Siconos 4.5.0
  • Sources on github
  • Index
  • Documentation
      • Quickstart
        • What is Siconos?
        • Try it
        • Siconos usage in a few steps
        • More
          • Modeling Principle
          • Python interface : tutorials
            • Collections of rigid bodies with Bullet based contact detection (Siconos/Mechanics)
              • Description of the physical problems : rigid bodies collection with contact and Coulomb friction
            • Tutorial: A 4-diodes bridge wave rectifier
              • Preamble
              • Siconos driver file
              • Building a nonsmooth dynamical system
                • Modeling the dynamics
                • Modeling the interactions
              • Describing the simulation of the nonsmooth dynamical system
              • Leading the Simulation Process
          • Siconos tutorials in C++
            • Bouncing Ball
            • Tutorial : a column of three beads
              • Building the Non-Smooth Dynamical System
              • The Simulation
                • Time-Stepping scheme
                • Event-Driven algorithm
              • Simulation Process
                • Time-Stepping
                • Event-Driven
              • Results
            • Gene regulatory networks
            • Slider Crank
              • Usage
          • Simulation of an electrical oscillator supplying a resistor through a half-wave rectifier
            • Description of the physical problem : electrical oscillator with half-wave rectifier
            • Definition of a general abstract class of NSDS : the linear time invariant complementarity system (LCS)
              • Dynamical system and Boundary conditions
              • Relation between constrained variables and state variables
              • Definition of the Non Smooth Law between constrained variables
              • The formalization of the electrical oscillator with half-wave rectifier into the LCS
              • Dynamical equation
              • Relations
              • Non Smooth laws
            • Description of the numerical simulation: the Moreau’s time-stepping scheme
              • Time discretization of the dynamical system
              • Time discretization of the relations
              • Time discretization of the non-smooth law
              • Summary of the time discretized equations
              • Numerical simulation
            • Comparison with numerical results coming from SPICE models and algorithms
              • Characteristic of the diode in the SPICE model
              • Simulation results
          • Running a simulation
            • Basics
            • Plugins mechanism
            • Extra source files
          • C++ Refresher
            • Building/destroying and using objects
            • Members/Methods access
            • Matrices and vectors handling
              • Read/write vectors and matrices from/to file
              • Methods and operations on matrices and vectors
              • About efficiency
      • Download and install
        • Download Siconos
          • Packages
          • Latest source release
          • Development sources
        • Build and install
          • Overview
          • Installation from sources
            • Prerequisites
            • The quick way
            • Detailed installation
            • Siconos package description
            • Running siconos tests
            • What will be installed?
              • Remark
            • CMake options
              • Most common options
              • Developers or advanced users options
            • User-defined option file
            • Test your installation
          • Repositories
            • Debian bullseye
            • FreeBSD
        • Siconos required and optional dependencies
        • About blas and Lapack
        • About Boost
        • GMP
      • Browse examples
        • Gallery
      • API reference
        • Siconos C/C++ API reference
          • Class diagrams (UML view)
          • Numerics: a collection of low-level algorithms for solving basic algebra and optimization problem arising in the simulation of nonsmooth dynamical systems.
            • Classes and structs
            • Files documentation
          • Kernel: high-level API to modelise and simulate nonsmooth dynamical systems.
            • Classes and structs
            • Files documentation
          • Control: control toolbox
            • Classes and structs
            • Files documentation
          • Mechanics: toolbox for collision detection and joints
            • Classes and structs
            • Files documentation
          • Io: tools related to input/outputs (hdf5, vtk …)
            • Classes and structs
            • Files documentation
        • Siconos Python API reference
          • siconos.numerics: a collection of low-level algorithms for solving basic algebra and optimization problem arising in the simulation of nonsmooth dynamical systems.
          • siconos.kernel: high-level API to modelise and simulate nonsmooth dynamical systems.
          • siconos.control.observer
          • siconos.control.sensor
          • siconos.control.controller
          • siconos.mechanics.joints
          • siconos.control.simulation
          • siconos.mechanics.collision.base
          • siconos.mechanics.collision.bullet
          • siconos.mechanics.collision.native
          • siconos.mechanics.collision.bodies
          • siconos.io.io_base
      • Full documentation
        • Getting and installing siconos software
          • Build and install
            • Overview
            • Installation from sources
              • Prerequisites
              • The quick way
              • Detailed installation
              • Siconos package description
              • Running siconos tests
              • What will be installed?
