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HP35s - Regression and Geometric Program
06-21-2016, 01:26 PM
Post: #1
HP35s - Regression and Geometric Program
Hi all!

I wrote a (huge) program to calculate different regression curves for xy-pairs and some geometric and mechanic values (if the xy-pairs represent a closed polygon). In detail this program calculates:
* Regression with inverse function y=A+B/x
* Regression with constant function y=A
* Regression with linear function y=A+B.x
* Regression with quadratic function y=A+Bx+C.x^2
* Regression with logarithmic function y=A+B.ln(x)
* Regression with exponential function y=A.exp(B.x)
* Regression with ab-power-function y=A.B^x
* Regression with power function y=A.x^B
* Circumference of polygon
* Area of polygon
* Center of gravity coordinates (x,y)
* Second moments of inertia of area (Ixx, Iyy, Ixy)

I got most formulas from http://keisan.casio.com/menu/system/000000000395 (unfortunately a casio page) and https://en.wikipedia.org/wiki/Second_moment_of_area

The whole program is menu driven (see attachment; similar to the programs of stefanv):
* Main menu: SUM+ - c LR x^y^ G (add xy-pair, remove xy-pair, clear all, calculate parameters of regression, predict y and x values, calculate geometric data)
* Submenu calculate parameters: POLYNOM POWER (polynomical- or power-regression)
* Submenu calculate polynomical regression: x^-1 x^0 x^1 x^2 (inverse, constant, linear quadratic regression)
* Submenu calculate power regression: LN EXP AB PWR (logarithmic, exponential, ab-power, power)
* Submenu geometric: C A CGxy MD (circumference, area, center of gravity, moments of deviation)

Actually this program is close to the limits of the HP35s. I had to use EQN-formulas for prediction to use less then 1000 lines per label. "Meanwhile calculation" during the input of the xy-pairs needs "a second".

As this program does not use the intrinsic regression module of the HP35s, inputs with the SUM+-key are not possible ... instead 3 keys have to be pressed (R/S 1 R/S).

Example - Linear regression for x1,y1=1,4 and x2,y2=2,5:
* XEQs ENTER 3 R/S ... start and clear all
* 4 ENTER 1 R/S 1 R/S ... enter first yx-pair (the display shows n=1, and x,y=1i4 the last pair in "complex view")
* 5 ENTER 2 R/S 1 R/S ... enter second yx-pair (display: 2, 2i5)
* R/S 4 R/S 1 R/S 3 R/S ... to calculate linear coefficients A=3 and B=1
* 0 R/S 5 R/S ... predicts y=3 (and x=-3) value for x=0 (and y=0)

Used flags:
* Flag 0: clear...SUM+, set...SUM-

Used direct variables
* a:A
* b:B
* c:C
* d:a…
* e:xmv
* f:ymv, Gtmp
* g:x2mv, Gtmp
* h:...mv, Gtmp
* i:i indir
* j:j indir
* k:type
* l:loop counter
* m:max indir. var (27)
* n:n
* o:Sxx
* p:Sxy
* q:Sxx2
* r:Sx2x2
* s:Sx2y
* t: S…denominator, tmp
* u:x1
* v:y1
* w:xold
* x:x
* y:y
* z:yold

* Used indirect variables
1:SUMx
2:SUMy
3:SUMx^2
4:SUMy^2
5:SUMxy
6:SUMx^3
7:SUMx^4
8:SUMx^2y
9:SUMlnx
10:SUMlnx.y
11:SUM(lnx)^2
12:SUMlny
13:SUMln(y^2)
14:SUMx.lny
15:SUMlnx.lny
16:SUM1/x
17:SUM1/x^2
18:SUMy/x
19:SUM(lnx)^2
20:c
21:a
22:CGx
23:Cgy
24:Ixx
25:Iyy
26:Ixy


PROGRAM CODE (short version) - S – (Sums) LN=3172

[MAIN MENU]
LBLs STOx Rdown STOy 27 STOm STOi STO(i) CLx SF10 „EQN: SUM+ - c LR x^y^ G“ CF10 1 x=y? GTOs042 Rdown 2 x=y? GTOs041 Rdown 3

x=y? GTOs289 Rdown 4 x=y? GTOs304 Rdown 5 x=y? GTOs766 Rdown 6 x=y? GTOs842 GTOs001

