WP43 Alternative key layout --> C43

[Walter]

Another use of Σ+ and Σ- is vector arithmetics in 2D. Many HP manuals contain examples and also the OM does.

[rprosperi]

The other main use for sigma-plus and minus is for adding and subtracting lists of real numbers using sum-x, or complex numbers / 2D vectors, using sum-x and sum-y. On modern calculators there are other ways to do this, but I expect that quite a few people are in the habit of working this way.

I'm sure I remember a problem involving tomato numbers and costs that was worked using this technique from one of the early HP manuals!

Nigel (UK)

This is a nice reminder of how we can use functions effectively even if not using them for the task intended, thanks Nigel.

The RefMan does state some of this for Σ+, but not for Σ-, and as Walter points out below, the OwnMan does explain it as well.

@Walter - I'd recommend these small enhancements be added into both manuals, for both commands, so there is thorough discussion of reasonably likely use of these functions beyond the intended straightforward add-to and subtract-from the statistics totals registers.

That being said, for the WP43C additional functionality (storing all data points, inevitable data point browser, etc.) I'd say it still makes sense to not remove an invalid data point, since in that case this would seem to be more important than the implied possible use for other functions, but it too should be clearly noted, especially since this behavior would then deviate from the nominal WP43S behavior. Ultimately, the ideal situation would be to make this optional behavior one could select via a system flag, etc. but possibly is not worth that extra effort.

[Jaymos]

The other main use for sigma-plus and minus is for adding and subtracting lists of real numbers using sum-x, or complex numbers / 2D vectors, using sum-x and sum-y. On modern calculators there are other ways to do this, but I expect that quite a few people are in the habit of working this way.

I'm sure I remember a problem involving tomato numbers and costs that was worked using this technique from one of the early HP manuals!

Nigel (UK)

This is a nice reminder of how we can use functions effectively even if not using them for the task intended, thanks Nigel.

The RefMan does state some of this for Σ+, but not for Σ-, and as Walter points out below, the OwnMan does explain it as well.

@Walter - I'd recommend these small enhancements be added into both manuals, for both commands, so there is thorough discussion of reasonably likely use of these functions beyond the intended straightforward add-to and subtract-from the statistics totals registers.

That being said, for the WP43C additional functionality (storing all data points, inevitable data point browser, etc.) I'd say it still makes sense to not remove an invalid data point, since in that case this would seem to be more important than the implied possible use for other functions, but it too should be clearly noted, especially since this behavior would then deviate from the nominal WP43S behavior. Ultimately, the ideal situation would be to make this optional behavior one could select via a system flag, etc. but possibly is not worth that extra effort.

The problem is what to do with Σ- when the stats points are recorded for the purposes of plotting and saving to a file.

After reading the responses, I think what is needed to make the Sigma keys work as expected, is to define a statistics mode and a vector mode, i.e. a mode setting as which can be added, as rprosperi rightly alludes to. This setting for Σ- could be part of another selection, of what kind of plot you want:

It can be a radio button setting for the PLOT type, i.e.: VECT / SCAT / LINE / C.FIT.

• VECT: Plots from the origin, a line from (0,0) to (0+x1,0+y1), then a line to (0+x1+x2,0+y1+y2), etc. In this mode +- stores the vector x,y and Σ- stores -x,-y.
• SCAT: Plots a cross at every point x,y. Stores coordinates.
• LINE: Connects the dots of a scatter plot. Stores coordinates.
• C.FIT: Plots a cross at every point x,y; Plots the last selected curve fit type as a line through the scatter plot. Stores coordinates.

