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Casio Basic C.Basic

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#521 acapde

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Posted 10 December 2019 - 03:57 PM

Hi sentaro21

 

Gauss-Cronrod has week point with periodical function.

Please check out following article;

https://egadget.blog...icFunc_Integral

 

This is in Japanese, so you are OK, but for anyone else please use Google translation.

 

Hi Krtyski,

 

Unfortunately all numerical integration approximations have some weak points, especially when there are discontinuities or even periodicity, that's why it's required to do some prior analysis of the function to be numerically integrated, In the case  of periodic functions it's possible to limit the integration to the area of one period (keeping in mind any change of sign) and then multiply the result by the number of periods.

 

In my tests Gauss-Kronrod Quadrature is the most robust algorithm for almost every situation and that's probably the reason TI and Casio are using it. I will try to post a Romberg algorithm version tomorrow, Romberg has been traditionally used by HP and it works well for any well-behaved function but not as robust as Gauss-Kronrod in some tricky situations.

 

Stay tuned.

Thanks!



#522 acapde

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Posted 10 December 2019 - 10:02 PM

Here it is....

 

Romberg Integration method
Ported from HP41 PPC ROM/Module
 
Before running ROMBERG, the function must be loaded as a program, similar to this:
 
Filename:FX
sin X→X
Return
 
 
 
 
'ProgramMode:RUN
"A"?->A /Lower limit
"B"?->B /Upper limit
"Accuracy"?->E% /this is the minimum number of decimal places of accuracy / precision. 1 means 1 dec place, 2 means two and so on.
/Typical results are far better than this minimum threshold 
E%+1->E%
0->D% /if D% = 0 then no intermediate results are shown, if not 0 then they are shown
(B-A)/4->P
(B+A)/2->Q
{12,1}->Dim Mat A
0->O
0->K
0->Mat A[1,1] /Not mandatory but I put it here for clarity
(-)1->I%
Do
For I%->Z% To 0
1->S
2->N
2^(-)K->T
T*N->N
T-1->L
Do
S-L^<2>->M
(M+2)*L*P+Q->X
Prog "FX"
(X*M)+O->O
L+N->L
LpWhile L<1
K->M
1->L
K+1->K
1->U
O*P*1.5*N->T
Do
U*4->U
Mat A[L,1]->S
T->Mat A[L,1]
((T-S)/(U-1))+Mat A[L]->T
L+1->L
L>12=>Goto 4 /I know, this is ugly, it's there as a (temporary ;) emergency exit if enough convergence is not reached, it can be replaced by an error routine
M-1->M
LpWhile M>0
T->Mat A[L]
Next
0->I%
If D%<>0 Then    /these 3 lines are optional, it just displays intermediate results if D<>0
Disp TDisps
IfEnd
LpWhile RndFix(T,Sci E%)<>RndFix(S,Sci E%) /this checks if the desired accuracy has been reached.
Lbl 4
"IG="
T
Return 


#523 sentaro21

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Posted 11 December 2019 - 07:24 AM

@Krtysk
@acapde
Thanks! :D
I would like to be able to select two methods from the perspective of accuracy. ^_^
 
by the way,
This is the Kronrod program from @acapde, but the accuracy of the Gauss21 results is remarkably poor, but is there something wrong?
 
[FX]:sin X->X
A:0
B:1
Accurate :0.4596976941
Gauss21  :0.4455341995
Kronrod51:0.4596976941
 
