A Math Question

[ivor]

I have a math question.  I'm not good at math, but I have a problem and I don't even know how to ask the question properly.

I have two graphs that I want to be able to analyze mathematically.  At some point the graphs may be the same but not necessarily at the same point on the X axis.  The Y axis may also be higher or lower at the point on the X axis where they converge.  The two graphs will differ slightly or even more than a little.  The point of my question is how to find the points on the graphs where they converge the most.  Does any one know how to put this question in the proper terminology so I can find an equation that can compare the two graphs mathematically?  I need to find the delta between the X and Y axes of the two graphs where they converge.

I'm sure I could do this with a program by brute force but I'm looking for something fast and elegant.

[goat starer]

its still 'maths' not math. I thougt we had agreed this 

[beagle]

its still 'maths' not math. I thougt we had agreed this 

Oh, the irony...


I suspect we'll need Swato for this one. So far I'm not sure what MB means by "converge" and "converge the most" and "same".

Are you trying to find the x point at which the y values of the two graphs are closest?

Or

The x point at which one graph is moving most rapidly in the direction of obtaining the value of the other at that same x point.

Or

Are you trying to get a best match of the shape of one line segment of one graph in any part of the x-y space against the most similar shape in the other graph at any part of the x-y space?
(Your mention of the delta seems to imply this one). If so then you'd need to define how to penalise differences between line segments' shapes, how long the line segment has to be, and other evil stuff like that.

Or

Something else...


Maybe you should describe the high level goal, then I'll explain why I haven't a clue, and pass control to Swato.

[ivor]

Are you trying to get a best match of the shape of one line segment of one graph in any part of the x-y space against the most similar shape in the other graph at any part of the x-y space?
(Your mention of the delta seems to imply this one). If so then you'd need to define how to penalise differences between line segments' shapes, how long the line segment has to be, and other evil stuff like that.

That's it exactly.

[Bob in a quantum-state-of-faith]

I have a math question.  I'm not good at math, but I have a problem and I don't even know how to ask the question properly.

I have two graphs that I want to be able to analyze mathematically.  At some point the graphs may be the same but not necessarily at the same point on the X axis.  The Y axis may also be higher or lower at the point on the X axis where they converge.  The two graphs will differ slightly or even more than a little.  The point of my question is how to find the points on the graphs where they converge the most.  Does any one know how to put this question in the proper terminology so I can find an equation that can compare the two graphs mathematically?  I need to find the delta between the X and Y axes of the two graphs where they converge.

I'm sure I could do this with a program by brute force but I'm looking for something fast and elegant.

Send a PM to Aphos... he has at least one advanced Math(s) degree, I think.

[beagle]

Sounds like good advice. 

Do you have the equations of the two graphs, or are they drawn from discrete measured values?

In the second case you might have to choose an interpolation method to give you aproximations to the two functions, and then work with those to find similar regions.

If you're trying to prove that the second graph is following the first, but with a time delay I guess you could minimise the difference in the areas under the two graphs in a loop where you rebase the y and time origins of the second in a loop shifted leftwards relative to the time axis of the first to find the best match. Either mechanically with a program or algorithmically.

I'd see what Aphos and/or Swato and/or Agujim and/or anyone else who has done this in the last twenty years say.  If they say polynomial interpolation and calculus of variations my advice is to run away quite fast.

[Aggie]

I'd see what Aphos and/or Swato and/or Agujim and/or anyone else who has done this in the last twenty years say.  If they say polynomial interpolation and calculus of variations my advice is to run away quite fast.

I took Calc 1 twice.  

_{I didn't actually fail the first time, and did OK the second time (got 75% on the final exam, because I finished 75% of it in the 3 hours allotted - stupid chalkboard-grunting, sandal-wearing old mathnazi-hippie professor), but I'd need to take it a third time to actually recall any of it.}

I understand what you're looking to do, but can't recommend anything better than brute-force-and-ignorance.  If I had number sets I could possibly browbeat Excel into doing something with the data, but that's largely based on my presumption that I can browbeat Excel into doing anything.

[Griffin NoName]

If they say polynomial interpolation and calculus of variations my advice is to run away quite fast.

If I say that too, run away even faster.

I'd use irriducible reductionism too.

Or

Draw a rectangle or parallelogram around each such that it touches on all four sides for each. Work out which bits don't fit for each. Throw them away. What you have left is the answer. You'll at least have some interesting equations along the way.

Oh, sorry, it's math not maths, ignore all that

Draw the graphs on tracing paper. Place graph A over graph B.

[Sibling Zono (anon1mat0)]

Do you have the equations of the two graphs, or are they drawn from discrete measured values?

If you have the equations it should be pretty easy to go through and use a delta on for the crossing (sorry for the poor drawing).

[Swatopluk]

I better keep out of this. I am weak in turning verbal descriptions of mathematical stuff into formula, especially if I am not accustomed to the exact terminology (and in English at least I am not).

[ivor]

Thanks for your help everybody!

I like that picture Zono, that's about right.

I don't really have any equations.  It's all discrete data.

[Sibling Zono (anon1mat0)]

Then the only problem is the space between points (if you have them) and determine if you need a simple line or estimate a rounded curve. There is an algorithm that gives you that curve between those points (which I believe is used by Excel) and you would only need to do a direct comparison (I forgot the name of the method though  ).

[goat starer]

its still 'maths' not math. I thougt we had agreed this 

Oh, the irony...

who keeps giving beagle hugs? he does not deserve them.

[anthrobabe]

its still 'maths' not math. I thougt we had agreed this 

Oh, the irony...

who keeps giving beagle hugs? he does not deserve them.

                                                                                             
poor dear----- 
but you know can't leave bagle out--