LIP: The Livermore Interpolation Package Version 1.1

Fritsch, F N

关键词: COMPATIBILITY;    DESIGN;    EFFICIENCY;    FUNCTIONALS;    INTERPOLATION;   

DOI  :  10.2172/957617
RP-ID  :  LLNL-TR-406719-REV-1
PID  :  OSTI ID: 957617
Others  :  TRN: US201002%%309

学科分类：社会科学、人文和艺术（综合）

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来源: SciTech Connect

【 摘 要 】

This report describes LIP, the Livermore Interpolation Package. Because LIP is a standalone version of the interpolation package in the Livermore Equation of State (LEOS) access library, the initials LIP alternatively stand for the 'LEOS Interpolation Package'. LIP was totally rewritten from the package described in. In particular, the independent variables are now referred to as x and y, since the package need not be restricted to equation of state data, which uses variables {rho} (density) and T (temperature). LIP is primarily concerned with the interpolation of two-dimensional data on a rectangular mesh. The interpolation methods provided include piecewise bilinear, reduced (12-term) bicubic, and bicubic Hermite (biherm). There is a monotonicity-preserving variant of the latter, known as bimond. For historical reasons, there is also a biquadratic interpolator, but this option is not recommended for general use. In addition to direct interpolation of two-dimensional data, LIP includes a facility for inverse interpolation (at present, only in the second independent variable). For completeness, however, the package also supports a compatible one-dimensional interpolation capability. Parametric interpolation of points on a two-dimensional curve can be accomplished by treating the components as a pair of one-dimensional functions with a common independent variable. LIP has an object-oriented design, but it is implemented in ANSI Standard C for efficiency and compatibility with existing applications. First, a 'LIP interpolation object' is created and initialized with the data to be interpolated. Then the interpolation coefficients for the selected method are computed and added to the object. The current version has options to instead estimate derivative values or merely store data in the object. It is then possible to pass the object to functions that interpolate or invert the interpolant at an arbitrary number of points. The first section of this report describes the overall design of the package, including both forward and inverse interpolation. Sections 2-5 describe each interpolation method in detail. The software that implements this design is summarized function-by-function in Section 6. For a complete example of package usage, refer to Section 7. The report concludes with a few brief notes on possible software enhancements. For guidance on adding other functional forms to LIP, refer to Appendix B. The reader who is primarily interested in using LIP to solve a problem should skim Section 1, then skip to Sections 6.1-4. Finally, jump ahead to Section 7 and study the example. The remaining sections can be referred to in case more details are desired. Changes since the previous version of this document include the new Section 1.4 that discusses partial setup options and Section 6.3 that discusses the new function lip{_}setup{_}interp that implements them. Section 6.1 and the example in Section 7 have been modified accordingly.