extracting data point from the plot and then some

[jasius-disabled]

Hi,

I would like some help and advice with the following problem:

I have two data series plotted (see attached). Those are the point I obtained experimentally. My first question is if I can connect those point with a line (scatter plot connected by lines, somehow I couldn't) and extract that point data with a selected interval between the points (so my data instead of scatter becomes linear plot)

and second

I need to show the difference between those two data series. they are comprised of two parabole, on centered at ~1.1 and the other one at 1.5. I would need somehow to show where and when this inflection at 1.3 appears (I have more data series in between and at some point parabole at 1.3 moves down and this inflection apperas). I need to somehow show that onset. Would first or second derivative show that? How do I proceed with this data (that's why I wanted to extract linear points to the try derivatives on them

hectic but would appreciate any help

JOnas

[ptc-1368288]

>Oh my... Now I feel guilty <<br> ___________________________

Guilty for what ? many collabs read this forum, cheaper and more instructive than the "London Times" or else paper. Your data aren't collected, then. What you did wrong is to calculate at too far away points. Maybe there is no need for any fit, and you will get all your stuff right from the original equation(s), that you must provide obviously !
Back to square one: show the function(s)

jmG

[TomGutman]

Another approach. You are interested in the extrema of the PE curve, which are at the roots of the derivative of the PE curve. Assuming that the quartic fit is a sufficiently good approximation the derivative is a cubic. If the cubic has three real roots (in the region of interest) then the PE curve will have a maximum between the two energy minima and the first minimum will represent a more or less stable state. If it has only one root there is just a single minimum and only that one stable state.

If you look at the Cardan solution for the cubic, there arises a quantity known as the discriminant. IIRC a negative discriminant means three real roots, a positive discriminant means on real and two complex roots, and a zero discriminant means two roots, one of them a double root. If you plot the discriminant against z the zero crossing should be the z value separating single stable state solutions from two stable state solutions.

Because the discriminant is based on the relative position of the roots a horizontal shift along the x axis does not change it. Hence the actual x values are not material, as long as they are scaled the same. Further, because the discriminant is for the derivative of the energy curve the absolute height of the curve (the normalization to zero) makes no difference -- the constant terms drops out when differentiated. I don't have the formula for the discriminant in my head, it's something that would need to be looked up (or worked out).
__________________
� � � � Tom Gutman

[ptc-1368288]

>I don't have the formula for the discriminant in my head, it's something that would need to be looked up (or worked out)<.
___________________________

Below Marlett is what I have just added before leaving. The synthetic cubic root solver is also given. The Cardan solver is excluded whereas some of the columns will fail with Cardan. Considering the quartic fit should be used as very adequate, the Maximize/Minimize will solve the problem.
If the maths/physics behind the project can produce more columns of data, the function is then f(x,y) ... from which then: local 2d min/max can be found from again Maximize/Minimize Mathcad built-in functions, directly from the surface plots.

Conclusion:
the project is in hand but not the generating maths/physics

jmG

[RichardJ]

On 9/10/2009 9:42:48 PM, jasius wrote:
>Oh my... Now I feel guilty
>that I posted this question
>here...

Don't worry about that.

Tom makes a couple of good points about the data though.

1) Some of the vectors do not have the same number of entries. Unfortunately, they are ones close to the value of interest so we need them. You need to post the correct vectors. If your other piece of software can write them to a text file, just post that.

2) Post the non-normalized data. Normalizing each vector individually could affect the results of subsequent calculations, so don't do it unless you have a very good reason. If you do want to normalize, find the offset of the lowest minimum, and subtract that from all the data.

Richard

[ptc-1368288]

Richard,

>You need to post the correct vectors<<br>
We need the f(x,y) formula that generates the vectors, and easy to get the local min/max of the project directly, as explained in my reply to Tom about Cardan. In fact, the collab never realised that Mathcad could do so much, so easily. The intermediate approach is a !!!generous data set !!! and then spline. That is in case there would be proprietary information about the generating formula.

Jean

[jasius-disabled]

Gents,

you are not getting my point. I am calculating series of values with quantum chemical methods and combining them in these vectors. Those are abstract values. So you understand what I am talking about, I attached an output file from quantum chemical software package. There is a value called total: -817.46092406325488. I take it and 16 other values from the same set of calculations, offset everything to the lowest value and make it zero, so I get what's called relative values. these are the numbers I plotted and these are the values I need halp with interpreting, when this Inflection (or whatever you call it) appears

Jonas

[ptc-1368288]

>Gents,

You are not getting my point. I am calculating series of values with quantum chemical methods and combining them in these vectors.<<br> _______________________

That's what I was asking for: +++++ vectors of values, so to get the surface plot and get your min/max ! peanut doing in Mathcad. Better some collab might get the formula working, bingo !

jmG

[RichardJ]

On 9/11/2009 1:08:23 PM, jasius wrote:
>Gents,
>
>you are not getting my point.

