help mata mm_polint()
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Title

    mm_polint() -- Polynomial interpolation and extrapolation


Syntax

        real vector mm_polint(x, y, xnew [, degree])

    where

            x:  real vector containing strictly monotone increasing or
                decreasing x-values

            y:  real vector containing associated y-values

         xnew:  real vector containing evaluation points

            d:  real scalar specifying degree of the polynomial (default: 1)


Description

    mm_polint() evaluates the interpolating polynomial through d+1
    (x,y)-points at the value xnew. x should be strictly monotone increasing
    or decreasing. The set of data points is chosen such that the x-values
    are centered around xnew. However, the set is bounded by 1 at the left
    and length(x) at the right. Furthermore, choosing a centered set of data
    points is only possible if d is uneven. In this case (d+1)/2 points are
    on each side of xnew. If d is even and x is in ascending order, then
    d/2+1 points are below xnew and d/2 above. If x is in descending order
    d/2 points are below and d/2+1 above.  Therefore, if d is even, the
    returned result depends on whether x is increasing or decreasing.

    d is the degree of the polynomial. The default is to use a polynomial of
    degree one, i.e. to compute the linear interpolation (d=1).


Remarks

    mm_polint() is based on a translation into Mata of the polint rountine
    given in Press et al. (1992:109-110).


Conformability

    mm_polint(x, y, xnew, degree):
           x: n x 1 or 1 x n
           y: n x 1 or 1 x n
        xnew: m x 1 or 1 x m
      degree: 1 x 1
      result: m x 1 or 1 x m.


Diagnostics

    mm_polint() requires x be in ascending or descending order.

    d must be an integer equal to one or larger and must be smaller than the
    number of input data points (i.e., d<length(x)).


Source code

    mm_polint.mata


References

    Press, William H., Saul A. Teukolsky, William T. Vetterling, Brian P.
        Flannery (1992). Numerical Recipes in C. The Art of Scientific
        Computing. Second Edition. Cambridge University Press.  
        http://www.numerical-recipes.com/


Author

    Ben Jann, ETH Zurich, jann@soz.gess.ethz.ch


Also see

    Online:  help for ipolate, mm_ipolate(), spline3(), [M-4] utility,