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I am trying to use FFTw3 in Visual Studio using the Intel Fortran compiler.
I am confused about normalization.
I have setup a r2r spectral to grid plan for sinx siny components.

 plan_spectral_to_grid_sin_sin = fftwf_plan_r2r_2d(Ny, Nx, dummy, dummy, FFTW_RODFT00, FFTW_RODFT00, FFTW_MEASURE)

 plan_grid_to_spectral_sin_sin = fftwf_plan_r2r_2d(Ny, Nx, dummy, dummy, FFTW_RODFT00, FFTW_RODFT00, FFTW_MEASURE)

(Note the reversal of the x, y dimensions since this is a C library and FORTRAN is column-major)

I understand (maybe this is incorrect) that the normalization factor is

```sin_sin_norm = (2.0 * REAL(currentDims%IXMAX + 1) * 2.0 * REAL(currentDims%IYMAX + 1))```

So if I divide my spectral components ```A(k,l)sinkxsinly``` by this value and do the transform

```call fftwf_execute_r2r(plan_spectral_to_grid_sin_sin, horzArr%G1, horzArr%G1)```

I should be able to do the transform back

```call fftwf_execute_r2r(plan_grid_to_spectral_sin_sin, horzArr%G1, horzArr%G1)```

and get the original spectral components WITHOUT normalization. But that is not what I am seeing.

For reference

``` horzArr%G1 is a 2-d array of dimension currentDims%IXMAX, currentDims%IYMAX```

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I can't recall which normalisation convention FFTW3 uses for that r2r transform. If you take it on a round trip without trying to normalise it at all what factor does it get multiplied by? Fence post errors are all too easy in C/FORTRAN hybrid interface code.

Martin Brown
– Martin Brown

2025年10月29日 17:20:28 +00:00
Commented Oct 29, 2025 at 17:20
2

What are you seeing? Is your result simply different by a multiplicative factor? Can you compute the factor? The normalisation in FFTW always requires the logical transform size.

Vladimir F Героям слава
– Vladimir F Героям слава

2025年10月29日 18:44:54 +00:00
Commented Oct 29, 2025 at 18:44
1

Note that I have no idea what currentDims%IXMAX is and how it is related to Nx. Try to show a minimal reproducible example.

Vladimir F Героям слава
– Vladimir F Героям слава

2025年10月29日 18:47:18 +00:00
Commented Oct 29, 2025 at 18:47
@VladimirFГероямслава I guess I should have put horzArr%G1 is a 2-d array of dimension currentDims%IXMAX, currentDims%IYMAX. I was careless.

Brian Reinhold
– Brian Reinhold

2025年10月30日 13:41:35 +00:00
Commented Oct 30, 2025 at 13:41
@MartinBrown Good idea and that's exactly how I am trying to approach it. I am doing a spectral meteorological model and there one typically does spectral to grid, compute nonlinear terms, and then grid to spectral. Since we work in spectral space the 'inverse' transform is the grid to spectral which is opposite of the documentation definition. That confused me for a while. Given that, I have lined up some code that does spectral to grid and then grid to spectral one after the other. That way I can find out what the normalization is with the help of the debugger.

Brian Reinhold
– Brian Reinhold

2025年10月30日 13:46:44 +00:00
Commented Oct 30, 2025 at 13:46

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