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It looks like the spffte documentation for the G and W arrays is incorrect. According to the documentation
Lines 39 to 44 in 2344525
| C> @param[out] W complex amplitudes if IDIR>0 | |
| C> @param[out] G real values if IDIR<0 | |
| C> @param IDIR direction flag | |
| C> - IDIR=0 to initialize trigonometric data | |
| C> - IDIR>0 to transform from Fourier to physical space | |
| C> - IDIR<0 to transform from physical to Fourier space |
W should return complex amplitudes in Fourier space if IDIR > 0 or G should return real values if IDIR < 0. However, if IDIR > 0, then the transform should be going from Fourier to real space, and if IDIR < 0, then the transform should be going from real space to Fourier. This implies that either the algorithm is misdocumented (i.e. IDIR > 0 means we are going to Fourier space) or the variables are misdocumented.
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