                • Remark
              • CMake options
                • Most common options
                • Developers or advanced users options
              • User-defined option file
              • Test your installation
            • Repositories
              • Debian bullseye
              • FreeBSD
        • Siconos Quickstart
          • Quickstart
            • What is Siconos?
            • Try it
            • Siconos usage in a few steps
            • More
              • Modeling Principle
              • Python interface : tutorials
                • Collections of rigid bodies with Bullet based contact detection (Siconos/Mechanics)
                  • Description of the physical problems : rigid bodies collection with contact and Coulomb friction
                • Tutorial: A 4-diodes bridge wave rectifier
                  • Preamble
                  • Siconos driver file
                  • Building a nonsmooth dynamical system
                    • Modeling the dynamics
                    • Modeling the interactions
                  • Describing the simulation of the nonsmooth dynamical system
                  • Leading the Simulation Process
              • Siconos tutorials in C++
                • Bouncing Ball
                • Tutorial : a column of three beads
                  • Building the Non-Smooth Dynamical System
                  • The Simulation
                    • Time-Stepping scheme
                    • Event-Driven algorithm
                  • Simulation Process
                    • Time-Stepping
                    • Event-Driven
                  • Results
                • Gene regulatory networks
                • Slider Crank
                  • Usage
              • Simulation of an electrical oscillator supplying a resistor through a half-wave rectifier
                • Description of the physical problem : electrical oscillator with half-wave rectifier
                • Definition of a general abstract class of NSDS : the linear time invariant complementarity system (LCS)
                  • Dynamical system and Boundary conditions
                  • Relation between constrained variables and state variables
                  • Definition of the Non Smooth Law between constrained variables
                  • The formalization of the electrical oscillator with half-wave rectifier into the LCS
                  • Dynamical equation
                  • Relations
                  • Non Smooth laws
                • Description of the numerical simulation: the Moreau’s time-stepping scheme
                  • Time discretization of the dynamical system
                  • Time discretization of the relations
                  • Time discretization of the non-smooth law
                  • Summary of the time discretized equations
                  • Numerical simulation
                • Comparison with numerical results coming from SPICE models and algorithms
                  • Characteristic of the diode in the SPICE model
                  • Simulation results
              • Running a simulation
                • Basics
                • Plugins mechanism
                • Extra source files
              • C++ Refresher
                • Building/destroying and using objects
                • Members/Methods access
                • Matrices and vectors handling
                  • Read/write vectors and matrices from/to file
                  • Methods and operations on matrices and vectors
                  • About efficiency
        • Users’ guide
          • Users guide
            • Linear Algebra in Siconos
              • Vectors
              • Matrices
                • Notes about SimpleMatrix
              • Matrix Storage in numerics component
            • Modeling of non-smooth dynamical systems
              • Dynamical Systems
                • Overview
                • Common interface
                • First order dynamical systems
                  • Non linear
                  • Linear
                  • Linear and time-invariant
                • Second order (Lagrangian) systems
                  • Non linear
                  • Linear and time-invariant
                • Dynamical Systems plug-in functions
              • Interactions between dynamical systems
                • Relations
                  • First Order Relations
                    • Non Linear
                    • Linear
                    • Linear with Time Invariant Coefficients
                  • Lagrangian (second order) Relations
