About

fortran2

My name is Jacob and I am an astrodynamicist and software developer. This is my personal blog. All opinions expressed here are my own!

Contact Info

Email: jacob [at] degenerateconic [dot] com
Twitter: DegenerateConic
Mastodon: @jacobwilliams
BlueSky: degenerateconic.bsky.social

Projects

fortran2

I maintain several open source projects for modern, object-oriented Fortran (i.e., Fortran 2003/2008). All of these have BSD-style licenses, and are hosted on GitHub:

Catagory	Library	Description
Interpolation	bspline-fortran	1D-6D B-Spline Interpolation
Interpolation	regridpack	1D-4D linear and cubic interpolation
Interpolation	finterp	1D-6D Linear Interpolation
Interpolation	PCHIP	Piecewise Cubic Hermite Interpolation Package
Interpolation	splpak	Multidimensional least-squares cubic spline fitting
Plotting	pyplot-fortran	Make plots from Fortran using Matplotlib
File I/O	json-fortran	Read and write JSON files
File I/O	csv-fortran	Read and write CSV Files (formerly named `fortran-csv-module`)
Optimization	slsqp	SLSQP Optimizer
Optimization	conmin	CONMIN Optimizer
Optimization	conmax	CONMAX Optimizer
Optimization	psqp	PSQP Optimizer
Optimization	optgra	OPTGRA Optimizer
Optimization	fmin	Derivative free 1D function minimizer
Optimization	pikaia	Pikaia Genetic Algorithm
Optimization	simulated-annealing	Simulated Annealing Algorithm
Optimization	lbfgsb	L-BFGS-B Nonlinear Optimizater
One Dimensional Root-Finding	roots-fortran	Roots of continuous scalar functions of a single real variable, using derivative-free methods
Polynomial Roots	polyroots-fortran	Root finding for real and complex polynomial equations
Nonlinear equations	nlesolver-fortran	Nonlinear Equation Solver
Linear Equations	LSQR	Sparse linear systems solver
Linear Equations	lusol	LU factors of a square or rectangular sparse matrix
Ordinary Differential Equations	dop853	An explicit Runge-Kutta method of order 8(5,3)
Ordinary Differential Equations	ddeabm	DDEABM Adams-Bashforth algorithm
Ordinary Differential Equations	rklib	Suite of fixed and variable-step Runge-Kutta solvers
Numerical Differentiation	NumDiff	Numerical differentiation with finite differences
Numerical integration	quadpack	Modernized QUADPACK Library for 1D numerical quadrature
Numerical integration	quadrature-fortran	1D-6D Adaptive Gaussian Quadrature
Random numbers	mersenne-twister-fortran	Mersenne Twister pseudorandom number generator
Astrodynamics	Fortran-Astrodynamics-Toolkit	Modern Fortran Library for Astrodynamics
Astrodynamics	astro-fortran	Standard models used in fundamental astronomy
Geodesy	geodesic-fortran	Geodesic routines
Graph Theory	daglib	Directed Acyclic Graphs
System	popen-fortran	Simple module for `popen`
System	fortran-mach	Machine Constants

Also check out the full list of my GitHub projects.

Publications

Selected conference papers, journal articles, etc.

