FFTW3 plug-in
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Package yfftw (in yfftw.i) -
Index of documented functions or symbols:
DOCUMENT y= fftw(x, ljdir, rjdir, &plan, nosave=, fcplx=, keep=)
main yorick_fftw(3) interface, much of it similar to fft.i.
returns Y the complex Fastest Fourier Transform of array X.
If FCPLX==1 input arrays X==array(float,2,..) are treated
as float-complex.
PLAN == array(long, 2)
where plan(1) is 0 if there is no dir=+1 transforms
or is a casted pointer to an fftw plan
where plan(2) is 0 if there is no dir=-1 transforms
or is a casted pointer to an fftw plan
*ATTN* plan differ for in- and out-of-place transforms!!
USAGE TABLE: OUT-of-place IN-place
--planning and execution:.....................................
y= fftw(x, dir) fftw, x, dir
y= fftw(x, ljdir, rjdir) fftw, x, ljdir, rjdir
--planning only:..............................................
*attn* *plan is different out- or in-place*
plan= fftw(dimsof(x), dir) fftw, dimsof(x), dir, [], plan
plan= fftw(dimsof(x), ljdir, rjdir) fftw, dimsof(x), ljdir, rjdir, plan
--plan execution only:........................................
y= fftw(x, dir,[], plan) fftw, x, dir,[],plan
y= fftw(x, ljdir, rjdir, plan) fftw, x, ljdir, rjdir, plan
NOTE ABOUT USAGE TABLE ABOVE:
+ X is of type==complex OR array(float,[nd+1,2,d_1,...,d_nd])
+ right-column usage in-place
+ left-column usage out-of-place
+ setting plan=[0,0] on input forces planning
+ Since plans are archived as soon as they are optimized it is
NOT a good idea not to do repeated calls to planning. If it
is required use NOSAVE==1 to turn off wisdom caching.
DIRECTION determines which direction the transform is in --
e.g.- from time to frequency or vice-versa -- see below:
DIRECTION meaning
--------- -------
1 "forward" transform (coefficients of exp(+i * 2*pi*kl/N))
on every dimension of X
-1 "backward" transform (coefficients of exp(-i * 2*pi*kl/N))
on every dimension of X
[1,-1,1] forward transform on first and third dimensions of X,
backward transform on second dimension of X (any other
dimensions remain untransformed)
[-1,0,0,1] backward transform on first dimension of X, forward
transform on fourth dimension of X
etc.
The third positional argument, if present, allows the direction
of dimensions of X to be specified relative to the final dimension
of X, instead of relative to the first dimension of X. In this
case, both LJDIR and RJDIR must be vectors of integers -- the
scalar form is illegal:
LJDIR RJDIR meaning
----- ----- -------
[] [1] forward transform last dimension of X
[1] [] forward transform first dimension of X
[] [-1,-1] backward transform last two dimensions of X,
leaving any other dimensions untransformed
[-1,0,0,1] [] backward transform on first dimension of X,
forward transform on fourth dimension of X
[] [-1,0,0,1] backward transform 4th to last dimension of X,
forward transform on last dimension of X
etc.
Note that the final element of RJDIR corresponds to the last dimension
of X, while the initial element of LJDIR corresponds to the first
dimension of X.
The explicit meaning of "forward" transform -- the coefficients of
exp(+i * 2*pi*kl/N) -- is:
for j=1,...,n ; result(j)= sum from k=1,...,n of
x(k)*exp(-i*(j-1)*(k-1)*2*pi/n)
where i=sqrt(-1)
Note that the result is unnormalized. Applying the "backward"
transform to the result of a "forward" transform returns N times
the original vector of length N. Equivalently, applying either
the "forward" or "backward" transform four times in succession
yields N^2 times the original vector of length N.
Performing transforms requires PLANNING, which can be set up
beforehand by calling fftw on a dimsof(X) array. This allow fftw
to be called more than once with arrays X of the same shape with
KEEP==1.
SEE ALSO: fft, fft_inplace, fft_setup, fftw[f]_init_wisdom, fftw_wisdom, _fftwfI, _fftwfO, _fftwfP, _fftwfE, _fftwfD, _fftwfS, _fftwfC, _fftwT, _fftwI, _fftwO, _fftwP, _fftwE, _fftwD, _fftwS, _fftwC
DOCUMENT fftwf_init_wisdom (nlimit)
Optimization and caching of FFTW plans for n-equi-dimensional arrays.
nlimit==[log2_1d_nmax, log2_2d_nmax,....log2_md_nmax].
nlimit defaults to [FFTW_NLIMIT_1D, FFTW_NLIMIT_2D].
Plans are saved to the wisdom file. (See FFTW_WISDOM_FNM.)
example: fftw_init_wisdom, [4,3];
saves plans for fftw{array(complex,[1,4-or-8-or-16])}
and fftw{array(complex,[2,4-or-8,4-or-8])}
and for in-place or out-of-place fft's.
DOCUMENT fftw_clean, p, fcplx=; free-up memory space allocated by FFTW plan P. FCPLX=1 if the plan was for a float-complex transform. Once space is deallocated, returns a null plan P==[0,0];
DOCUMENT func init_fftw_wisdom(nlimit)
Optimization and caching of FFTW plans for n-equi-dimensional arrays.
nlimit==[log2_1d_nmax, log2_2d_nmax,....log2_md_nmax].
nlimit defaults to [FFTW_NLIMIT_1D, FFTW_NLIMIT_2D].
Plans are saved to the wisdom file. (See FFTW_WISDOM_FNM.)
example: fftw_init_wisdom, [4,3];
saves plans for fftw{array(complex,[1,4-or-8-or-16])}
and fftw{array(complex,[2,4-or-8,4-or-8])}
and for in-place or out-of-place fft's.
SEE ALSO: _init_fftw_plans, fftwf_init_wisdom
DOCUMENT func fftw_wisdom(void) this function will run each time this file is included. It reads wisdom files. To create wisdom files in case they do not exist, call _init_fftwf_plans, this will create optimized FFTW plans and save them in the wisdom files if wisdom files are not found.
SEE ALSO: _init_fftwf_plans, fftw_init_wisdom, fftw,