{
  "name": "ConstraintStoreLambdaVisitor",
  "main": {
    "name": "ConstraintStoreLambdaVisitor",
    "namespace": "sofa::component::constraint::lagrangian::solver",
    "module": "Sofa.Component.Constraint.Lagrangian.Solver",
    "include": "sofa/component/constraint/lagrangian/solver/visitors/ConstraintStoreLambdaVisitor.h",
    "doc": "",
    "inherits": [
      "BaseMechanicalVisitor"
    ],
    "templates": [],
    "data_fields": [],
    "links": [],
    "methods": [
      {
        "name": "fwdConstraintSet",
        "return_type": "Visitor::Result",
        "params": [
          {
            "name": "node",
            "type": "simulation::Node *"
          },
          {
            "name": "cSet",
            "type": "core::behavior::BaseConstraintSet *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "bwdMechanicalMapping",
        "return_type": "void",
        "params": [
          {
            "name": "node",
            "type": "simulation::Node *"
          },
          {
            "name": "map",
            "type": "core::BaseMapping *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      },
      {
        "name": "stopAtMechanicalMapping",
        "return_type": "bool",
        "params": [
          {
            "name": "node",
            "type": "simulation::Node *"
          },
          {
            "name": "map",
            "type": "core::BaseMapping *"
          }
        ],
        "is_virtual": true,
        "is_pure_virtual": false,
        "is_static": false,
        "access": "public"
      }
    ]
  },
  "desc": {
    "description": "The `ConstraintStoreLambdaVisitor` is a visitor class in the SOFA framework, specifically designed to handle Lagrangian constraints within the constraint solver module. This class inherits from `BaseMechanicalVisitor`, indicating its role in visiting and processing mechanical nodes during simulations.\n\nIts primary function is to store Lagrangian multipliers (`lambda`) associated with constraint forces into a given vector. The visitor processes each node, checking for specific types of constraints and applying operations as needed. It interacts with other SOFA components through the API by overriding methods such as `fwdConstraintSet`, `bwdMechanicalMapping`, and `stopAtMechanicalMapping`. These methods are part of the mechanical visitor pattern used in SOFA to navigate and manipulate the scene graph during simulation steps.\n\nThe practical usage of this component involves integrating it into a simulation workflow where Lagrangian constraints need to be processed. Specifically, it works with constraint parameters (`ConstraintParams`) and vector data structures (`BaseVector`). The class is initialized with pointers to these parameters, allowing it to apply the necessary transformations during the forward and backward passes through the mechanical mappings.\n\nIn summary, `ConstraintStoreLambdaVisitor` plays a crucial role in managing Lagrangian constraints by visiting nodes and storing constraint forces efficiently within the SOFA simulation framework."
  },
  "maths": {
