PDL::FFTW - PDL interface to the Fastest Fourier Transform in the West v2.x
This is a means to interface PDL with the FFTW library. It's similar to the standard FFT routine but it's usually faster and has support for real transforms. It works well for the types of PDLs for which was the library was compiled (otherwise it must do conversions).
use PDL::FFTW
load_wisdom("file_name");
out_cplx_pdl = fftw(in_cplx_pdl); out_cplx_pdl = ifftw(in_cplx_pdl);
out_cplx_pdl = rfftw(in_real_pdl); out_real_pdl = irfftw(in_cplx_pdl);
cplx_pdl = nfftw(cplx_pdl); cplx_pdl = infftw(cplx_pdl);
cplx_pdl = Cmul(a_cplx_pdl, b_cplx_pdl); cplx_pdl = Cconj(a_cplx_pdl); real_pdl = Cmod(a_cplx_pdl); real_pdl = Cmod2(a_cplx_pdl);
Please refer to the FFTW documentation for a better understanding of these functions.
Note that complex numbers are represented as piddles with leading dimension size 2 (real/imaginary pairs).
Loads the wisdom from a file for better FFTW performance.
The wisdom
is automatically saved when the program ends. It will be automagically
called when the variable $PDL::FFT::wisdom
is set to a file name.
For example, the following is a useful idiom to have in your .perldlrc
file:
$PDL::FFT::wisdom = "$ENV{HOME}/.fftwisdom"; # save fftw wisdom in this file
Explicit usage:
load_wisdom($fname);
calculate the complex FFT of a real piddle (complex input, complex output)
$pdl_cplx = fftw $pdl_cplx;
Complex inverse FFT (complex input, complex output).
$pdl_cplx = ifftw $pdl_cplx;
Complex inplace FFT (complex input, complex output).
$pdl_cplx = nfftw $pdl_cplx;
Complex inplace inverse FFT (complex input, complex output).
$pdl_cplx = infftw $pdl_cplx;
Real FFT. For an input piddle of dimensions [n1,n2,...] the output is [2,(n1/2)+1,n2,...] (real input, complex output).
$pdl_cplx = fftw $pdl_real;
Real inverse FFT. Have a look at rfftw to understand the format. USE ONLY an even n1! (complex input, real output)
$pdl_real = ifftw $pdl_cplx;
Real inplace FFT. If you want a transformation on a piddle with dimensions [n1,n2,....] you MUST pass in a piddle with dimensions [2*(n1/2+1),n2,...] (real input, complex output).
Use with care due to dimension restrictions mentioned below. For details check the html docs that come with the fftw library.
$pdl_cplx = nrfftw $pdl_real;
Real inplace inverse FFT. Have a look at nrfftw to understand the format. USE ONLY an even first dimension size! (complex input, real output)
$pdl_real = infftw $pdl_cplx;
ND convolution using real ffts from the FFTW library
$conv = rfftwconv $im, kernctr $im, $k; # kernctr is from PDL::FFT
ND convolution using complex ffts from the FFTW library
Assumes real input!
$conv = fftwconv $im, kernctr $im, $k; # kernctr is from PDL::FFT
Signature: (a(n); b(n); [o]c(n))
Complex multiplication
$out_pdl_cplx = Cmul($a_pdl_cplx,$b_pdl_cplx);
Signature: (a(n); b(); [o]c(n))
Complex by real multiplation.
Cscale($a_pdl_cplx,$b_pdl_real);
Signature: (a(n); b(n); [o]c(n))
Complex division.
$out_pdl_cplx = Cdiv($a_pdl_cplx,$b_pdl_cplx);
Signature: (a(n); b(n))
Complex inplace multiplication.
Cbmul($a_pdl_cplx,$b_pdl_cplx);
Signature: (a(n); b())
Complex inplace multiplaction by real.
Cbscale($a_pdl_cplx,$b_pdl_real);
Signature: (a(n); [o]c(n))
Complex conjugate.
$out_pdl_cplx = Cconj($a_pdl_cplx);
Signature: (a(n))
Complex inplace conjugate.
Cbconj($a_pdl_cplx);
Signature: (a(n); [o]c(n))
Complex exponentation.
$out_pdl_cplx = Cexp($a_pdl_cplx);
Signature: (a(n))
Complex inplace exponentation.
$out_pdl_cplx = Cexp($a_pdl_cplx);
Signature: (a(n); [o]c())
modulus of a complex piddle.
$out_pdl_real = Cmod($a_pdl_cplx);
Signature: (a(n); [o]c())
argument of a complex number.
$out_pdl_real = Carg($a_pdl_cplx);
Signature: (a(n); [o]c())
Returns squared modulus of a complex number.
$out_pdl_real = Cmod2($a_pdl_cplx);
Copyright (C) 1999 Christian Pellegrin, 2000 Christian Soeller. All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDL distribution. If this file is separated from the PDL distribution, the copyright notice should be included in the file.