MtxVec is vectorized object oriented numerical library for .NET, Borland Delphi and Borland C++ Builder users. The library features complete support for complex numbers for all functions in single or double precision. Matrix operations: Solving a system of linear equations with refinment and condition number via LU, QR or SVD decomposition, Inverse of the matrix, Eigenvalues and eigenvectors, Sylvester equation, Teoplitz system solver, 2D FFT, Inverse 2D FFT, 2D real FFT, Square root of the matrix, Logarithm of the matrix... Vector operations: autocorrelation, circular convolution, cross correlation, forward and inverse discrete cosine transform, forward and inverse FFT, Geortz'el algorithm, Hilbert transform... Probability distributions PDF, CDF and Inverse CDF: binomial, geometric, hypergeometric, negative binomial, Poisson, discrete uniform, beta ,Cauchy, chi-squared, exponential, F, gamma, Maxwell, normal, Pareto, Rayleigh, Student (T), Continuous uniform, Weibull.. Sparse matrix operations: Solver for banded sparse matrices, Iterative sparse solvers: SGS, CG, BC, CS, GMRES, OM with LU preconditioning. Direct sparse solver for non-symmetric matrices. Conversions supported between: Banded, Dense, Sparse and Triplets matrix formats. Performance features: CPU specific optimizations, Critical functions optimized in assembler, symmetric multiprocessing, block processing support for vectors, fast object create and destroy, thin object layer, vector/matrix design. Special functions: complete elliptic integrals, Jacoby elliptic functions, Airy function and its derivative, Airy function of second kind and its derivative, Bessel functions: J, Y, I, K and H, associated Legendre polynomials. Math parser capable of parsing equations with real and complex numbers. Customizable operators, functions and variables. Polynomials: Finding roots, polynomial evaluation, Cubic splines, Linear and cubic interpolation algorithms, construction and evaluation of piece-wise polynoms, polynomial division. Optimization: Brent, BFGS...
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