Home > freetb4matlab > polynomial > spline.m

spline

PURPOSE ^

%

SYNOPSIS ^

function ret = spline (x, y, xi)

DESCRIPTION ^

% -*- 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

CROSS-REFERENCE INFORMATION ^

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