I think we are, but you are not getting ours.

>I am calculating series of
>values with quantum chemical
>methods and combining them in
>these vectors.

I had guessed the results came form some computational chemistry package.

>Those are
>abstract values.

I think you mean they are on arbitrary scales?

>So you
>understand what I am talking
>about, I attached an output
>file from quantum chemical
>software package. There is a
>value called total:
>-817.46092406325488. I take it
>and 16 other values from the
>same set of calculations,
>offset everything to the
>lowest value and make it zero,
>so I get what's called
>relative values. these are the
>numbers I plotted and these
>are the values I need halp
>with interpreting, when this
>Inflection (or whatever you
>call it) appears

The fact that all the vectors are on arbitrary scales does not matter as long as they are all on the same arbitrary scale. So there are a couple of possibilities:

1) Each vector was on a different arbitrary scale before you did any normalization. That's potentially a problem. We need to interpolate on the concentration-energy axes, and that means all the energies must be on a common scale. If the only difference between the scales is the offsets then in this case it will not affect the analysis. It would seriously screw up a lot of other possible analyses though. If the arbitrary scales have different scaling factors, what you want to do cannot work.

2) Each vector was on the same arbitrary scale before you did any normalization. If you have subtracted a different number from each one they are now not on the same arbitrary scale. As it happens, the different offsets will not matter for this analysis, but in general they will.

And we still don't have replacement vectors for the short ones: z_2 and z_5. We need those to proceed. It's not possible to interpolate two vectors that don't have the same number of points.

What you want to do can be done in Mathcad, but not without the right data.

Richard

[ptc-1368288]

Right, Richard:

We need either the abundant data set for spline surface in case there is proprietary information or the best would be the function that generates the data set.

jmG

[RichardJ]

The data is not generated using a simple function.

Richard

[ptc-1368288]

On 9/12/2009 12:20:21 PM, rijackson wrote:
>The data is not generated
>using a simple function.
>
>Richard
__________________________

I can see that from the monster file "job.last" . So far, the collab has complied 3 vectors, we need more. Maybe he should have that software produce automatically what he is doing manually. and for the part that this software can't do, Mathcad will. For what it looks and the scope of the project, this software must be reprogrammed

In the mean time, I'm gone up until ++++ vectors.

jmG

[TomGutman]

But we don't have to interpolate between the vectors. All we want is the z value where the curve changes from one peak to three peaks. We only need to interpolate the discriminant -- which can be done regardless of the lengths of the vectors involved.
__________________
� � � � Tom Gutman

[TomGutman]

And here is the result of calculating the discriminants.
__________________
� � � � Tom Gutman

[RichardJ]

If Jonas posts the two correct vectors it will be interesting to compare you solution to the one found by interpolation.

Richard

[ptc-1368288]

On 9/13/2009 9:14:10 AM, rijackson wrote:
>If Jonas posts the two correct
>vectors it will be interesting
>to compare you solution to the
>one found by interpolation.
>
>Richard
_______________________________

I was on the impression that Data XX(1519) were from Jonas, except for two vectors missing one (1) point each.



jmG

[RichardJ]

On 9/13/2009 10:11:56 AM, jmG wrote:

>I was on the impression that Data
>XX(1519) were from Jonas,

Yes

>except for two
>vectors missing one (1) point each.

Except that that "except" is a very big except!

Richard

[TomGutman]

The data in xx(1519) are all from Jonas, including the two short vectors. It was just a massive copy and paste job to put the data into some sort of structure. No data were modified, omitted, or invented.
__________________
� � � � Tom Gutman

[ptc-1368288]

On 9/13/2009 3:56:20 PM, Tom_Gutman wrote:
>The data in xx(1519) are all
>from Jonas, including the two
>short vectors. It was just a
>massive copy and paste job to
>put the data into some sort of
>structure. No data were
>modified, omitted, or
>invented.
>__________________
>� � � � Tom Gutman
______________________________

I must have missed them.. it does happen that in the transmission, part of the work sheet shifts down very far and if the top part makes sense, then the remaining is missed. Sorry for Jonas but Data[1], and Data[2] are short of on value each and can't be invented.

Thanks for your reminder.

jmG

[TomGutman]

Since the data plot makes it fairly clear that the two short vectors are just missing the first x value, you can remove the first value from the other vectors (including a) and then you have uniform length vectors. You can put that into a matrix and use a 2D cubic spline interpolation, or a set of 1D cubic spines (which could be done even with unequal length vectors), or whatever other interpolation scheme you deem useful. That first point won't make much of a difference.
__________________
� � � � Tom Gutman