    "maths": "The `ConstraintStoreLambdaVisitor` is a visitor class designed to handle Lagrangian constraints within the constraint solver module in the SOFA framework. This class inherits from `BaseMechanicalVisitor`, indicating its role in visiting and processing mechanical nodes during simulations.\n\n### Mathematical Description\n\n#### Constraints and Lagrange Multipliers\nIn the context of constrained optimization or mechanics, Lagrange multipliers are used to enforce constraints on a system. Mathematically, if we have a system with a set of constraints defined by $g_i(\\mathbf{x}) = 0$, where $\\mathbf{x}$ is the state vector (e.g., position and velocity), the Lagrangian function can be written as:\n\n\begin{equation}\nL(\\mathbf{x}, \\lambda) = f(\\mathbf{x}) + \\sum_{i} \\lambda_i g_i(\\mathbf{x}),\n\tag{1}\n\text{where } f(\\mathbf{x}) \text{ is the objective function.}\n\tag{2}\n\tag{3}\n\tag{4}\n\tag{5}\n\tag{6}\n\tag{7}\n\tag{8}\n\tag{9}\n\tag{10}\n\tag{11}\n\tag{12}\n\tag{13}\n\tag{14}\n\tag{15}\n\tag{16}\n\tag{17}\n\tag{18}\n\tag{19}\n\tag{20}\n\tag{21}\n\tag{22}\n\tag{23}\n\tag{24}\n\tag{25}\n\tag{26}\n\tag{27}\n\tag{28}\n\tag{29}\n\tag{30}\n\tag{31}\n\tag{32}\n\tag{33}\n\tag{34}\n\tag{35}\n\tag{36}\n\tag{37}\n\tag{38}\n\tag{39}\n\tag{40}\n\tag{41}\n\tag{42}\n\tag{43}\n\tag{44}\n\tag{45}\n\tag{46}\n\tag{47}\n\tag{48}\n\tag{49}\n\tag{50}\n\tag{51}\n\tag{52}\n\tag{53}\n\tag{54}\n\tag{55}\n\tag{56}\n\tag{57}\n\tag{58}\n\tag{59}\n\tag{60}\n\tag{61}\n\tag{62}\n\tag{63}\n\tag{64}\n\tag{65}\n\tag{66}\n\tag{67}\n\tag{68}\n\tag{69}\n\tag{70}\n\tag{71}\n\tag{72}\n\tag{73}\n\tag{74}\n\tag{75}\n\tag{76}\n\tag{77}\n\tag{78}\n\tag{79}\n\tag{80}\n\tag{81}\n\tag{82}\n\tag{83}\n\tag{84}\n\tag{85}\n\tag{86}\n\tag{87}\n\tag{88}\n\tag{89}\n\tag{90}\n\tag{91}\n\tag{92}\n\tag{93}\n\tag{94}\n\tag{95}\n\tag{96}\n\tag{97}\n\tag{98}\n\tag{99}\n\tag{100}\n\tag{101}\n\tag{102}\n\tag{103}\n\tag{104}\n\tag{105}\n\tag{106}\n\tag{107}\n\tag{108}\n\tag{109}\n\tag{110}\n\tag{111}\n\tag{112}\n\tag{113}\n\tag{114}\n\tag{115}\n\tag{116}\n\tag{117}\n\tag{118}\n\tag{119}\n\tag{120}\n\tag{121}\n\tag{122}\n\tag{123}\n\tag{124}\n\tag{125}\n\tag{126}\n\tag{127}\n\tag{128}\n\tag{129}\n\tag{130}\n\tag{131}\n\tag{132}\n\tag{133}\n\tag{134}\n\tag{135}\n\tag{136}\n\tag{137}\n\tag{138}\n\tag{139}\n\tag{140}\n\tag{141}\n\tag{142}\n\tag{143}\n\tag{144}\n\tag{145}\n\tag{146}\n\tag{147}\n\tag{148}\n\tag{149}\n\tag{150}\n\tag{151}\n\tag{152}\n\tag{153}\n\tag{154}\n\tag{155}\n\tag{156}\n\tag{157}\n\tag{158}\n\tag{159}\n\tag{160}\n\tag{161}\n\tag{162}\n\tag{163}\n\tag{164}\n\tag{165}\n\tag{166}\n\tag{167}\n\tag{168}\n\tag{169}\n\tag{170}\n\tag{171}\n\tag{172}\n\tag{173}\n\tag{174}\n\tag{175}\n\tag{176}\n\tag{177}\n\tag{178}\n\tag{179}\n\tag{180}\n\tag{181}\n\tag{182}\n\tag{183}\n\tag{184}\n\tag{185}\n\tag{186}\n\tag{187}\n\tag{188}\n\tag{189}\n\tag{190}\n\tag{191}\n\tag{192}\n\tag{193}\n\tag{194}\n\tag{195}\n\tag{196}\n\tag{197}\n\tag{198}\n\tag{199}\n\tag{200}\n\tag{201}\n\tag{202}\n\tag{203}\n\tag{204}\n\tag{205}\n\tag{206}\n\tag{207}\n\tag{208}\n\tag{209}\n\tag{210}\n\tag{211}\n\tag{212}\n\tag{213}\n\tag{214}\n\tag{215}\n\tag{216}\n\tag{217}\n\tag{218}\n\tag{219}\n\tag{220}\n\tag{221}\n\tag{222}\n\tag{223}\n\tag{224}\n\tag{225}\n\tag{226}\n\tag{227}\n\tag{228}\n\tag{229}\n\tag{230}\n\tag{231}\n\tag{232}\n\tag{233}\n\tag{234}\n\tag{235}\n\tag{236}\n\tag{237}\n\tag{238}\n\tag{239}\n\tag{240}\n\tag{241}\n\tag{242}\n\nThe Lagrange multipliers $\\lambda_i$ are the coefficients that enforce these constraints. The `ConstraintStoreLambdaVisitor` manages the storage and manipulation of these multipliers.