% -*- texinfo -*-
% @deftypefn {Function File} {@var{yi} =} interp1 (@var{x}, @var{y}, @var{xi})
% @deftypefnx {Function File} {@var{yi} =} interp1 (@dots{}, @var{method})
% @deftypefnx {Function File} {@var{yi} =} interp1 (@dots{}, @var{extrap})
% @deftypefnx {Function File} {@var{pp} =} interp1 (@dots{}, 'pp')
%
% One-dimensional interpolation. Interpolate @var{y}, defined at the
% points @var{x}, at the points @var{xi}. The sample points @var{x}
% must be strictly monotonic. If @var{y} is an array, treat the columns
% of @var{y} separately.
%
% Method is one of:
%
% @table @asis
% @item 'nearest'
% Return the nearest neighbor.
% @item 'linear'
% Linear interpolation from nearest neighbors
% @item 'pchip'
% Piece-wise cubic hermite interpolating polynomial
% @item 'cubic'
% Cubic interpolation from four nearest neighbors
% @item 'spline'
% Cubic spline interpolation--smooth first and second derivatives
% throughout the curve
% @end table
%
% Appending '*' to the start of the above method forces @code{interp1}
% to assume that @var{x} is uniformly spaced, and only @code{@var{x}
% (1)} and @code{@var{x} (2)} are referenced. This is usually faster,
% and is never slower. The default method is 'linear'.
%
% If @var{extrap} is the string 'extrap', then extrapolate values beyond
% the endpoints. If @var{extrap} is a number, replace values beyond the
% endpoints with that number. If @var{extrap} is missing, assume NA.
%
% If the string argument 'pp' is specified, then @var{xi} should not be
% supplied and @code{interp1} returns the piece-wise polynomial that
% can later be used with @code{ppval} to evaluate the interpolation.
% There is an equivalence, such that @code{ppval (interp1 (@var{x},
% @var{y}, @var{method}, 'pp'), @var{xi}) == interp1 (@var{x}, @var{y},
% @var{xi}, @var{method}, 'extrap')}.
%
% An example of the use of @code{interp1} is
%
% @example
% @group
% xf = [0:0.05:10];
% yf = sin (2*pi*xf/5);
% xp = [0:10];
% yp = sin (2*pi*xp/5);
% lin = interp1 (xp, yp, xf);
% spl = interp1 (xp, yp, xf, 'spline');
% cub = interp1 (xp, yp, xf, 'cubic');
% near = interp1 (xp, yp, xf, 'nearest');
% plot (xf, yf, 'r', xf, lin, 'g', xf, spl, 'b',
% xf, cub, 'c', xf, near, 'm', xp, yp, 'r*');
% legend ('original', 'linear', 'spline', 'cubic', 'nearest')
% @end group
% @end example
%
% @seealso{interpft}
% @end deftypefn