C++ VectorX类代码示例

	void PGSSolver::solve(const MatrixX& _A, const VectorX& _B, VectorX& _x, int _interationCount) const
	{
		int size = _B.getSize();

		//initialize x
		_x.setSize(size);
		_x.set(0);

		//make the required number of iteration
		for (int iteration = 0; iteration < _interationCount; ++iteration)
		{
			//loop through each element of x
			for (int i = 0; i < size; ++i)
			{
				//compute a(i, j) * x(j)
				float ax = 0;
				for (int j = 0; j < size; ++j)
					ax += _A(i, j) * _x(j);

				//compute x(i) = (b(i) - ax) / a(i, i)
				float res = (_B(i) - ax) / _A(i, i);
				_x(i, res);
			}
		}

	}

void AttachmentConstraint::PBDProject(VectorX& x, const SparseMatrix& inv_mass, unsigned int ns)
{
	// LOOK
	ScalarType k_prime = 1 - std::pow(1-*(m_p_pbd_stiffness), 1.0/ns);
	
	EigenVector3 p = x.block_vector(m_p0);
	EigenVector3 dp = m_fixd_point-p;

	x.block_vector(m_p0) += k_prime * dp;
}

template <typename PointSource, typename PointTarget, typename MatScalar> inline void
pcl::registration::TransformationEstimationLM<PointSource, PointTarget, MatScalar>::estimateRigidTransformation (
    const pcl::PointCloud<PointSource> &cloud_src,
    const std::vector<int> &indices_src,
    const pcl::PointCloud<PointTarget> &cloud_tgt,
    const std::vector<int> &indices_tgt,
    Matrix4 &transformation_matrix) const
{
  if (indices_src.size () != indices_tgt.size ())
  {
    PCL_ERROR ("[pcl::registration::TransformationEstimationLM::estimateRigidTransformation] Number or points in source (%lu) differs than target (%lu)!\n", indices_src.size (), indices_tgt.size ());
    return;
  }

  if (indices_src.size () < 4)     // need at least 4 samples
  {
    PCL_ERROR ("[pcl::IterativeClosestPointNonLinear::estimateRigidTransformationLM] ");
    PCL_ERROR ("Need at least 4 points to estimate a transform! Source and target have %lu points!",
               indices_src.size ());
    return;
  }

  int n_unknowns = warp_point_->getDimension ();  // get dimension of unknown space
  VectorX x (n_unknowns);
  x.setConstant (n_unknowns, 0);

  // Set temporary pointers
  tmp_src_ = &cloud_src;
  tmp_tgt_ = &cloud_tgt;
  tmp_idx_src_ = &indices_src;
  tmp_idx_tgt_ = &indices_tgt;

  OptimizationFunctorWithIndices functor (static_cast<int> (indices_src.size ()), this);
  Eigen::NumericalDiff<OptimizationFunctorWithIndices> num_diff (functor);
  //Eigen::LevenbergMarquardt<Eigen::NumericalDiff<OptimizationFunctorWithIndices> > lm (num_diff);
  Eigen::LevenbergMarquardt<Eigen::NumericalDiff<OptimizationFunctorWithIndices>, MatScalar> lm (num_diff);
  int info = lm.minimize (x);

  // Compute the norm of the residuals
  PCL_DEBUG ("[pcl::registration::TransformationEstimationLM::estimateRigidTransformation] LM solver finished with exit code %i, having a residual norm of %g. \n", info, lm.fvec.norm ());
  PCL_DEBUG ("Final solution: [%f", x[0]);
  for (int i = 1; i < n_unknowns; ++i) 
    PCL_DEBUG (" %f", x[i]);
  PCL_DEBUG ("]\n");

