Methods

{
  "name": "NaturalOrderingMethod",
  "namespace": "sofa::component::linearsolver::ordering",
  "module": "Sofa.Component.LinearSolver.Ordering",
  "include": "sofa/component/linearsolver/ordering/NaturalOrderingMethod.h",
  "doc": "Natural order (no permutation). Corresponding to an identity matrix.",
  "inherits": [
    "BaseOrderingMethod"
  ],
  "templates": [],
  "data_fields": [],
  "links": [],
  "methods": [
    {
      "name": "methodName",
      "return_type": "int",
      "params": [],
      "is_virtual": false,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "public"
    },
    {
      "name": "computePermutation",
      "return_type": "void",
      "params": [
        {
          "name": "inPattern",
          "type": "const SparseMatrixPattern &"
        },
        {
          "name": "outPermutation",
          "type": "int *"
        },
        {
          "name": "outInversePermutation",
          "type": "int *"
        }
      ],
      "is_virtual": true,
      "is_pure_virtual": false,
      "is_static": false,
      "access": "public"
    }
  ],
  "description": "The `NaturalOrderingMethod` is a component within the SOFA framework's linear solver ordering module (`Sofa.Component.LinearSolver.Ordering`). Its primary role is to maintain the natural order of matrix elements, which corresponds to an identity permutation (no reordering). This method inherits from the `BaseOrderingMethod`, implementing a straightforward approach where no changes are made to the original indices. The component defines two methods: `methodName` returns a string representing the name of the method, and `computePermutation` calculates the natural ordering for input sparse matrix patterns by setting both permutation and inverse-permutation arrays to their respective identity values. This component is useful when no reordering is desired in linear system solving processes.",
  "maths": "The `NaturalOrderingMethod` is a component within the SOFA framework's linear solver ordering module (`Sofa.Component.LinearSolver.Ordering`). Its primary role is to maintain the natural order of matrix elements, which corresponds to an identity permutation (no reordering). This method inherits from the `BaseOrderingMethod`, implementing a straightforward approach where no changes are made to the original indices. The component defines two methods: `methodName` returns a string representing the name of the method, and `computePermutation` calculates the natural ordering for input sparse matrix patterns by setting both permutation and inverse-permutation arrays to their respective identity values.\n\n### Mathematical Description:\n\nThe role of the `NaturalOrderingMethod` is to preserve the original order of indices in a linear system. This means that if we have a matrix \\( A \\) with elements arranged according to some ordering, the natural ordering method ensures that no permutation occurs, i.e., the index mapping remains identity.\n\nIn terms of mathematical notation:\n- Let \\( P \\) be the permutation matrix used for reordering. For the `NaturalOrderingMethod`, \\( P \\) is simply the identity matrix \\( I \\).\n- Given a linear system represented by the equation \\( A x = b \\), where \\( A \\) is the matrix and \\( x, b \\) are vectors, the natural ordering method ensures that \\( A \\) remains unchanged after any reordering process.\n\n### Constitutive or Kinematic Laws:\n- The `NaturalOrderingMethod` does not involve constitutive laws (such as stress-strain relationships), kinematic measures (like deformation gradients), or specific material models. It is purely a numerical method for maintaining the original order of matrix elements.\n\n### Role in FEM Pipeline:\n- In the context of the global FEM pipeline, this component operates during the linear solve phase to ensure that no reordering occurs in the stiffness matrix \\( K \\) or mass matrix \\( M \\). This is particularly useful when the inherent structure and sparsity pattern of the matrices are already optimized for efficient solution.\n\n### Numerical Methods:\n- The `computePermutation` method iterates through the indices of the input sparse matrix pattern (`inPattern`) and sets both the permutation array (`outPermutation`) and inverse-permutation array (`outInversePermutation`) to the identity values, i.e., \\( outPermutation[i] = i \\) and \\( outInversePermutation[i] = i \\).\n\n### Variational/Lagrangian Mechanics Framework:\n- The `NaturalOrderingMethod` does not directly contribute to the variational or Lagrangian mechanics framework. It is a support component that helps maintain the integrity of matrix ordering, which can indirectly affect the efficiency and stability of iterative linear solvers used in the nonlinear solve phase.\n\n### Summary:\n- This component ensures no reordering occurs, preserving the natural index order of matrices. It does not introduce any physical or constitutive laws but provides a straightforward identity permutation that is useful for maintaining matrix structure during linear system solving.",
  "abstract": "The `NaturalOrderingMethod` maintains the natural order of matrix elements, corresponding to an identity permutation, ensuring no reordering occurs during linear system solving processes.",
  "sheet": "# NaturalOrderingMethod\n\n## Overview\n\nThe `NaturalOrderingMethod` is a component within the SOFA framework's linear solver ordering module (`Sofa.Component.LinearSolver.Ordering`). Its primary role is to maintain the natural order of matrix elements, which corresponds to an identity permutation (no reordering). This method inherits from the `BaseOrderingMethod`, implementing a straightforward approach where no changes are made to the original indices.\n\n## Parameters and Data\n\nThe `NaturalOrderingMethod` does not expose any significant data fields. It relies on its methods to ensure that the natural order is maintained without altering the matrix elements' arrangement."
}