In normal statistics mode (PLOT OPTION: SCAT/LINE/C.FIT):

• Σ+ action would simply record a x,y point in the list, and to do the STAT sums:
• Σ- action would:
  • Subtract the sums and if the to-be-removed point is found in the list, remove it from the list.
  • If not found in the list - beep to indicate loss of synchronicity in the graph but proceed. (comments may suggest to abort the point removal ??)
  • If beeped, there would then be point(s) in the data set and plot which were deleted from the STAT sums.
  • This would still result in a correct curve fit excluding the Σ- points, as the sums were updated and the points are not used for the curve fit.
  • 2D vector / 1D sums will still work as sums, but will not work in the graph, and there will be beeping. Better to use VECT mode.

In vector mode (PLOT OPTION: VECT):

• Σ+ stores +x,+y, and updates the STAT sums,
• Σ- stores -x,-y, and updates the STAT sums,
• the point search and delete is simply not done.

Thoughts?

[Walter]

This is a nice reminder of how we can use functions effectively even if not using them for the task intended, thanks Nigel.

The RefMan does state some of this for Σ+, but not for Σ-, and as Walter points out below, the OwnMan does explain it as well.

@Walter - I'd recommend these small enhancements be added into both manuals, for both commands, so there is thorough discussion of reasonably likely use of these functions beyond the intended straightforward add-to and subtract-from the statistics totals registers.

@Bob: Please see the ReM, p. 95, footnote 27. And the OM, pp. 126ff. It's all in for quite some time already. BTW, I don't rate these cases as "small enhancements" since these applications go back to the HP-25 Owner's Handbook of 1975.

[Nigel (UK)]

Calculators in the HP48 series accumulate data points in matrices, so that matrix editing commands can be used to add or remove points. Statistical functions then take the name of a matrix as an argument and the column or columns to be analysed. I don't know what the HP43S matrix editing facilities will be like - perhaps they won't be suited to editing a matrix with 400 rows by hand, but there are sure to be programmable commands for adding rows and finding elements. It might be possible to use the matrix editing commands when implementing the statistics and graphing modes that retain each entered point.

I think having both the matrix approach and the normal "accumulate sums" approach would be interesting. I can't think of another calculator that has both; perhaps there is a good reason for this...

Nigel (UK)

[rprosperi]

This is a nice reminder of how we can use functions effectively even if not using them for the task intended, thanks Nigel.

The RefMan does state some of this for Σ+, but not for Σ-, and as Walter points out below, the OwnMan does explain it as well.

@Walter - I'd recommend these small enhancements be added into both manuals, for both commands, so there is thorough discussion of reasonably likely use of these functions beyond the intended straightforward add-to and subtract-from the statistics totals registers.

@Bob: Please see the ReM, p. 95, footnote 27. And the OM, pp. 126ff. It's all in for quite some time already. BTW, I don't rate these cases as "small enhancements" since these applications go back to the HP-25 Owner's Handbook of 1975.

Sorry I wasn't clear - by 'small enhancements', I meant to add small additions to the manual to cover these alternate uses.

I suppose if a user read every single page, and every footnote, of both manuals, they might have discovered all the references. But no one does that... If they wondered how Σ+ and/or Σ- work, they'd likely look them up in the table of commands, like I did when this came up, and not find all the references, for example Σ- does not mention vector or matrix use. Having a brief mention there of other possible uses could point the reader at other sections in the manuals to better understand how those alternate uses could work.

Despite the truly excellent nature of your manuals, it's just a simple fact that no one else knows them as well as you do, so when small issues like this come up, I think it's sensible for us readers to make suggestions for improvement, that will help us and future readers use it more effectively.

I've no intention to insult your manuals (I love them), and there is no need to defend them; we both want them to be better for everyone to use.

[Walter]

No problem, Bob - once you wrote what you meant I can comprehend your intentions

Please allow me quoting footnote 27 from the very same page where Σ+ and Σ- are explained in the ReM (and directly referenced from Σ+ and Σ-):

Σ+ and Σ− return temporary information as shown in Section 2 of the OM and disable
automatic stack lift. Both commands may also be used for 2D vector adding and subtracting
(see SUM and the corresponding example in Section 2 of the OM).

(emphasis added)

Now what else shall I do? What do you miss?

