A report on the computer routine INTERP3 is presented. The routine is designed to linearly interpolate a variable which is a function of three independent variables. The variables within the parameter arrays do not have to be distinct, or equally spaced, and the array variables can be in increasing or decreasing order

Hill, D. C.

Morris, S. J., Jr.

English

NASA Technical Reports Server

NASA Technical Memorandum 80070 
(N AS A-TH-800 70) INTERP3 : A COHPUTFE N79- 2 1 800 
R O U T I N E  FOR LINEAR IITERPCILATTOI O F  
T R I V A R I A T E  FUNCTIONS DEFINED ET NONDISTXICT 
U N E Q U 4 L L Y  SPACED VARIABLES (NASA) 15 p RC Unclas 
A92/nF A01 CSCL 09E G3/61 23952 
IfJTERP3 - A CMPUTER ROUTINE FOR 
LINEAR INTERPOLATION OF TRIVARIATE 
FUNCTIONS DEFINED BY NOND ISTIWCT 
UNEQUALLY SPACED VARIABLES 
~ E N I S E  C, HILL AND SHELBY J, MORRIS, JR, 
MARCH 1979 
National AerGnaurics and 
Space Adrninistrdtion 
Langley Research Center 
Hamp!on. Virginia 23665 
https://ntrs.nasa.gov/search.jsp?R=19790013629 2020-03-22T00:15:12+00:00Z
INTERP3 - A COMPUTER ROUTINE FOR LINEAR INTERPOLATION 
OF TRIVARIATE FUNCTIONS DEFINED BY NONOISTINCT 
UNEQUALLY SPACED VARIABLES 
Denise C. H i l l  and Shelby J. Morr is,  Jr. 
Langley Research Center 
Ham?ton, V i r g i n i a  23665 
SUMMARY 
INTERP3 i s  a computer rou t i ne  designed t o  l i n e a r l y  i n t e r p o l a t e  a var iab le  
which i s  a func t ion  o f  three independent parameters. 
var iab les wit!,in the parameter arrays do n o t  have t o  be d i s t i n c t ,  o r  equal ly  
spaced, and the array var iab les can be i n  increas ing o r  decreasing order. 
It i s  unique i n  t h a t  the  
INTRODUCTION 
The type o f  t r i v a r i a t e  funct ions which can be evaluated by e x i s t i n g  in te rpo la -  
t i o n  rout ines i s  severely l i m i t e d  by r e s t r i c t i o n s  imposed by the rout ines.  I n  
the Langley computer complex, the-e rou t ines  inc lude I T R I ,  which requires the 
parameter var iab les t o  be d i s t i n c t  and i n  a lgeb ra i ca l l y  increas ing order, and 
FUNGEN which assumes t h a t  the funct ion i s  known f o r  equal i n t e r v a l s  o f  the 
parameter var iables.  
The des i re  t o  use the computer f o r  l i n e a r  i n t e r p o l a t i o n  i n  a data tab le  o f  
p rope l le r  s l ipst ream charac ter is t i cs  generated the need f o r  a computer rou t ine  
t o  in te rpo la te  a t r i v a r i a t e  funccion def ined by nond is t inc t ,  unequally spaced 
parameter var iables.  INTERP3 i s  desigrted t o  f u l f i l l  t h a t  need. Furthermore, 
t h i s  rou t ine  allows th2 paralmter var iab les t o  be i n  increas ing o r  decreasing 
order. 
Descr ipt ion o f  Program 
This proaram performs l i n e a r  i n te rpo la t i on  f o r  a se t  o f  funct ions defined over 
the same se t  o f  independent parameter po ints .  By the use o f  m u l t i p l e  en t ry  
statements, IhTERP3 evaluates the funct ion a t  the po in t  (XIND, Y IND,  ZIND), 
producing a value WD, where: 
XIND = The inpu t  x parameter where i n t e r p o l a t i o n  i s  des i red 
YIND = The inpu t  y parameter where i n t e r p o l a t i o n  i s  des i red 
ZIND = The inpu t  t parameter where i n t e r p o l a t i o n  i s  des i red 
WD = The output in te rpo la ted  value o f  the  func t i on  a t  the  
p o i n t  (XIND, YIND, ZIND). 
Th is  program does no t  a l l ow  ext rapolat ion.  
data tab le  range, a warning i s  p r i n t e d  and WD w i l l  no t  be calc l r lated, bu t  
given the value of zero. 
If any inpu t  parameter exceeds the  
The names and descr ip t ions o f  the  subroutines are as follows: 
INTERP3 - Oumny main program t o  i n i t i a t e  ca lcu lat ions.  Control 
re tu rns  t o  t h i s  rou t i ne  a f t e r  evaluat ion o f  each i n p u t  
po int .  
XSEAR - Main rout ine.  Loads data tab le  and performs i n t e r -  
po la t i on  i n  X parameter array. 
YZSEAR - Performs i n t e r p o l a t i o n  i n  Y and 2 parameter arrays. 
WSEAR - Performs i n t e r p o l a t i o n  i n  W array. 