J. Williams, T. F. Dawn, A. L. Batcha, "A History of Orion Mission Design, Copernicus Development, and the Artemis I Trajectory", AAS/AIAA Astrodynamics Specialist Conference, August 2023, AAS 23-241.
Q. Moore, B. Killeen, J. Williams, "A New Architecture for Parallelization of Complex Spacecraft Trajectory Optimization Scans", AAS/AIAA Astrodynamics Specialist Conference, August 9-12, 2023.
J. Williams, S. L. Smallwood, D. E. Lee, M. V. Widner, "A New Eclipse Algorithm for use in Spacecraft Trajectory Optimization", AAS/AIAA Astrodynamics Specialist Conference, August 2023, AAS 23-243.
A. L. Batcha, J. Williams, T. F. Dawn, J. P. Gutkowski, M. V. Widner, S. L. Smallwood, B. J. Killeen, E. C. Williams, and R. E. Harpold, "Artemis I Trajectory Design and Optimization", AAS/AIAA Astrodynamics Specialist Conference, August 9-12, 2020, AAS 23-649
J. Williams, A. Kamath, R. Eckman, G. Condon, R. Mathur, D. Davis, "Copernicus 5.0: Latest Advances in JSC's Spacecraft Trajectory Optimization and Design System", 2019 AAS/AIAA Astrodynamics Specialist Conference, Portland, ME, August 11-15, 2019, AAS 19-719
D. G. Murri, G. L. Condon, J. Williams, A. H. Kamath, R. A. Eckman, R. Mathur, "Improvements to the Copernicus Trajectory Design and Optimization System for Complex Space Trajectories", NASA/TM 2019-220247, Jan 1, 2019
J. Williams, R. D. Falck, and I. B. Beekman. "Application of Modern Fortran to Spacecraft Trajectory Design and Optimization", 2018 Space Flight Mechanics Meeting, AIAA SciTech Forum, (AIAA 2018-1451)
T. F. Dawn, J. Gutkowski, A. Batcha, J. Williams, and S. Pedrotty. "Trajectory Design Considerations for Exploration Mission 1", 2018 Space Flight Mechanics Meeting, AIAA SciTech Forum, (AIAA 2018-0968)
J. Williams, D. E. Lee, R. J. Whitley, K. A. Bokelmann, D. C. Davis, and C. F. Berry. "Targeting cislunar near rectilinear halo orbits for human space exploration", AAS 17-267
J. Williams, "A New Plugin Architecture for the Copernicus Spacecraft Trajectory Optimization Program", AAS/AIAA Astrodynamics Specialist Conference, Vail, Colorado, Aug. 2015. AAS 15-606.
R. Whitley, J. Gutkowski, S. Craig, T. Dawn, J. Williams, W. B. Stein, D. Litton, R. Lugo, M. Qu, "Combining Simulation Tools for End-to-End Trajectory Optimization", AAS/AIAA Astrodynamics Specialist Conference, Vail, Colorado, Aug. 2015. AAS 15-662.
G. L. Condon, J. Williams, "Asteroid Redirect Crewed Mission Nominal Design and Performance", SpaceOps Conference, 5-9 May 2014, Pasadena, CA. AIAA 2014-1696.
J. Williams, G. L. Condon, "Contingency Trajectory Planning for the Asteroid Redirect Crewed Mission", SpaceOps Conference, 5-9 May 2014, Pasadena, CA. AIAA 2014-1697.
H. D. Hinkel, S. P. Cryan, C. D'Souza, D. P. Dannemiller, J. P. Brazzel, G. L. Condon, W. L. Othon, J. Williams, "Rendezvous and Docking Strategy for Crewed Segment of the Asteroid Redirect Mission", SpaceOps Conference, 5-9 May 2014, Pasadena, CA.
J. Williams, J. S. Senent, D. E. Lee, "Recent Improvements to the Copernicus Trajectory Design and Optimization System", Advances in the Astronautical Sciences, 2012.
R. J. Whitley, C. A. Ocampo, J. Williams, "Performance of an Autonomous Multi-Maneuver Algorithm for Lunar Trans-Earth Injection", Journal of Spacecraft and Rockets, Vol. 49, No. 1 (2012), pp. 165-174.
R. J. Whitley, J. Williams. "Implementation of an Autonomous Multi-Maneuver Targeting Sequence for Lunar Trans-Earth Injection", AIAA Guidance Navigation and Control Conference, 2-5 Aug. 2010, Toronto, Ontario, Canada.
J. Williams, J. S. Senent, C. Ocampo, R. Mathur, E. C. Davis. "Overview and Software Architecture of the Copernicus Trajectory Design and Optimization System", 4th International Conference on Astrodynamics Tools and Techniques, 3-6 May 2010, Madrid, Spain
C. Ocampo, J. S. Senent, J. Williams. "Theoretical Foundation of Copernicus: A Unified System for Trajectory Design and Optimization", 4th International Conference on Astrodynamics Tools and Techniques, 3-6 May 2010, Madrid, Spain.
J. Williams, S. M. Stewart, D. E. Lee, E. C. Davis, G. E. Condon, J. S. Senent. "The Mission Assessment Post Processor (MAPP): A New Tool for Performance Evaluation of Human Lunar Missions", 20th AAS/AIAA Space Flight Mechanics Meeting, 14-17 February 2010, San Diego, CA.
G. Condon, J. Williams, S. M. Stewart. "Mission Design and Performance Assessment for the Constellation Lunar Architecture", 20th AAS/AIAA Space Flight Mechanics Meeting, 14-17 February 2010, San Diego, CA.
S. M. Stewart, J. S. Senent, J. Williams, G. E. Condon, D. E. Lee. "Evaluation of Dual-Launch Lunar Architectures Using the Mission Assessment Post Processor", 20th AAS/AIAA Space Flight Mechanics Meeting, 14-17 February 2010, San Diego, CA.
J. Williams, E. C. Davis, D. E. Lee, G. L. Condon, T. Dawn, M. Qu. "Global Performance Characterization of the Three Burn Trans-Earth Injection Maneuver Sequence over the Lunar Nodal Cycle", AAS/AIAA Astrodynamics Specialist Conference, 9-13 Aug. 2009, Pittsburgh, PA.
O. Montenbruck, M. Garcia-Fernandez, J. Williams. "Performance Comparison of Semi-Codeless GPS Receivers for LEO Satellites". GPS Solutions. Volume 10, Number 4. November, 2006
O. Montenbruck, J. Williams, T. Wang, G. Lightsey, "Preflight Validation of the IGOR GPS Receiver for TerraSAR-X", DLR-GSOC GTN-TST-0200, Deutsches Zentrum für Luft- und Raumfahrt, Oberpfaffenhofen. May 2, 2005.
J. Williams, E. G. Lightsey, S. Yoon, R. E. Schutz. "Testing of the ICESat BlackJack GPS Receiver Engineering Model", ION GPS 2002 Conference, September 24-27, 2002, Portland, Oregon.

