fft2du(3F)

NAME
     scfft2du, dzfft2du - 2D, Real to Complex, Direct Fast Fourier Transforms.

SYNOPSYS
     Fortran :
     subroutine scfft2du( sign, n1, n2, array, lda, coef )
          integer            sign, n1, n2, lda
          real      array(lda,n2), coef((n1+15)+2*(n2+15))

     subroutine dzfft2du( sign, n1, n2, array, lda, coef )
          integer            sign, n1, n2, lda
          real*8  array(lda,n2), coef((n1+15)+2*(n2+15))


     C :
     #include <fft.h>
     int scfft2du ( int sign, int n1, int n2, float *array,
                    int lda, float *coef);
     int dzfft2du ( int sign, int n1, int n2, double *array,
                    int lda, double *coef);


DESCRIPTION
     scfft2du and dzfft2du compute in place the complex Fourier transform of
     real 2D sequence of size N1 x N2.  The value F{k,l} of the transform of
     the 2D sequence f{i,j} is equal to:
          F{k,l} = Sum ( W1^(i*k) * W2^(j*l) * f{i,j} ),
                  for i =0,...,(N1-1), j=0,...,(n2-1)
              W1 = exp( (Sign*2*sqrt(-1)*PI) / N1 )
              W2 = exp( (Sign*2*sqrt(-1)*PI) / N2 )


Storage
     It is assumed that the (N1 x N2) 2D sequence is stored along dimension
     N1.  So the index {i+1,j} has an offset of 1 element with respect to
     {i,j}, and {i,j+1} an offset of lda elements with respect to {i,j}.
     NOTE : lda must be larger (or equal) to 2*((N1+2)/2).


Algorithm
     The real-to-complex Direct 2D Fourier transform is computed with a row-
     column approach.
      - First, N2 FFTs real-to-complex of size N1 are evaluated, stride = 1
      and leading_dimension=lda.
      - then, N1 FFTs complex-to-complex of size N2 are preformed,
     stride=lda/2, and leading_dimension=1.

     As the input sequence has real values, only half of the results are
     computed since the sample {(N1-k),l} of the real-to-complex transform
     would be the conjugate of the sample {k,l}.
     However, some extra space is necessary, and the relation
     (lda>=2*((N1+2)/2)) must hold.
PARAMETERS
     SIGN Integer specifying which sign to be used for the expression of W
     (see above) - must be either +1 or -1.
     Unchanged on exit.

     N1 Integer, the first dimension size of the 2D sequence.
     Unchanged on exit.

     N2 Integer, the second dimension size of the 2D sequence.
     Unchanged on exit.

     ARRAY Array containing the samples of the 2D sequence to be transformed.
     On input, the element {i,j} of the sequence is stored as A(i,j) in
     Fortran , and A[i+j*lda] in C.
     On exit, the array is overwritten by its transform.

     LDA Integer, leading dimension: increment between the samples of two
     consecutive sub-sequences (e.g between {i,j+1} and {i,j} ).
     Unchanged on exit.

     COEFF Array of at least ( (N1+15)+2*(N2+15) ) elements.  On entry it
     contains the Sines/Cosines and factorization of N1 and N2. COEFF needs to
     be initialized with a call to scfft2dui or dzfft2dui.  Unchanged on exit.


Example of Calling Sequence
     2D FFTs computed on a 64*1024 sequence of real values. The elements of
     each sequence are stored with increment (stride) 1, and the offset
     between the first element of two succesive sequence (leading dimension)
     is 1026.
     Note : 1026 >= 1024+2 .
     Fortran
          real array(0:1026-1,0:64-1), coeff(1024+15 + 2*(64+15))
          call scfft2dui( 1024, 64, coeff)
          call scfft2du( -1, 1024, 64, array, 1026, coeff)

     C
          #include <fft.h>
          float array[64*1026], *coeff;
          coeff = scfft2dui( 1024, 64, NULL);
          scfft2du( -1, 1024, 64, array, 1026, coeff);

SEE ALSO
     fft, scfft2dui, dzfft2dui, scfft1du, dzfft1du, csfft2du, zdfft2du