[WP 34s] Trapezoidal approximation of area under curve
06-01-2015, 01:53 PM (This post was last modified: 06-01-2015 02:31 PM by Marcio.)
Post: #1
 Marcio Senior Member Posts: 438 Joined: Feb 2015
[WP 34s] Trapezoidal approximation of area under curve
Hello all,

Is it possible to have access to data keyed into the calc using the $$\sum +$$ for other procedures other than stat functions? If so, I am planning on creating a program that would take advantage of that so it would be possible to easily calculate the area under a curve defined by data, as shown below:

$\int_{x_1}^{x_n} y(x) dx \approx \frac{1}{2} \sum_{k=1}^{n-1} (x_{k+1}-x_{k})(y_{k+1}+y_{k})$

Many thanks

Marcio
06-01-2015, 03:54 PM
Post: #2
 Marcus von Cube Senior Member Posts: 754 Joined: Dec 2013
RE: [WP 34s] Trapezoidal approximation of area under curve
(06-01-2015 01:53 PM)Marcio Wrote:  Is it possible to have access to data keyed into the calc using the $$\sum +$$ for other procedures other than stat functions?
The SUMS catalog has all the accumulated data ready for access. All commands in this catalog are programmable.

Marcus von Cube
Wehrheim, Germany
http://www.mvcsys.de
http://wp34s.sf.net
http://mvcsys.de/doc/basic-compare.html
06-01-2015, 05:36 PM
Post: #3
 Dave Britten Senior Member Posts: 893 Joined: Dec 2013
RE: [WP 34s] Trapezoidal approximation of area under curve
(06-01-2015 03:54 PM)Marcus von Cube Wrote:
(06-01-2015 01:53 PM)Marcio Wrote:  Is it possible to have access to data keyed into the calc using the $$\sum +$$ for other procedures other than stat functions?
The SUMS catalog has all the accumulated data ready for access. All commands in this catalog are programmable.

The problem is that the trapezoidal approximation appears to require the individual data points, and not just the sums. You'll probably have to write a custom program that accumulates its own sums, either on the fly, or by using a block of registers to store x and y data points.
06-01-2015, 06:56 PM (This post was last modified: 06-01-2015 07:06 PM by Thomas Klemm.)
Post: #4
 Thomas Klemm Senior Member Posts: 949 Joined: Dec 2013
RE: [WP 34s] Trapezoidal approximation of area under curve
(06-01-2015 01:53 PM)Marcio Wrote:  If so, I am planning on creating a program that would take advantage of that so it would be possible to easily calculate the area under a curve defined by data, as shown below:

$\int_{x_1}^{x_n} y(x) dx \approx \frac{1}{2} \sum_{k=1}^{n-1} (x_{k+1}-x_{k})(y_{k+1}+y_{k})$

You could use something like:
Code:
001 LBL'TPZ' 002 CLΣ 003 LBL 00 004 STOP 005 R↑ 006 RCL+ Z 007 R↑ 008 RCL- Z 009 Σ+ 010 R↓ 011 R↓ 012 GTO 00 013 END

Usage:
$$y_1$$ ENTER $$x_1$$ XEQ'TPZ'
$$y_2$$ ENTER $$x_2$$ R/S
(...)
$$y_n$$ ENTER $$x_n$$ R/S
Σxy
-2 ÷

Not a sophisticated program but I hope you get the idea.

Cheers
Thomas
06-02-2015, 02:46 AM
Post: #5
 Marcio Senior Member Posts: 438 Joined: Feb 2015
RE: [WP 34s] Trapezoidal approximation of area under curve
Works like a charm.
Thank you
06-02-2015, 09:23 PM
Post: #6
 Dieter Senior Member Posts: 2,078 Joined: Dec 2013
RE: [WP 34s] Trapezoidal approximation of area under curve
(06-01-2015 06:56 PM)Thomas Klemm Wrote:  Not a sophisticated program but I hope you get the idea.

A bit of sophistication can be added by using the 34s' complex functions:

Code:
01 LBL"TRP" 02 CLΣ 03 CLSTK 04 STOP 05 LBL 01 06 STOP 07 cplx x<> Z 08 +/- 09 cplx RCL+ Z 10 Σ+ 11 cplx DROP 12 GTO 01

XEQ"TRP"
y1 ENTER x1 R/S
y2 ENTER x2 R/S
...
Σxy 2 ÷

Dieter
06-16-2015, 10:47 AM (This post was last modified: 06-16-2015 10:49 AM by Marcio.)
Post: #7
 Marcio Senior Member Posts: 438 Joined: Feb 2015
RE: [WP 34s] Trapezoidal approximation of area under curve
Hello again,

Does anyone know how to do $$RCL+ Z$$ on the 35s? From what I saw in the manual, one has to use the EQN inside the program in order to recall the $$z$$-register, which is somewhat dangerous.

Thanks.
06-16-2015, 11:31 AM
Post: #8
 Dieter Senior Member Posts: 2,078 Joined: Dec 2013
RE: [WP 34s] Trapezoidal approximation of area under curve
(06-16-2015 10:47 AM)Marcio Wrote:  Does anyone know how to do $$RCL+ Z$$ on the 35s?

Yes. You can't. Recall-arithmetics is not available for the stack registers.
Of course you can do a RCL+Z with variable Z, but that's a completely different story.

Dieter
06-16-2015, 12:38 PM
Post: #9
 Thomas Klemm Senior Member Posts: 949 Joined: Dec 2013
RE: [WP 34s] Trapezoidal approximation of area under curve
(06-16-2015 10:47 AM)Marcio Wrote:  Does anyone know how to do $$RCL+ Z$$ on the 35s?

You can use the following program:

Code:
T001 LBL T T002 CLΣ T003 STOP T004 REGY+REGT T005 REGY-REGT T006 Σ+ T007 R↓ T008 R↓ T009 GTO T003

Usage:
$$y_1$$ ENTER $$x_1$$ XEQ T
$$y_2$$ ENTER $$x_2$$ R/S
(...)
$$y_n$$ ENTER $$x_n$$ R/S
Σxy
2 ÷

Cheers
Thomas
06-16-2015, 12:57 PM
Post: #10
 Marcio Senior Member Posts: 438 Joined: Feb 2015
RE: [WP 34s] Trapezoidal approximation of area under curve
Thank you Thomas.

I myself created a program with more than 2 times as many lines as yours, which is not only simpler but also much more elegant.

Very much appreciated.

Marcio
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