |
| |
| Matrix3N mat3N(3,size), mcross3N(3,size); |
| mat3N.setRandom(); |
| mcross3N = mat3N.colwise().cross(vec3); |
| VERIFY_IS_APPROX(mcross3N.col(i), mat3N.col(i).cross(vec3)); |
| |
| MatrixN3 matN3(size,3), mcrossN3(size,3); |
| matN3.setRandom(); |
| mcrossN3 = matN3.rowwise().cross(vec3); |
| VERIFY_IS_APPROX(mcrossN3.row(i), matN3.row(i).cross(vec3)); |
| } |
| |
| EIGEN_DECLARE_TEST(geo_orthomethods) |
| { |
| for(int i = 0; i < g_repeat; i++) { |
| CALL_SUBTEST_1( orthomethods_3<float>() ); |
| CALL_SUBTEST_2( orthomethods_3<double>() ); |
| CALL_SUBTEST_4( orthomethods_3<std::complex<double> >() ); |
| CALL_SUBTEST_1( (orthomethods<float,2>()) ); |
| CALL_SUBTEST_2( (orthomethods<double,2>()) ); |
| CALL_SUBTEST_1( (orthomethods<float,3>()) ); |
| CALL_SUBTEST_2( (orthomethods<double,3>()) ); |
| CALL_SUBTEST_3( (orthomethods<float,7>()) ); |
| CALL_SUBTEST_4( (orthomethods<std::complex<double>,8>()) ); |
| CALL_SUBTEST_5( (orthomethods<float,Dynamic>(36)) ); |
| CALL_SUBTEST_6( (orthomethods<double,Dynamic>(35)) ); |
| } |
| } |