# Robin K S Hankin

#### 31 packages on CRAN

Performs Bayesian prediction of complex computer codes when fast approximations are available. It uses a hierarchical version of the Gaussian process, originally proposed by Kennedy and O'Hagan (2000), Biometrika 87(1):1.

The BACCO bundle of packages is replaced by the BACCO package, which provides a vignette that illustrates the constituent packages (emulator, approximator, calibrator) in use.

Handles very large numbers in R. Real numbers are held using their natural logarithms, plus a logical flag indicating sign. The package includes a vignette that gives a step-by-step introduction to using S4 methods.

Performs Bayesian calibration of computer models as per Kennedy and O'Hagan 2001. The package includes routines to find the hyperparameters and parameters; see the help page for stage1() for a worked example using the toy dataset. A tutorial is provided in the calex.Rnw vignette; and a suite of especially simple one dimensional examples appears in inst/doc/one.dim/.

A suite of routines for Clifford algebras, using the 'Map' class of the Standard Template Library. Canonical reference: Hestenes (1987, ISBN 90-277-1673-0, "Clifford algebra to geometric calculus"). Special cases including Lorentz transforms, quaternion multiplication, and Grassman algebra, are discussed. Conformal geometric algebra theory is implemented.

A suite of elliptic and related functions including Weierstrass and Jacobi forms. Also includes various tools for manipulating and visualizing complex functions.

Allows one to estimate the output of a computer program, as a function of the input parameters, without actually running it. The computer program is assumed to be a Gaussian process, whose parameters are estimated using Bayesian techniques that give a PDF of expected program output. This PDF is conditional on a training set of runs, each consisting of a point in parameter space and the model output at that point. The emphasis is on complex codes that take weeks or months to run, and that have a large number of undetermined input parameters; many climate prediction models fall into this class. The emulator essentially determines Bayesian posterior estimates of the PDF of the output of a model, conditioned on results from previous runs and a user-specified prior linear model. A vignette is provided and the help pages include examples.

Provides functionality for manipulating elements of the free group (juxtaposition is represented by a plus) including inversion, multiplication by a scalar, group-theoretic power operation, and Tietze forms. The package is fully vectorized.

The Lorentz transform in special relativity; also the gyrogroup structure of three-velocities following Ungar (2006) <doi:10.1088/0143-0807/27/3/L02>. For general relativity, see the 'schwarzschild' package.

A collection of efficient, vectorized algorithms for the creation and investigation of magic squares and hypercubes, including a variety of functions for the manipulation and analysis of arbitrarily dimensioned arrays. The package includes methods for creating normal magic squares of any order greater than 2. The ultimate intention is for the package to be a computerized embodiment all magic square knowledge, including direct numerical verification of properties of magic squares (such as recent results on the determinant of odd-ordered semimagic squares). Some antimagic functionality is included. The package also serves as a rebuttal to the often-heard comment "I thought R was just for statistics".

Fast manipulation of symbolic multivariate polynomials using the 'Map' class of the Standard Template Library. The package uses print and coercion methods from the 'mpoly' package (Kahle 2013, "Multivariate polynomials in R". The R Journal, 5(1):162), but offers speed improvements. It is comparable in speed to the 'spray' package for sparse arrays, but retains the symbolic benefits of 'mpoly'.

Quaternions and Octonions are four- and eight- dimensional extensions of the complex numbers. They are normed division algebras over the real numbers and find applications in spatial rotations (quaternions) and string theory and relativity (octonions). The quaternions are noncommutative and the octonions nonassociative. See RKS Hankin 2006, Rnews Volume 6/2: 49-51, and the package vignette, for more details.

Additive partitions of integers. Enumerates the partitions, unequal partitions, and restricted partitions of an integer; the three corresponding partition functions are also given. Set partitions are now included.

Manipulates invertible functions from a finite set to itself. Can transform from word form to cycle form and back.

Provides functionality for working with differentials, k-forms, wedge products, Stokes's theorem, and related concepts from the exterior calculus. The canonical reference would be: M. Spivak (1965, ISBN:0-8053-9021-9). "Calculus on Manifolds", Benjamin Cummings.