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## @deftypefnx {Function File} {@var{yi} =} interp1 (@var{y}, @var{xi})
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## @deftypefnx {Function File} {@var{yi} =} interp1 (@dots{}, @var{method})
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## @deftypefnx {Function File} {@var{yi} =} interp1 (@dots{}, @var{extrap})
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## @deftypefnx {Function File} {@var{yi} =} interp1 (@dots{}, "left")
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## @deftypefnx {Function File} {@var{yi} =} interp1 (@dots{}, "right")
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## @deftypefnx {Function File} {@var{pp} =} interp1 (@dots{}, "pp")
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## One-dimensional interpolation. Interpolates to determine the value of
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## @var{yi} at the points, @var{xi}. If not specified, @var{x} is taken
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## to be the indices of @var{y}. If @var{y} is a matrix or an N-dimensional
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## array, the interpolation is performed on each column of @var{y}.
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## One-dimensional interpolation.
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## Interpolate input data to determine the value of @var{yi} at the points
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## @var{xi}. If not specified, @var{x} is taken to be the indices of @var{y}.
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## If @var{y} is a matrix or an N-dimensional array, the interpolation is
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## performed on each column of @var{y}.
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## Method is one of:
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## @item @qcode{"nearest"}
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## Return the nearest neighbor.
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## Return the nearest neighbor
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## @item @qcode{"linear"}
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## Linear interpolation from nearest neighbors
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## throughout the curve
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## Appending '*' to the start of the above method forces @code{interp1}
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## Adding '*' to the start of any method above forces @code{interp1}
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## to assume that @var{x} is uniformly spaced, and only @code{@var{x}(1)}
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## and @code{@var{x}(2)} are referenced. This is usually faster,
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## and is never slower. The default method is @qcode{"linear"}.
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## If @var{extrap} is the string @qcode{"extrap"}, then extrapolate values
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## beyond the endpoints. If @var{extrap} is a number, replace values beyond
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## the endpoints with that number. If @var{extrap} is missing, assume NA.
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## beyond the endpoints using the current @var{method}. If @var{extrap} is a
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## number, then replace values beyond the endpoints with that number. When
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## unspecified, @var{extrap} defaults to NA.
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## If the string argument @qcode{"pp"} is specified, then @var{xi} should not be
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## supplied and @code{interp1} returns the piecewise polynomial that
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## can later be used with @code{ppval} to evaluate the interpolation.
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## If the string argument @qcode{"pp"} is specified, then @var{xi} should not
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## be supplied and @code{interp1} returns a piecewise polynomial object. This
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## object can later be used with @code{ppval} to evaluate the interpolation.
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## There is an equivalence, such that @code{ppval (interp1 (@var{x},
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## @var{y}, @var{method}, @qcode{"pp"}), @var{xi}) == interp1 (@var{x}, @var{y},
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## @var{xi}, @var{method}, @qcode{"extrap"})}.
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yi = shiftdim (yi, 1);
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error ("interp1: invalid method '%s'", method);
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if (! ischar (extrap))
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## determine which values are out of range and set them to extrap,
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## unless extrap == "extrap".
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minx = min (x(1), x(nx));
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maxx = max (x(1), x(nx));
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if (! ispp && ! ischar (extrap))
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## determine which values are out of range and set them to extrap,
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## unless extrap == "extrap".
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minx = min (x(1), x(nx));
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maxx = max (x(1), x(nx));
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outliers = xi < minx | ! (xi <= maxx); # this catches even NaNs
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if (size_equal (outliers, yi))
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yi(outliers) = extrap;
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yi = reshape (yi, szx);
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elseif (!isvector (yi))
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yi(outliers, :) = extrap;
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yi(outliers.') = extrap;
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outliers = xi < minx | ! (xi <= maxx); # this even catches NaNs
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if (size_equal (outliers, yi))
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yi(outliers) = extrap;
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yi = reshape (yi, szx);
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elseif (! isvector (yi))
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yi(outliers, :) = extrap;
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yi(outliers.') = extrap;
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%! h = plot (x, interp1 (x1, y1, x), 'b', x1, y1, 'sb');
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%! g = plot (x, interp1 (x2, y2, x), 'r', x2, y2, '*r');
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%! legend ([h(1), g(1)], {'left-continous', 'right-continuous'}, ...
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%! 'location', 'east')
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%! axis ([0.5 3.5 -0.5 1.5])
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%! legend ([h(1), g(1)], {'left-continuous', 'right-continuous'}, ...
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%! 'location', 'northwest')
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%! %--------------------------------------------------------
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%! % red curve is left-continuos and blue is right-continuous at x = 2
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%! % red curve is left-continuous and blue is right-continuous at x = 2
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##FIXME: add test for n-d arguments here
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%!# test linear extrapolation
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## test extrapolation (linear)
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%!assert (interp1 ([1:5],[3:2:11],[0,6],"linear","extrap"), [1, 13], eps)
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%!assert (interp1 (xp, yp, [-1, max(xp)+1],"linear",5), [5, 5])
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## Basic sanity checks
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%!assert (interp1 (1:2,1:2,1.4,"nearest"), 1)
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%!assert (interp1 (1:2,1:2,1.4,"linear"), 1.4)
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%!assert (interp1 (1:4,1:4,1.4,"cubic"), 1.4)
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%!assert (interp1 (1:2,1:2,1.1, "spline"), 1.1)
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%!assert (interp1 (1:2,1:2,1.1,"spline"), 1.1)
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%!assert (interp1 (1:3,1:3,1.4,"spline"), 1.4)
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%!assert (interp1 (1:2:4,1:2:4,1.4,"*nearest"), 1)
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%!assert (interp1 ([3,2,1],[3,2,2],2.5), 2.5)
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%!assert (interp1 ([1,2,2,3,4],[0,1,4,2,1],[-1,1.5,2,2.5,3.5], "linear", "extrap"), [-2,0.5,4,3,1.5])
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%!assert (interp1 ([4,4,3,2,0],[0,1,4,2,1],[1.5,4,4.5], "linear"), [1.75,1,NA])
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%!assert (interp1 (0:4, 2.5), 1.5)
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## Left and Right discontinuities
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%!assert (interp1 ([1,2,2,3,4],[0,1,4,2,1],[-1,1.5,2,2.5,3.5], "linear", "extrap", "right"), [-8,2,4,3,1.5])
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%!assert (interp1 ([1,2,2,3,4],[0,1,4,2,1],[-1,1.5,2,2.5,3.5], "linear", "extrap", "left"), [-2,0.5,1,1.5,1.5])
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%% Test input validation
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%!error interp1 ()
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%!error interp1 (1,1,1, "linear")
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%!error interp1 (1,1,1, "*nearest")
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%!error interp1 (1,1,1, "*linear")
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%!error interp1 (1:2,1:2,1, "bogus")
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%!error interp1 (1,2,3,4,5,6,7)
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%!error <table too short> interp1 (1,1,1, "linear")
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%!error <table too short> interp1 (1,1,1, "*nearest")
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%!error <table too short> interp1 (1,1,1, "*linear")
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%!warning <multiple discontinuities> interp1 ([1 1 1 2], [1 2 3 4], 1);
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%!error <discontinuities not supported> interp1 ([1 1],[1 2],1, "pchip")
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%!error <discontinuities not supported> interp1 ([1 1],[1 2],1, "cubic")
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%!error <discontinuities not supported> interp1 ([1 1],[1 2],1, "spline")
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%!error <invalid method> interp1 (1:2,1:2,1, "bogus")
added
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scripts/general/interp1.m
