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    /*
       FFT.I
       Yorick interface to Swarztrauber FFT routines, modified for strides.

       $Id: fft.i,v 1.1 1993/08/06 23:13:12 munro Exp $
     */
    /*    Copyright (c) 1994.  The Regents of the University of California.
                        All rights reserved.  */

    /* ------------------------------------------------------------------------ */

    /* MAKE-INSTRUCTIONS
    SRCS = cfft2.c cfftb.c cfftf.c cffti.c roll2.c
    LIB =
    DEPLIBS =
    */

    /* ------------------------------------------------------------------------ */

    func fft (x, ljdir, rjdir, setup=)
    /* DOCUMENT fft(x, direction)
                fft(x, ljdir, rjdir)

             or fft(x, ljdir, rjdir, setup=workspace)

         returns the complex Fast Fourier Transform of array X.
         The DIRECTION determines which direction the transform is in --
         e.g.- from time to frequency or vice-versa -- as follows:

         DIRECTION    meaning
         ---------    -------

             1        "forward" transform (coefficients of exp(+i * 2*pi*kl/N))
    	          on every dimension of X

            -1        "backward" transform (coefficients of exp(-i * 2*pi*kl/N))
    	          on every dimension of X
         [1,-1,1]     forward transform on first and third dimensions of X,

                      backward transform on second dimension of X (any other
    		  dimensions remain untransformed)
         [-1,0,0,1]   backward transform on first dimension of X, forward
                      transform on fourth dimension of X
    	etc.

         The third positional argument, if present, allows the direction
         of dimensions of X to be specified relative to the final dimension
         of X, instead of relative to the first dimension of X.  In this
         case, both LJDIR and RJDIR must be vectors of integers -- the
         scalar form is illegal:

            LJDIR    RJDIR      meaning
            -----    -----      -------
    	[]        [1]       forward transform last dimension of X
    	[1]        []       forward transform first dimension of X
    	[]        [-1,-1]   backward transform last two dimensions of X,
    	                    leaving any other dimensions untransformed
         [-1,0,0,1]    []       backward transform on first dimension of X,
                                forward transform on fourth dimension of X
            []      [-1,0,0,1]  backward transform on 4th to last dimension of X,
                                forward transform on last dimension of X
    	etc.

         Note that the final element of RJDIR corresponds to the last dimension
         of X, while the initial element of LJDIR corresponds to the first
         dimension of X.

         The explicit meaning of "forward" transform -- the coefficients of

         exp(+i * 2*pi*kl/N) -- is:

         result for j=1,...,n

                    result(j)=the sum from k=1,...,n of

                          x(k)*exp(-i*(j-1)*(k-1)*2*pi/n)

                                where i=sqrt(-1)

         Note that the result is unnormalized.  Applying the "backward"
         transform to the result of a "forward" transform returns N times
         the original vector of length N.  Equivalently, applying either
         the "forward" or "backward" transform four times in succession
         yields N^2 times the original vector of length N.

         Performing the transform requires some WORKSPACE, which can be

         set up beforehand by calling fft_setup, if fft is to be called
         more than once with arrays X of the same shape.  If no setup
         keyword argument is supplied, the workspace allocation and setup
         must be repeated for each call.

       SEE ALSO: roll, fft_setup, fft_inplace
     */
    {
      result= complex(x);

      fft_inplace, result, ljdir, rjdir, setup=setup;
      return result;
    }

    func fft_inplace (x, ljdir, rjdir, setup=)

    /* DOCUMENT fft_inplace, x, direction

             or fft_inplace, x, ljdir, rjdir

    	 or fft_inplace, x, ljdir, rjdir, setup=workspace

         is the same as the fft function, except that the transform is

         performed "in_place" on the array X, which must be of type complex.