[CALCULATE SUMS]
[s037] FS?0 +/- STO+(i) RTN
[s041] SF0
[s042] 1 FS?0 +/- STO+n
1 STOi RCLx XEQs037
2 STOi RCLy XEQs037
3 STOi RCLx x2 XEQs037
4 STOi RCLy x2 XEQs037
5 STOi RCLx RCLy * XEQs037
6 STOi RCLx 3 y^x XEQs037
7 STOi RCLx 4 y^x XEQs037
8 STOi RCLx x2 RCLy * XEQs037
9 STOi RCLx x>0? LN XEQs037
10 STOi RCLx x>0? LN RCLy * XEQs037
11 STOi RCLx x>0? LN x2 XEQs037
12 STOi RCLy x>0? LN XEQs037
13 STOi RCLy x2 x>0? LN XEQs037
14 STOi RCLy x>0? LN RCLx * XEQs037
15 STOi RCLx x>0? LN RCLy x>0? LN * XEQs037
16 STOi RCLx x<>0? 1/x XEQs037
17 STOi RCLx x2 x<>0? 1/x XEQs037
18 STOi RCLy RCLx x<>0? / XEQs037
19 STOi RCLx x>0? LN x2 XEQs037
FS0? GTOs171 GTOs174
[s171] 1 STO+n GTO191
[s174] 1 RCLn x=y? GTO179 GTO186
[s179] RCLx STOu STOw RCLy STOv STOz GTOs191
[s186] XEQs196 RCLx STOw RCLy STOz
[s191] RCLn eqn:X+i*Y CF0 STOP GTOs001
[s196] 20 STOi RCLx RCLw – x2 RCLy RCLz – x2 + SQRTx XEQs037
21 STOi RCLy RCLw * RCLx RCLz * – STOh XEQs037
22 STOi RCLx RCLw + RCLh * XEQs037
23 STOi RCLy RCLz + RCLh * XEQs037
24 STOi RCLy x2 RCLy RCLz * + RCLz x2 + RCLh * XEQs037
25 STOi RCLx x2 RCLx RCLw * + RCLw x2 + RCLh * XEQs037
26 STOi RCLx RCLz * RCLx RCLy * 2 * + RCLw RCLz * 2 * + RCLw RCLy * + RCLh * XEQs037 RTN

[CLEAR ALL]
[s289] RCLm 1 - STOi
[s293] RCLi x<=0? GTOs301 0 STO(i) 1 STO-i GTOs293
[s301] CLVARS STOP GTOs001

[SUBMENU]
[s304] CLx SF10 „EQN: POLYNOM POWER“ CF10 1 x=y? GTOs316 Rdown 2 x=y? GTOs557 GTOs001

[SUBMENU - POLYGON]
[s316] CLx SF10 „eqn: x-1 x0 x1 x2“ CF10 1 x=y? GTOs336 Rdown 2 x=y? GTOs389 Rdown 3 x=y? GTOs401 Rdown 4 x=y? GTOs447 GTOs001

[CALCULATE REGRESSION COEFFICIENTS - POLYNOM]
[s336] 1 STOk 17 STOi 16 STOj RCL(i) RCL(j) x2 RCLn / - STOt 18 STOi 2 STOj RCL(i) RCL(j) 16 STOi RCL(i) x<>y Rdown RCLn / * -

RCLt / STOb RCLn / 16 STOi RCL(i) x<>y Rdown * +/- 2 STOi RCL(i) x<>y Rdown RCLn / + STOa RCLb x<>y STOP GTOs001
[s389] 2 STOk 2 STOi RCL(i) RCLn / STOa 0 x<>y STOP GTOs001
[s401] 3 STOk 1 STOi RCL(i) RCLn / STOe 2 STOi RCL(i) RCLn / STOf 3 STOi RCL(i) RCLn / RCLe x2 – STOo 5 STOi RCL(i) RCLn / RCLe

RCLf * - STOp RCLo / STOb RCLe * +/- RCLf + STOa RCLb x<>y STOP GTOs001
[s447] 4 STOk 1 STOi RCL(i) RCLn / STOe 2 STOi RCL(i) RCLn / STOf 3 STOi RCL(i) RCLn / STOg 3 STOi RCL(i) RCLn / RCLe x2 – STOo

5 STOi RCL(i) RCLn / RCLe RCLf * - STOp 6 STOi RCL(i) RCLn / RCLe RCLg * - STOq 7 STOi RCL(i) RCLn / RCLg x2 – STOr 8 STOi RCL

(i) RCLn / RCLg RCLf * - STOs RCLo RCLr * RCLq x2 – STOt RCLp RCLr * RCLs RCLq * - RCLt / STOb RCLs RCLo * RCLp RCLq * - RCLt /

