Python Wrapper around the Fortran TSPACK.

The primary purpose of TSPACK is to construct a smooth function which interpolates a discrete set of data points. The function may be required to have either one or two con- tinuous derivatives, and, in the C-2 case, several options are provided for selecting end conditions. If the accuracy of the data does not warrant interpolation, a smoothing func- tion (which does not pass through the data points) may be constructed instead. The fitting method is designed to avoid extraneous inflection points (associated with rapidly varying data values) and preserve local shape properties of the data (monotonicity and convexity), or to satisfy the more general constraints of bounds on function values or first derivatives. The package also provides a parametric representation for con- structing general planar curves and space curves.

The fitting function h(x) (or each component h(t) in the case of a parametric curve) is defined locally, on each interval associated with a pair of adjacent abscissae (knots), by its values and first derivatives at the endpoints of the interval, along with a nonnegative tension factor SIGMA associated with the interval (h is a Hermite interpolatory tension spline). With SIGMA = 0, h is the cubic function defined by the endpoint values and derivatives, and, as SIGMA increases, h approaches the linear interpolant of the endpoint values. Since the linear interpolant preserves positivity, monotonicity, and convexity of the data, h can be forced to preserve these properties by choosing SIGMA sufficiently large. Also, since SIGMA varies with intervals, no more tension than necessary is used in each interval, resulting in a better fit and greater efficiency than is achieved with a single constant tension factor.