       SEE ALSO: fft, fft_setup
     */
    {

      if (structof(x)!=complex) error, "expecting complex argument";

      /* form list of dimension lengths (dims) and corresponding list of
         transform directions (dirs) */
      dims= dimsof(x);
      ndims= dims(1);
      if (ndims<1) return;

      dirs= fft_dirs(ndims, ljdir, rjdir);

      list= where(dirs);  /* list of dimensions to be transformed */
      n= numberof(list);
      if (!n) return;

      /* setup the workspace now if it hasn't already been done */

      if (is_void(setup)) setup= fft_setup(dims, dirs);

      /* get the strides associated with each dimension */
      dims= dims(2:0);
      stds= array(1, ndims);
      for (i=1 ; i<ndims ; i++) stds(i+1)= stds(i)*dims(i);
      tops= numberof(x)/(stds*dims);

      /* do the requested transforms */
      nlist= *setup(1);
      setup= *setup(2);

      if (is_void(setup)) error, "no workspace for any dimension length";
      for (i=1 ; i<=n ; i++) {
        j= list(i);
        ndims= dims(j);  /* clobbers original ndims */
        ws= setup(where(nlist==ndims)(1));

        if (is_void(ws)) error, "no workspace for dimension length "+pr1(ndims);

        fft_raw, dirs(j), x, stds(j), ndims, tops(j), ws;
      }
    }

    func fft_setup (dims, ljdir, rjdir)

    /* DOCUMENT workspace= fft_setup(dimsof(x))

             or workspace= fft_setup(dimsof(x), direction)

             or workspace= fft_setup(dimsof(x), ljdir, rjdir)

         allocates and sets up the workspace for a subsequent call to

                fft(X, DIRECTION, setup=WORKSPACE)
         or

                fft(X, LJDIR, RJDIR, setup=WORKSPACE)
         The DIRECTION or LJDIR, RJDIR arguments compute WORKSPACE only for
         the dimensions which will actually be transformed.  If only the

         dimsof(x) argument is supplied, then WORKSPACE will be enough to
         transform any or all dimensions of X.  With DIRECTION or LJDIR, RJDIR
         supplied, WORKSPACE will only be enough to compute the dimensions
         which are actually to be transformed.  The WORKSPACE does not

         depend on the sign of any element in the DIRECTION (or LJDIR, RJDIR),
         so you can use the same WORKSPACE for both "forward" and "backward"
         transforms.

         Furthermore, as long as the length of any dimensions of the array
         X to be transformed are present in WORKSPACE, it may be used in

         a call to fft with the array.  Thus, if X were a 25-by-64 array,

         and Y were a 64-vector, the following sequence is legal:

              ws= fft_setup(dimsof(x));
    	  xf= fft(x, 1, setup=ws);
    	  yf= fft(y, -1, setup=ws);

         The WORKSPACE required for a dimension of length N is 6*N+15 doubles.

       SEE ALSO: fft, dimsof, fft_inplace
     */
    {
      ndims= dims(1);

      if (ndims<1) return array(pointer, 2);

      dirs= fft_dirs(ndims, ljdir, rjdir);

      list= where(dirs);  /* list of dimensions to be transformed */
      n= numberof(list);
      if (!n) return array(pointer, 2);
      dims= dims(1+list);
      if (n>1) {
        dims= dims(sort(dims));
        list= grow([0],dims)(dif);
        /* eliminate duplicate dimension lengths */
        dims= dims(where(list));
        n= numberof(dims);
      }
      setup= array(pointer, n);
      for (i=1 ; i<=n ; i++) {
        ndims= dims(i);
        ws= array(0.0, 6*ndims+15);
        fft_init, ndims, ws;
        setup(i)= &ws;
      }
      return [&dims, &setup];
    }

    func fft_dirs (ndims, ljdir, rjdir)
    {
      nolj= is_void(ljdir);
      norj= is_void(rjdir);

      if (nolj && norj) return array(1, ndims);  /* mostly for fft_setup --
    					        also makes fft(x) work */
      if (nolj || dimsof(ljdir)(1)) {
        /* detailed direction list present */

        dirs= array(0, ndims);          /* all 0 initially */
        if (!nolj) {                    /* fill in left-justified directions */
          list= where(ljdir);
          dirs(list)= ljdir(list);
        }
        if (!norj) {                    /* fill in right-justified directions */
          list= where(rjdir);

          dirs(list-numberof(rjdir) + ndims)= rjdir(list);
        }
      } else {
        /* all dimensions get the same direction */
        dirs= array(ljdir, ndims);
      }
      return dirs;
    }

    extern fft_init ;
    /* PROTOTYPE
       void cffti(long n, double array ws)
     */
    /* DOCUMENT fft_init, n, wsave