STOc RCLf RCLb RCLe * - RCLc RCLg * - STOa RCLc RCLb RCLa STOP GTOs001

[SUBMENU - POWER]
[s557] CLx SF10 „eqn: LN EXP AB PWR“ CF10 1 x=y? GTOs577 Rdown 2 x=y? GTOs623 Rdown 3 x=y? GTOs670 Rdown 4 x=y? GTOs719 GTOs001

[CALCULATE REGRESSION COEFFICIENTS - POWER]
[577] 5 STOk 9 STOi RCL(i) RCLn / STOe 2 STOi RCL(i) RCLn / STOf 11 STOi RCL(i) RCLn / RCle x2 – STOo 10 STOi RCL(i) RCLn /

RCLe RCLf * - STOp RCLo / STOb RCLe * +/- RCLf + STOa RCLb x<>y STOP GTOs001
[623] 6 STOk 1 STOi RCL(i) RCLn / STOe 12 STOi RCL(i) RCLn / STOf 3 STOi RCL(i) RCLn / RCLe x2 – STOo 14 STOi RCL(i) RCLn /

RCLe RCLf * - STOp RCLo / STOb RCLe * +/- RCLf + ex STOa RCLb x<>y STOP GTOs001
[670] 7 STOk 1 STOi RCL(i) RCLn / STOe 12 STOi RCL(i) RCLn / STOf 3 STOi RCL(i) RCLn / RCLe x2 – STOo 14 STOi RCL(i) RCLn /

RCLe RCLf * - STOp RCLo / ex STOb LN RCLe * +/- RCLf + ex STOa RCLb x<>y STOP GTOs001
[719] 8 STOk 9 STOi RCL(i) RCLn / STOe 12 STOi RCL(i) RCLn / STOf 19 STOi RCL(i) RCLn / RCLe x2 – STOo 15 STOi RCL(i) RCLn /

RCLe RCLf * - STOp RCLo / STOb RCLe * +/- RCLf + ex STOa RCLb x<>y STOP GTOs001

[PREDICTION SPREAD]
[s766] RCLk 1 x=y? GTOs799 Rdown 2 x=y? GTOs803 Rdown 3 x=y? GTOs806 Rdown 4 x=y? GTOs810 Rdown 5 x=y? GTOs826 Rdown 6 x=y?

GTOs830 Rdown 7 x=y? GTOs834 Rdown 8 x=y? GTOs838 GTOs001

[CALCULATE PREDICTION]
[s799] eqn:A*B/X eqn:B/(X-A) STOP GTOs001
[s803] RCLa STOP GTOs001
[s806] eqn:A+B*X eqn: (X-A)/B STOP GTOS001
[s810] SQ(B)-4*A*C STOt x>0? GTOs817 x=0? GTOs819 GTOs821
[s817] eqn: (-B+SQRT(T))/2/C+i*(-B-SQRT(T))/2/C GTOs822
[s819] eqn:-B/2/C GTOs822
[s821] 9,9999
[s822] eqn:C*SQ(X)+B*X+A x<>y STOP GTOs001
[s826] eqn:A+B*LN(X) eqn:EXP((X-A)/B) STOP GTOs001
[s830] eqn:A*EXP(B*X) eqn:LN(X/A)/B STOP GTOs001
[s834] eqn:A*B^X eqn:LN(X/A)/LN(B) STOP GTOs001
[s838] eqn:A*X^B eqn:EXP(LN(X/A)/B) STOP GTOs001

[CALCULATE GEOMETRICS]
[s842] RCLu STOx RCLv STOy XEQs196
[s847] CLx SF10 „eqn:C A CGxy MD“ CF10 1 x=y? GTOs867 Rdown 2 x=y? GTOs872 Rdown 3 x=y? GTOs879 Rdown 4 x=y? GTOs901 GTOs847
[s867] 20 STOi RCL(i) STOP GTOs847
[s872] 21 STOi RCL(i) 2 / STOP GTOs847
[s879] 22 STOi 21 STOj RCL(i) RCL(j) / 3 / STOe
23 STOi 21 STOj RCL(i) RCL(j) / 3 / RCLe STOP GTOs847
[901] 24 STOi RCL(i) 12 / STOe 25 STOi RCL(i) 12 / STOf 26 STOi RCL(i) 24 / RCLf RCLe STOP GTOs847


Maybe someone can use this or parts of it. If someone finds a bug please drop an answer. I did not make the program very resistant against "misuse" (I only captured some "divisions by 0" and "log(0)" during sums-calculation).

Regards
deetee

PS: To release the occupied indirect memory (approx. 1 kB) press: shiftright CLEAR 6 (CLVARx) 000 and 0 STO I STO(I).


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