C++ Matrix3f::colPivHouseholderQr方法代码示例

void transformOrientationToGroundFrame(const VirtualRobot::RobotPtr& robot,
                                       const Eigen::Matrix6Xf& leftFootTrajectory,
                                       const VirtualRobot::RobotNodePtr& leftFoot,
                                       const VirtualRobot::RobotNodePtr& rightFoot,
                                       const VirtualRobot::RobotNodeSetPtr& bodyJoints,
                                       const Eigen::MatrixXf& bodyTrajectory,
                                       const Eigen::Matrix3Xf& trajectory,
                                       const std::vector<SupportInterval>& intervals,
                                       Eigen::Matrix3Xf& relativeTrajectory)
{
    Eigen::Matrix4f leftInitialPose = bodyJoints->getKinematicRoot()->getGlobalPose();
    int N = trajectory.cols();
    int M = trajectory.rows();
    relativeTrajectory.resize(M, N);

    BOOST_ASSERT(M > 0 && M <= 3);

    auto intervalIter = intervals.begin();
    for (int i = 0; i < N; i++)
    {
        while (i >= intervalIter->endIdx)
        {
            intervalIter = std::next(intervalIter);
        }
        // Move basis along with the left foot
        Eigen::Matrix4f leftFootPose = Eigen::Matrix4f::Identity();
        VirtualRobot::MathTools::posrpy2eigen4f(1000 * leftFootTrajectory.block(0, i, 3, 1),
                                                leftFootTrajectory.block(3, i, 3, 1),  leftFootPose);
        robot->setGlobalPose(leftFootPose);
        bodyJoints->setJointValues(bodyTrajectory.col(i));
        Eigen::Matrix3f worldToRef = computeGroundFrame(leftFoot->getGlobalPose(),
                                                        rightFoot->getGlobalPose(),
                                                        intervalIter->phase).block(0, 0, 3, 3);
        relativeTrajectory.block(0, i, M, 1) = worldToRef.colPivHouseholderQr().solve(trajectory.col(i)).block(0, 0, M, 1);
    }
}

        {
          
          Eigen::Matrix3f mM3;
          Eigen::Vector3f x3NL;
          
          x3NL(0) = dMt.x03(0,1);
          x3NL(1) = dMt.x03(1,1);
          x3NL(2) = dMt.x03(2,1);
          
          // c0 + c1*nl + c2*nl^2
          mM3 <<
            1, 0, 0,
            1, 2, 4,
            1, 4, 16;
          
          Eigen::Vector3f ci3 = pow(4,-3)*mM3.colPivHouseholderQr().solve(x3NL);
          
          // NL^0
          REQUIRE(  ci3(0) == Approx( -198.7068 ) );
          // NL^1
          REQUIRE(  ci3(1) == Approx( 26.9239 ) );
          // NL^2
          REQUIRE(  ci3(2) == Approx( -0.65269 ) );
        }

      SECTION( "Four-loop zm4 = c0 + c1*L + c2*L^2 + c3*L^3 + c4*L^4" )
        {
          
          ////
          /// 4-loop
          // 

int main(int argc, char** argv) {

    ros::init(argc, argv, "eigen_test");
    ros::NodeHandle nh_jntPub; // node handle for joint command publisher

 //   ros::Publisher pub_joint_commands; //
//    pub_joint_commands = nh_jntPub.advertise<atlas_msgs::AtlasCommand>("/atlas/atlas_command", 1, true); 
    
    ROS_INFO("test eigen program");
    
    Eigen::Matrix3f A;
    Eigen::Vector3f b;
    A << 1,2,3, 4,5,6, 7,8,10;
    
    A(1,2)=0; // how to access one element of matrix; start from 0; no warning out of range...
    
 
    b << 3,3,4;
    std::cout <<"b = "<<b <<std::endl;   
    
    // column operaton: replace first column of A with vector b:
    A.col(0)= b;  // could copy columns of matrices w/ A.col(0) = B.col(0);
    
    std::cout <<"A = "<<A <<std::endl;

    Eigen::MatrixXd mat1 = Eigen::MatrixXd::Zero(6, 6); //6x6 matrix full of zeros
    Eigen::MatrixXd mat2 = Eigen::MatrixXd::Identity(6, 6); //6x6 identity matrix  

    std::cout<<mat1<<std::endl;
    std::cout<<mat2<<std::endl;

    Eigen::Vector3f xtest = A.colPivHouseholderQr().solve(b);
    std::cout<<"soln xtest = "<<xtest<<std::endl;
    
    Eigen::Vector3f x = A.partialPivLu().solve(b); //dec.solve(b); //A.colPivHouseholderQr().solve(b);
    std::cout<<"soln x = "<<x<<std::endl;
    
    Eigen::Vector3f btest = A*x;
    std::cout<<"test soln: A*x = " <<btest<<std::endl;
    
