Computer Programs
NEA-0590 AKIMA'S-SPLINE.
last modified: 01-JUL-1980 | catalog | categories | new | search |

# NEA-0590 AKIMA'S-SPLINE.

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

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1. NAME OR DESIGNATION OF PROGRAM:  AKIMA'S-SPLINE.
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2. COMPUTERS
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Program name Package id Status Status date
AKIMA'S-SPLINE NEA-0590/01 Tested 01-JUL-1980

Machines used:

Package ID Orig. computer Test computer
NEA-0590/01 IBM 3033 IBM 3033
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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.
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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.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM:
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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.)
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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.
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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
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9. STATUS
Package ID Status date Status
NEA-0590/01 01-JUL-1980 Tested on behalf of NEADB
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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, included references:
- 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)
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11. MACHINE REQUIREMENTS

The number of words required for each sub- routine is:
INTRPL    600
CURVFT    800
ITPLBV   1600
SFCFIF   1400
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NEA-0590/01 FORTRAN-IV
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:
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15. NAME AND ESTABLISHMENT OF AUTHOR

T. Ise, T. Tsutsui and N. Saitoh
Division of Reactor Engineering
Tokai Research Establishment
JAERI
Japan.
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16. MATERIAL AVAILABLE
NEA-0590/01
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
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17. CATEGORIES
• O. Experimental Data Processing
• P. General Mathematical and Computing System Routines

Keywords: data processing, interpolation, polynomials.