NEA-0590: AKIMA'S-SPLINE, Curve and Surface Fit of Uni-Variate and Bi-Variate Function

OECD Nuclear Energy Agency / L'Agence pour l'énergie nucléaire

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NEA-0590 AKIMA'S-SPLINE. (Abstract last modified 01-JUL-1980)

AKIMA'S-SPLINE, Curve and Surface Fit of Uni-Variate and Bi-Variate Function

Abstract Table of Contents:

OPERATING SYSTEM

OTHER RESTRICTIONS

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

2. COMPUTER FOR WHICH PROGRAM IS DESIGNED AND OTHER MACHINE VERSION PACKAGES AVAILABLE -

To request or retrieve programs click on the one of the active versions below. A password and special authorization is required.

Explanation of the status codes.

Program-name Package-ID Status AKIMA'S-SPLINE NEA-0590/01 Tested

Machines used: Package-ID Orig.Computer Test Computer NEA-0590/01 IBM 3033 IBM 3033

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

9. STATUS
NEA-0590/01: 01-JUL-1980 Tested on behalf of NEADB

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).
NEA-0590/01:
- 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

12. PROGRAMMING LANGUAGE(S) USED -
NEA-0590/01: FORTRAN-IV

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.

16. MATERIAL AVAILABLE -
NEA-0590/01:
NEA0590_01.001    INFORMATION                                        11 records
NEA0590_01.002    INTRPL ROUTINE SOURCE (F4,EBCDIC)                 166 records
NEA0590_01.003    CURVFT ROUTINE SOURCE (F4,EBCDIC)                 206 records
NEA0590_01.004    ITPLBV ROUTINE SOURCE (F4,EBCDIC)                 500 records
NEA0590_01.005    SFCFIT ROUTINE SOURCE (F4,EBCDIC)                 403 records
NEA0590_01.006    TEST PROGRAM SOURCE FOR INTRPL (F4,EBCDIC)         42 records
NEA0590_01.007    SAMPLE INPUT FOR INTRPL PROBLEM                    14 records
NEA0590_01.008    SAMPLE OUTPUT OF INTRPL PROBLEM                    25 records
NEA0590_01.009    TEST PROGRAM SOURCE FOR CURVFT (F4,EBCDIC)         44 records
NEA0590_01.010    SAMPLE INPUT FOR CURVFT PROBLEM                     6 records
NEA0590_01.011    SAMPLE OUTPUT OF CURVFT PROBLEM                    25 records
NEA0590_01.012    TEST PROGRAM SOURCE FOR ITPLBV (F4,EBCDIC)         58 records
NEA0590_01.013    SAMPLE INPUT FOR ITPLBV PROBLEM                    34 records
NEA0590_01.014    SAMPLE OUTPUT OF ITPLBV PROBLEM                    71 records
NEA0590_01.015    TEST PROGRAM SOURCE FOR SFCFIT (F4,EBCDIC)         70 records
NEA0590_01.016    SAMPLE INPUT FOR SFCFIT PROBLEM                    28 records
NEA0590_01.017    SAMPLE OUTPUT OF SFCFIT PROBLEM                    97 records

17. CATEGORIES -

- O. Experimental Data Processing
- P. General Mathematical and Computing System Routines

Keywords: DATA PROCESSING, INTERPOLATION, POLYNOMIALS

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