NAME

PDL::FFTW - PDL interface to the Fastest Fourier Transform in the West v2.x

DESCRIPTION

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).

SYNOPSIS

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);

FFTW documentation

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).

load_wisdom

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);

fftw

calculate the complex FFT of a real piddle (complex input, complex output)

$pdl_cplx = fftw $pdl_cplx;

ifftw

Complex inverse FFT (complex input, complex output).

$pdl_cplx = ifftw $pdl_cplx;

nfftw

Complex inplace FFT (complex input, complex output).

$pdl_cplx = nfftw $pdl_cplx;

infftw

Complex inplace inverse FFT (complex input, complex output).

$pdl_cplx = infftw $pdl_cplx;

rfftw

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;

irfftw

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;

nrfftw

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;

inrfftw

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;

rfftwconv

ND convolution using real ffts from the FFTW library

$conv = rfftwconv $im, kernctr $im, $k; # kernctr is from PDL::FFT

fftwconv

ND convolution using complex ffts from the FFTW library

Assumes real input!

$conv = fftwconv $im, kernctr $im, $k; # kernctr is from PDL::FFT

Complex multiplication

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

EOD );

pp_def('Cscale', Pars => 'a(n); b(); [o]c(n);', Code => ' if ($SIZE(n)!=2) barf("This function works only on complex\n"); threadloop %{ $c(n => 0)= $a(n => 0)*$b(); $c(n => 1)= $a(n => 1)*$b(); %} ', Doc => <<'EOD', =for ref

Complex by real multiplation.

Cscale($a_pdl_cplx,$b_pdl_real);
EOD
    );

pp_def('Cdiv', Pars => 'a(n); b(n); [o]c(n);', Code => ' $GENERIC() divi;

if ($SIZE(n)!=2) barf("This function works only on complex\n"); threadloop %{ divi = $b(n => 0)*$b(n => 0) + $b(n => 1)*$b(n => 1);

$c(n => 0)= ( $a(n => 0)*$b(n => 0) + $a(n => 1)*$b(n => 1) ) / divi; $c(n => 1)= ( $a(n => 1)*$b(n => 0) - $a(n => 0)*$b(n => 1) ) / divi; %} ', Doc => <<'EOD', =for ref

Complex division.

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

EOD );

pp_def('Cbmul', Pars => 'a(n); b(n);', Code => ' $GENERIC() tmp1,tmp;

if ($SIZE(n)!=2) barf("This function works only on complex\n"); threadloop %{ tmp = $a(n => 0); tmp1 = $a(n => 1); $a(n => 0)= tmp * $b(n => 0) - tmp1 * $b(n => 1); $a(n => 1)= tmp * $b(n => 1) + tmp1 * $b(n => 0); %} ', Doc => <<'EOD', =for ref

Complex inplace multiplication.

Cbmul($a_pdl_cplx,$b_pdl_cplx);
EOD
   );

pp_def('Cbscale', Pars => 'a(n); b();', Code => ' $GENERIC() tmp1,tmp,divi;

if ($SIZE(n)!=2) barf("This function works only on complex\n"); threadloop %{ $a(n => 0) *= $b(); $a(n => 1) *= $b(); %} ', Doc => <<'EOD', =for ref

Complex inplace multiplaction by real.

Cbscale($a_pdl_cplx,$b_pdl_real);
EOD
   );

pp_def('Cconj', Pars => 'a(n); [o]c(n);', Code => ' if ($SIZE(n)!=2) barf("This function works only on complex\n"); threadloop %{ $c(n => 0)= $a(n => 0); $c(n => 1)= -$a(n => 1); %} ', Doc => <<'EOD', =for ref

Complex conjugate.

$out_pdl_cplx = Cconj($a_pdl_cplx);
EOD
   );

pp_def('Cbconj', Pars => 'a(n);', Code => ' if ($SIZE(n)!=2) barf("This function works only on complex\n"); threadloop %{ $a(n => 1)= -$a(n => 1); %} ', Doc => <<'EOD', =for ref

Complex inplace conjugate.

Cbconj($a_pdl_cplx);
EOD
   );

pp_def('Cexp', Pars => 'a(n); [o]c(n);', Code => ' if ($SIZE(n)!=2) barf("This function works only on complex\n"); threadloop %{ $c(n => 0)= exp($a(n => 0)) * cos($a(n => 1)); $c(n => 1)= exp($a(n => 0)) * sin($a(n => 1)); %} ', Doc => <<'EOD', =for ref

Complex exponentation.

$out_pdl_cplx = Cexp($a_pdl_cplx);
EOD
   );

pp_def('Cbexp', Pars => 'a(n);', Code => ' if ($SIZE(n)!=2) barf("This function works only on complex\n"); threadloop %{ double re = $a(n => 0); double im = $a(n => 1);

$a(n => 0)= exp(re) * cos(im); $a(n => 1)= exp(re) * sin(im); %} ', Doc => <<'EOD', =for ref

Complex inplace exponentation.

$out_pdl_cplx = Cexp($a_pdl_cplx);
EOD
   );

pp_def('Cmod', Pars => 'a(n); [o]c();', Code => ' if ($SIZE(n)!=2) barf("This function works only on complex\n"); threadloop %{ $c()= sqrt ( $a(n => 0)*$a(n => 0) + $a(n => 1)*$a(n => 1) ); %} ', Doc => <<'EOD', =for ref

modulus of a complex piddle.

$out_pdl_real = Cmod($a_pdl_cplx);
EOD
    );

pp_def('Carg', Pars => 'a(n); [o]c();', Code => ' if ($SIZE(n)!=2) barf("This function works only on complex\n"); threadloop %{ $c()= atan2($a(n=>1),$a(n=>0)); %} ', Doc => <<'EOD', =for ref

argument of a complex number.

$out_pdl_real = Carg($a_pdl_cplx);
EOD
   );

pp_def('Cmod2', Pars => 'a(n); [o]c();', Code => ' if ($SIZE(n)!=2) barf("This function works only on complex\n"); threadloop %{ $c()= ( $a(n => 0)*$a(n => 0) + $a(n => 1)*$a(n => 1) ); %} ', Doc => <<'EOD', =for ref

Returns squared modulus of a complex number.

$out_pdl_real = Cmod2($a_pdl_cplx);
EOD
   );

### real fftw