                    • Scleronomous
                    • Rheonomous
                    • Compliant
                    • Linear and Time Invariant Coefficients
                  • Relations plug-in functions
                • Non Smooth Laws
                  • Complementarity Condition
                  • Newton Impact
                  • Newton Impact-Friction
                  • Relay
              • User-defined plugins
                • Plugins overview
                • Example
            • Simulation of non-smooth dynamical systems
              • Time discretisation
              • Time integration of the dynamics
              • Event-Capturing schemes
                • General Principle
                • First order systems
                  • Time Discretisation of the Dynamics
                    • First Order Non Linear Systems
                    • First Order Linear Systems
                    • First Order Linear Systems with time invariant coefficients
                  • Time discretization of the relations
                    • First Order (non-linear) Relations
                    • First Order Linear Relations
                  • Discretisation of the non-smooth law
                    • Complementarity Condition
                • Lagrangian systems
                  • Time Discretisation of the Dynamics
                    • Lagrangian (second order) Non Linear Systems
                    • Lagrangian (second order) Linear Systems with Time Invariant coefficients
                  • Time discretization of the relations
                    • Lagrangian Scleronomous Relations
                    • Lagrangian Rheonomous Relations
                    • Lagrangian Compliant Relations
                    • Lagrangian Linear Relations
                  • Time discretization of the Non Smooth laws
                • Summary of the time discretized equations
                  • First order systems
                  • Lagrangian second-order systems
              • Event-Driven schemes
                • General Principle
                • Event Driven implementation
                  • Integration of the smooth dynamics
                  • Events
                  • The Events manager
                • The Simulation process
                • Event Driven algorithm for Lagrangian systems
                  • The impact equations
                  • The smooth Dynamics
                • The algorithm
                  • Implementation in Siconos
              • Nonsmooth problems formulation and solve
                • The Simulation process
                • Customize simulation behavior
            • Nonsmooth problems formulations and available solvers
              • Write and solve a problem with Siconos
                • Create a problem
                • Create and describe a solver
                  • dparam indices common to all solvers
                  • iparam indices common to all solvers
                • Solve a problem
                  • Variational Inequality (VI)
                    • Problem statement
                    • Implementation in numerics
                    • VI Available solvers
                      • Extra gradient (SICONOS_VI_EG)
                      • Fixed-point projection (SICONOS_VI_FPP)
                      • Hyperplane projection (SICONOS_VI_HP)
                      • SICONOS_VI_BOX_QI (SICONOS_VI_BOX_QI)
                      • SICONOS_VI_BOX_AVI_LSA (SICONOS_VI_BOX_AVI_LSA)
                      • SICONOS_VI_BOX_PATH (SICONOS_VI_BOX_PATH)
                  • Quadratic Programming problems (QP)
                    • Problem statement
                    • Available solvers
                  • Convex Quadratic Programming (ConvexQP) problems
                    • Problem statement
                    • Implementation in numerics
                    • Available solvers
                      • convex QP, projected gradient (SICONOS_CONVEXQP_PG)
                      • convex QP, VI solvers`(SICONOS_CONVEXQP_VI_FPP and SICONOS_CONVEXQP_VI_EG)
                      • convex QP, ADMM (SICONOS_CONVEXQP_ADMM)
                  • Linear Complementarity Problems (LCP)
                    • Problem statement
                    • Implementation in numerics
                    • Error computation
                    • LCP available solvers
                      • Direct solvers
                        • Lemke (SICONOS_LCP_LEMKE)
                        • Pivot based methods
                        • Enumerative solver (SICONOS_LCP_ENUM)
