Math Library Features

The Extreme Optimization Numerical Libraries for .NET includes classes for the following subject areas. Also see the detailed vector and matrix, data analysis and statistics feature lists.

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General

  • Machine floating-point constants.
  • Common mathematical constants.
  • Extended elementary functions.
  • Algorithm support functions: iteration, tolerance, convergence tests.

Complex numbers

  • Double-precision complex number value type.
  • Overloaded operators for all arithmetic operations.
  • Static operator functions for languages that don’t support operator overloading.
  • Extension of functions in System.Math to complex argument.
  • Support for complex infinity and complex Not-a-Number (NaN).
  • Complex vector and matrix classes.

Numerical integration and differentiation

  • Numerical differentiation.
  • Numerical integration using Simpson’s rule and Romberg’s method.
  • Non-adaptive Gauss-Kronrod numerical integrator.
  • Adaptive Gauss-Kronrod numerical integrator.
  • Integration over infinite intervals.
  • Optimizations for functions with singularities and/or discontinuities.
  • Six integration rules to choose from, or provide your own.
  • Integration in 2 or more dimensions. Updated!

Curve fitting and interpolation

  • Interpolation using polynomials, cubic splines, piecewise constant and linear curves.
  • Barycentric rational interpolation.
  • Linear least squares fit using polynomials or arbitrary functions.
  • Nonlinear least squares using predefined functions or your own.
  • Predefined nonlinear curves: exponential, rational, Gaussian, Lorentz, 4 and 5 parameter logistic.
  • Weighted least squares, with 4 predefined weight functions.
  • Scaling of curve parameters.
  • Constraints on curve parameters.

Curves

  • Object-oriented approach to working with mathematical curves.
  • Methods for: evaluation, derivative, definite integral, tangent, roots.
  • Many basic types of curves: constants, lines, quadratics, polynomials, cubic splines, Chebyshev approximations, linear combinations of arbitrary functions.

Solving equations

  • Real and complex roots of polynomials.
  • Roots of arbitrary functions: bisection, false positive, Dekker-Brent and Newton-Raphson methods.
  • Systems of simultaneous linear equations.
  • Systems of nonlinear equations: Powell’s hybrid ‘dogleg’ method, Newton’s method.
  • Least squares solutions.

Optimization

  • Optimization in 1 dimension: Brent’s algorithm, Golden Section search.
  • Quasi-Newton method in N dimensions: BFGS and DFP variants. Updated!
  • Conjugate gradient method in N dimensions: Fletcher-Reeves and Polak-Ribière variants.
  • Powell’s conjugate gradient method.
  • Downhill Simplex method of Nelder and Mead. Updated!
  • Levenberg-Marquardt method for nonlinear least squares. New!
  • Line search algorithms: Moré-Thuente, quadratic, unit.
  • Linear program solver: Based on the Revised Simplex method.
  • Linear program solver: Import from MPS files.

Signal processing

  • Real 1D and 2D Fast Fourier Transform
  • Complex 2D Fast Fourier Transform
  • Special code for factors 2, 3, 4, 5
  • Real and complex convolution
  • Managed, 32bit and 64bit native implementations

Special functions

  • Over 40 special functions not included in the standard .NET Framework class library.
  • Functions from combinatorics: factorial, combinations, variations, more.
  • Functions from number theory: greatest common divisor, least common multiple, decomposition into prime factors, primality testing.
  • Gamma and related functions, including incomplete and regularized gamma function, digamma function, beta function, harmonic numbers.
  • Hyperbolic and inverse hyperbolic functions for real and complex numbers.
  • Ordinary and Modified Bessel functions of the first and second kind.
  • Airy functions and their derivatives.
  • Exponential integral, sine and cosine integral, logarithmic integral.