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## -*- texinfo -*-
## @deftypefn  {} {} conv (@var{a}, @var{b})
## @deftypefnx {} {} conv (@var{a}, @var{b}, @var{shape})
## Convolve two vectors @var{a} and @var{b}.
##
## When @var{a} and @var{b} are the coefficient vectors of two polynomials, the
## convolution represents the coefficient vector of the product polynomial.
##
## The size of the result is determined by the optional @var{shape} argument
## which takes the following values
##
## @table @asis
## @item @var{shape} = @qcode{"full"}
## Return the full convolution.  (default)
## The result is a vector with length equal to
## @code{length (@var{a}) + length (@var{b}) - 1}.
##
## @item @var{shape} = @qcode{"same"}
## Return the central part of the convolution with the same size as @var{a}.
##
## @item @var{shape} = @qcode{"valid"}
## Return only the parts which do not include zero-padded edges.
## The size of the result is
## @code{max (size (@var{a}) - size (@var{b}) + 1, 0)}.
## @end table
##
## @seealso{deconv, conv2, convn, fftconv}
## @end deftypefn

function y = conv (a, b, shape = "full")

  if (nargin < 2 || nargin > 3)
    print_usage ();
  endif

  if (! (isvector (a) && isvector (b)))
    error ("conv: both arguments A and B must be vectors");
  elseif (nargin == 3 && ! any (strcmpi (shape, {"full", "same", "valid"})))
    error ('conv: SHAPE argument must be "full", "same", or "valid"');
  endif

  y = conv2 (a(:), b(:), shape);

  if (strcmpi (shape, "full"))
    ## Adapt the shape to the longest input argument, if necessary.
    if ((length (a) > length (b) && isrow (a)) ...
        || (length (a) <= length (b) && isrow (b)))
      y = y.';
    endif
  elseif (isrow (a))
    ## Adapt the shape to the first input argument, if necessary.
    y = y.';
  endif

endfunction


%!test
%! x = ones (3,1);
%! y = ones (1,3);
%! b = 2;
%! c = 3;
%! assert (conv (x, x), [1; 2; 3; 2; 1]);
%! assert (conv (y, y), [1, 2, 3, 2, 1]);
%! assert (conv (x, y), [1, 2, 3, 2, 1]);
%! assert (conv (y, x), [1; 2; 3; 2; 1]);
%! assert (conv (c, x), [3; 3; 3]);
%! assert (conv (c, y), [3, 3, 3]);
%! assert (conv (x, c), [3; 3; 3]);
%! assert (conv (y, c), [3, 3, 3]);
%! assert (conv (b, c), 6);

%!shared a,b
%!test
%! a = 1:10;
%! b = 1:3;
%!assert (size (conv (a,b)), [1, numel(a)+numel(b)-1])
%!assert (size (conv (b,a)), [1, numel(a)+numel(b)-1])

%!test
%! a = (1:10).';
%!assert (size (conv (a,b)), [numel(a)+numel(b)-1, 1])
%!assert (size (conv (b,a)), [numel(a)+numel(b)-1, 1])

%!test
%! a = 1:10;
%! b = (1:3).';
%!assert (size (conv (a,b)), [1, numel(a)+numel(b)-1])
%!assert (size (conv (b,a)), [1, numel(a)+numel(b)-1])

%!test
%! a = 1:10;
%! b = 1:3;

%!assert (conv (a,b,"full"), conv (a,b))
%!assert (conv (b,a,"full"), conv (b,a))

%!assert (conv (a,b,"same"), [4, 10, 16, 22, 28, 34, 40, 46, 52, 47])
%!assert (conv (b,a,"same"), [28, 34, 40])

%!assert (conv (a,b,"valid"), [10, 16, 22, 28, 34, 40, 46, 52])
%!assert (conv (b,a,"valid"), zeros (1,0))


## Test input validation
%!error conv (1)
%!error conv (1,2,3,4)
%!error <A and B must be vectors> conv ([1, 2; 3, 4], 3)
%!error <A and B must be vectors> conv (3, [1, 2; 3, 4])
%!error <SHAPE argument must be> conv (2, 3, "INVALID_SHAPE")
