How to find maximum values in 3D plot?

Questions
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1

Dear All,

May I ask you something? I plotted a runoff (q) probability in 3D. I am expecting that the obtained result will show the variation of q.
Thus, may I know how to extract the values of q in the peak time, like in this case time to peak is around 39. Please refer to attach. for the illustration of my obtained figure plotted in 3D.

If I plot it by using 2D, I could obtained the maximum values for both, q and t, by using FindMaximum command. However, I am not sure how to obtain the maximum values for plotting in 3D. Please kindly let me know if you know how to do so. Thanks in advance for your kind help.

Best Regards,
Intan

2

Dear Intan,

I guess that I would need more information, on what exactly the problem is. The figure in the attached pptx document does not help.

In Maximize or NMaximize tend to work in 3D example. Let’s look at:

Plot3D[Cos[x^2 + y^2]*Exp[-0.3 (x^2 + y^2)], {x, -6, 6}, {y, -6, 6}, PlotRange -> All]

ScreenShot2015-02-19at10.41.11.png
ScreenShot2015-02-19at10.41.11.png383×295 30.3 KB

If you then simply use the Maximize function you get:

Maximize[{Cos[x^2 + y^2]*Exp[-0.3 (x^2 + y^2)] && -6 < x < 6 && -6 < y < 6}, {x, y}]
(*{1., {x -> -1.06836*10^-8, y -> -7.75192*10^-9}}*)

which says that the maximum value of 1 is reached at (numerically) {0,0}.

Cheers,
Marco

3

Dear Marco,

Thanks a lot for your reply. I am still not sure if Minimize command works for my case or not. If I am not wrong, for your example case, there is only 1 peak value which is 1 and it is occurred at x=0 and y=0. So what I would like to know, how if 1 plot consists of many peak values, like ensemble case, and I want to find out the maximum and the minimum values including the coordinate points of those max and min values. Thanks in advance for your help.

Best Regards,
Intan

4

Maximize worked for me for a different function (using t, Q as example variables with example ranges)-

Maximize[{ Function [ ], 0<t<200 && 0<Q<1000}, {Q,t}]

5

What was the function used to create the plot?

6

Hello Marco,
I found your reply here really helpful for me. May I ask you a followup question? Is there any way to indicate in the diagram the level of x and y where the maximum is achieved, and also the maximum?
Thanks!
Best,
Hyun Woong