NEA-0590 AKIMA'S-SPLINE.

1. NAME OR DESIGNATION OF PROGRAM:  AKIMA'S-SPLINE.

3. DESCRIPTION OF PROBLEM OR FUNCTION

Interpolation from a given set  of data points in a plane and fitting a smooth curve to the points.

4. METHOD OF SOLUTION

The method is based on a piecewise function composed of a set of polynomials, each of degree three, at most, and applicable to successive intervals of the given points. The slope of the curve is determined at each given point locally, and each polynomial representing a portion of the curve between a pair of given points is determined by the coordinates of and the slopes at the points. Comparison indicates that the curve obtained by this method is closer to a manually drawn curve than curves found using other mathematical methods.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM:

6. TYPICAL RUNNING TIME

0.065 secs. for INTRPL with L = 10, N = 46.
0.070 secs. for CURVFT with L = 10, N = 46, MD = 1, M = 5.
0.1 secs for ITPLBV with N = 17, LX = 11, LY = 9.
0.2 secs. for SFCFIT with MX = 2, MY = 2, LX = 11, LY = 9.
(Times on the FACOM 230/75.)

7. UNUSUAL FEATURES OF THE PROGRAM

The method requires only straight- forward procedures rather than iterative solutions of equations with preassigned error tolerances which are required by some other methods.

8. RELATED AND AUXILIARY PROGRAMS

The code contains the following subroutines:

    INTRPL    Interpolates for uni-variate functions
    CURVFT    Curve fits for uni-variate functions
    ITPLBV    Interpolates for bi-variate functions
    SFCFIT    Surface fits for bi-variate functions

10. REFERENCES

- H. Akima:
  "A433, Interpolation and Smooth Curve Fitting Based on Local
   Procedures"
  Comm. ACM, 15, 10,914 (1972).
- H. Akima:
  "Method of Bivariate Interpolation and Smooth Surface Fitting
   Based on Local Procedures"
  Comm. ACM, 17, 18 (1974).
- H. Akima:
"A474, Bivariate Interpolation and Smooth Surface Fitting Based on     Local Procedures"
  Comm. ACM, 17, 26 (1974).
- T. Ise and T. Fujimura:
  "Recent Algorithms and Computer Programs for Interpolation"
  Information Processing Society of Japan, 17, 417 (1976)
  (in Japanese).

- H. Akima:
  "A New Method of Interpolation and Smooth Curve Fitting Based on
  Local Procedures"
  J. ACM 17, 589-602 (1970).
- T. Ise, T. Tsutsui and N. Saitoh:
  "How to Use Akima's Interpolation Program Package (AKIMA'S
  SPLINE)"
- T. Ise and T. Tsutsui:
  "Computer Programs for Interpolations (Development and Benchmark
  Test of SSL, No. 3)"
  JAERI-M 7419 (extract of pages in English - incomplete) (1977)

11. MACHINE REQUIREMENTS

The number of words required for each sub- routine is:
INTRPL    600
CURVFT    800
ITPLBV   1600
SFCFIF   1400

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:

15. NAME AND ESTABLISHMENT OF AUTHOR

          T. Ise, T. Tsutsui and N. Saitoh
          Division of Reactor Engineering
          Tokai Research Establishment
          JAERI
          Japan.

File name	File description	Records
NEA0590_01.001	INFORMATION	11
NEA0590_01.002	INTRPL ROUTINE SOURCE (F4,EBCDIC)	166
NEA0590_01.003	CURVFT ROUTINE SOURCE (F4,EBCDIC)	206
NEA0590_01.004	ITPLBV ROUTINE SOURCE (F4,EBCDIC)	500
NEA0590_01.005	SFCFIT ROUTINE SOURCE (F4,EBCDIC)	403
NEA0590_01.006	TEST PROGRAM SOURCE FOR INTRPL (F4,EBCDIC)	42
NEA0590_01.007	SAMPLE INPUT FOR INTRPL PROBLEM	14
NEA0590_01.008	SAMPLE OUTPUT OF INTRPL PROBLEM	25
NEA0590_01.009	TEST PROGRAM SOURCE FOR CURVFT (F4,EBCDIC)	44
NEA0590_01.010	SAMPLE INPUT FOR CURVFT PROBLEM	6
NEA0590_01.011	SAMPLE OUTPUT OF CURVFT PROBLEM	25
NEA0590_01.012	TEST PROGRAM SOURCE FOR ITPLBV (F4,EBCDIC)	58
NEA0590_01.013	SAMPLE INPUT FOR ITPLBV PROBLEM	34
NEA0590_01.014	SAMPLE OUTPUT OF ITPLBV PROBLEM	71
NEA0590_01.015	TEST PROGRAM SOURCE FOR SFCFIT (F4,EBCDIC)	70
NEA0590_01.016	SAMPLE INPUT FOR SFCFIT PROBLEM	28
NEA0590_01.017	SAMPLE OUTPUT OF SFCFIT PROBLEM	97