Module rgsl::types::interpolation
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Interpolation
This chapter describes functions for performing interpolation. The library provides a variety of interpolation methods, including Cubic splines and Akima splines. The interpolation types are interchangeable, allowing different methods to be used without recompiling. Interpolations can be defined for both normal and periodic boundary conditions. Additional functions are available for computing derivatives and integrals of interpolating functions.
These interpolation methods produce curves that pass through each datapoint. To interpolate noisy data with a smoothing curve see Basis Splines.
Introduction
Given a set of data points (x_1, y_1) \dots (x_n, y_n) the routines described in this section compute a continuous interpolating function y(x) such that y(x_i) = y_i. The interpolation is piecewise smooth, and its behavior at the end-points is determined by the type of interpolation used.
Index Look-up and Acceleration
The state of searches can be stored in a gsl_interp_accel object, which is a kind of iterator for interpolation lookups. It caches the previous value of an index lookup. When the subsequent interpolation point falls in the same interval its index value can be returned immediately.
Higher-level Interface
The functions described in the previous sections required the user to supply pointers to the x and y arrays on each call. The following functions are equivalent to the corresponding gsl_interp functions but maintain a copy of this data in the gsl_spline object. This removes the need to pass both xa and ya as arguments on each evaluation.
References and Further Reading
Descriptions of the interpolation algorithms and further references can be found in the following books:
C.W. Ueberhuber, Numerical Computation (Volume 1), Chapter 9 “Interpolation”, Springer (1997), ISBN 3-540-62058-3. D.M. Young, R.T. Gregory A Survey of Numerical Mathematics (Volume 1), Chapter 6.8, Dover (1988), ISBN 0-486-65691-8.
Structs
| Interp | |
| InterpAccel |
evaluation accelerator |
| InterpType | |
| Spline |
general interpolation object |