Technical notes

LVLH Transformations -- This technical note derives the equations for transformation of state vectors to and from a Local Vertical Local Horizontal (LVLH) frame. An implementation of the algorithms in Fortran is also included.

See also

My ResearchGate page

Copyright and License Info

Unless otherwise indicated, the original sourcecode on Degenerate Conic by Jacob Williams is licensed under the following license:

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
The names of its contributors may not be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Fortran Compilers

fortran

Intel Fortran Compiler (ifort) - a commercial product.
- Currently supports all of the current Fortran 2008 standard and some of the upcoming Fortran 2018 standard.
- There are free licenses available for academia and open source contributors.
GNU Fortran Compiler (gfortran) - opensource.
- Currently supports some of Fortran 2003/2008/2018.
- Binaries of gfortran for MacOS X are available here: http://hpc.sourceforge.net and here: http://coudert.name/.
- Gfortran can also be installed on a Mac using Homebrew (either via gcc, or OpenCoarrays).
LFortran - Modern interactive LLVM-based Fortran compiler
- Currently in development

Fortran References

Books

E. Jorgensen, Introduction to Programming using Fortran 95/2003/2008, March 2018, Version 3.0.51
R. J. Hanson, Numerical Computing With Modern Fortran, SIAM-Society for Industrial and Applied Mathematics, 2013.
A. Markus, Modern Fortran in Practice, Cambridge University Press, 2012.
D. Rouson, J. Xia, X. Xu, Scientific Software Design: The Object-Oriented Way, Cambridge University Press, 2011.
M. Metcalf, J. Reid, M. Cohen, Modern Fortran Explained, Oxford University Press, 2011.
N. S. Clerman, W. Spector, Modern Fortran: Style and Usage, Cambridge University Press, 2011.
G. Hager, G. Wellein, Introduction to High Performance Computing for Scientists and Engineers, CRC Press, 2011.
R. A. Vowels, Algorithms and Data Structures in F and Fortran, Unicomp, 1998.

Articles

J. Reid, The New Features of Fortran 2018, ISO/IEC JTC1/SC22/WG5 N2161, 2 August 2018.
J. Williams, R. D. Falck, and I. B. Beekman. "Application of Modern Fortran to Spacecraft Trajectory Design and Optimization", 2018 Space Flight Mechanics Meeting, AIAA SciTech Forum, (AIAA 2018-1451)
M. Metcalf, "The Seven Ages of Fortran", JCS&T Vol. 11 No. 1, April 2011
J. Reid, "The New Features of Fortran 2008", ISO/IEC JTC1/SC22/WG5 N1729, May 27, 2008.
M. Cohen, "Fortran Matters", SD Times, April 15, 2004.

Websites

fortran-lang.org
An introduction to modern Fortran programming
Overview about Fortran 90/95 for C/C++ programmers
Fortran Wiki, an open venue for discussing all aspects of the Fortran programming language.
Fortran Specialist Group
Programming in Modern Fortran, A HyperText-based introduction to programming in Fortran 2003, 2008, and 2018 on Unix.

Forums

Fortran Discourse
Intel Fortran Compiler Forum
Other Intel developer forums
comp.lang.fortran -- Usenet Group [Note: Google stopping mirroring Usenet groups in 2024 so the Google Group ends there]
COMP-FORTRAN-90

Fortran Standards

J3 US Fortran Standards Committee (formerly known as ANSI X3J3)
- Mailing list
- Github page
JTC1/SC22/WG5 The ISO Home of Fortran Standards