[Jaymos]

Following the posts above re 2D vector sums, and my proposal posted above to split the use of the sigma operator for statistical plotting and regression, and for vector arithmetic, I edited my stats graph code to include a VECT mode, where a vector series is plotted starting from the origin and following the vectors in the table.

"VECT mode" would be used with Σ+ and Σ-, to determine the solution for the thrust vector in the example on the 43S OM, on pp. 128 & 129 (of 319) rev U:
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Clipboard18i.png (2.39 KiB) Viewed 3457 times

Vector sum. This illustrates the vector input mode where Σ+ adds to the vector table x,y and Σ- adds to the vector table -x,-y (instead of removing a point from the table).
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Something to note from the sketch in the manual is the navigational vector graph on p129 with 0 degrees (N) on the vertical axis, with clockwise rotation. The graph that I produced on the 43C, has the 0 degree line horisontal, with anticlockwise rotation. Not sure what to do there?
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Below a more complex example of vectors programmatically added using Σ+.:
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Clipboard17.png (3.04 KiB) Viewed 3457 times

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Thoughts on whether this is useful or wanted?

[Jaymos]

Calculators in the HP48 series accumulate data points in matrices, so that matrix editing commands can be used to add or remove points. Statistical functions then take the name of a matrix as an argument and the column or columns to be analysed. I don't know what the HP43S matrix editing facilities will be like - perhaps they won't be suited to editing a matrix with 400 rows by hand, but there are sure to be programmable commands for adding rows and finding elements. It might be possible to use the matrix editing commands when implementing the statistics and graphing modes that retain each entered point.

I think having both the matrix approach and the normal "accumulate sums" approach would be interesting. I can't think of another calculator that has both; perhaps there is a good reason for this...

Nigel (UK)

Interesting. The data structure for the 400 points is not defined in the ReM so I am picking my own structure, which currently is not accessible in the stack and register memory. To optimise memory usage I do certain simplifications in the memory allocation, so the structures are not 400 x 2 x 34 digits reals, which would take up way too much space, therefore it possibly will not be possible to store 800 reals to fit a matrix. There are no other real number structures, so we cannot store those in normal register/matrix space and are thus are stuck without matrix access.

I have no idea how the matrix editor would look like, so I would not venture into that. I'll wait and see.

The only very flexible way I can see to manage the stats data is to have a standard text file STAT.CSV or something like that in which the data will be written as data is entered via Sigma. The way I would like it, is that the data is mastered in the file. This file is automatically loaded into the volatile graphic memory, so you could in fact prep this file on pc and the calculator would import that data. You can also import the graphic memory into the STATS sums by pressing IMPORT, which means you can then work on regression or whatever powerful stats functions are available in the calculator.

[rprosperi]

No problem, Bob - once you wrote what you meant I can comprehend your intentions

Please allow me quoting footnote 27 from the very same page where Σ+ and Σ- are explained in the ReM (and directly referenced from Σ+ and Σ-):

Σ+ and Σ− return temporary information as shown in Section 2 of the OM and disable
automatic stack lift. Both commands may also be used for 2D vector adding and subtracting
(see SUM and the corresponding example in Section 2 of the OM).

(emphasis added)

Now what else shall I do? What do you miss?

Thanks for the extra details Walter. I must admit that the comments at the end of the footnote do indeed convey what I was suggesting. When I looked up the commands in the ReM, I read the explanations in the table for the commands and admit I did not read the footnote, expecting only the oft-repeated (as is appropriate) warning about disabling stack-lift.

My point is that this relatively important facet of these commands, as this whole discussion seems to imply, is too important to relegate to a footnote. I imagine most other readers would skip the footnote too, though of course some would read it.

So this is a style issue, and I'm only trying to convey that despite the information being there, in a case like this it wasn't obvious enough to be found by me, and that other readers would likely miss it as well. Of course you can't promote every detail of every command into the table itself, but this is a case where I would say it's worth it.