'ProgramMode:RUN
'KRONROD
10->N
'Number of subintervals
"A"?->A
'Lower limit
"B"?->B
'Upper limit
'Load 64 nodes and weights
{64,1}->Dim Mat A
1.231760537267155E-1->Mat A[1]
6.158081806783294Exp(-)2->Mat A[2]
6.147118987142532Exp(-)2->Mat A[3]
6.154448300568508Exp(-)2->Mat A[4]
1.222424429903100Exp(-)1->Mat A[5]
6.112850971705305Exp(-)2->Mat A[6]
1.228646926107104Exp(-)1->Mat A[7]
6.053945537604586Exp(-)2->Mat A[8]
1.837189394210489Exp(-)1->Mat A[9]
1.194557635357848Exp(-)1->Mat A[10]
5.972034032417406Exp(-)2->Mat A[11]
2.438668837209884Exp(-)1->Mat A[12]
5.868968002239421Exp(-)2->Mat A[13]
3.030895389311078Exp(-)1->Mat A[14]
1.148582591457116Exp(-)1->Mat A[15]
5.743711636156783Exp(-)2->Mat A[16]
3.611723058093878Exp(-)1->Mat A[17]
5.595081122041232Exp(-)2->Mat A[18]
4.178853821930377Exp(-)1->Mat A[19]
1.085196244742637Exp(-)1->Mat A[20]
5.425112988854549Exp(-)2->Mat A[21]
4.730027314457150Exp(-)1->Mat A[22]
5.236288580640748Exp(-)2->Mat A[23]
5.263252843347192Exp(-)1->Mat A[24]
1.005359490670506Exp(-)1->Mat A[25]
5.027767908071567Exp(-)2->Mat A[26]
5.776629302412230Exp(-)1->Mat A[27]
4.798253713883671Exp(-)2->Mat A[28]
6.268100990103174Exp(-)1->Mat A[29]
9.102826198296365Exp(-)2->Mat A[30]
4.550291304992179Exp(-)2->Mat A[31]
6.735663684734684Exp(-)1->Mat A[32]
4.287284502017005Exp(-)2->Mat A[33]
7.177664068130844Exp(-)1->Mat A[34]
8.014070033500102Exp(-)2->Mat A[35]
4.008382550403238Exp(-)2->Mat A[36]
7.592592630373576Exp(-)1->Mat A[37]
3.711627148341554Exp(-)2->Mat A[38]
7.978737979985001Exp(-)1->Mat A[39]
6.803833381235692Exp(-)2->Mat A[40]
3.400213027432934Exp(-)2->Mat A[41]
8.334426287608340Exp(-)1->Mat A[42]
3.079230016738749Exp(-)2->Mat A[43]
8.658470652932756Exp(-)1->Mat A[44]
5.490469597583519Exp(-)2->Mat A[45]
2.747531758785174Exp(-)2->Mat A[46]
8.949919978782754Exp(-)1->Mat A[47]
2.400994560695322Exp(-)2->Mat A[48]
9.207471152817016Exp(-)1->Mat A[49]
4.093915670130631Exp(-)2->Mat A[50]
2.043537114588284Exp(-)2->Mat A[51]
9.429745712289743Exp(-)1->Mat A[52]
1.684781770912830Exp(-)2->Mat A[53]
9.616149864258425Exp(-)1->Mat A[54]
2.635498661503214Exp(-)2->Mat A[55]
1.323622919557168Exp(-)2->Mat A[56]
9.766639214595175Exp(-)1->Mat A[57]
9.473973386174152Exp(-)3->Mat A[58]
9.880357945340772Exp(-)1->Mat A[59]
1.139379850102629Exp(-)2->Mat A[60]
5.561932135356714Exp(-)3->Mat A[61]
9.95556969790498Exp(-)1->Mat A[62]
1.987383892330316Exp(-)3->Mat A[63]
9.992621049926098Exp(-)1->Mat A[64]
 
 
0->D
0->E
A->H
(B-A)/(2*N)->G
Do
 G+H->H
 64->I
 1->F
 Do
  G*Mat A[I]->J
  H-J->X
  Prog "FX"
  X->K
  H+J->X
  Prog "FX"
  X+K->J
  I-1->I
  Mat A[I]*J+E->E
  -F->F
  If F>=0Then 
   I-1->I
   Mat A[I]*J+D->D
  IfEnd
  I-1->I
 LpWhile I>2
 H->X
 Prog "FX"
 X->J
 Mat A[I]*J+E->E
 J*Mat A[I]+D->D
 G+H->H
 N-1->N
LpWhile N>0
G*D->D
G*E->E
Disp D:'Shows Gauss21-Integral result
Disp E:'Shows Kronrod51-Integral result

Edited by sentaro21, 11 December 2019 - 07:24 AM.


#524 acapde

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Posted 11 December 2019 - 01:24 PM

Hi Sentaro21,
 
I found an error:
 
 Mat A[I]*J+E->E
 J*Mat A[I]+D->D -----> this should be J*Mat A[ 1 ]+D->D  the I must be replaced by 1
 G+H->H
 
Please try again and let me know.
Best regards.
 


#525 sentaro21

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Posted 12 December 2019 - 12:15 AM

Thanks!