Fortran Software

Alan Miller's Fortran Software
ARPACK collection of Fortran77 subroutines designed to solve large scale eigenvalue problems (see also arpack-ng)
BLAS (Basic Linear Algebra Subprograms)
CERNLIB (CERN Program Library)
CMLIB (NBS Core Math Library)
David G. Simpson software
Derivative-Free Optimization several Fortran codes listed
EISPACK for computing eigenvalues and eigenvectors of matrices
Ernst Hairer’s Fortran codes for solving ordinary differential equations
filterSD a software package for solving Nonlinear Programming Problems and Linearly Constrained Problems in continuous optimization
FLIBS collection of Fortran modules
FortranCL OpenCL interface for Fortran 90
Fortran Wiki software listings
Fortran Tools from Mining & Exploration Geological Modelling Services
F90GL public domain implementation of the official Fortran 90 bindings for OpenGL
F03GL Fortran 2003 Interface to OpenGL
gnuplotfortran the Fortran 95 interface to Gnuplot
GnuFor2 Gnuplot/Fortran 90 interface
GPF General Purpose Fortran Collection
gtk-fortran aims to offer scientists programming in Fortran a cross-platform library to build Graphical User Interfaces (GUI).
Harwell Subroutine Library (not free) and HSL Archive (free)
High-Precision Software by David H. Bailey
Implicit Filtering (DIRECT and IFFCO) at the Kanpur Genetic Algorithms Laboratory
John Burkardt's FORTRAN 77 and Fortran 90 software
json-fortran (A Fortran 2003/2008 JSON API)
Karin's FORTRAN gems
LAPACK (Linear Algebra PACKage)
LINPACK for solving linear equations and linear least-squares problems
LUSOL A sparse LU factorization for square and rectangular matrices
MATH77 Fortran library from JPL.
MESA Modules for Experiments in Stellar Astrophysics
MINPACK for solving systems of nonlinear equations
M.J.D. Powell software for derivative-free minimization
modFileSys modern Fortran wrappers around the file system interface of libc.
NAG Fortran 90 Software Repository
NCAR Classic Libraries for Geophysics
Netlib collection of mathematical software
NIST Software - various libraries
NOVAS (Naval Observatory Vector Astrometry Subroutines)
NSWC (Naval Surface Warfare Center Mathematical Library)
ODEPACK for solving systems of initial value ordinary differential equations, for stiff and non-stiff problems
OpenCoarrays an open-source software project for developing, porting and tuning transport layers that support coarray Fortran (CAF) compilers
Optimization subroutines from Ladislav Luksan
ORDERPACK for unconditional, unique, and partial ranking, sorting, and permutation
PROPACK for computing the singular value decomposition of large and sparse or structured matrices
PSBLAS Parallel Sparse Basic Linear Algebra Subroutines
SLATEC a library of over 1400 general purpose mathematical and statistical routines (see listing)
SOFA (Standards of Fundamental Astronomy)
SPICELIB from JPL
STARPAC for statistical data analysis
SWIFT (and Swifter) solar system integration software package

Fortran Build & Documentation Tools

foraytool (An advanced build tool for Fortran developers) [defunct]
SCons - a Software Construction Tool
FoBiS (Fortran projects building system for poor men)
FORD (Automatically generates FORtran Documentation from comments within the code)
The Meson Build system an open source build system meant to be both extremely fast, and, even more importantly, as user friendly as possible
Fortran Package Manager a package manager and build system for Fortran.

See also fortran-lang Build tools

Other Programming Resources

txt2re - regular expression generator
regular expressions 101
JSONLint - the JSON Validator
Semantic Versioning
Fortran questions on stackoverflow.com
NIST Digital Library of Mathematical Functions

General Scientific Software

NIST Guide to Available Mathematical Software
Local Optimization Software
Global Optimization Software
Freely Available Software for Linear Algebra
NA-Digest -- collection of articles on topics related to numerical analysis and those who practice it.

Other Interesting Blogs

Other References

K.M. Borkowski, "Accurate Algorithms to Transform Geocentric to Geodetic Coordinates", Bull. Geod., 63 (1989).
R.H. Gooding, "A Procedure for the Solution of Lambert’s Orbital Boundary-Value Problem", Celestial Mechanics, Vol. 48, Number 2, 1990.
S.W. Shepperd, "Universal Keplerian State Transition Matrix", Celestial Mechanics, Vol. 35, Feb. 1985.
T. Vincenty, "Direct and Inverse Solutions of Geodesics on the Ellipsoid with Application of Nested Equations". Survey Review XXII. 176, April 1975. [sourcecode from the U.S. National Geodetic Survey].
J. Oliver, "An algorithm for numerical differentiation of a function of one real variable". Journal of Computational and Applied Mathematics, Volume 6, Issue 2, June 1980, Pages 145–160. [Original sourcecode from NIST. Updated version here].
D. Kraft, "A Software Package for Sequential Quadratic Programming", DFVLR-FB-88-28, 1988.