A FORTRAN l i s t i n g  o f  t h i s  program i s  presented i n  Appendix A, and a f low char t  
i s  presented i n  f i g u r e  1. 
Descr ip t ion of Data F i l e  
The data f i l e  contains a l l  tabu la r  values i n  the X, Y, 2, and W arrays.  The 
purpose o f  FORMAT 601 i s  t o  read these parameter values i n  the sequence x, y, 
z, w f o r  each record. To ensure t h a t  a l l  parameter values are read i n t o  the 
program, a record must be added t o  the end of the data tab le  f i l e  w i t h  dummy 
values t h a t  do not  equal the respect ive x, y, z, w values o f  the l a s t  t r u e  
record. 
the program. 
This ed i ted f i l e  must be placed a t  TAPES, p r i o r  t o  execution o f  
A sample case inc lud ing  data f i l e  and input/output l i s t i n g s  i s  presented i n  
Appendix B. 
CONCLUSION 
INTERP3 i s  a program designed t o  l i n e a r l y  i n te rpo la te  a var iab le  which i s  a 
funct ion o f  three independent parameters. 
the parameter arrays do no t  have t o  be d i s t i n c t ,  o r  equal ly  spaced and array 
values can be e i t h e r  a lgeb ra i ca l l y  increasing o r  decreasing. These features 
It i s  unique i n  t h a t  values w i t h i n  
2 
o f  INTERP3 give it a capacity o f  interpolating many di f ferent  kinds o f  tri- 
variate functions. 
3 
4 
d 0 0 0 0 d 0 0 
Z z 2 2 z z t z 
H Y U c( U U H U 
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4 
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APPENDIX 6 - SAHPLE CASE 
(a)  Data File Listing 
The following data f i l e  i s  listed as i t  would appear a t  TAPE5. 
FORMAT 601 reads the values x,y,z,w, respectively. 
arrangement of the values in each paramter array, and the last 
f i l e  record, which contains dumny values. 
Note the 
X 
5000 . 5000 
.5000 . 5000 
05000 
o5000 
5000 
.5000 
5 0 0 0  
.5500 
r5500 
5 500 
5 5 0 0  
a5500 
05500 
0 5 5 0 0  
.5500 
0 5 5 0 0  
5 500 
5 5 0 0  
5 500 
5 5 0 0  
05500 
05500  
05500 
6SOO 
06500 
0 6 5 0 0  
06  500 
0 6 5 0 0  
06500 
e 6 5 0 0  
e 6 5 0 0  
r6S00 
0 6 5 0 3  
ob500 
0 6 5 0 0  
0 6 5 0 0  
0.0000 
Y 
0 .oooo 
0 . 0000 
0.0060 
.2000 . zoo0 
.2000 . 2000 . 2000 
3.  coo0 
3 . 0000 
3 . 0000 
3 .OOOO 
3 .0000 
3 0000 
3 . 2 0 0 0  
3 2030 
3 02000 
3 2000 
3 0200G 
3 4000 
3 a 4 0 0 0  
3 C O O 0  
3 04000  
3 4000 
3 . 2 0 0 0  
3 .  2000 
", . 2000 
3 .  2000 
3 2000 
3 2 0 0 0  
3 . 2 0 0 0  
3 200C 
3 8 0 0 0  
3 .  8000 
3 .eo00 
3 . eo00 
0.0000 
o . aooo 
3 . eooo 
z 
2070 
0 3 4 2 0  
0 5 0 3 1  
e 6 8 4  8 
02000  . 4000 
6000 
8 0 0 0  
1.0000 
04 883 
06777 
1 0 6 7 5  
1 . 4 7 0 6  
1 . 8 8 6 1  
2.3118 . 3994 
1 .0255  
l e  4662 
1 9 2 0 4  
2 . 3 8 4 8  
3 0 0 8  
7 5 8 1  
1 .2318  
10 7 2 0 4  
2 . 2 2 1 7  
6 1 4 6  
0 8 3 1 8  
1.0530 
1 . 2 7 8 2  
1.5C70 
1 . 7 3 9 7  
1.9751 
2 . 2 1 3 2  
0 4 2 1 5  
9095 
1 . 5 7 5 8  
2 . 1 7 7 8  
2. 791 5 
0 .0000  
W 
e3280  
e4361  
0 5 1 4 2  
0 5 3 2 4  
e2905  
04 5 8 0  
05660 
6 1 4 0  
061 80 
0 1 3 4 5  
0 1 9 4 0  
0 3 0 5 6  
e4082 
05030  . 5 8 9 9  
e1564 
0 2 3 9 6  
0 3 8 4 8  
04 862 
05766 
a 0 5 5 5  
0 1 8 7 7  
308 7 
0 4 2 0 1  
0 5 2 1 7  
0 1 6 0 7  
0 2 2 2 7  
0 2  82 5 
03395 
394 1 
04469  
04 9 7 0  
5 4 4 1  
00 7 1  9 
0 2  1 6 0  
0 3 4 7 1  
. 4 6 5 5  
o s  72 G 
0 .0000  
11 
APPENDIX B - Concluded 
(b) Input /Output  Listing 
Compare the following input/output values to those presented in 
the sample data f i l e .  
extrapolation i s  attempted. 
Error messages will be printed whenever 
XIND. e 5 5 0 0  YIND. 3e0000 Z I N l  7 l e 4 7 0 0  WD* e 4 0 8 0  
XIND. e3000 YINO. 0 2 C O O  Z I N D B  e3000 YO. e 3 7 4 3  
XIND. e 5 5 0 0  YIND. 3.3000 ZING.  2.0000 HD. e 5 0 1 7  
I N P U T  VALUE OF X I N D  OUT OF X T A B L E  R A N G E  
XINO. e7000 Y I N D .  2 e 8 0 0 0  Z I N D B  a 2 5 0 0  W D ~ O e O 0 0 0  
12 
3 
0 
13 


INTERP3: A computer routine for linear interpolation of trivariate functions defined by nondistinct unequally spaced variables

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