It works well! :D

 

Furthermore, I made a mistake in initializing Mat A [ 1].  :P

 


'KRONROD
10->N
'Number of subintervals
"A"?->A
'Lower limit
"B"?->B
'Upper limit
'Load 64 nodes and weights
{64,1}->Dim Mat A
1.231760537267155Exp(-)1->Mat A[1]
6.158081806783294Exp(-)2->Mat A[2]
6.147118987142532Exp(-)2->Mat A[3]
6.154448300568508Exp(-)2->Mat A[4]
1.222424429903100Exp(-)1->Mat A[5]
6.112850971705305Exp(-)2->Mat A[6]
1.228646926107104Exp(-)1->Mat A[7]
6.053945537604586Exp(-)2->Mat A[8]
1.837189394210489Exp(-)1->Mat A[9]
1.194557635357848Exp(-)1->Mat A[10]
5.972034032417406Exp(-)2->Mat A[11]
2.438668837209884Exp(-)1->Mat A[12]
5.868968002239421Exp(-)2->Mat A[13]
3.030895389311078Exp(-)1->Mat A[14]
1.148582591457116Exp(-)1->Mat A[15]
5.743711636156783Exp(-)2->Mat A[16]
3.611723058093878Exp(-)1->Mat A[17]
5.595081122041232Exp(-)2->Mat A[18]
4.178853821930377Exp(-)1->Mat A[19]
1.085196244742637Exp(-)1->Mat A[20]
5.425112988854549Exp(-)2->Mat A[21]
4.730027314457150Exp(-)1->Mat A[22]
5.236288580640748Exp(-)2->Mat A[23]
5.263252843347192Exp(-)1->Mat A[24]
1.005359490670506Exp(-)1->Mat A[25]
5.027767908071567Exp(-)2->Mat A[26]
5.776629302412230Exp(-)1->Mat A[27]
4.798253713883671Exp(-)2->Mat A[28]
6.268100990103174Exp(-)1->Mat A[29]
9.102826198296365Exp(-)2->Mat A[30]
4.550291304992179Exp(-)2->Mat A[31]
6.735663684734684Exp(-)1->Mat A[32]
4.287284502017005Exp(-)2->Mat A[33]
7.177664068130844Exp(-)1->Mat A[34]
8.014070033500102Exp(-)2->Mat A[35]
4.008382550403238Exp(-)2->Mat A[36]
7.592592630373576Exp(-)1->Mat A[37]
3.711627148341554Exp(-)2->Mat A[38]
7.978737979985001Exp(-)1->Mat A[39]
6.803833381235692Exp(-)2->Mat A[40]
3.400213027432934Exp(-)2->Mat A[41]
8.334426287608340Exp(-)1->Mat A[42]
3.079230016738749Exp(-)2->Mat A[43]
8.658470652932756Exp(-)1->Mat A[44]
5.490469597583519Exp(-)2->Mat A[45]
2.747531758785174Exp(-)2->Mat A[46]
8.949919978782754Exp(-)1->Mat A[47]
2.400994560695322Exp(-)2->Mat A[48]
9.207471152817016Exp(-)1->Mat A[49]
4.093915670130631Exp(-)2->Mat A[50]
2.043537114588284Exp(-)2->Mat A[51]
9.429745712289743Exp(-)1->Mat A[52]
1.684781770912830Exp(-)2->Mat A[53]
9.616149864258425Exp(-)1->Mat A[54]
2.635498661503214Exp(-)2->Mat A[55]
1.323622919557168Exp(-)2->Mat A[56]
9.766639214595175Exp(-)1->Mat A[57]
9.473973386174152Exp(-)3->Mat A[58]
9.880357945340772Exp(-)1->Mat A[59]
1.139379850102629Exp(-)2->Mat A[60]
5.561932135356714Exp(-)3->Mat A[61]
9.95556969790498Exp(-)1->Mat A[62]
1.987383892330316Exp(-)3->Mat A[63]
9.992621049926098Exp(-)1->Mat A[64]
 
 
0->D
0->E
A->H
(B-A)/(2*N)->G
Do
 G+H->H
 64->I
 1->F
 Do
  G*Mat A[I]->J
  H-J->X
  Prog "FX"
  X->K
  H+J->X
  Prog "FX"
  X+K->J
  I-1->I
  Mat A[I]*J+E->E
  -F->F
  If F>=0Then 
   I-1->I
   Mat A[I]*J+D->D
  IfEnd
  I-1->I
 LpWhile I>2
 H->X
 Prog "FX"
 X->J
 Mat A[I]*J+E->E
 J*Mat A[1]+D->D
 G+H->H
 N-1->N
LpWhile N>0
G*D->D
G*E->E
Disp D'Shows Gauss21-Integral result
Disp E'Shows Kronrod51-Integral result

 


  • acapde likes this

#526 acapde

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Posted 12 December 2019 - 04:04 AM


[/quote]
Furthermore, I made a mistake in initializing Mat A [ 1].  :P
[/quote]

Good catch! I had missed that one!