  // Return the correct transformation
  warp_point_->setParam (x);
  transformation_matrix = warp_point_->getTransform ();

  tmp_src_ = NULL;
  tmp_tgt_ = NULL;
  tmp_idx_src_ = tmp_idx_tgt_ = NULL;
}

bool BCCoreSiconos::callSolver(MatrixX& Mlcp, VectorX& b, VectorX& solution, VectorX& contactIndexToMu, ofstream& os)
{
#ifdef BUILD_BCPLUGIN_WITH_SICONOS
  int NC3 = Mlcp.rows();
  if(NC3<=0) return true;
  int NC = NC3/3;
  int CFS_DEBUG = 0;
  int CFS_DEBUG_VERBOSE = 0;
  if(CFS_DEBUG)
  {
    if(NC3%3 != 0           ){ os << "   warning-1 " << std::endl;return false;}
    if(       b.rows()!= NC3){ os << "   warning-2 " << std::endl;return false;}
    if(solution.rows()!= NC3){ os << "   warning-3 " << std::endl;return false;}
  } 
  for(int ia=0;ia<NC;ia++)for(int i=0;i<3;i++)prob->q [3*ia+i]= b(((i==0)?(ia):(2*ia+i+NC-1)));
  for(int ia=0;ia<NC;ia++)                    prob->mu[  ia  ]= contactIndexToMu[ia];
  prob->numberOfContacts = NC;

  if( USE_FULL_MATRIX )
  {
    prob->M->storageType = 0;
    prob->M->size0       = NC3;
    prob->M->size1       = NC3;
    double* ptmp = prob->M->matrix0 ;
    for(int ia=0;ia<NC;ia++)for(int i =0;i <3 ;i ++)
    {
      for(int ja=0;ja<NC;ja++)for(int j =0;j <3;j ++) 
      {
        ptmp[NC3*(3*ia+i)+(3*ja+j)]=Mlcp(((i==0)?(ia):(2*ia+i+NC-1)),((j==0)?(ja):(2*ja+j+NC-1)));
      }
    }
  }
  else
  {
    prob->M->storageType = 1;
    prob->M->size0       = NC3;
    prob->M->size1       = NC3;
    sparsify_A( prob->M->matrix1 , Mlcp , NC , &os);
  }
  
  fc3d_driver(prob,reaction,velocity,solops, numops);
  
  double* prea = reaction ;
  for(int ia=0;ia<NC;ia++)for(int i=0;i<3;i++) solution(((i==0)?(ia):(2*ia+i+NC-1))) = prea[3*ia+i] ;
  if(CFS_DEBUG_VERBOSE)
  {
    os << "=---------------------------------="<< std::endl; 
    os << "| res_error =" << solops->dparam[1] <<  std::endl;
    os << "=---------------------------------="<< std::endl; 
  }
#endif
  return true;
}

// sping gradient: k*(current_length-rest_length)*current_direction;
void SpringConstraint::EvaluateGradient(const VectorX& x, VectorX& gradient)
{
	// TODO
	//EigenVector3 g_i = (*(m_p_stiffness))*(x.block_vector(m_p0) - m_fixd_point);
    //gradient.block_vector(m_p0) += g_i;

	EigenVector3 p1=x.block_vector(m_p1);
	EigenVector3 p2=x.block_vector(m_p2);
	float currentLength=(p1-p2).norm();
	float force=(*this->m_p_stiffness)*(currentLength-this->m_rest_length);
	EigenVector3 n1=p1-p2,n2=p2-p1;
	n1.normalize();n2.normalize();
	gradient.block_vector(m_p1)+=n1*force;
	gradient.block_vector(m_p2)+=n2*force;
}

void VelocityTrackingObjective<Scalar>::setVelRefInWorldFrame(const VectorX& velRefInWorldFrame)
{
  assert(velRefInWorldFrame.size()==model_.getNbSamples());
  assert(velRefInWorldFrame==velRefInWorldFrame);

  velRefInWorldFrame_ = velRefInWorldFrame;
}

GMMExpectationMaximization::Real GMMExpectationMaximization::gauss(const VectorX & mean,
  const MatrixX & cov,const VectorX & pt) const
{
  Real det = cov.determinant();
  uint dim = mean.size();
  // check that the covariance matrix is invertible
  if (std::abs(det) < std::pow(m_epsilon,dim) * 0.1)
    return 0.0; // the gaussian has approximately zero width: the probability of any point falling into it is approximately 0.
 
