Road to Release

Mathematics.NET is closer to its first release, but a number of important features still need to be implemented.

Core Features

Here are some core features that will be included in the first release and their current status. Note that a number of basic operations are not icluded in this list.

Numerical Types

• Core types
  • Real numbers
  • Complex numbers
  • Rational numbers

AutoDiff

• Reverse-mode autodiff
  • Gradient Tapes
    • Parallelization
    • Checkpointing
  • Hessian Tapes
    • Parallelization
    • Checkpointing
• Forward-mode autodiff
  • Dual numbers
  • Hyper-dual numbers

Linear Algebra

• Vectors
  • Two, three, and four-element vectors
  • AutoDiff vectors
  • Vectors in polar, cylindrical, and spherical coordinates
• Matrices
• Multi-dimensional arrays

Differential Geometry

• Rank one, two, three, and four tensors
• DifGeo methods
  • Index raising and lowering
  • Index contractions
  • Covariant derivatives
  • Contravariant derivatives
  • Tensor products
• Christoffel symbols
• Riemann curvature tensors
• Metric tensors
• Levi-Civita symbols

Other Features

• Solvers
  • Runge-Kutta solvers
    • Solvers for differential geometry
• QR decomposition
  • Gram-Schmidt process
  • Householder reflections
  • Givens rotations