GNU Info

(gnuplot.info)acsplines

---

Next: bezier Prev: smooth Up: smooth

---

Enter node , (file) or (file)node

 The `acsplines` option approximates the data with a "natural smoothing spline".
 After the data are made monotonic in x (see `smooth unique`
 (Note: unique )), a curve is piecewise constructed from segments of cubic
 polynomials whose coefficients are found by the weighting the data points; the
 weights are taken from the third column in the data file.  That default can be
 modified by the third entry in the `using` (Note: using ) list, e.g.,
       plot 'data-file' using 1:2:(1.0) smooth acsplines

 Qualitatively, the absolute magnitude of the weights determines the number
 of segments used to construct the curve.  If the weights are large, the
 effect of each datum is large and the curve approaches that produced by
 connecting consecutive points with natural cubic splines.  If the weights are
 small, the curve is composed of fewer segments and thus is smoother; the
 limiting case is the single segment produced by a weighted linear least
 squares fit to all the data.  The smoothing weight can be expressed in terms
 of errors as a statistical weight for a point divided by a "smoothing factor"
 for the curve so that (standard) errors in the file can be used as smoothing
 weights.

 Example:
       sw(x,S)=1/(x*x*S)
       plot 'data_file' using 1:2:(sw($3,100)) smooth acsplines