         Swarztrauber's cffti.  This actually requires wsave=array(0.0, 4*n+15),

         instead of the 6*n+15 doubles of storage used by fft_raw to handle the
         possibility of multidimensional arrays.  If the storage matters, you

         can call cfftf and/or cfftb as the Yorick functions fft_fraw and/or
         fft_braw.
     */

    extern fft_fraw ;
    /* PROTOTYPE

       void cfftf(long n, complex array c, double array ws)
     */
    /* DOCUMENT fft_fraw, n, c, wsave
         Swarztrauber's cfftf.  You can use this to avoid the additional
         2*N storage incurred by fft_setup.
     */

    extern fft_braw ;
    /* PROTOTYPE

       void cfftb(long n, complex array c, double array ws)
     */
    /* DOCUMENT fft_braw, n, c, wsave
         Swarztrauber's cfftb.  You can use this to avoid the additional
         2*N storage incurred by fft_setup.
     */

    extern fft_raw ;
    /* PROTOTYPE

       void cfft2(long idir, complex array c, long istd, long n, long n2,
                  pointer ws)
     */

    /* ------------------------------------------------------------------------ */

    func roll (x, ljoff, rjoff)
    /* DOCUMENT roll(x, ljoff, rjoff)
             or roll, x, ljoff, rjoff
    	 or roll(x)
    	 or roll, x

         "rolls" selected dimensions of the array X.  The roll offsets
         LJOFF and RJOFF (both optional) work in the same fashion as the

         LJDIR and RJDIR arguments to the fft function:

            A scalar LJDIR (and nil RJDIR) rolls all dimensions of X by
            the specified offset.
    	Otherwise, the elements of the LJDIR vector [ljoff1, ljoff2, ...]

    	are used as the roll offsets for the first, second, etc.
    	dimensions of X.
    	Similarly, the elements of the RJDIR vector [..., rjoff1, rjoff0]
    	are matched to the final dimensions of X, so the next to last
    	dimension is rolled by rjoff1 and the last dimension by rjoff0.

    	As a special case (mostly for use with the fft function), if
    	both LJDIR and RJDIR are nil, every dimension is rolled by
    	half of its length.  Thus,
    	   roll(x)
    	it equivalent to

    	   roll(x, dimsof(x)(2:0)/2)

         The result of the roll function is complex if X is complex, otherwise

         double (i.e.- any other array type is promoted to type double).  If

         roll is invoked as a subroutine, the operation is performed in place.

       SEE ALSO: fft
     */
    {
      /* get array to be transformed */
      if (structof(x)==complex) {
        stds1= 2;

        if (!am_subroutine()) x= complex(x);  /* copy to avoid clobbering */
      } else {
        stds1= 1;

        if (!am_subroutine()) x= double(x);  /* copy to avoid clobbering */
        else if (structof(x)!=double)

          error, "in-place roll needs double or complex argument";
      }
      dims= dimsof(x);
      ndims= dims(1);
      n= numberof(x);
      if (ndims<1 || n<2) return x;
      dims= dims(2:0);

      /* get offset arguments */

      if (is_void(ljoff) && is_void(rjoff)) ljoff= dims/2;

      else ljoff= fft_dirs(ndims, ljoff, rjoff);
      ljoff%= dims;
      if (noneof(ljoff)) return x;

      /* get strides */

      stds= array(stds1, ndims);   /* note extra factor of 2 for complex */
      for (i=1 ; i<ndims ; i++) stds(i+1)= stds(i)*dims(i);
      tops= (stds1*n)/(stds*dims);

      /* perform roll operation */

      px= &x;   /* avoids complex<-->double type conversion problems */

      ws= array(0.0, max(dims(where(ljoff))));
      for (i=1 ; i<=ndims ; i++)

        _roll2, px, ljoff(i), stds(i), dims(i), tops(i), ws;

      return x;
    }

    extern _roll2 ;
    /* PROTOTYPE
       void roll2(pointer a, long ioff, long istd, long n, long n2,
                  double array ws)
     */