What would an integrated development environment for numerical algorithms look like? To me it looks a lot like Fedora. That’s right, Fedora Linux is your integrated development environment. Oh, separate programs in an operating system isn't integrated enough for you? They ought to be, Python or Bash are right there waiting to glue it all together.
An implementer or developer of numerical methods ought to have a good computer algebra system(CAS) available. This is where the high-level algorithm design needs to take place. All the rest of the low level coding needs to be automated as much as possible. You as the human in the loop need to spend time thinking about the bigger picture and get Maxima to code Fortran for you.
Numerical software needs testing. Lots of rigorous testing. You can use your (CAS) to generate unit tests by evaluating the expressions you converted to Fortran for specific cases, and then converting these answers to Fortran too. Then you can easily wrap those routines in a unit testing framework using F2Py.
This approach lets you automate the generation of the low-level functions that will be in your inner loops (which need to be in Fortran for performance sake). Then use Python's powerful standard library and additional packages for things like parsing input decks, file reading and creation, setting up parallel jobs and generating graphics. All things which can be a real pain in Fortran. The real benefit is that the human effort is kept focused where it is most profitably employed: at the higher levels of abstraction of the mathematical concepts rather than the low level coding.
There it is, a complete "environment" in three building blocks: Maxima, Fortran and Python. Almost completely automated from governing equations in the CAS to low-level number crunching in Fortran. Some human intervention required to bring it all together into a working program, but that’ll be in Python, which is easy.
This is the basic method used in the second half of the magnetron problem. I'll post some more simple examples of the whole work-flow in use after the holidays.