Home > freetb4matlab > polynomial > pchip.m

pchip

PURPOSE ^

%

SYNOPSIS ^

function ret = pchip (x, y, xi)

DESCRIPTION ^

% -*- texinfo -*-
% @deftypefn {Function File} {@var{pp} =} pchip (@var{x}, @var{y})
% @deftypefnx {Function File} {@var{yi} =} pchip (@var{x}, @var{y}, @var{xi})
%
% Piecewise Cubic Hermite interpolating polynomial.  Called with two
% arguments, the piece-wise polynomial @var{pp} is returned, that may
% later be used with @code{ppval} to evaluate the polynomial at
% specific points.
%
% The variable @var{x} must be a strictly monotonic vector (either
% increasing or decreasing).  While @var{y} can be either a vector or
% array.  In the case where @var{y} is a vector, it must have a length
% of @var{n}.  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
% 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 in this matrix is then treated separately.  Note that this
% is exactly the opposite treatment than @code{interp1} and is done
% for compatibility.
%
% Called with a third input argument, @code{pchip} evaluates the 
% piece-wise polynomial at the points @var{xi}.  There is an equivalence
% between @code{ppval (pchip (@var{x}, @var{y}), @var{xi})} and
% @code{pchip (@var{x}, @var{y}, @var{xi})}.
%
% @seealso{spline, ppval, mkpp, unmkpp}
% @end deftypefn

CROSS-REFERENCE INFORMATION ^

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