Re^8: Any idea for predicting the peak points in the graph by perl

Strawman?

Our discussion here is in reply to the parent who made a claim that the second derivative was useful in finding extrema. I have posted so that future readers will not believe this, as I believe it to be untrue. In reply to my claim you have posted a number interesting things - but none seemingly address the claims of the parent, or myself.

The OP claims that the second derivative is useful for determining extrema. His claim suggests that looking at toggling signs on the resulting series indicates extrema. I claim this as *false*.

I also claim that it is possible to find extrema using the first derivative. Any time the derivative crosses the X axis there will be a maxima or minima present within the source series. I do *not* claim that this will find all extrema - I do claim that it will also require additional processing to capture all extrema of interest. Are you claiming this is false?

Your above program is quite a bit shorter than mine. I have a different type of data, but I am pretty sure that looking at deltas like this is a more precise and efficient way of solving the problem than using first derivatives - I disagree that it's more accurate, but that's nitpicking. Overall it is better than doing solely a first derivative and picking from that.

Finally, I strongly disagree that using inverted graphs (even if that's what's used in computer graphics) is a good way to prove your point about much of anything. That said, had you labelled your graph and explained what it was I we both could have saved some time

Comment on Re^8: Any idea for predicting the peak points in the graph by perl

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Re^9: Any idea for predicting the peak points in the graph by perl by BrowserUk (Patriarch) on Jul 16, 2012 at 09:36 UTC
Strawman? Hardly. You said 2nd derivative was no good and that 1st derivative was the way to go. I demonstrated that neither is a good mechanism for the data in question. You countered: "your graph is upside down" -- a strawman if ever. I demonstrated that of the 7 inversion points in the data; first derivative only sees 5 of them. And of those 5; three are substantially inaccurate. Indeed, if you draw a few vertical lines on your own linked graph -- which is now at least accessible -- you can see both problems: missed turning points and inaccurately discovered ones. The age old problem with first (and second) deritives -- along with many other numerical methods -- is that they have a tendency to discover values that don't exist in the dataset. Ie. calculated values that fall between the discrete values that are actually in the dataset. Whilst this is fine for theoretical discussion -- rounded to some number of sig.fig. -- it leaves real-world applications with the need to fall back upon heuristics -- ie. guesses -- in order to "correct" calculated values and align them with the actual data. Imagine the dataset represents clock-speed (or power drain) from a deep-bin sort of newly minted cpus. -- ie. when cpus are manufactured, there is some considerable variability in their electrical performance; and manufacturers can sort the parts by their actual performance, and charge premium prices for the better ones. In the many all-too-real scenarios like this that crop up in manufacturing every day, having calculated maxima and minima that fall at theoretical points on the curve; between the actual values that are there, isn't very useful for the selection processes that are the reason for performing the calculation in the first place. So no, not a strawman. A legitimate and relevant discussion in context. I accept that my original graph was, as presented, difficult to interpret. But I anticipated that anyone interested would produce their own graph to verify the accuracy of my quick plots and conclusions. Which you did. Inspect their own plots carefully and notice the obvious discrepancies that I noticed in mine. Which you did not. That's the trouble with "pretty graphs". People get so impressed by the pictures, they forget to inspect them closely and take note of why they produced them in the first place. With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday' Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error. "Science is about questioning the status quo. Questioning authority". In the absence of evidence, opinion is indistinguishable from prejudice. The start of some sanity?	[reply]

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Re^9: Any idea for predicting the peak points in the graph by perl
by BrowserUk (Patriarch) on Jul 16, 2012 at 09:36 UTC

Strawman?

Hardly.

You said 2nd derivative was no good and that 1st derivative was the way to go.
I demonstrated that neither is a good mechanism for the data in question.
You countered: "your graph is upside down" -- a strawman if ever.
I demonstrated that of the 7 inversion points in the data; first derivative only sees 5 of them. And of those 5; three are substantially inaccurate.
Indeed, if you draw a few vertical lines on your own linked graph -- which is now at least accessible -- you can see both problems: missed turning points and inaccurately discovered ones.

The age old problem with first (and second) deritives -- along with many other numerical methods -- is that they have a tendency to discover values that don't exist in the dataset. Ie. calculated values that fall between the discrete values that are actually in the dataset.

Whilst this is fine for theoretical discussion -- rounded to some number of sig.fig. -- it leaves real-world applications with the need to fall back upon heuristics -- ie. guesses -- in order to "correct" calculated values and align them with the actual data.

Imagine the dataset represents clock-speed (or power drain) from a deep-bin sort of newly minted cpus. -- ie. when cpus are manufactured, there is some considerable variability in their electrical performance; and manufacturers can sort the parts by their actual performance, and charge premium prices for the better ones.

In the many all-too-real scenarios like this that crop up in manufacturing every day, having calculated maxima and minima that fall at theoretical points on the curve; between the actual values that are there, isn't very useful for the selection processes that are the reason for performing the calculation in the first place.

So no, not a strawman. A legitimate and relevant discussion in context.

I accept that my original graph was, as presented, difficult to interpret. But I anticipated that anyone interested would

produce their own graph to verify the accuracy of my quick plots and conclusions.
Which you did.
Inspect their own plots carefully and notice the obvious discrepancies that I noticed in mine.
Which you did not.

That's the trouble with "pretty graphs". People get so impressed by the pictures, they forget to inspect them closely and take note of why they produced them in the first place.

With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority".

In the absence of evidence, opinion is indistinguishable from prejudice.

The start of some sanity?

[reply]