  // else, compute pdf
  MatrixX inverse_cov = cov.inverse();
  VectorX dist = pt - mean;
  Real exp = - (dist.dot(inverse_cov * dist)) / 2.0;
  Real den = std::sqrt(std::pow(2.0 * M_PI,dim) * std::abs(det));
  return std::exp(exp) / den;
}

void TrajectoryWalkgen<Scalar>::setState(const VectorX& state)
{
  assert(state==state);
  assert(state.size()==3);

  noDynModel_.setState(state);
}

void Simulation::computeForces(const VectorX& x, VectorX& force)
{
    VectorX gradient;

    gradient.resize(m_mesh->m_system_dimension);
    gradient.setZero();

    // springs
    for (std::vector<Constraint*>::iterator it = m_constraints.begin(); it != m_constraints.end(); ++it)
    {
        (*it)->EvaluateGradient(x, gradient);
    }

    // external forces
    gradient -= m_external_force;

    force = -gradient;
}

void MotionConstraint<Scalar>::computeFunction(const VectorX& x0, VectorX& func,
                                               Scalar velLimit, Scalar accLimit)
{
  int N = model_.getNbSamples();

  const LinearDynamic<Scalar>& dynBaseVel = model_.getVelLinearDynamic();
  const LinearDynamic<Scalar>& dynBaseAcc = model_.getAccLinearDynamic();

  tmp_.fill(velLimit);
  tmp2_.fill(accLimit);

  func.noalias() = -getGradient()*x0;
  func.segment(0, N).noalias() += tmp_;
  func.segment(0, N).noalias() -= dynBaseVel.S * model_.getState();
  func.segment(N, N).noalias() += tmp2_;
  func.segment(N, N).noalias() -= dynBaseAcc.S * model_.getState();

}

const MatrixX& Jacobian::GetNullspace()
{
	if(computeNullSpace_)
	{
		computeNullSpace_ = false;
		/*jacobianInverseNoDls_ = jacobian_;
		PseudoInverse(jacobianInverseNoDls_); // tmp while figuring out how to chose lambda*/
		//ComputeSVD();
		MatrixX id = MatrixX::Identity(jacobian_.cols(), jacobian_.cols());
		ComputeSVD();
		//Eigen::JacobiSVD<MatrixX> svd(jacobian_, Eigen::ComputeThinU | Eigen::ComputeThinV);
		MatrixX res = MatrixX::Zero(id.rows(), id.cols());
		for(int i =0; i < svd_.matrixV().cols(); ++ i)
		{
			VectorX v = svd_.matrixV().col(i);
			res += v * v.transpose();
		}
		Identitymin_ = id - res;
		//Identitymin_ = id - (jacobianInverseNoDls_* jacobian_);
	}
	return Identitymin_;
}

bool Solver_LP_abstract::readLpFromFile(const std::string& filename,
                                        VectorX &c, VectorX &lb, VectorX &ub,
                                        MatrixXX &A, VectorX &Alb, VectorX &Aub)
{
  std::ifstream in(filename.c_str(), std::ios::in | std::ios::binary);
  typename MatrixXX::Index n=0, m=0;
  in.read((char*) (&n),sizeof(typename MatrixXX::Index));
  in.read((char*) (&m),sizeof(typename MatrixXX::Index));
  c.resize(n);
  lb.resize(n);
  ub.resize(n);
  A.resize(m,n);
  Alb.resize(m);
  Aub.resize(m);
  in.read( (char *) c.data() , n*sizeof(typename MatrixXX::Scalar) );
  in.read( (char *) lb.data() , n*sizeof(typename MatrixXX::Scalar) );
  in.read( (char *) ub.data() , n*sizeof(typename MatrixXX::Scalar) );
  in.read( (char *) A.data() , m*n*sizeof(typename MatrixXX::Scalar) );
  in.read( (char *) Alb.data() , m*sizeof(typename MatrixXX::Scalar) );
  in.read( (char *) Aub.data() , m*sizeof(typename MatrixXX::Scalar) );
  in.close();
  return true;
}

TYPED_TEST(TestSecondOrderMultinomialLogisticRegression, MinimizerOverfitSmall) {
    MatrixX<TypeParam> X(2, 10);
    VectorXi y(10);

    X << 0.6097662 ,  0.53395565,  0.9499446 ,  0.67289898,  0.94173948,
         0.56675891,  0.80363783,  0.85303565,  0.15903886,  0.99518533,
         0.41655682,  0.29256121,  0.36103228,  0.29899503,  0.4957268 ,
         -0.04277318, -0.28038614, -0.12334621, -0.17497722,  0.1492248;
    y << 0, 0, 0, 0, 0, 1, 1, 1, 1, 1;
    std::vector<MatrixX<TypeParam> > X_var;
    for (int i=0; i<10; i++) {
        //X_var.push_back(MatrixX<TypeParam>::Random(2, 2).array().abs() * 0.01);
        //X_var.push_back(MatrixX<TypeParam>::Zero(2, 2));
        VectorX<TypeParam> a = VectorX<TypeParam>::Random(2).array() * 0.01;
        X_var.push_back(
            a * a.transpose()
        );
    }

