Degenerate Conic

Interpolation

Just in case you find yourself needing to do some multidimensional data interpolation with modern Fortran:

• I just published a modernized version of REGRIDPACK, a library for "regriding" 1D-4D data sets using linear and spline interpolation. The original version of this library (which used to be called TLCPACK) was formerly available from the UCAR website, but it is now nowhere to be seen. It was a well-written library, and had the nice feature of being able to specify linear or spline interpolation independently for each dimension. My refactoring is simply an update of the old code to modern standards.
• I also recently added nearest neighbor interpolation to my Finterp library. So, now you can perform linear and nearest neighbor interpolation/extrapolation on 1D-6D data sets.
• My Bspline-Fortran library can also be used for interpolation/extrapolation of 1D-6D data sets using B-splines. This library is being used by several people for CFD work, it seems.

There are precious few modern Fortran libraries for other types of interpolation. Here are a couple:

• FOLLIA -- Fortran Library for Lagrange Interpolation
• curvefit -- A library for fitting functions to sets of data.

There are also any number of old school FORTRAN 77 codes out there that haven't been updated in decades, but still work fine for what they do, including:

• PCHIP -- Piecewise Cubic Hermite Interpolation Package from SLATEC.
• PPPACK -- Piecewise polynomial interpolation code from from A Practical Guide to Splines by C. de Boor.
• FITPACK -- a collection of FORTRAN programs for curve and surface fitting with splines and tensor product splines.

See also

• Multidimensional Linear Interpolation (Part 2) [earlier post].
• John C. Adams, "TLCPACK: Software for regridding array data is now available", SDC Computing News, Scientific Computing Division, National Center for Atmospheric Research, Vol. 15, No. 1, Spring 1994.

Latest Library Updates

I just released some updates to my two most popular Fortran libraries on GitHub: JSON-Fortran and bspline-fortran. Coincidently, both are now at v5.2.0. Details of the updates are:

JSON-Fortran

There are several new features in this release. The biggest update is that now the code can parse JSON files that include comments (it just ignores them). You can even specify the character that identifies a comment. For example, if using # as a comment character, the following file can now be parsed just fine:

{
    "t": 0.12345,  # this is the time
    "x": 123.7173  # this is the state
}

Technically, comments are not part of the JSON standard. Douglas Crockford, the creator of JSON, had his reasons [1] for not including them, which I admit I don't understand (something about parsing directives and interoperability?) I mainly use JSON for configuration files, where it is nice to have comments. Crockford's suggestion for this use case is to pipe your commented JSON files through something called JSMin before parsing, a solution which seems somewhat ridiculous for Fortran users. So, never fear, now we can have comments in our JSON files and continue not using JavaScript for anything.

Another big change is the addition of support for the RFC 6901 "JSON Pointer" path specification [2]. This can be used to retrieve data from a JSON structure using its path. Formerly, JSON-Fortran used a simple path specification syntax, which broke down if the keys contained special characters such as ( or ). The new way works for all keys.

Bspline-Fortran

A minor update to Bspline-Fortran is the addition of an extrapolation mode. Formerly, if an interpolation was requested outside the bounds of the data, an error was returned. Now, the user has the option of enabling extrapolation.

See also

1. D. Crockford, "Comments in JSON", Apr 30, 2012 [Google Plus]
2. JavaScript Object Notation (JSON) Pointer, RFC 6901, April 2013 [IETF]