Research Interests
My primary area of research interest is the numerical computation of multiple integrals. These integrals arise in a wide variety application areas that include electromagnetics, chemistry, physics and statistics. I have developed and implemented many different types of algorithms for the computation of multiple integrals. I am also interested in related problems in multivariate approximation theory.
Alan Genz Software
QSIMVNEF: A Matlab function with supporting functions, for the numerical computation of multivariate normal distribution expected values. The method used is similar to the method used for qsimvn, but qsimvnef also computes the expected value of a user speficied function.
SPHRUL: A Matlab function, with supporting functions, for the computation of spherical surface integrals. SPHRLR is a randomized version of SPHRUL.
TVPACK: A set of Fortran subroutines, with sample driver program, for the computation of univariate, bivariate and trivariate normal and t-probabilities.
TVTL: A set of Matlab functions, for the computation of univariate, bivariate and trivariate normal and t-probabilities. Minor bug for bvtl special cases fixed 12/20/04.
TVNL: A set of Matlab functions, for the computation of univariate, bivariate and trivariate normal probabilities. TVNLS is a simpler but less accurate version of this software.
QSIMVT: A Matlab function with supporting functions, for the numerical computation of multivariate t distribution values. The method used is similar to the method used by the Fortran MVTDST software, but the quasi-random integration point set is different. Tiny variance scaling problem fixed 5/9/6.
QSCMVT: A Matlab function with supporting functions, for the numerical computation of multivariate t distribution values. The method used is similar to the method used by the Fortran MVTDST software, but the quasi-random integration point set is different. The integration region may be specified by a set of linear inequalities in the form a < c*x < b, where a and b are m-vectors and c is an mxn matrix. QSCMVTV is a vectorized version of this software which is usually at lot faster than QSCMVT.
QSIMVN: A Matlab function with supporting functions, for the numerical computation of multivariate normal distribution values. The method used is similar to the method used by the Fortran MVNDST software, but the quasi-random integration point set is different. QSIMVNV is a vectorized version of this software which is usually at lot faster than QSIMVN. Tiny variance scaling problem fixed 5/9/6.
QSCMVN: A Matlab function with supporting functions, for the numerical computation of multivariate normal distribution values. The method used is similar to the method used by the Fortran MVNDST software, but the quasi-random integration point set is different and the integration region may be specified by a set of linear inequalities in the form a < c*x < b, where a and b are m-vectors and c is an mxn matrix. QSCMVNV is a vectorized version of this software which is usually at lot faster than QSCMVN.
MVNLPS: A Matlab function for the numerical computation of multivariate normal distribution values for ellipsoidal integration regions.
MVSTAT: A set of Fortran 90 subroutines for the numerical computation of multivariate t integrals, with maximum dimension 100. This is a conversion of the best MVTDST sofware, with modifications that allow the integration regions to be specified using a set of linear inequalities. This software may also be used to compute multivariate normal integrals and critical values. A illustrative example program is also available. Revised 6/02 with the addition of functions for trivariate distributions and 3rd order bounds, and some minor bugs fixed. A revision 11/05 fixed parameter bug for dimensions 25-100.
SMPINT: A set of Fortran subroutines, with sample driver program, for the numerical integration of a vector of integrals over a collection of simplices. This software uses the integration rules and subdivision methods described in the paper by Alan Genz and Ronald Cools, An Adaptive Numerical Cubature Algorithm for Simplices (Postscript).
PATSYM: A set of Fortran subroutines, with sample driver program, for the numerical integration of a vector of integrals over a hyper-rectangular region. This software uses the integration rules described in the paper by Alan Genz, Fully Symmetric Interpolatory Rules for Multiple Integrals, SIAM J. Numer. Anal. 23 (1986), pp. 1273-1283.
CUBPACK: website for the CUBPACK research project. The purpose of this project with Ronald Cools and Ann Haegemans, is to develop and implement algorithms for the numerical computation of multiple integrals.
ParInt: website for NSF supported ParInt research project. The purpose of this project with Elise de Doncker and Ajay Gupta, is to develop and implement parallel algorithms for the numerical computation of multiple integrals.
MVTDST: A set of Fortran subroutines, with sample driver program, for the numerical computation of multivariate t integrals, with maximum dimension 100. This is an assimilation of the best sofware in MVTPACK. This software may also be used to compute multivariate normal integrals. Revised 8/00 to include a bivariate t distribution function. A revision 11/05 fixed parameter bug for dimensions 25-100. A revision 7/7 increased the maximum dimension to 1000.
MVNEXP: A Fortran subroutine and function, with sample driver program, for the numerical computation of the expected values for the variables for a multivariate normal distribution, with maximum dimension 100. This must be compiled with the MVNDST file, without the MVNDST driver program.
MVNDST: A set of Fortran subroutines, with sample driver program, for the numerical computation of multivariate normal integrals, with maximum dimension 100. A revision 11/98 allows for positive semidefinite correlation matrices. A revision 1/3 increased the maximum dimension to 500. A revision 11/5 fixed parameter bug for dimensions 25-100. Minor bug for dimensions > 100 fixed 7/7
RANRTH: A Fortran subroutine for the numerical computation of a vector integrals over an infinite region with a Gaussian weight function. This software is described in the paper "A Stochastic Algorithm for High Dimensional Multiple Integrals over Unbounded Regions with Gaussian Weight".
HRMSYM: A Fortran subroutine for the numerical computation of a vector integrals over an infinite region with a Gaussian weight function. This is software for an implementation of rules described in the paper "Fully Symmetric Interpolatory Rules for Multiple Integrals over Infinite Regions with Gaussian Weight". Also included is software for Gauss-Hermite product rules for a maximum of fifty points in each variable.
DECUHR: A set of Fortran subroutines, with sample driver program, for the numerical computation of singular multiple integrals. This software uses methods described in the paper by Espelid, T. and Genz, A. (1994), An Algorithm for Automatic Integration of Singular Functions over a Hyperrectangular Region, published in Numerical Algorithms 8, pp. 201-220.
DCUHRE: A set of Fortran subroutines, with sample driver program, for the numerical computation of multiple integrals. This software is described in the paper by Berntsen, J., Espelid, T. and Genz, A. (1991), An Adaptive Multidimensional Integration Routine for a Vector of Integrals, published in ACM Trans. Math. Softw. 17, pp. 452-456.
MULTST: A multiple integration subroutine test package, with sample driver program and early version of ADAPT.