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SUBROUTINE GRFGD (X1,X,X2, Y1,Y,Y2, N, WORK, NINT, SIGMA, PL2)
C$ (Graph Derivative with Tensioned Spline Interpolation)
C$ Plot a graph by connecting interpolated values of the
C$ derivative of the splined curve by straight lines. The
C$ points defining the graph are taken from two arrays, one
C$ holding the X-values and one holding the Y-values. The
C$ respective scales are indicated by the values to be
C$ assigned to the margins of the graph.
C$
C$ Ordinarily, the margins would be given rounded values
C$ slightly larger than the extreme data values. However, the
C$ graph may be centered in various ways by assigning one or
C$ more margins considerably larger values. Likewise,
C$ excerpts from the graph may be chosen by giving the margins
C$ lesser values than the extremes. The arguments are:
C$
C$ X1..........X lower limit.
C$ X(N)........Array of X values in ascending order with no
C$ two values equal. This is necessary for the
C$ spline interpolation.
C$ X2..........X upper limit.
C$ Y1..........Y lower limit.
C$ Y(N)........Array of Y values.
C$ Y2..........Y upper limit.
C$ N...........Number of points.
C$ WORK(N,3)...Scratch array.
C$ NINT........Number of points to interpolate between X(1)
C$ and X(N).
C$ SIGMA.......Tensioned spline parameter (see FITC1
C$ comments).
C$ PL2.........2-D pen movement subroutine, usually PL2CA.
C$
C$ The derivative curve is determined by evaluating the
C$ derivatives of the tensioned spline function at the input
C$ data points, then resplining these to give an new
C$ interpolant which is then plotted. This is more
C$ satisfactory than plotting the derivative of the original
C$ interpolant, because that function has a linear first
C$ derivative and constant second derivative. The resplined
C$ derivative has a quadratic first derivative and linear
C$ second derivative.
C$ (21-JAN-83)