INTRP 1.50
A library of interpolation routines for the HP48G/GX
By Matthew Willis
29 October 1995
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Library: INTRP (#1658)
Version: 1.50
Purpose: Simple, powerful linear interpolation routines
Easy to use "input form" based interpolation,
Lookup table interpolation
Compatability: G/GX
Author: Matt Willis (mbw8@cornell.edu)
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Preamble:
Often in my studies I have had to look values up in tables.
For example, I might be interested in the density of water as a
function of temperature. If I have data specified in 5 degree (C)
increments, and I wanted to know the density at 21C then I'd have
to interpolate between the density at 20C and the density at 25C.
It's a trivial exercise to show that given any two points we can
specify a line. It's a repetitive, mistake-prone calculation,
though, and amenable to any shortcuts we can find. This library
includes three tools that will make interpolating a snap...
Overview:
INTRP - an interpolation tool you can use from
programs or the stack
e.g.
[ 1 2 ]
[ 2 2.5 ] 1.5 INTRP ---> 2.25
IINTRP - an interactive interpolation program that uses
the HP48G friendly input forms. Very easy to use.
LINTRP - an interpolation routine for a lookup table. You
can enter a whole table into your HP and let the HP
do all the figuring!
e.g.
[[ 1 1.5 ]
[ 2 2.0 ]
[ 4 3.0 ]] 3 LINTRP ---> 2.5
Using water density as an example, we could put all the
densities for 0 to 100C and then let the HP find the
density as a function of Temperature. More on this
later on.
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INSTALLING THE LIBRARY
I made this a library so that it would be easy to install. It
will run from any port, but for simplicity we'll assume you only
have port 0 on your calculator.
1) download the library onto your calculator from your computer
(use the pc link software)
the file is INTRP15.LIB
2) recall the library object to the stack, you should see
1: Library 1658: INT...
3) Type 0 STO
This will store the library in the 0 port
4) Turn your HP off, then on again
The library should be installed. You can verify this by looking
at the LIBRARY menu (right shift, library)
VERSION HISTORY
1.50
Rewritten in Sysrpl. Added error protection and checking.
Should be faster, more robust.
1.00
First version, mostly USER RPL code.
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COMMAND CATALOG:
INTRP
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Command line version of the interpolation routine.
Inputs
5: Real (X1)
4: Real (Y1)
3: complex 3: row vector 3: Real (X2)
2: complex 2: row vector 2: Real (Y2)
1: real 1: real 1: Real (X)
Returns
--> real --> real --> real
(or row vector)
Note that the real component of the complex number is the X
value and the imaginary component is the function.
Example: water density as a function of temperature.
Temp Density
20C 998.21kg/m3
25C 997.05kg/m3
Say we want the density at 21 degrees C:
(20,998.21) (25,997.05) 21 INTRP
gives F(21): 997.98
If we wanted to interpolate more than one variable, use the row
vector notation. Say we wanted to also find the absolute
viscosity at T=21C:
Temp Density Viscosity
20C 998.21kg/m3 1.000cp
25C 997.05kg/m3 0.890cp
To get the values at 21C:
[ 20 998.21 1.000 ] [ 25 997.05 0.890 ] 21 INTRP
gives
[ 21 997.98 0.978 ]
(To extract one of the numbers use ARRY-> or 2 GET, etc.)
If this all seems too hard, then look at IINTRP instead. It's
much much friendlier.
Note:
INTRP will extrapolate - but make sure you know what you're
doing. Ask yourself: does it make sense to extrapolate here?
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COMMAND CATALOG:
IINTRP
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Friendly, forms based interpolation. Very easy to use. You
don't have to remember the syntax of INTRP this way. Example:
*****interpolate*****
X1 1.0 F1 3.5
X2 3.0 F2 5.5 ----> 4.5
X 2
To start the IINTRP command:
1) type IINTRP, or
open the library menu (right shift, 2)
press INTRP, then IINTRP
How to use this screen to find the density of water at 21C:
X1: put the first temperature, 20, here
F1: put the first density, 998.21, here
X2: put the second temperature, 25, here
F2: put the second density, 997.05, here
X : put 21 here (what we actually want)
i.e. your screen should look like this:
*****interpolate*****
X1 20 F1 998.21
X2 25 F2 997.05
X 21
Now press the soft key with the "OK" on it.
You'll get your answer.
When you want to get really efficient:
1) start IINTRP
2) type 20, hit ENTER type 998.21, hit ENTER, type 25, hit
ENTER, type 997.05, hit ENTER, type 21 and hit ENTER twice.
Note:
IINTRP will extrapolate. Make sure you know that extrapolation
is valid for your data, or else your numbers won't mean much. For
example, does it make sense to extrapolate based on unemployment
figures in 1930 and 1935 to get unemployment figures in 1995?
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COMMAND CATALOG:
LINTRP
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The lookup interpolater. You can use this is any application
where you'd have to go look something up in a table. Think of it
as a replacement for tables. You enter the table of data on your
HP and the HP finds the proper points to interpolate between.
Note that this is pretty different from linear regression.
Input:
2: Matrix
1: Real
Output:
1: Row vector
Example:
I have some stream gauging data, depth as a function of X. I
want a function that returns the linearly interpolated depth as a
function of X.
1) store the stream data in a variable, 'STRM' with X data in
the first column of a matrix and depth in the second column:
'STRM'
[[ 0 0 ]
[ 2 0.5 ]
[ 3 0.6 ]
[ 5 0.2 ]
[ 6 0 ]]
2) create a user function that uses this data table:
'Sdepth'
<< -> X
<< STRM X LINTRP >>
>>
Now you can use the interpolant as a function, like 'Sdepth(x)'
Other uses:
You could put entire database for water characteristics as a
matrix, then could get viscosity, density, etc., from an HP
function rather than by looking it up in a table in a book.
Notes:
Unlike the first two programs, this one won't extrapolate.
This program doesn't check to see if your data is sorted. If
your data isn't sorted then your answer will not make sense.
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