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## -*- texinfo -*-
## @deftypefn  {} {@var{b} =} unwrap (@var{x})
## @deftypefnx {} {@var{b} =} unwrap (@var{x}, @var{tol})
## @deftypefnx {} {@var{b} =} unwrap (@var{x}, @var{tol}, @var{dim})
##
## Unwrap radian phases by adding or subtracting multiples of 2*pi as
## appropriate to remove jumps greater than @var{tol}.
##
## @var{tol} defaults to pi.
##
## Unwrap will work along the dimension @var{dim}.  If @var{dim}
## is unspecified it defaults to the first non-singleton dimension.
## @end deftypefn

function retval = unwrap (x, tol, dim)

  if (nargin < 1)
    print_usage ();
  endif

  if (! isnumeric (x))
    error ("unwrap: X must be a numeric matrix or vector");
  endif

  if (nargin < 2 || isempty (tol))
    tol = pi;
  endif

  ## Don't let anyone use a negative value for TOL.
  tol = abs (tol);

  nd = ndims (x);
  sz = size (x);
  if (nargin == 3)
    if (!(isscalar (dim) && dim == fix (dim))
        || !(1 <= dim && dim <= nd))
      error ("unwrap: DIM must be an integer and a valid dimension");
    endif
  else
    ## Find the first non-singleton dimension.
    (dim = find (sz > 1, 1)) || (dim = 1);
  endif

  rng = 2*pi;
  m = sz(dim);

  ## Handle case where we are trying to unwrap a scalar, or only have
  ## one sample in the specified dimension.
  if (m == 1)
    retval = x;
    return;
  endif

  ## Take first order difference to see so that wraps will show up
  ## as large values, and the sign will show direction.
  idx = repmat ({':'}, nd, 1);
  idx{dim} = [1,1:m-1];
  d = x(idx{:}) - x;

  ## Find only the peaks, and multiply them by the appropriate amount
  ## of ranges so that there are kronecker deltas at each wrap point
  ## multiplied by the appropriate amount of range values.
  p = round (abs (d)./rng) .* rng .* (((d > tol) > 0) - ((d < -tol) > 0));

  ## Now need to "integrate" this so that the deltas become steps.
  r = cumsum (p, dim);

  ## Now add the "steps" to the original data and put output in the
  ## same shape as originally.
  retval = x + r;

endfunction


%!shared i, t, r, w, tol
%! i = 0;
%! t = [];
%! r = [0:100];                         ## original vector
%! w = r - 2*pi*floor ((r+pi)/(2*pi));  ## wrapped into [-pi,pi]
%! tol = 1e3*eps;

%!assert (r,  unwrap (w),  tol)
%!assert (r', unwrap (w'), tol)
%!assert ([r',r'], unwrap ([w',w']), tol)
%!assert ([r; r ], unwrap ([w; w ], [], 2), tol)
%!assert (r + 10, unwrap (10 + w), tol)

%!assert (w', unwrap (w', [], 2))
%!assert (w,  unwrap (w,  [], 1))
%!assert ([w; w], unwrap ([w; w]))

## Test that small values of tol have the same effect as tol = pi
%!assert (r, unwrap (w, 0.1), tol)
%!assert (r, unwrap (w, eps), tol)

## Test that phase changes larger than 2*pi unwrap properly
%!assert ([0;  1],        unwrap ([0;  1]))
%!assert ([0;  4 - 2*pi], unwrap ([0;  4]))
%!assert ([0;  7 - 2*pi], unwrap ([0;  7]))
%!assert ([0; 10 - 4*pi], unwrap ([0; 10]))
%!assert ([0; 13 - 4*pi], unwrap ([0; 13]))
%!assert ([0; 16 - 6*pi], unwrap ([0; 16]))
%!assert ([0; 19 - 6*pi], unwrap ([0; 19]))
%!assert (max (abs (diff (unwrap (100*pi * rand (1000, 1))))) < pi)

%!test
%! A = [pi*(-4), pi*(-2+1/6), pi/4, pi*(2+1/3), pi*(4+1/2), pi*(8+2/3), pi*(16+1), pi*(32+3/2), pi*64];
%! assert (unwrap (A), unwrap (A, pi));
%! assert (unwrap (A, pi), unwrap (A, pi, 2));
%! assert (unwrap (A', pi), unwrap (A', pi, 1));

%!test
%! A = [pi*(-4); pi*(2+1/3); pi*(16+1)];
%! B = [pi*(-2+1/6); pi*(4+1/2); pi*(32+3/2)];
%! C = [pi/4; pi*(8+2/3); pi*64];
%! D = [pi*(-2+1/6); pi*(2+1/3); pi*(8+2/3)];
%! E(:, :, 1) = [A, B, C, D];
%! E(:, :, 2) = [A+B, B+C, C+D, D+A];
%! F(:, :, 1) = [unwrap(A), unwrap(B), unwrap(C), unwrap(D)];
%! F(:, :, 2) = [unwrap(A+B), unwrap(B+C), unwrap(C+D), unwrap(D+A)];
%! assert (unwrap (E), F);

%!test
%! A = [0, 2*pi, 4*pi, 8*pi, 16*pi, 65536*pi];
%! B = [pi*(-2+1/6), pi/4, pi*(2+1/3), pi*(4+1/2), pi*(8+2/3), pi*(16+1), pi*(32+3/2), pi*64];
%! assert (unwrap (A), zeros (1, length (A)));
%! assert (diff (unwrap (B), 1) < 2*pi, true (1, length (B)-1));

## Test input validation
%!error <Invalid call> unwrap ()
%!error unwrap ("foo")