Misc.

  • complex number
  • scientific notatoin
  • arbitrary precision support
  • interval arithmetics
  • a Math table data structure to store table values
  • Ordinary Least Square solver
  • sequence
    • Fibonacci sequence
  • uniroot finding algorithm:
    • Brent
    • Halley
    • Newton
  • common physical constants

Linear Algebra

  • vector
  • vector space
  • various matrix representations:
    • bi-diagonal
    • diagonal
    • tri-diagonal
    • Givens
    • Hilbert
    • lower/upper triangular
    • permutation
  • sparse vector representations:
  • sparse matrix representations:
    • CSR
    • DOK
    • LIL
  • iterative sparse matrix solver:
    • stationary
      • Jacobi
      • Gauss-Seidel
      • SOR
      • SSOR
    • non-stationary
      • Steepest Descent
      • BiCG
      • BiCGStabl
      • CGNE
      • CGNR
      • CG
      • CGS
      • GCR
      • GMRES
      • MinRes
      • QMR
    • pre-conditioner support
      • Jacobi
      • SSOR
      • customized
  • matrix elementary operations
  • Householder transformation
  • matrix inverse
  • matrix measures:
    • determinant
    • rank
    • trace
    • max
    • min
  • power of matrix
  • matrix pseudoinverse
  • matrix bi-diagonalization
  • matrix tri-diagonalization
  • Cholesky decomposition
  • Doolittle factorization
  • Eigen factorization
  • Gauss-Jordan elimination
  • SVD factorization (for asymmetric matrix)
  • Gram-Schmidt factorization
  • Hessenberg factorization
  • LDL decomposition
  • LU decomposition
  • QR decomposition

Curve Fitting & Interpolation

  • curve fitting
    • least-squares
  • online interpolation
    • the Neville method
  • univariate
    • linear
    • Newton polynomial
    • (natural) cubic spline
    • cubic Hermite spline
  • bivariate grid
    • bilinear
    • bicubic
    • bicubic spline
  • multivariate grid
    • multi-linear
    • multi-cubic spline
    • general recursive grid interpolation

Geometry

  • comprehensive collection of trigonometric functions (complementary to Java’s Math class)
  • point and line segment
  • polygonal chain
    • Ramer-Douglas-Peucker algorithm

Functions

  • polynomial
  • polynomial evaluation using Horner scheme
  • polynomial root finding using analytical formulae up to degree 4
  • polynomial root finding using the Jenkins Traub method
  • continued fraction
  • special functions:
    • Beta
    • regularized Beta
    • inverse of regularized Beta
    • cumulative Normal
    • inverse of cumulative Normal
    • Digamma
    • Erf
    • inverse of Erf
    • Gamma
    • lower incomplete Gamma
    • regularized Gamma P
    • inverse of regularized Gamma P
    • regularized Gamma Q
    • incomplete upper Gamma
    • Gaussian
    • logBeta
    • logGamma
    • Lanczos method

Calculus

  • finite difference
  • differentiation using Ridders’ method
  • derivaties of functions for:
    • Beta
    • Beta Regularized
    • Erf
    • Gamma
    • Gaussian
  • multivariate differentiation:
    • (bordered) Hessian
    • gradient
    • Jacobian
  • Riemann integration
  • Riemann integration using substitution rules:
    • Double-Exponential rule
    • Exponential rule
    • Power law singularity
    • Map to the Standard interval
  • integration using Romberg’s method
  • integration using Newton-Cotes formula
    • Simpson’s rule
    • Trapezoidal rule
    • Midpoint rule
  • integration using Gaussian quadrature
    • Legendre polynomials
    • Chebyshev polynomials
    • Laguerre polynomials
    • Hermite polynomials