POLY_SMOOTH

       Apply a least-squares (Savitzky-Golay) polynomial smoothing filter

       Reduce noise in 1-D data (e.g. time-series, spectrum) but retain
       dynamic range of variations in the data by applying a least squares
       smoothing polynomial filter,
       Also called the Savitzky-Golay smoothing filter, cf. Numerical
       Recipes (Press et al. 1992, Sec.14.8)
       The low-pass filter coefficients are computed by effectively
       least-squares fitting a polynomial in moving window,
       centered on each data point, so the new value will be the
       zero-th coefficient of the polynomial. Approximate first derivates
       of the data can be computed by using first degree coefficient of
       each polynomial, and so on. The filter coefficients for a specified
       polynomial degree and window width are computed independent of any
       data, and stored in a common block. The filter is then convolved
       with the data array to result in smoothed data with reduced noise,
       but retaining higher order variations (better than SMOOTH).
       This procedure became partially obsolete in IDL V5.4 with the
       introduction of the SAVGOL function, which computes the smoothing
       coefficients.

       spectrum = poly_smooth( data, [ width, DEGREE = , NLEFT = , NRIGHT =
                                       DERIV_ORDER = ,COEFF = ]

       data = 1-D array, such as a spectrum or time-series.
       width = total number of data points to use in filter convolution,
               (default = 5, using 2 past and 2 future data points),
               must be larger than DEGREE of polynomials, and a guideline is to
               make WIDTH between 1 and 2 times the FWHM of desired features.

       DEGREE = degree of polynomials to use in designing the filter
               via least squares fits, (default DEGREE = 2)
               The higher degrees will preserve sharper features.
       NLEFT = # of past data points to use in filter convolution,
               excluding current point, overrides width parameter,
               so that width = NLEFT + NRIGHT + 1.  (default = NRIGHT)
       NRIGHT = # of future data points to use (default = NLEFT).
       DERIV_ORDER = order of derivative desired (default = 0, no derivative).

       COEFFICIENTS = optional output of the filter coefficients applied,
               but they are all stored in common block for reuse, anyway.

       Function returns the data convolved with polynomial filter coefs.

       Given a wavelength - flux spectrum (w,f), apply a 31 point quadratic
       smoothing filter and plot
       IDL> plot, w, poly_smooth(f,31)

       common poly_smooth, degc, nlc, nrc, coefs, ordermax

       As described in Numerical Recipies, 2nd edition sec.14.8,
       Savitsky-Golay filter.
       Matrix of normal eqs. is formed by starting with small terms
       and then adding progressively larger terms (powers).
       The filter coefficients of up to derivative ordermax are stored
       in common, until the specifications change, then recompute coefficients.
       Coefficients are stored in convolution order, zero lag in the middle.

       Written, Frank Varosi NASA/GSFC 1993.
       Converted to IDL V5.0   W. Landsman   September 1997

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