/usr/include/SurgSim/Math/OdeEquation.h is in libopensurgsim-dev 0.7.0-6ubuntu1.
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// Copyright 2013, SimQuest Solutions Inc.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#ifndef SURGSIM_MATH_ODEEQUATION_H
#define SURGSIM_MATH_ODEEQUATION_H
#include <memory>
#include "SurgSim/Math/SparseMatrix.h"
#include "SurgSim/Math/Matrix.h"
#include "SurgSim/Math/Vector.h"
namespace SurgSim
{
namespace Math
{
class OdeState;
/// Enum to identify which of the data need to be updated by the OdeEquation::update()
enum OdeEquationUpdate
{
ODEEQUATIONUPDATE_F = 1<<0,
ODEEQUATIONUPDATE_M = 1<<1,
ODEEQUATIONUPDATE_D = 1<<2,
ODEEQUATIONUPDATE_K = 1<<3,
ODEEQUATIONUPDATE_FMDK = ODEEQUATIONUPDATE_F | ODEEQUATIONUPDATE_M | ODEEQUATIONUPDATE_D | ODEEQUATIONUPDATE_K
};
/// Ode equation of 2nd order of the form \f$M(x,v).a = F(x, v)\f$ with \f$(x0, v0)\f$ for initial conditions
/// and a set of boundary conditions. The problem is called a Boundary Value Problem (BVP).
/// This ode equation is solved as an ode of order 1 by defining the state vector
/// \f$y = \left(\begin{array}{c}x\\v\end{array}\right)\f$:
/// \f[
/// y' = \left(\begin{array}{c} x' \\ v' \end{array}\right) =
/// \left(\begin{array}{c} v \\ M(x, v)^{-1}.f(t, x, v) \end{array}\right)
/// \f]
/// \note To allow the use of explicit and implicit solver, we need to be able to evaluate
/// \note \f$M(x, v)\f$, \f$f(t, x, v)\f$ but also \f$K = -dF/dx(x, v)\f$ and \f$D = -dF/dv(x, v)\f$
/// \note Models wanting the use of implicit solvers will need to compute these Jacobian matrices.
class OdeEquation
{
public:
/// Virtual destructor
virtual ~OdeEquation() {}
/// Retrieves the ode initial conditions \f$(x0, v0)\f$ (i.e the initial state)
/// \return The initial state
const std::shared_ptr<OdeState> getInitialState() const;
/// Calculate the product C.b where C is the compliance matrix with boundary conditions
/// applied. Note that this can be rewritten as (Bt)(M^-1)(B.b) = (Bt)((M^-1)(B.b)) = x,
/// where (M^-1)(B.b) = y is simply the solution to M.y = B.b and Bt.y = x.
/// \param state \f$(x, v)\f$ the current position and velocity to evaluate the various terms with
/// \param b The input matrix
/// \return The matrix \f$C.b\f$
virtual Matrix applyCompliance(const OdeState& state, const Matrix& b) = 0;
/// Update the OdeEquation (and support data) based on the given state.
/// \param state \f$(x, v)\f$ the current position and velocity to evaluate the various terms with
/// \param options Flag to specify which of F, M, D, K needs to be updated.
virtual void updateFMDK(const OdeState& state, int options);
/// \return The vector containing \f$f(x, v)\f$
const Vector& getF() const;
/// \return The matrix \f$M(x,v)\f$
const SparseMatrix& getM() const;
/// \return The matrix \f$D = -\frac{\partial f}{\partial v}(x,v)\f$
const SparseMatrix& getD() const;
/// \return The matrix \f$K = -\frac{\partial f}{\partial x}(x,v)\f$
const SparseMatrix& getK() const;
protected:
/// Evaluation of the RHS function \f$f(x, v)\f$ for a given state
/// \param state \f$(x, v)\f$ the current position and velocity to evaluate the function \f$f(x,v)\f$ with
virtual void computeF(const OdeState& state) = 0;
/// Evaluation of the LHS matrix \f$M(x,v)\f$ for a given state
/// \param state \f$(x, v)\f$ the current position and velocity to evaluate the matrix \f$M(x,v)\f$ with
virtual void computeM(const OdeState& state) = 0;
/// Evaluation of \f$D = -\frac{\partial f}{\partial v}(x,v)\f$ for a given state
/// \param state \f$(x, v)\f$ the current position and velocity to evaluate the Jacobian matrix with
virtual void computeD(const OdeState& state) = 0;
/// Evaluation of \f$K = -\frac{\partial f}{\partial x}(x,v)\f$ for a given state
/// \param state \f$(x, v)\f$ the current position and velocity to evaluate the Jacobian matrix with
virtual void computeK(const OdeState& state) = 0;
/// Evaluation of \f$f(x,v)\f$, \f$M(x,v)\f$, \f$D = -\frac{\partial f}{\partial v}(x,v)\f$ and
/// \f$K = -\frac{\partial f}{\partial x}(x,v)\f$.
/// When all the terms are needed, this method can perform optimization in evaluating everything together
/// \param state \f$(x, v)\f$ the current position and velocity to evaluate the various terms with
/// \note computeF(), computeM(), computeD(), computeK()
virtual void computeFMDK(const OdeState& state) = 0;
/// The initial state (which defines the ODE initial conditions \f$(x0, v0)\f$)
/// \note MUST be set by the derived classes
std::shared_ptr<OdeState> m_initialState;
/// The vector containing \f$f(x, v)\f$
Vector m_f;
/// The matrix \f$M(x,v)\f$
SparseMatrix m_M;
/// The The matrix \f$D = -\frac{\partial f}{\partial v}(x,v)\f$
SparseMatrix m_D;
/// The The matrix \f$K = -\frac{\partial f}{\partial x}(x,v)\f$
SparseMatrix m_K;
};
}; // namespace Math
}; // namespace SurgSim
#endif // SURGSIM_MATH_ODEEQUATION_H
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