Hi Hans, Two additional packages are TaylorSeries (not in METADATA right now) and HyperDualNumbers, which I 'derived' from the C code by the authors (see below links).
The entry in your list could look like: > ### HyperDualNumbers 0.1.1 > ------------------- -------------------------------------------------- > Hyper, eps1,eps1eps2 Automated 1st & 2nd order Differentiation > [if the function accepts dual numbers] The c++ code can be found at http://adl.stanford.edu/hyperdual/hyperdual.h . The paper itself at http://adl.stanford.edu/hyperdual/Fike_AIAA-2011-886.pdf . The Julia package can be found at: https://github.com/goedman/HyperDualNumbers.jl.git . Regards, Rob J. Goedman goed...@icloud.com On Apr 21, 2014, at 1:20 AM, Hans W Borchers <hwborch...@gmail.com> wrote: > I would like to use Julia mostly on applied numerical math problems. I think > what I need is an overview of what is available in Base and contributed > packages. Therefore I decided to write a short "vignette" listing all > relevant functions and packages, possibly with a short description, usage, > and one or two examples. > > I have identified the items in the following list. I would welcome any > suggestions of functions I have overlooked in this area. > (Optimization at the moment is not covered by intention.) > > ### Julia Base 0.2.0 > ------------------- -------------------------------------------------- > sin, cos, ... Trigonometric, hyperbolic functions, square root, > exponential and logarith functions, etc. > factor, gcd, primes Number-theoretic and combinatorial functions > factorial, binomial > ... > gamma, airy, bessel Special functions > beta, eta, zeta > ... > > quadgk Gauss-Kronrod adaptive integration > > ### Calculus 0.1.3 > ------------------- -------------------------------------------------- > derivative, ... finite-differences numerical derivatives > gradient, hessian second-order, gradients and hessians > [unfortunately:] finite_difference and complex_step not exported! > > integrate adaptive Simpson, Monte-Carlo integration > differentiate symbolic differentiation > > ### DualNumbers 0.0.0 (??) > ------------------- -------------------------------------------------- > Dual, epsilon Automated Differentiation > [if the function accepts dual numbers] > > ### Cubature 1.0.1 > ------------------- -------------------------------------------------- > h/pquadrature one- and multidimensional adaptive integration > h/pcubature (Gauss-Kronrod, Genz-Malik, Clenshaw-Curtis) > > ### Grid 0.2.8 > ------------------- -------------------------------------------------- > InterpGrid function interpolation on (regular) grids > [a simpler interp1d() function for irregular > grids might still be helpful] > > ### BSplines 0.0.0 (??) > ------------------- -------------------------------------------------- > linear/quadratic/ > cubicSplineBFE > > ### ApproxFun 0.0.0 (??) > ------------------- -------------------------------------------------- > Fun generates an approximating function > diff, cumsum differentiate or integrate the approximation > > ### Polynomial 0.0.0 (??) > ------------------- -------------------------------------------------- > Poly, poly construct polynomial from coefficients resp. roots > polyval evaluate the polynomial (Horner scheme) > polyint, polyder derivative, anti-derivative of a polynomial > roots determine the roots/zeros of the polynomial > (as eigenvalues of the companion matrix) > [missing is a polyfit() function] > > ### PowerSeries > ------------------- -------------------------------------------------- > series, restrict generates or truncates a (finite) power series > (used to determine the Taylor series) > > ### Roots 0.1.0 > ------------------- -------------------------------------------------- > find_zero, fzero bracketing/derivative-free root finding methods > [Ridders' method is not implemented !] > newton, halley derivative-based root finding methods > multroot multiple roots of (inexact) polynomials > > ### NLsolve 0.1.1 > ------------------- -------------------------------------------------- > nlsolve solves systems of nonlinear equations, based on > Newton and trust-region approaches > > ### ODE 0.0.0 (??) > ------------------- -------------------------------------------------- > ode23 Runge-Kutta (2, 3)-method with variable step size > ode4 Runge-Kutta of order 4 (with fixed step size?) > > ### Elliptic 0.2.0 > ------------------- -------------------------------------------------- > K, F, E, Pi (in)complete elliptic integrals of 1. and 2. kind > > ### GSL 0.1.1 > ------------------- -------------------------------------------------- > interface to the GNU Scientific Library(GSL) > e.g., hypergeom Gauss' hypergeometric function 2F1