    SecondOrderLogisticRegressionApproximation<TypeParam> mlr(X, X_var, y, 0);
    MatrixX<TypeParam> eta = MatrixX<TypeParam>::Zero(2, 3);

    GradientDescent<SecondOrderLogisticRegressionApproximation<TypeParam>, MatrixX<TypeParam>> minimizer(
        std::make_shared<
            ArmijoLineSearch<
                SecondOrderLogisticRegressionApproximation<TypeParam>,
                MatrixX<TypeParam>
            >
        >(),
        [](TypeParam value, TypeParam gradNorm, size_t iterations) {
            return iterations < 5000;
        }
    );
    minimizer.minimize(mlr, eta);

    EXPECT_GT(0.1, mlr.value(eta));
}

  virtual void SetUp()
  {
    using namespace MPCWalkgen;

    int nbSamples = 3;
    Real samplingPeriod = 1.0;
    bool autoCompute = true;
    VectorX variable;
    variable.setZero(2*nbSamples);
    Real feedbackPeriod = 0.5;

    vectorOfVector2 p(3);
    p[0] = Vector2(1.0, 1.0);
    p[1] = Vector2(-1.0, 1.0);
    p[2] = Vector2(1.0, -1.0);

    HumanoidFeetSupervisor<Real> feetSupervisor(nbSamples,
                                                samplingPeriod);
    feetSupervisor.setLeftFootCopConvexPolygon(ConvexPolygon<Real>(p));
    feetSupervisor.setRightFootCopConvexPolygon(ConvexPolygon<Real>(p));


    feetSupervisor.updateTimeline(variable, feedbackPeriod);

    LIPModel<Real> lip(nbSamples, samplingPeriod, autoCompute);
    lip.setFeedbackPeriod(feedbackPeriod);

    HumanoidCopConstraint<Real> copCtr(lip, feetSupervisor);

    VectorX x0 = VectorX::Zero(6);

    function_ = copCtr.getFunction(x0);
    gradient_ = copCtr.getGradient(x0.rows());
    supBounds_ = copCtr.getSupBounds(x0);
    infBounds_ = copCtr.getInfBounds(x0);
  }

  void HumanoidFootConstraint<Scalar>::computeBoundsVectors(const VectorX& x0)
  {
    int M = feetSupervisor_.getNbPreviewedSteps();

    assert(x0.rows()==2*M);

    supBound_.setConstant(2*M, Constant<Scalar>::MAXIMUM_BOUND_VALUE);
    infBound_.setConstant(2*M, -Constant<Scalar>::MAXIMUM_BOUND_VALUE);

    for(int i = 0; i<M; ++i)
    {
      const ConvexPolygon<Scalar>& cp = feetSupervisor_.getKinematicConvexPolygon(i);

      supBound_(i) = cp.getXSupBound();
      supBound_(i + M) = cp.getYSupBound();
      infBound_(i) = cp.getXInfBound();
      infBound_(i + M) = cp.getYInfBound();

      // This if-else statement adds the required terms to vectors supBound_ and infBound_
      // so that constraints are expressed in world frame
      if(i==0)
      {
        supBound_(i) += feetSupervisor_.getSupportFootStateX()(0);
        supBound_(i + M) += feetSupervisor_.getSupportFootStateY()(0);
        infBound_(i) += feetSupervisor_.getSupportFootStateX()(0);
        infBound_(i + M) += feetSupervisor_.getSupportFootStateY()(0);
      }
      else
      {
        supBound_(i) += x0(i - 1);
        supBound_(i + M) += x0(M + i - 1);
        infBound_(i) += x0(i - 1);
        infBound_(i + M) += x0(M + i - 1);
      }
    }

    // As we optimize a variation dX_ of the QP variable X_ (such that X_ = x0 + dX_),
    // the bound constraints need to be translated of x0 too.
    supBound_ -= x0;
    infBound_ -= x0;
  }