Computes the inverse Discrete Fourier Transform of several complex or real sequences.

Function Return Value

Complex array containing the inverse of the Discrete Fourier Transform of the sequences in X.  If X is an assumed shape complex array of rank 2, 3 or 4, the result is a complex array of the same shape and rank consisting of the inverse DFT for each of the last rank's indices.  (Output)

Required Argument

X — Box containing the sequences for which the inverse transform is to be computed.  X is an assumed shape complex array of rank 2, 3 or 4.  If X is real or double, it is converted to complex internally prior to the computation. (Input)

Optional Arguments, Packaged Options

WORK — A COMPLEX array of the same precision as the data.  For rank-1 transforms the size of  WORK is n+15.  To define this array for each problem, set WORK(1) = 0. Each additional rank adds the dimension of the transform plus 15. Using the optional argument WORK increases the efficiency of the transform.

The option and derived type names are given in the following tables:

Option Names for IFFT	Option Value
Options_for_fast_dft	1

 

Name of Unallocated Option Array to Use for Setting Options	Use	Derived Type
?_ifft_box_options(:)	Use when setting options for calls hereafter.	?_options
?_ifft_box_options_once(:)	Use when setting options for next call only.	?_options

For a description on how to use these options, see Matrix Optional Data Changes.  See fast_dft located in Chapter 6, “Transforms”  for the specific options for this routine.

FORTRAN 90 Interface

IFFT_BOX (X [,…])

Description

Computes the inverse of the Discrete Fourier Transform of a box of complex sequences.  This function uses fast_dft, fast_2dft, and fast_3dft from Chapter 6.

Parallel Example

 

      use rand_gen_int

      use fft_box_int

      use ifft_box_int

      use linear_operators

      use mpi_setup_int

 

      implicit none

 

! This is FFT_BOX example.

 

      integer i,j

      integer, parameter :: n=40, nr=4

      real(kind(1e0)) :: err(nr), one=1e0

      real(kind(1e0)) :: a(n,1,nr), b(n,nr), c(n,1,nr), yy(n,n,nr)

      complex(kind(1e0)), dimension(n,nr) :: f, fa, fb, cc, aa

 

      real(kind(1e0)),parameter::zero_par=0.e0

      real(kind(1e0))::dummy_par(0)

      integer iseed_par

      type(s_options)::iopti_par(2)

 

 

! setup for MPI

      MP_NPROCS = MP_SETUP()

 

! Set Random Number generator seed

 

      iseed_par = 53976279

      iopti_par(1)=s_options(s_rand_gen_generator_seed,zero_par)

      iopti_par(2)=s_options(iseed_par,zero_par)

 

      call rand_gen(dummy_par,iopt=iopti_par)

 

! Generate two random periodic sequences 'a' and 'b'.

      a=rand(a); b=rand(b)

 

! Compute the convolution 'c' of 'a' and 'b'.

     do i=1,nr

      aa(1:,i) = a(1:,1,i)

      yy(1:,1,i)=b(1:,i)

      do j=2,n

        yy(2:,j,i)=yy(1:n-1,j-1,i)

        yy(1,j,i)=yy(n,j-1,i)

      end do

     end do

 

      c=yy .x. a

 

! Compute f=inverse(transform(a)*transform(b)).

      fa = fft_box(aa)

      fb = fft_box(b)

      f=ifft_box(fa*fb)

 

! Check the Convolution Theorem:

! inverse(transform(a)*transform(b)) = convolution(a,b).

      do i=1,nr

       cc(1:,i) = c(1:,1,i)

      end do

      err = norm(cc-f)/norm(cc)

      if (ALL(err <= sqrt(epsilon(one))) .AND. MP_RANK == 0) then

         write (*,*) 'FFT_BOX is correct.'

      end if

 

       MP_NPROCS = MP_SETUP('Final')

      end

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