I have received from Graeme Dennes another update to his Tanh-Sinh Quadrature spreadsheet, offering fast and convenient numerical integration functions. The spreadsheet can be downloaded from: Tanh-Sinh Quadrature (including, as usual, full open source code). Here is Graeme’s description of the changes:
Tanh-Sinh Quadrature v3.0 by Graeme Dennes
To the best of this author’s knowledge, this V3.0 package is the fastest, most powerful, most accurate and comprehensive general-purpose quadrature package available today at no cost. It includes full open source code and extensive documentation.
A number of improvements have been incorporated into this release:
1. Nine new quadrature programs have been included in the total of 13.
2. Double Exponential (DE) semi-infinite interval (a,inf) and (-inf,b) programs and infinite interval (-inf,inf) programs for both non-periodic and periodic functions are included.
3. The Tanh-Sinh finite interval (a,b) program and the DE programs are (still) the star attractions for combined speed and accuracy!
4. The Quadpack QAGI infinite interval program has also been included for the three infinite intervals. Its speed is about a quarter of the DE programs.
5. A “modern” quadrature program, RMS (Recursive Monotone Stable), has been included for the finite interval. Its speed is about twice as fast as the Quadpack QAGE program on which it is based, but is about a quarter of the speed of the Tanh-Sinh program.
6. The finite interval Gauss-Kronrod program now uses a modified version of the Quadpack QAGE program for a performance improvement. It’s the accuracy champion!
7. A new automatic error management feature has been added to improve accuracy and reliability of all programs.
8. The array data used by the programs (except Romberg) are generated and/or loaded at workbook open time, improving the overall performance of these programs.
9. A simple function plotting tool has been included in the Tanh-Sinh worksheet to enable the selected function to be easily plotted and observed. It uses the same test function data as used by the Tanh-Sinh program, and can assist decisions regarding “difficult” integrals.
10. The suite of test integrals has been comprehensively expanded.
As always, Graeme’s work is very thorough and comes with extensive documentation, both on the worksheet and throughout the code. In addition to the integration functions Graeme has also put much work into the error checking, graphics and benchmarking routines, and these are well worth a close look even for those who don’t need to do numerical integration.
I have attached some screenshots below, but please download the spreadsheet and have a good look.
For earlier posts on this spreadsheet search the blog for Tanh-Sinh, or trace back from: Tanh-Sinh Quadrature V2.1.