The Museum of HP Calculators The Museum of HP Calculators
This program was written by Jose M.Perez, Xose.
This program is supplied without representation or warranty of any kind. The author and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.
'Fitter' is the proper tool to FIT any data to any function in the way: y = a1 × f1(x) + a2 × f2(x) + a3 × f3(x) + .... The functions f1, f2, f3,... must be programmed in a very simple way: the index will be passed to the functions program through register 00, the program will then jump to the specified function that will operate over X (at register X) and Y (at register Y). A sample:
Imagine we are trying to fit some data to a function of the kind: y = a + b × sin(x) + c × cos(x), all we have to do is to write a program like this:
LINE KEYS 000 { 19-Byte Prgm } 001 ▶LBL "FNC" ; 002 GTO IND 00 ; 003 LBL 01 ; f1(x) 004 1 ; 005 RTN ; 006 LBL 02 ; f2(x) 007 SIN ; 008 RTN ; 009 LBL 03 ; f3(x) 010 COS ; 011 RTN ; 012 END ;
Notice the first function is index 1, not 0!!
Although this is the general template to use sometimes we can save a few bytes.
For instance, a program to fit data to any polinomy can be written this way:
LINE KEYS 000 { 14-Byte Prgm } 001 ▶LBL "POLY" ; 002 RCL 00 ; 003 1 ; 004 - ; 005 yx ; 006 RTN ; 007 END ;
Later, on the menu we will be able to specify the grade of the polinomy by setting the number of functions.
Input: Through menu...
Sum+: enters data pair (just like normal sum+)
Sum-: deletes or corrects data.
#F: enters number of funcions (X register), resets data.
FNC: allows you to enter the name of the program with the
functions definitions.
CLsum: deletes global variables from memory.
GO: calculates coeficients.
(EXIT to EXIT ;)
Output:
X: [ ?x1 Matrix ], matrix with the calculated coeficients (a1 = 1:1, a2 = 2:1, ...)
Once inside the program menu the first thing you have to do is indicate the name the program which contains the functions and the number of them (options 'FNC' and '#F'). Then begin to enter data pairs the same way as usual statistics (X value, Y value and 'sum+'), if you enter wrong data by mistake just press 'R↓' (the data pair remains in registers Y and Z) and then 'sum-'.
One important thing: exiting the program (by pressing 'EXIT' or 'GO') does not delete previous entered data. '#F' resets data and 'CLsum' purges data variables.
How to manipulate data before enter it with functions such as 'LN' or '1/X' which are on the top row?
Since exiting the program does not clear data variables, just press 'EXIT', manipulate the data and re-enter 'FITTER', then press 'sum+' (do not re-inicialize with '#F'!)
How to reset data variables
Just re-enter the number of functions and press '#F'.
We've got the following data:
X | Y
----+----
3 | 26
4 | 46
5 | 72
6 | 104
7 | 142
and we want to fit it to a second degree polynomy or parabola. First introduce the program 'POLY' we've already talked about. Then enter FITTER (XEQ FTTR).
3 #F FNC NOPQ P NOPQ O JKLM L WXYZ Y R/S
Then begin to enter data pairs (there's an about 6 seconds delay after each entry):
3 ENTER 26 SUM+
4 ENTER 46 SUM+
5 ENTER 62 SUM+
R↓ SUM-
5 ENTER 72 SUM+
6 ENTER 104 SUM+
7 ENTER 142 SUM+
As you can see, I made a mistake when entering the third pair, so I deleted it and re-entered the correct data.
GO SHIFT MATRIX EDIT
(element 1:1 is 2)
→ (element 2:1 is -1)
→ (element 3:1 is 3)
EXIT EXIT
So the parabola is y = 2 - X + 3 × X2, which fits exactly (it does not have to fit exactly in general, the program will give the best approximation, but in this case the data pairs were calculated from the parabola itself so the answer is exact).
XEQ FTTR CLSUM EXIT
As I have already told there's a short delay after each entry (about 6 seconds for the sample problem). The delay depends mainly on the number of functions and their complexity. Of course you can accelerate the calculator in fast-mode (but pressing 'EXIT' will return it to its normal state...)
