% -*- texinfo -*- % @deftypefn {Function File} {@var{pp} =} spline (@var{x}, @var{y}) % @deftypefnx {Function File} {@var{yi} =} spline (@var{x}, @var{y}, @var{xi}) % % Return the cubic spline interpolant of @var{y} at points @var{x}. % If called with two arguments, @code{spline} returns the piece-wise % polynomial @var{pp} that may later be used with @code{ppval} to % evaluate the polynomial at specific points. % If called with a third input argument, @code{spline} evaluates the % spline at the points @var{xi}. There is an equivalence % between @code{ppval (spline (@var{x}, @var{y}), @var{xi})} and % @code{spline (@var{x}, @var{y}, @var{xi})}. % % The variable @var{x} must be a vector of length @var{n}, and @var{y} % can be either a vector or array. In the case where @var{y} is a % vector, it can have a length of either @var{n} or @code{@var{n} + 2}. % If the length of @var{y} is @var{n}, then the 'not-a-knot' end % condition is used. If the length of @var{y} is @code{@var{n} + 2}, % then the first and last values of the vector @var{y} are the values % of the first derivative of the cubic spline at the end-points. % % If @var{y} is an array, then the size of @var{y} must have the form % @iftex % @tex % $$[s_1, s_2, \cdots, s_k, n]$$ % @end tex % @end iftex % @ifnottex % @code{[@var{s1}, @var{s2}, @dots{}, @var{sk}, @var{n}]} % @end ifnottex % or % @iftex % @tex % $$[s_1, s_2, \cdots, s_k, n + 2].$$ % @end tex % @end iftex % @ifnottex % @code{[@var{s1}, @var{s2}, @dots{}, @var{sk}, @var{n} + 2]}. % @end ifnottex % The array is then reshaped internally to a matrix where the leading % dimension is given by % @iftex % @tex % $$s_1 s_2 \cdots s_k$$ % @end tex % @end iftex % @ifnottex % @code{@var{s1} * @var{s2} * @dots{} * @var{sk}} % @end ifnottex % and each row of this matrix is then treated separately. Note that this % is exactly the opposite treatment than @code{interp1} and is done % for compatibility. % @seealso{ppval, mkpp, unmkpp} % @end deftypefn

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