    //extend to 6x6 test: v = M*z, find z using 2 methods
    // use double-precision matrices/vectors
    Eigen::MatrixXd M = Eigen::MatrixXd::Random(6,6);

    std::cout<<"test 6x6: M = "<<M<<std::endl;
    Eigen::VectorXd v(6);   
    v << 1,2,3,4,5,6;
    std::cout<<"v = "<<v<<std::endl;
    Eigen::VectorXd z(6); 
    Eigen::VectorXd ztest(6);   
    ztest = M.colPivHouseholderQr().solve(v);
    std::cout<<"soln ztest = "<<ztest<<std::endl;
    z = M.partialPivLu().solve(v);   
    std::cout<<"soln 6x6: z = "<<z<<std::endl;
    Eigen::VectorXd vtest(6);
    vtest = M*z;
    std::cout<<"test soln: M*z = "<<vtest<<std::endl;

    // .norm() operator...
    double relative_error = (M*z - v).norm() / v.norm(); // norm() is L2 norm
    std::cout << "The relative error is:\n" << relative_error << std::endl;

    
    std::cout<<"dot prod, v, z: "<< v.dot(z)<<std::endl;
    std::cout<<"cross prod, b-cross-x: " << b.cross(x)<<std::endl;
    
    
    
    return 0;
}

template <typename PointInT, typename PointNT, typename PointOutT, typename IntensitySelectorT> void
pcl::IntensityGradientEstimation <PointInT, PointNT, PointOutT, IntensitySelectorT>::computePointIntensityGradient (
  const pcl::PointCloud <PointInT> &cloud, const std::vector <int> &indices,
  const Eigen::Vector3f &point, float mean_intensity, const Eigen::Vector3f &normal, Eigen::Vector3f &gradient)
{
  if (indices.size () < 3)
  {
    gradient[0] = gradient[1] = gradient[2] = std::numeric_limits<float>::quiet_NaN ();
    return;
  }

  Eigen::Matrix3f A = Eigen::Matrix3f::Zero ();
  Eigen::Vector3f b = Eigen::Vector3f::Zero ();

  for (size_t i_point = 0; i_point < indices.size (); ++i_point)
  {
    PointInT p = cloud.points[indices[i_point]];
    if (!pcl_isfinite (p.x) ||
        !pcl_isfinite (p.y) ||
        !pcl_isfinite (p.z) ||
        !pcl_isfinite (intensity_ (p)))
      continue;

    p.x -= point[0];
    p.y -= point[1];
    p.z -= point[2];
    intensity_.demean (p, mean_intensity);

    A (0, 0) += p.x * p.x;
    A (0, 1) += p.x * p.y;
    A (0, 2) += p.x * p.z;

    A (1, 1) += p.y * p.y;
    A (1, 2) += p.y * p.z;

    A (2, 2) += p.z * p.z;

    b[0] += p.x * intensity_ (p);
    b[1] += p.y * intensity_ (p);
    b[2] += p.z * intensity_ (p);
  }
  // Fill in the lower triangle of A
  A (1, 0) = A (0, 1);
  A (2, 0) = A (0, 2);
  A (2, 1) = A (1, 2);

//*
  Eigen::Vector3f x = A.colPivHouseholderQr ().solve (b);
/*/

  Eigen::Vector3f eigen_values;
  Eigen::Matrix3f eigen_vectors;
  eigen33 (A, eigen_vectors, eigen_values);

  b = eigen_vectors.transpose () * b;

  if ( eigen_values (0) != 0)
    b (0) /= eigen_values (0);
  else
    b (0) = 0;

  if ( eigen_values (1) != 0)
    b (1) /= eigen_values (1);
  else
    b (1) = 0;

  if ( eigen_values (2) != 0)
    b (2) /= eigen_values (2);
  else
    b (2) = 0;


  Eigen::Vector3f x = eigen_vectors * b;

//  if (A.col (0).squaredNorm () != 0)
//    x [0] /= A.col (0).squaredNorm ();
//  b -= x [0] * A.col (0);
//
//
//  if (A.col (1).squaredNorm ()  != 0)
//    x [1] /= A.col (1).squaredNorm ();
//  b -= x[1] * A.col (1);
//
//  x [2] = b.dot (A.col (2));
//  if (A.col (2).squaredNorm () != 0)
//    x[2] /= A.col (2).squaredNorm ();
  // Fit a hyperplane to the data

//*/
//  std::cout << A << "\n*\n" << bb << "\n=\n" << x << "\nvs.\n" << x2 << "\n\n";
//  std::cout << A * x << "\nvs.\n" << A * x2 << "\n\n------\n";
  // Project the gradient vector, x, onto the tangent plane
  gradient = (Eigen::Matrix3f::Identity () - normal*normal.transpose ()) * x;
}