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 CW$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);

Cmul does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  Signature: (a(n); b(); [o]c(n))

Complex by real multiplation.

  Cscale($a_pdl_cplx,$b_pdl_real);

Cscale does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  Signature: (a(n); b(n); [o]c(n))

Complex division.

  $out_pdl_cplx = Cdiv($a_pdl_cplx,$b_pdl_cplx);

Cdiv does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  Signature: (a(n); b(n))

Complex inplace multiplication.

   Cbmul($a_pdl_cplx,$b_pdl_cplx);

Cbmul does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  Signature: (a(n); b())

Complex inplace multiplaction by real.

   Cbscale($a_pdl_cplx,$b_pdl_real);

Cbscale does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  Signature: (a(n); [o]c(n))

Complex conjugate.

   $out_pdl_cplx = Cconj($a_pdl_cplx);

Cconj does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  Signature: (a(n))

Complex inplace conjugate.

   Cbconj($a_pdl_cplx);

Cbconj does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  Signature: (a(n); [o]c(n))

Complex exponentation.

   $out_pdl_cplx = Cexp($a_pdl_cplx);

Cexp does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  Signature: (a(n))

Complex inplace exponentation.

   $out_pdl_cplx = Cexp($a_pdl_cplx);

Cbexp does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  Signature: (a(n); [o]c())

modulus of a complex piddle.

  $out_pdl_real = Cmod($a_pdl_cplx);

Cmod does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  Signature: (a(n); [o]c())

argument of a complex number.

   $out_pdl_real = Carg($a_pdl_cplx);

Carg does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

  Signature: (a(n); [o]c())

Returns squared modulus of a complex number.

   $out_pdl_real = Cmod2($a_pdl_cplx);

Cmod2 does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

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.