Glad that it`s working well now.

#527 CalcLoverHK

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Posted 12 December 2019 - 05:11 AM

Hi sentaro21

 

Bunch of questions:

- What is the format and usage of WriteGraph and DotGet/DotTrim/DotPut/CellSum?

- What does PopUpWin looks like and its syntax? (And what does n in PopUpWin(n) mean? It seems like the following situation exceed 5, such as PopUpWin(11,"Message1"[,"Message1"])→A)

 

Cheers

CalcLoverHK


Edited by CalcLoverHK, 12 December 2019 - 08:46 AM.


#528 sentaro21

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Posted 12 December 2019 - 11:44 AM

@acapde
Thanks. :D
 
 
@CalcLoverHK
The (example) in the manual is nearly the (format). ^_^
(Format 1) WriteGraph x,y,dx,dy,Mat A ,P1[,P2]
  Draw data of Mat A in width dx, the range of height dy from coordinate (x,y) of the graphic screen.
  P1 parameter.(Can not be omitted.)
   [,N] normal
   [,R] reverse
   [,M] mesh
  P2 parameter.(Can omitted.)
   [omit] over
   [,X] xor
   [,O] or
   [,A] and
 
(Format 2) WriteGraph x,y,dx,dy,Mat A[m,n] ,P1[,P2]
Draw data from Mat A[m,n].
 
(Format) DotGet(px1,py1, px2,py2)->Mat A[x,y]
  area of (px1, py1)-(px2, py2) to Mat A[x,y].
 
(Format 1) DotPut (Mat A,x,y,px1,py1,px2,py2)
  Draw (px1, py1)-(px2, py2) of the screen as the starting element of Mat A[x,y].
(Format 2) DotPut(Mat A[x,y],mx1,my1,mx2,my2)->Mat B
  transfer to element Mat B[mx1,my1]-[mx2,my2] as the starting element of Mat A[x,y].
 
(Format 1)DotTrim(Mat A,x1,y1,x2,y2)->Mat B
  Trim the rectangular area of nonzero data in the [X1,y1]-[x2,y2] element of range in the Mat A and copy it to the Mat B.
  If the Mat B to be copied is not secured, it is newly allocated.
 
(Format 1)DotTrim(px1,py1,px2,py2)->Mat A
  This is a trimming input from the graphics screen range of (px1,py1)-(px2,py2).
 
 
The pop-up window is the same shape as the error display pop-up. ^_^
When the range of n of PopUpWin(n) is,
1-6, normal pop-up (1 line to 6 lines).
0, current vram store to the screen buffer.
9, resore from the screen buffer.
11, EXIT popup with comment(max 2 line).
10, [Yse/No] popup with comment(max 2 line), return value is [Yes:1]/[No:0]. 
 


#529 CalcLoverHK

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Posted 13 December 2019 - 08:58 AM

Hi sentaro21

 

- Can I write something up to 6 lines in a normal pop-up?

- I forgot about DotLife/CellSum. How do they work?

- How does KeyRow( work and what is its syntax?

- What is exactly the difference between TicksWait 4 and TicksWait -4? I see both can do a 32 fps loop. Can you give me some processing showcases?

- Does IsExist("*.<extension>") return values to both Mat Ans and N? And what does "When the extension is left out, the file name becomes [.bin] to eight characters." mean?\

 

Cheers

CalcLoverHK



#530 sentaro21

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Posted 13 December 2019 - 01:37 PM

Thanks CalcLoverHK :D

- Can I write something up to 6 lines in a normal pop-up?

A normal pop-up is blank and must be written with the Locate/Text command. :)
 
 
CelSum()/DotLife() commands are implement for the following programs and is not versatile. :P
(Format) CellSum(Mat A[X,Y])->C
 return value is sum of 8 element of around Mat A[X,Y].

(Format) DotLife(Mat A,x1,y1,x2,y2)->Mat B
 Calculate Life game in element Mat A[x1,y1]-[x2,y2].
 