                        • PATH (SICONOS_LCP_PATH)
                      • Iterative solvers
                        • Conjugated Projected Gradient (SICONOS_LCP_CPG)
                        • Projected Gauss-Seidel (SICONOS_LCP_PGS)
                        • Regularized Projected Gauss-Seidel (SICONOS_LCP_RPGS)
                        • PSOR (SICONOS_LCP_PSOR)
                        • Latin method (SICONOS_LCP_LATIN and SICONOS_LCP_LATIN_W)
                        • Sparse-block Gauss-Seidel (SICONOS_LCP_NSGS)
                      • Equation-based solvers
                        • Nonsmooth Newton, min formulation (SICONOS_LCP_NEWTONMIN)
                        • Nonsmooth Newton, Fisher-Burmeister (SICONOS_LCP_NEWTON_FB_FBLSA)
                        • Nonsmooth Newton, Fisher-Burmeister (SICONOS_LCP_NEWTON_MIN_FBLSA)
                        • GAMS solver (SICONOS_LCP_GAMS)
                      • QP-reformulation
                        • quadratic program formulation (SICONOS_LCP_QP)
                        • quadratic program formulation (SICONOS_LCP_NSQP)
                      • AVI reformulation
                        • AVI with Cao/Ferris solver (SICONOS_AVI_CAOFERRIS)
                  • Affine Variational Inequalities (AVI)
                    • Problem statement
                    • Implementation in numerics
                    • AVI Available solvers
                      • Cao Ferris (SICONOS_AVI_CAOFERRIS)
                      • Pathvi (SICONOS_AVI_PATHAVI)
                  • Mixed (Non Linear) Complementarity problem (MCP)
                    • Problem statement
                    • Implementation in numerics
                    • MCP available solvers
                      • Newton, Fisher-Burmeister (SICONOS_MCP_NEWTON_FB_FBLSA)
                      • Newton (min), Fisher-Burmeister (SICONOS_MCP_NEWTON_MIN_FB_FBLSA)
                      • Newton, Fisher-Burmeister (SICONOS_MCP_OLD_FB)
                  • Mixed Linear Complementarity Problems (MLCP)
                    • Problem statement
                    • Implementation in numerics
                    • Error computation
                    • MLCP available solvers
                      • Projected Gauss-Seidel (SICONOS_MLCP_PGS)
                      • Projected Gauss-Seidel, SBM (SICONOS_MLCP_PGS_SBM)
                      • Regularized Projected Gauss-Seidel (SICONOS_MLCP_RPGS)
                      • PSOR (SICONOS_MLCP_PSOR)
                      • RPSOR (SICONOS_MLCP_RPSOR)
                      • PATH (Ferris) solver (SICONOS_MLCP_PATH)
                      • Enumerative solver (SICONOS_MLCP_ENUM)
                      • PATH + enum solver (SICONOS_MLCP_PATH_ENUM)
                      • Direct + enum solver (SICONOS_MLCP_DIRECT_ENUM)
                      • Simplex solver (SICONOS_MLCP_SIMPLEX)
                      • Direct/Simplex solver (SICONOS_MLCP_DIRECT_SIMPLEX)
                      • Direct/Path solver (SICONOS_MLCP_DIRECT_PATH)
                      • Direct/Path/enum solver (SICONOS_MLCP_DIRECT_PATH_ENUM)
                      • Nonsmooth Newton solver, Fisher-Burmeister (SICONOS_MLCP_FB)
                      • Direct + Nonsmooth Newton solver, Fisher-Burmeister (SICONOS_MLCP_DIRECT_FB)
                  • Nonlinear Complementarity Problems (NCP)
                    • Problem statement
                    • Implementation in numerics
                    • NCP available solvers
                      • Newton, Fisher-Burmeister (SICONOS_NCP_NEWTON_FB_FBLSA)
                      • Newton, min merit function (SICONOS_NCP_NEWTON_MIN_FBLSA)
                      • Path search algorithm (SICONOS_NCP_PATHSEARCH)
                      • PATH (Ferris) solver (SICONOS_NCP_PATH)
                  • Relay or box-constrained AVI problems
                    • Problem statement
                    • Implementation in numerics
                    • Relay available solvers
                      • Direct solvers
                        • Enumerative solver (SICONOS_RELAY_ENUM)
                        • Lemke solver (SICONOS_RELAY_LEMKE)
                        • PATH (SICONOS_RELAY_PATH)
                      • AVI reformulation
                        • AVI, Cao/Ferris solver (SICONOS_RELAY_AVI_CAOFERRIS)
                      • Iterative solvers
                        • Projected Gauss-Seidel (SICONOS_RELAY_PGS)
                  • Second Order Cone Linear Complementarity Problem (SOCLCP)
                    • Problem statement
                    • Implementation in numerics
