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## Purpose

Quadratic interpolation of X,Y vectors onto a new X grid

## Explanation

Interpolate a function Y = f(X) at specified grid points using an
average of two neighboring 3 point quadratic (Lagrangian) interpolants.
Use LINTERP for linear interpolation

## Calling Sequence

QUADTERP, Xtab, Ytab, Xint, Yint, [ MISSING = ]

## Input

Xtab - Vector (X TABle) containing the current independent variable
Must be either monotonic increasing or decreasing
Ytab - Vector (Y TABle) containing the dependent variable defined
at each of the points of XTAB.
Xint - Scalar or vector giving the values of X for which interpolated
Y values are sought

## Output

Yint - Interpolated value(s) of Y, same number of points as Xint

## Optional Input Keyword

MISSING - Scalar specifying Yint value(s) to be assigned, when Xint
value(s) are outside of the range of Xtab. Default is to
truncate the out of range Yint value(s) to the nearest value
of Ytab. See the help for the INTERPOLATE function.

## Method

3-point Lagrangian interpolation. The average of the two quadratics
derived from the four nearest points is returned in YTAB. A single
quadratic is used near the end points. VALUE_LOCATE is used
to locate center point of the interpolation.

## Notes

QUADTERP provides one method of high-order interpolation. The
RSI interpol.pro function includes the following alternatives:
interpol(/LSQUADRATIC) - least squares quadratic fit to a 4 pt
neighborhood
interpol(/QUADRATIC) - quadratic fit to a 3 pt neighborhood
interpol(/SPLINE) - cubic spline fit to a 4 pt neighborhood
Also, the IDL Astro function HERMITE fits a cubic polynomial and its
derivative to the two nearest points.

## Restrictions

Unless MISSING keyword is set, points outside the range of Xtab in
which valid quadratics can be computed are returned at the value
of the nearest end point of Ytab (i.e. Ytab[0] and Ytab[NPTS-1] ).

## Example

A spectrum has been defined using a wavelength vector WAVE and a
flux vector FLUX. Interpolate onto a new wavelength grid, e.g.
IDL> wgrid = [1540.,1541.,1542.,1543.,1544.,1545.]
IDL> quadterp, wave, flux, wgrid, fgrid

FGRID will be a 5 element vector containing the quadratically
interpolated values of FLUX at the wavelengths given in WGRID.
EXTERNAL ROUTINES:
ZPARCHECK

## Revision History

31 October 1986 by B. Boothman, adapted from the IUE RDAF
12 December 1988 J. Murthy, corrected error in Xint
September 1992, W. Landsman, fixed problem with double precision
August 1993, W. Landsman, added MISSING keyword
June, 1995, W. Landsman, use single quadratic near end points
Converted to IDL V5.0 W. Landsman September 1997
Fix occasional problem with integer X table,
YINT is a scalar if XINT is a scalar W. Landsman Dec 1999
Use VALUE_LOCATE instead of TABINV W. Landsman Feb. 2000

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