Add FFTW-based synthesis and analysis

[ahbarnett]

Hi Michael,

It took a little while to get build on linux going. Here's suggestions for tweaks to library (not worth a pull request). I only tested on ubuntu 16.04.

Append to Make.inc:

ifeq ($(UNAME), Linux)
LDLIBS += -lm
CFLAGS += -I/usr/lib/openblas-base
LDFLAGS += -L/usr/lib/openblas-base
endif

You'll also need to add in the ifeq windows block:
UNAME := Windows

Also, you'll want to add instructions to type in the shell:
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:.

Otherwise the executable can't find the .so

My tests now all run, although I don't understand the output.

PS It's not apparent from your docs how to do a simple spherical harmonic eval or projection onto a tensor product grid. Am I supposed to do sph to Fourier then do FFT2 on grid? I would have to guess the normalization, etc. An example of that would be very helpful.

PPS Good to see you at ICOSAHOM!

[MikaelSlevinsky]

This is really helpful, thanks!

The plan is to port over the synthesis and analysis from FFTW as in the Julia package https://github.com/MikaelSlevinsky/FastTransforms.jl/blob/master/src/SphericalHarmonics/synthesisanalysis.jl

[MikaelSlevinsky]

The repository now builds and runs the tests on Travis' linux infrastructure. FFTW-based synthesis and analysis are forthcoming and will be available as part of a first release.

[MikaelSlevinsky]

P.S. I started adding FFTW overrides for synthesis and analysis on the sphere. I'm not closing the issue because I still have to do the triangle and disk cases, but I also added an example that works through a simple case numerically illustrating the spherical harmonic addition theorem.