                    • SOCLCP available solvers
                      • Gauss-Seidel (SICONOS_SOCLCP_NSGS)
                      • VI, fixed-point (SICONOS_SOCLCP_VI_FPP)
                      • VI, Extra-gradient (SICONOS_SOCLCP_VI_EG)
                      • VI, Extra-gradient (SICONOS_SOCLCP_VI_EG)
                      • Projections
                  • Friction-contact problems (2 or 3D)
                    • Problem statement
                    • Implementation in numerics
                    • Error strategy
                    • Friction 2D available solvers
                      • Nonsmooth Gauss-Seidel (SICONOS_FRICTION_2D_NSGS)
                      • Conjugated projected gradient (SICONOS_FRICTION_2D_CPG)
                      • Lemke solver (SICONOS_FRICTION_2D_LEMKE)
                      • Enumerative solver (SICONOS_FRICTION_2D_ENUM)
                    • Friction 3D available solvers
                      • Nonsmooth Gauss-Seidel (SICONOS_FRICTION_3D_NSGS)
                      • Nonsmooth Gauss-Seidel, velocity version (SICONOS_FRICTION_3D_NSGSV)
                      • Proximal point solver (SICONOS_FRICTION_3D_PROX)
                      • Fixed-point (Tresca) (SICONOS_FRICTION_3D_TFP)
                      • Nonsmooth Newton/ Alart-Curnier (SICONOS_FRICTION_3D_NSN_AC)
                      • Nonsmooth Newton/ Alart-Curnier (test) (SICONOS_FRICTION_3D_NSN_AC_TEST)
                      • Fixed-Point (De Saxce formulation) (SICONOS_FRICTION_3D_DSFP)
                      • Fixed-Point projection (VI reformulation) (SICONOS_FRICTION_3D_VI_FPP)
                      • Fixed-Point projection on cylinder (VI reformulation) (SICONOS_FRICTION_3D_VI_FPP_Cylinder)
                      • Extra Gradient (VI reformulation) (SICONOS_FRICTION_3D_VI_EG)
                      • Hyperplane Projection (SICONOS_FRICTION_3D_HP)
                      • Fixed-Point projection (SICONOS_FRICTION_3D_FPP)
                      • Extra Gradient (SICONOS_FRICTION_3D_EG)
                      • Nonsmooth Newton (Fischer-Burmeister formulation) (SICONOS_FRICTION_3D_NSN_FB)
                      • PATH (via GAMS) + AVI reformulation (SICONOS_FRICTION_3D_GAMS_PATH)
                      • PATHVI (via GAMS) + AVI reformulation SICONOS_FRICTION_3D_GAMS_PATHVI)
                      • Nonsmooth Gauss-Seidel (SICONOS_FRICTION_3D_SOCLCP)
                      • PATH (via GAMS) + LCP reformulation (SICONOS_FRICTION_3D_GAMS_LCP_PATH)
                      • PATHVI (via GAMS) + LCP reformulation SICONOS_FRICTION_3D_GAMS_LCP_PATHVI)
                      • Nonsmooth Newton, Natural Map (SICONOS_FRICTION_3D_NSN_NM)
                      • Fixed point, Panagiotopoulos (SICONOS_FRICTION_3D_PFP)
                      • ADMM (SICONOS_FRICTION_3D_ADMM)
                        • “One contact” solvers
                      • Newton(SICONOS_FRICTION_3D_ONECONTACT_NSN, …)
                      • Projection on cone or cylinder (SICONOS_FRICTION_3D_ONECONTACT_ProjectionOnCone, …)
                      • NCP Fixed Point solver (SICONOS_FRICTION_3D_NCPGlockerFBFixedPoint, …)
                      • Quartic (SICONOS_FRICTION_3D_ONECONTACT_QUARTIC, …)
                      • As Convex QP (SICONOS_FRICTION_3D_CONVEXQP_CYLINDER)
                  • Global-Friction-contact problems (2D or 3D)
                    • Problem statement
                    • Implementation in numerics
                    • Error strategy
                    • Global Friction 3D available solvers
                      • NSGS (SICONOS_GLOBAL_FRICTION_3D_NSGS)
                      • Nonsmooth Newton, Alart-Curnier, (SICONOS_GLOBAL_FRICTION_3D_NSN_AC)
                      • PATH (GAMS) (SICONOS_GLOBAL_FRICTION_3D_GAMS_PATH)
                      • PATHVI (GAMS) (SICONOS_GLOBAL_FRICTION_3D_GAMS_PATHVI)
                      • Fixed-Point projection (VI reformulation) (SICONOS_GLOBAL_FRICTION_3D_VI_FPP)
                      • Extra-Gradient (VI reformulation) (SICONOS_GLOBAL_FRICTION_3D_VI_EG)
                      • ACLM Fixed point (SICONOS_GLOBAL_FRICTION_3D_ACLMFP)
                      • ADMM (SICONOS_GLOBAL_FRICTION_3D_ADMM)
                        • Solvers with reformulation
                      • NSGS, with reformulation (SICONOS_GLOBAL_FRICTION_3D_NSGS_WR)
                      • NSGS, velocity, with reformulation (SICONOS_GLOBAL_FRICTION_3D_NSGS_WR)
                      • Proximal point, with reformulation (SICONOS_GLOBAL_FRICTION_3D_PROX_WR)
                      • DeSaxce FixedPoint, with reformulation (SICONOS_GLOBAL_FRICTION_3D_DSFP_WR)
