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+# Copyright(c) 1986 Association of Universities for Research in Astronomy Inc.
+
+
+include	"bspln.h"
+
+.help fsplin	2	"math library"
+.ih
+NAME
+fsplin -- fast fit of b-spline interpolant.
+.ih
+USAGE
+fsplin (y, q, bspln)
+.ih
+PARAMETERS
+.ls y
+(real[n]).  Array of y-values of new data set.
+.le
+.ls q
+(real[(2*k-1)*n]).  Array containing the triangular factorization of the
+coefficient matrix of the linear system for the b-spline coefficients of
+the spline interpolant of dimension N and order K.  Q is produced by a
+prior call to SPLINE.
+.le
+.ls bspln
+(real[2*n+30]).  The spline descriptor array.  On input to FSPLIN, should
+contain a valid spline header (containing N, K, etc.), and knot array.
+As long as SPLINE is called before FSPLIN, the bspln array will be set up
+properly.  On output, the N b-spline coefficients are stored in BSPLN,
+ready for immediate input to SEVAL to evaluate the spline.
+.le
+.ih
+DESCRIPTION
+Fsplin is used following an initial SPLINE to efficiently fit a Kth order
+b-spline to a data set that differs from the data set input to SPLINE only
+in the y-values of the data points.  SPLINE and FSPLIN are used to
+interpolate an arbitrary array of data points (x,y), by fitting a piecewise
+Kth order curve, continuous in the first K-1 derivatives, through the
+data points.
+.ih
+SOURCE
+See Carl De Boor, "A Practical Guide to Splines", pg. 204-207.
+.ih
+SEE ALSO
+spline(2), seval(2)
+.endhelp ______________________________________________________________
+
+
+procedure fsplin (y, q, bspln)
+
+real	y[ARB], q[ARB]
+real	bspln[ARB]
+int	n, k, offset, i
+
+begin
+	offset = COEF1 - 1			#copy data into COEF array
+	do i = 1, NCOEF
+	    bspln[offset+i] = y[i]
+
+	n = NCOEF
+	k = ORDER
+
+	call banslv (q, 2*k - 1, n, k-1, k-1, bspln[offset+1])
+end