test/geo_orthomethods.cpp

// 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/.
// SPDX-License-Identifier: 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();
  v2 = rv1.template cast<Scalar>();
  VERIFY_IS_APPROX(v1.cross(v2), v1.cross(rv1));
  VERIFY_IS_APPROX(v2.cross(v1), rv1.cross(v1));
}

template <typename Scalar>
void orthomethods_2() {
  typedef typename NumTraits<Scalar>::Real RealScalar;
  typedef Matrix<Scalar, 2, 1> Vector2;
  typedef Matrix<Scalar, 3, 1> Vector3;

  Vector3 v30 = Vector3::Random(), v31 = Vector3::Random();
  Vector2 v20 = v30.template head<2>();
  Vector2 v21 = v31.template head<2>();

  VERIFY_IS_MUCH_SMALLER_THAN(v20.cross(v20), Scalar(1));
  VERIFY_IS_MUCH_SMALLER_THAN(v21.cross(v21), Scalar(1));
  VERIFY_IS_APPROX(v20.cross(v21), v30.cross(v31).z());

  Vector2 v20Rot90(numext::conj(-v20.y()), numext::conj(v20.x()));
  VERIFY_IS_APPROX(v20.cross(v20Rot90), v20.squaredNorm());
  VERIFY_IS_APPROX(v20.cross(-v20Rot90), -v20.squaredNorm());
  Vector2 v21Rot90(numext::conj(-v21.y()), numext::conj(v21.x()));
  VERIFY_IS_APPROX(v21.cross(v21Rot90), v21.squaredNorm());
  VERIFY_IS_APPROX(v21.cross(-v21Rot90), -v21.squaredNorm());

  // check mixed product
  typedef Matrix<RealScalar, 2, 1> RealVector2;
  RealVector2 rv21 = RealVector2::Random();
  v21 = rv21.template cast<Scalar>();
  VERIFY_IS_APPROX(v20.cross(v21), v20.cross(rv21));
  VERIFY_IS_APPROX(v21.cross(v20), rv21.cross(v20));
}

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_2<float>());
    CALL_SUBTEST_2(orthomethods_2<double>());
    CALL_SUBTEST_4(orthomethods_2<std::complex<double> >());
    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)));
  }
}