This program is speeded up using the DotPut/CelSum command.
Conway's Game of Life (ver.0.74) by Krtyski
And the following program is speeded up using DotLife command which commanded the core part.
Conway's Game of Life (ver.0.84) by Krtyski
(Format)  KeyRow(n)
 n:Row number 0~9
 Return value is the bit for the pressed key is enabled.
 
         bit6 bit5 bit4 bit3 bit2 bit1
   Row--------------------------------------Row
    09    F1    F2   F3   F4   F5   F6       09
    08    SHIFT OPTN VARS MENU <-  (up)      08
    07    ALPHA ^2   ^    EXIT (DW) ->       07
    06    XTT   log  ln   sin  cos  tan      06
    05    ab/c  F<>D  (    )    ,   ->       05
    04    7     8    9    DEL                04
    03    4     5    6    x    div           03
    02    1     2    3    +    -             02
    01    0     .    EXP  (-)  EXE           01
   Row--------------------------------------Row
 
The difference between "TicksWait 4" and "TicksWait -4",
"TicksWait 4" is just waiting for time.
However,
"TicksWait -4" is waiting for the time from the previous TicksWait. :)
If time has passed since the previous TicksWait, it will not wait.
 
IsExist("*.<extension>") return values is only Mat Ans. :)
If the extension is omitted it will be ".bin".

Edited by sentaro21, 47 minutes ago.


#531 CalcLoverHK

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Posted 13 December 2019 - 02:42 PM

Hi sentaro21

 

In TicksWait, you mean:

 

1.

TicksWait 128
TicksWait -32

If 128 ticks > 32 ticks, then program will skip "TicksWait -32".

 

2.

TicksWait 12
TicksWait -32

If 16 ticks < 32 ticks, then program will wait (32-12) ticks more.

 

3.

TicksWait 32
TicksWait -32

If both are the same, then program will wait (32-32) ticks, which is no difference at all.

 

Am I correct?

 

Cheers

CalcLoverHK



#532 sentaro21

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Posted 14 December 2019 - 12:55 AM

Regardless of the sign of the TicksWait argument, the waiting time is determined by the time after the last TicksWait command is executed.
In all cases it will wait for +32 ticks. :)
 
For example, if you create a loop that runs once a second,
If no use TicksWait -
Ticks->S
While 1
 ...
 Do:LpWihle Abs(Ticks-S)<128
 Ticks->S
WhileEnd
Temporary variable S is required as an initial value.
 
 
If use TicksWait -
While 1
 ...
 TicksWait -128
WhileEnd
The code is simplified and the temporary variable S is no longer needed. ^_^
 

If use TicksWait +
While 1
 ...
 TicksWait 128
WhileEnd
It will exceed 1 second depending on the content of the processing in the loop.
 

Edited by sentaro21, 14 December 2019 - 12:55 AM.


#533 CalcLoverHK

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Posted 14 December 2019 - 04:57 AM

Hi sentaro21

Got it. So I summarized the usage:

* TicksWait+ adds waiting time regardless in loop or individual without checking whether it is necessary.
* TicksWait- also adds waiting time in individual, but in loop it checks whether adding more waiting time is necessary depending on the processing in loop and its value.

Well, from the start of loop, TicksWait- is already in calculation, right?

Cheers
CalcLoverHK

#534 sentaro21

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Posted 14 December 2019 - 05:41 AM

* TicksWait+ adds waiting time regardless in loop or individual without checking whether it is necessary.
* TicksWait- also adds waiting time in individual, but in loop it checks whether adding more waiting time is necessary depending on the processing in loop and its value.

Well, from the start of loop, TicksWait- is already in calculation, right?

Thanks! :D

In addition,
The first TicksWait- has zero wait time. It works after the second time. ^_^


#535 CalcLoverHK

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Posted Yesterday, 07:15 AM

Hi sentaro21

 

Just found out a wild version of fx-9860GII: fx-9860GIIs.

This calculator is for Singapore examination. It does not support surd and pi form output. Other than that, it is nearly identical to fx-9860G.

 

Does C.Basic support this calculator? Then what is the model no. of it in C.Basic?

 

Cheers

CalcLoverHK



#536 sentaro21

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Posted Yesterday, 08:11 AM

Yes!

C.Basic supports all fx-9860G series. :D

So of course it seems to work in fx-9860GIIs.

Since there is only SH4A model, the System(-1) command return value is 3. ^_^







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