134 lines
4.7 KiB
C++
134 lines
4.7 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "main.h"
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#include <Eigen/Geometry>
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#include <Eigen/LU>
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#include <Eigen/SVD>
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/* this test covers the following files:
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Geometry/OrthoMethods.h
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*/
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template<typename Scalar> void orthomethods_3()
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{
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typedef typename NumTraits<Scalar>::Real RealScalar;
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typedef Matrix<Scalar,3,3> Matrix3;
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typedef Matrix<Scalar,3,1> Vector3;
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typedef Matrix<Scalar,4,1> Vector4;
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Vector3 v0 = Vector3::Random(),
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v1 = Vector3::Random(),
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v2 = Vector3::Random();
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// cross product
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VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v1), Scalar(1));
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VERIFY_IS_MUCH_SMALLER_THAN(v1.dot(v1.cross(v2)), Scalar(1));
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VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v2), Scalar(1));
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VERIFY_IS_MUCH_SMALLER_THAN(v2.dot(v1.cross(v2)), Scalar(1));
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VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(Vector3::Random()).dot(v1), Scalar(1));
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Matrix3 mat3;
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mat3 << v0.normalized(),
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(v0.cross(v1)).normalized(),
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(v0.cross(v1).cross(v0)).normalized();
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VERIFY(mat3.isUnitary());
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mat3.setRandom();
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VERIFY_IS_APPROX(v0.cross(mat3*v1), -(mat3*v1).cross(v0));
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VERIFY_IS_APPROX(v0.cross(mat3.lazyProduct(v1)), -(mat3.lazyProduct(v1)).cross(v0));
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// colwise/rowwise cross product
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mat3.setRandom();
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Vector3 vec3 = Vector3::Random();
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Matrix3 mcross;
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int i = internal::random<int>(0,2);
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mcross = mat3.colwise().cross(vec3);
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VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3));
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VERIFY_IS_MUCH_SMALLER_THAN((mat3.adjoint() * mat3.colwise().cross(vec3)).diagonal().cwiseAbs().sum(), Scalar(1));
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VERIFY_IS_MUCH_SMALLER_THAN((mat3.adjoint() * mat3.colwise().cross(Vector3::Random())).diagonal().cwiseAbs().sum(), Scalar(1));
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VERIFY_IS_MUCH_SMALLER_THAN((vec3.adjoint() * mat3.colwise().cross(vec3)).cwiseAbs().sum(), Scalar(1));
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VERIFY_IS_MUCH_SMALLER_THAN((vec3.adjoint() * Matrix3::Random().colwise().cross(vec3)).cwiseAbs().sum(), Scalar(1));
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mcross = mat3.rowwise().cross(vec3);
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VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3));
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// cross3
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Vector4 v40 = Vector4::Random(),
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v41 = Vector4::Random(),
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v42 = Vector4::Random();
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v40.w() = v41.w() = v42.w() = 0;
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v42.template head<3>() = v40.template head<3>().cross(v41.template head<3>());
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VERIFY_IS_APPROX(v40.cross3(v41), v42);
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VERIFY_IS_MUCH_SMALLER_THAN(v40.cross3(Vector4::Random()).dot(v40), Scalar(1));
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// check mixed product
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typedef Matrix<RealScalar, 3, 1> RealVector3;
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RealVector3 rv1 = RealVector3::Random();
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VERIFY_IS_APPROX(v1.cross(rv1.template cast<Scalar>()), v1.cross(rv1));
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VERIFY_IS_APPROX(rv1.template cast<Scalar>().cross(v1), rv1.cross(v1));
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}
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template<typename Scalar, int Size> void orthomethods(int size=Size)
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{
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typedef typename NumTraits<Scalar>::Real RealScalar;
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typedef Matrix<Scalar,Size,1> VectorType;
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typedef Matrix<Scalar,3,Size> Matrix3N;
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typedef Matrix<Scalar,Size,3> MatrixN3;
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typedef Matrix<Scalar,3,1> Vector3;
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VectorType v0 = VectorType::Random(size);
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// unitOrthogonal
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VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1));
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VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), RealScalar(1));
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if (size>=3)
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{
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v0.template head<2>().setZero();
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v0.tail(size-2).setRandom();
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VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1));
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VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), RealScalar(1));
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}
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// colwise/rowwise cross product
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Vector3 vec3 = Vector3::Random();
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int i = internal::random<int>(0,size-1);
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Matrix3N mat3N(3,size), mcross3N(3,size);
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mat3N.setRandom();
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mcross3N = mat3N.colwise().cross(vec3);
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VERIFY_IS_APPROX(mcross3N.col(i), mat3N.col(i).cross(vec3));
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MatrixN3 matN3(size,3), mcrossN3(size,3);
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matN3.setRandom();
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mcrossN3 = matN3.rowwise().cross(vec3);
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VERIFY_IS_APPROX(mcrossN3.row(i), matN3.row(i).cross(vec3));
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}
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EIGEN_DECLARE_TEST(geo_orthomethods)
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{
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1( orthomethods_3<float>() );
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CALL_SUBTEST_2( orthomethods_3<double>() );
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CALL_SUBTEST_4( orthomethods_3<std::complex<double> >() );
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CALL_SUBTEST_1( (orthomethods<float,2>()) );
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CALL_SUBTEST_2( (orthomethods<double,2>()) );
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CALL_SUBTEST_1( (orthomethods<float,3>()) );
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CALL_SUBTEST_2( (orthomethods<double,3>()) );
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CALL_SUBTEST_3( (orthomethods<float,7>()) );
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CALL_SUBTEST_4( (orthomethods<std::complex<double>,8>()) );
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CALL_SUBTEST_5( (orthomethods<float,Dynamic>(36)) );
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CALL_SUBTEST_6( (orthomethods<double,Dynamic>(35)) );
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}
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}
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