# Package jvx.numeric

Numerical algorithms and datastructures.

See: Description

- Interface Summary
  Interface | Description
  --- | ---
  PnLanczos.PnMatrixVectorProductIf | Interface encapsulating the product of a vector v with a square matrix A: A*v.

- Class Summary
  Class | Description
  --- | ---
  PnAlignmentEnergy | Alignment energy for non-conforming meshes.
  PnAreaEnergy | Area energy including gradient and hessian computations.
  PnAreaVolEnergy | Dirichlet energy with volume term is used to minimize area under a volume constraint.
  PnBandEigenSolver | Eigensolver computing a band instead the full spectrum of a matrix.
  PnBandEigenSolver_IP | Info panel for eigensolver computing a band instead the full spectrum of a matrix.
  PnBiconjugateGradient | Solve sparse linear equation systems using preconditioned biconjugate gradient method.
  PnConfEnergy | Conformal energy including gradient and hessian computations.
  PnConjugateGradient | Minimize functionals using conjugate gradient method.
  PnConjugateGradientMatrix | Solve symmetric sparse linear equation systems using preconditioned conjugate gradient method.
  PnDiriEnergy | Dirichlet energy including gradient and hessian computations.
  PnElementRK | Discrete Runge-Kutta solver on triangular element sets for integration of an element based vector field.
  PnEnergy | Energy functional on triangulated surfaces including gradient and hessian computations.
  PnEnergyMinimizer | Main class to vary a surface to minimize a given energy functional.
  PnEnergyMinimizer_IP | Info panel for energy minimization to control minimization process and print info.
  PnFunction | Abstract class for functions to be used numerical methods, e.g. in minimization classes.
  PnGaussEnergy | Gauss energy is the difference of the current Gauss curvature to a prescribed value.
  PnGeodesicRK | Discrete Runge-Kutta solver on triangular element sets.
  PnHodgeU | Energy to obtain potential function u.
  PnHodgeW | Energy to obtain potential function u.
  PnJacobi | Compute eigenvectors and eigenvalues of a given symmetric matrix and store in result vectors.
  PnJacobi_IP | Info panel holding interface elements for all user specified settings for `PnJacobi` eigensolver.
  PnLanczos | Lanczos method - computes (incomplete) tridiagonalization T of an symmetric input matrix A.
  PnLevelSet | Abstract class for all kinds of level sets.
  PnLIC | Line Integral Convolution for vector field visualization.
  PnMassMatrix | Mass matrix of triangulated surface and functions linear in each triangle.
  PnMatrix | Numerical routines for bigger matrix linear algebra problems.
  PnNoise | Generates 2D procedural white noise by hashtable-like method to generate a gradient on an integer lattice that is made continuous by smoothed interpolation.
  PnOde | Basic ode class with solver.
  PnOdeExpr | Extends basic ode class with ability to supply a string expression of the ode.
  PnPCA | Principal component analysis of an element set and tetra set.
  PnPreconditioner | Identity Preconditioner used by conjugate gradient and biconjugate gradient solver, all other Preconditioners should inherit from this.
  PnPreconditionerILU | Perform an ILU Preconditioning.
  PnPreconditionerJacobi | Perform a diagonal (Jacobi) preconditioning from the left to the a linear equation system smat.x=b.
  PnRootFinder | Find roots of a real-valued function in one variable or defined on a 1-dimensional curve.
  PnSparseMatrix | Sparse matrix representation.
  PnSpringEnergy | Spring energy including gradient computation.
  PnStiffAniso | Create and setup stiffness matrix for the anisotropic Laplace operator.
  PnStiffConformal | Create and setup stiffness matrix for conformal energy defined by John Hutchinson of a map from triangulation to C.
  PnStiffDiriConforming | Create and setup stiffness matrix for Dirichlet energy and area computations of a given conforming triangulated domain surface.
  PnStiffDiriNonConforming | Create and setup stiffness matrix for Dirichlet energy or area computations of a given non-conforming triangulated domain surface.
  PnStiffMatrix | Create and setup sparse representation of a stiffness matrix.
  PnStiffSpring | Create and setup stiffness matrix for spring energy of a given conforming triangulated domain surface.
  PnStraightestGeodesic | The exponential map on a PgElementSet.
  PnTranslationRK | Discrete Runge-Kutta method on element sets.
  PnVertexRK | Discrete Runge-Kutta solver on triangular element sets for integration of a vertex-based vector field.
  PnVertexRKIgnoreDirection | Discrete Runge-Kutta method on element sets.
  PnVolumeEnergy | Volume energy is the difference of the oriented volume of a surface with a given constant.

## Package jvx.numeric Description

Numerical algorithms and datastructures. Includes support for large matrices, sparse matrices and numerical linear algebra algorithms. Solution for variational problems and energy minimization.

Support for small vector and matrices including some 3D affine geometry is available in the package `jv.vecmath`.

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