LINE KEYS 000 { 316-Byte Prgm } 001 ▶LBL "FTTR" ; 002 CLMENU ; 003 "sum+" ; 004 KEY 1 XEQ 22 ; 005 "sum-" ; 006 KEY 2 XEQ 21 ; 007 "#F" ; 008 KEY 3 XEQ 23 ; 009 "FNC" ; 010 KEY 4 XEQ 24 ; 011 "CLsum" ; 012 KEY 5 XEQ 25 ; 013 "GO" ; 014 KEY 6 GTO 10 ; 015 KEY 9 GTO 11 ; 016 MENU ; 017 LBL 01 ; 018 STOP ; 019 GTO 01 ; 020 ▶LBL 10 ; GO 021 RCL "c" ; 022 RCL "a" ; 023 ÷ ; 024 ▶LBL 11 ; EXIT 025 CLMENU ; 026 EXITALL ; 027 RTN ; 028 ▶LBL 21 ; sum- 029 RCL "n" ; 030 X=0? ; 031 GTO 99 ; 032 SF 81 ; 033 ▶LBL 22 ; sum+ 034 FS? 81 ; 035 R↓ ; 036 STO 10 ; stores data 037 X⇔Y ; 038 STO 09 ; 039 X⇔Y ; 040 ENTER ; 041 SF 25 ; generates temporary matrix "b" 042 RCL "f" ; and inizilizes row counter 043 FS?C 25 ; 044 X=0? ; 045 GTO 99 ; 046 ENTER ; 047 STO 00 ; 048 NEWMAT ; 049 1 ; 050 + ; 051 STO "b" ; 052 LBL 02 ; 053 RCL 09 ; 054 RCL 10 ; 055 RCL 09 ; 056 SF 25 ; 057 XEQ IND "fx" ; calculates fn(X) 058 FC?C 25 ; 059 GTO 99 ; 060 RCL 00 ; 061 XEQ 30 ; multiplies actual row and column 062 XEQ 30 ; of "b" by fn(X) 063 INDEX "c" ; adds fn(X)×Y to actual row of "c" 064 1 ; 065 STOIJ ; 066 R↓ ; 067 RCLEL ; 068 RCL 10 ; 069 RCL× ST T ; 070 FS? 81 ; substracts if 'sum-' 071 +/- ; 072 + ; 073 STOEL ; 074 1 ; 075 STO- 00 ; 076 RCL 00 ; 077 X≠0? ; 078 GTO 02 ; 079 R↓ ; adds or substracts "b" to "a" 080 RCL "b" ; 081 FC?C 81 ; 082 GTO 03 ; 083 +/- ; 084 X⇔Y ; 085 +/- ; 086 X⇔Y ; 087 LBL 03 ; 088 STO+ "a" ; 089 X⇔Y ; 090 STO+ "n" ; 091 CLV "b" ; restores stack 092 RCL 09 ; 093 RCL 10 ; 094 RCL "n" ; shows actual data counter 095 RTN ; 096 ▶LBL 23 ; #F 097 IP ; 098 ENTER ; 099 X≤0? ; 100 GTO 99 ; 101 STO "f" ; stores new "f" 102 ENTER ; 103 1 ; 104 NEWMAT ; 105 STO "c" ; resets "c" 106 R↓ ; 107 ENTER ; 108 NEWMAT ; 109 STO "a" ; resets "a" 110 0 ; 111 STO "n" ; resets data counter 112 RTN ; 113 ▶LBL 24 ; FNC 114 CLA ; 115 SF 25 ; 116 RCL "fx" ; 117 CF 25 ; 118 STR? ; 119 ARCL ST X ; 120 AON ; 121 STOP ; 122 AOFF ; 123 ASTO "fx" ; 124 R↓ ; 125 RTN ; 126 ▶LBL 25 ; CLsum 127 CLV "c" ; 128 CLV "a" ; 129 CLV "n" ; 130 CLV "fx" ; 131 CTV "f" ; 132 RTN ; 133 ▶LBL 30 ; multiplies "b" matrix row (X) 134 INDEX "b" ; by a given number (Y) 135 1 ; 136 STOIJ ; 137 R↓ ; 138 LBL 04 ; 139 RCLEL ; 140 RCL× ST Z ; 141 STOEL ; 142 J+ ; 143 R↓ ; 144 FC? 76 ; 145 GTO 04 ; 146 RCL "b" ; 'rotates' the matrix to do the 147 TRANS ; same with the columns 148 STO "b" ; 149 R↓ ; 150 RTN ; 151 ▶LBL 99 ; error rutine 152 R↓ ; 153 TONE 0 ; 154 CF 81 ; 155 RTN ; 156 END ;
a: Matrix of Sum(fn(X)×fm(X))
b: Temporary matrix of fn(X)×fm(X) products
c: Matrix of Y×fn(X) products
fx: Contains the name of the program with the
functions definitions
f: Number of functions in 'fx'
n: Number of entered data pairs
00: Actual function (use it in 'fx')
25: Deactivates errors (system flag) 76: Indicates row jump on a matrix (system flag) 81: Set if sum-, cleared if sum+ (user flag)
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