One-dimensional Interpolation and Fitting, Splines

The routines for this sort of application (and their origins) are:

• PDA_BSPDOC (SLATEC/CAMSUN)
  Documentation for BSPLINE, a package of subprograms for working with piecewise polynomial functions in B-representation.
• PDA_DBINTK (SLATEC/CAMSUN)
  Compute the B-representation of a spline which interpolates given data. The knots must be given.
• PDA_DEFC (SLATEC/CAMSUN)
  Fit a piecewise polynomial curve to discrete data. The piecewise polynomials are represented as B-splines. The fitting is done in a weighted least squares sense.
• PDA_DBVALU (SLATEC/CAMSUN)
  Evaluate the B-representation of a B-spline at X for the function value or any of its derivatives.
• PDA_DBSQAD (SLATEC/CAMSUN)
  Compute the integral of a K-th order B-spline using the B-representation.

• PDA_CURFIT (DIERCKX/NETLIB)
  Determine a smooth spline approximation of degree k to the given set of data points. The knots can be given, or can be determined by the routine.
• PDA_SPLEV (DIERCKX/NETLIB)
  Evaluates in a number of points x(i) a spline s(x) of degree k, given in its B-spline representation.
• PDA_SPLDER (DIERCKX/NETLIB)
  Evaluates in a number of points x(i) the derivative of order NU of a spline s(x) of degree k, given in its B-spline representation.
• PDA_SPLINT (DIERCKX/NETLIB)
  Calculates the integral of a spline function s(x) of degree k, which is given in its normalised B-spline representation.

• PDA_DPLINT (SLATEC/CAMSUN)
  Produce the polynomial which interpolates a set of discrete data points.
• PDA_DPOLVL (SLATEC/CAMSUN)
  Calculate the value of a polynomial and its first NDER derivatives where the polynomial was produced by a previous call to PDA_DPLINT.
• PDA_DPOLCF (SLATEC/CAMSUN)
  Compute the coefficients of the polynomial fit (including Hermite polynomial fits) produced by a previous call to PDA_DPLINT.

• PDA_DPOLFT (SLATEC/CAMSUN)
  Fit discrete data in a least squares sense by polynomials in one variable. Uses weights.
• PDA_DP1VLU (SLATEC/CAMSUN)
  Use the coefficients generated by PDA_DPOLFT to evaluate the polynomial fit of degree L, along with the first NDER of its derivatives, at a specified point.
• PDA_DPCOEF (SLATEC/CAMSUN)
  Convert the PDA_DPOLFT coefficients to Taylor series form.