[Pw_forum] FFT - Help

[Aritz Leonardo Liceranzu]

Dear all,

I am trying to understand how Discrete Fourier Transform works in QE (in 
particular fftw) and there are several questions for which I would 
appreciate all kind of help.

I have used as a guidance for learning the nice presentation performed 
by prof. Giannozzi
http://www.fisica.uniud.it/%7Egiannozz/QE-Tutorial/tutorial_fft.pdf


So if I understood correctly once the Ecutoff is set, the file 
"gvectors.dat" contains the complete list of G vectors inside the sphere 
with a radius 4*Ecut where magnitudes such like density can be safely 
represented.

*Starting from here, how is the real-space grid generated?* I ask this 
because for my particular calculation there are around *3000 G different 
vectors* for a real space grid that has *nr1=nr2=nr3=24* points.

according to the definition:
r= (i-1)/nr1+(j-1)/nr2+(k-1)/nr3

The real space grid is denser than the reciprocal grid, so there has to 
be some kind of mapping from one to each other that I am missing. 
According to the above transparencies both grids should have equal 
amount of points.

I could still do (i think) brute force transformations using the forward 
and inverse transformations defined in transparency 5 but I if wanted to 
use fftw in order to be more efficient, shouldn't they be the same in size?

As I said, I would appreciate if somebody could address me a reference 
or notes to read where these issues are explained. Thanks!

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