Re: question about fft2df

A user contributed visualization of the fft2d is at:
    http://www.cgd.ucar.edu/~shea/fft2d_image_ncl

On 3/20/12 10:05 AM, 雷霆 wrote:
> Hi, Andy and All NCL users,
> With Andy's help, I think I find out the actual definition of
> output/return of ncl function fft2df ( it 's supposed to be the same as
> the sub rfft2f in the pack Andy provided). In their accompanying help
> document, it is found the definition for the 2d fft,
> ^^^^^^^^^^^^^^^^^^
>
> R Real output array of two dimensions. The full complex transform
> of r(i,j) is given by:
>
> L-1 M-1
> C(I,J) = 1/(L*M)*SUM SUM R(L1,M1)*
> L1=0 M1=0
>
> EXP(-SQRT(-1)*2*PI*(I*L1/L + J*M1/M))
>
> The complex transform of a real array has conjugate symmetry.
> That is, c(i,j) = congugate c(l-i,m-j) so only half the transform
> is computed and packed back into the original array R.
>
>
> VVVVVVVVVVVVVVVV
>
> The L and M are the size of the input . Namely L is the N in my original
> question.
> So, the actual output of this sub and fft2df of ncl is of size ( L, M) (
> or (N,M)). But, since they are symmetric,only
> (N, M/2+1) are output.
> This perfectly answer my previous question.
> I think it will be helpful for NCL staff to put the above definition of
> the 2d fft on the help webpage for function fft2df.
>
> Andy , your help is appreciated and pls correct any
> confusion/misunderstanding in the above.
>
> Best wishes,
> Ting
>
>
>
>
>
>
>
>
>
>
>
>
>
> > Date: Sat, 17 Mar 2012 20:42:28 -0600
> > From: mai@ucar.edu
> > To: leiting2002@hotmail.com
> > Subject: Re: [ncl-talk] question about fft2df
> >
> > On 03/17/2012 08:10 PM, 雷霆 wrote:
> >
> > > Would you pls tell me where I can see the fortran counterpart of
> the fft2df of NCL? So, I can
> > > understand why it has such dimension sizes.
> >
> > Two source files are attached. Why two? It's a long story. The one
> with comments (fftpack5.1.tar) is
> > not the version used in NCL. The one with no comments and explicit
> double precision
> > (fftpack5_dp.tar) is the one used in NCL. These were written at
> different times by the same two
> > people. The calling sequence is the same, I think. (See my test code
> and pay attention to the
> > leading dimension of the input array -- it must be larger than N
> because the output is complex
> > numbers which overwrite the input, a very bad programming style that
> was common many years ago. Paul
> > Swarztrauber died not very long ago. I talked to Richard Valent
> yesterday. He does not know or does
> > not remember much about these programs.)
> >
> > So I will also attach my little driver pro gram which prints out the
> same values as the NCL Example 1
> > and I will also attach a very slightly modified version of the NCL
> program (to get 64-bit floats
> > instead of 32-bit -- all actual calculations in NCL are done in
> 64-bit floating point precision,
> > even when the input is 32-bit). If you run the two program, you
> should see the same numbers coming out.
> >
> > You will have to build the libraries or at least get all of the
> needed routines into your compile. I
> > used gfortran because that is what is used to build NCL.
> >
> > Run the test NCL program like this:
> >
> > % ncl -n testfft.ncl
> >
> > Please do not hesitate to contact me again if you have any more
> questions.
> >
> > Andy
>
>
> _______________________________________________
> ncl-talk mailing list
> List instructions, subscriber options, unsubscribe:
> http://mailman.ucar.edu/mailman/listinfo/ncl-talk
_______________________________________________
ncl-talk mailing list
List instructions, subscriber options, unsubscribe:
http://mailman.ucar.edu/mailman/listinfo/ncl-talk
Received on Tue Mar 20 10:51:14 2012