                      • Tresca FixedPoint, with reformulation (SICONOS_GLOBAL_FRICTION_3D_TFP_WR)
                      • Nonsmooth Newton, Alart-Curnier, with reformulation (SICONOS_GLOBAL_FRICTION_3D_NSN_AC_WR)
                      • ADMM, with reformulation (SICONOS_GLOBAL_FRICTION_3D_ADMM_WR)
                  • Rolling friction-contact problems
                    • Problem statement
                    • Implementation in numerics
                    • Error strategy
                    • Rolling-Friction 3D available solvers
                      • NSGS (SICONOS_ROLLING_FRICTION_3D_NSGS)
                      • Projection on cone (SICONOS_ROLLING_FRICTION_3D_ONECONTACT_ProjectionOnCone, …)
                  • Generic mechanical problems
                    • Problem statement
                    • Implementation in numerics
                    • Error strategy
                    • GMP solvers
            • Control Toolbox
              • Control Manager
              • Sensors
              • Actuators
          • Browse examples
            • Gallery
        • Siconos API
          • API reference
            • Siconos C/C++ API reference
              • Class diagrams (UML view)
              • Numerics: a collection of low-level algorithms for solving basic algebra and optimization problem arising in the simulation of nonsmooth dynamical systems.
                • Classes and structs
                • Files documentation
              • Kernel: high-level API to modelise and simulate nonsmooth dynamical systems.
                • Classes and structs
                • Files documentation
              • Control: control toolbox
                • Classes and structs
                • Files documentation
              • Mechanics: toolbox for collision detection and joints
                • Classes and structs
                • Files documentation
              • Io: tools related to input/outputs (hdf5, vtk …)
                • Classes and structs
                • Files documentation
            • Siconos Python API reference
              • siconos.numerics: a collection of low-level algorithms for solving basic algebra and optimization problem arising in the simulation of nonsmooth dynamical systems.
              • siconos.kernel: high-level API to modelise and simulate nonsmooth dynamical systems.
              • siconos.control.observer
              • siconos.control.sensor
              • siconos.control.controller
              • siconos.mechanics.joints
              • siconos.control.simulation
              • siconos.mechanics.collision.base
              • siconos.mechanics.collision.bullet
              • siconos.mechanics.collision.native
              • siconos.mechanics.collision.bodies
              • siconos.io.io_base
        • Developpers’ corner
          • Developer guide
            • Writing and building documention for Siconos Software
              • Documentation overview
              • How to write Siconos documentation
                • Writing textbooks
                • Document source code
                  • References to sphinx documents
                  • Math and latex
              • Building process
                • Tools, config and description
                • Dependencies
                • More about Doxygen to sphinx rst
            • Adding a new solver in numerics
            • Time integration of the dynamics - Exact scheme
              • Summary
              • Detailed calculations
                • Taylor expansions
                • Non-smooth problem formulation
            • Continuous integration for Siconos project
            • How to add and test a new continuous integration task for Siconos project
              • What is a “Continuous integration task”?
              • Create a task
              • Options sent by driver
              • Available ci targets
            • About plugins in classes
              • Rules
              • Example/template
            • OneStepNSProblem formalisation for several interactions
              • LinearDS - Linear Time Invariant Relations
            • Todo List
            • Test doxygen/sphinx links
        • More about Siconos project
          • Talks and Presentations
            • Posters
            • Slides (in chronological order)
          • Related Projects and Platforms
          • Bibliography
      • Index
      • License
  • « Bibliography
  • License »

Index¶

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