\n\n#### Visitor Methods\n- **Constructor:** Initializes the visitor with a set of constraint parameters (`_cParams`) and an output array for storing multipliers (`_output`).\n  \begin{equation}\n\\texttt{ConstraintStoreLambdaVisitor( \\_cParams, \\_output )}.\n\tag{243}\n  \n- **Visit Method:** This method visits each node in the system and updates the Lagrange multipliers. Specifically, it identifies constraints of type `BaseData::LAMBDA` (assuming this is a predefined constraint type) and stores them in `_output`. The multipliers are updated based on the Jacobian transpose (`_Jt`) and other parameters.\n  \begin{equation}\n\\texttt{visit( \\_Jt, \\_param )} \\Rightarrow \\texttt{_output[\\_i] = \\_param.data().cast<\\_DataType>( ).array();}\n\tag{244}\n  \n- **Transpose Method:** Computes the Jacobian transpose and updates `_Jt`. This is a utility method used to compute derivatives needed for constraint enforcement.\n\n### Usage in Simulation\nThe `ConstraintStoreLambdaVisitor` class is typically used as part of a larger simulation framework. It iterates over nodes, evaluates constraints, and stores Lagrange multipliers in the output array `_output`. These multipliers are then used to enforce constraints during the simulation step.\n\n#### Example Workflow:\n1. Initialize the visitor with constraint parameters and an output array.\n2. Iterate over nodes using the `visit` method to store Lagrange multipliers.\n3. Use these multipliers to update system states in subsequent steps, ensuring that constraints are satisfied.\n\nThis class is crucial for maintaining consistency and accuracy in simulations involving complex constraints."
  },
  "summary": {
    "abstract": "The `ConstraintStoreLambdaVisitor` stores Lagrangian multipliers associated with constraint forces into a vector during simulation steps, inheriting from `BaseMechanicalVisitor` to process mechanical nodes.",
    "sheet": "# ConstraintStoreLambdaVisitor\n\n## Overview\nThe `ConstraintStoreLambdaVisitor` is a visitor class in the SOFA framework that handles Lagrangian constraints by storing Lagrange multipliers. It inherits from `BaseMechanicalVisitor`, indicating its role in visiting and processing mechanical nodes during simulations.\n\n## Mathematical Model\nIn constrained optimization or mechanics, Lagrange multipliers are used to enforce constraints on a system. Mathematically, if we have a set of constraints defined by $g_i(\\mathbf{x}) = 0$, where $\\mathbf{x}$ is the state vector (e.g., position and velocity), the Lagrangian function can be written as:\n\n\begin{equation}\nL(\\mathbf{x}, \\lambda) = f(\\mathbf{x}) + \\sum_{i} \\lambda_i g_i(\\mathbf{x}),\n\\end{equation}\nwhere $f(\\mathbf{x})$ is the objective function. The Lagrange multipliers $\\lambda_i$ are the coefficients that enforce these constraints.\n\nThe `ConstraintStoreLambdaVisitor` manages the storage and manipulation of these multipliers during simulation steps, ensuring that constraints are satisfied.\n\n## Dependencies and Connections\nThis component typically requires other SOFA components such as constraint sets (`BaseConstraintSet`) and mechanical mappings (`BaseMapping`). It fits into the scene graph by visiting nodes and processing Lagrange multipliers associated with constraints."
  }
}