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f(x, y) = positive random number, find df

Anonymous Tue 10 Nov 06:51:17 2020 No.12325277 View Reply Original Report

Quoted By: >>12325524 >>12325851 >>12325893 >>12326798

Mathfags help me out: I have blackbox program f(x, y), and each time I change the variable x and y, the result becomes somewhat random (large, small, but always positive numbers). X and y also will always be positive.

How to find df? Is slope formula my only chance? If so, can I use the slope formula onto the previous slope formula's result as a workaround to find the higher order slope?

Anonymous

Anonymous Tue 10 Nov 2020 09:22:20 No.12325524 Report

Quoted By: >>12325711

>>12325277
f is not differentiable sorry

Anonymous

Anonymous Tue 10 Nov 2020 11:18:16 No.12325711 Report

Quoted By: >>12325734

>>12325524
I see. Then, may I change the question: Since I cannot differentiate or solve the issue above, is it alright if I use the slope formula on the nonlinear/random lines, to find out how much the value has changed and how much the rate of change has changed? I dont really care about the equation, I just want to know what happened and what is happening.

Anonymous

Anonymous Tue 10 Nov 2020 11:32:34 No.12325734 Report

Quoted By: >>12327632

>>12325711
Differentiation is literally based on the slope formula. Differentiation is used for functions which
don't have constant slope throughout. It's not quite clear what you want. I would suggest a
polynomial interpolation for the function. And then differentiate that.

Anonymous

Anonymous Tue 10 Nov 2020 12:21:19 No.12325851 Report

Quoted By: >>12327632 >>12328173

>>12325277
run the function a decent number of times
plot the graph, so you can visualize it better
choose a good differentiable approximation
profit

Anonymous

Anonymous Tue 10 Nov 2020 12:33:17 No.12325893 Report

Quoted By: >>12327632

>>12325277
A basic way to do this is to evaluate the function with small steps, dx, and dy, to get the derivatives

[df/dx] = (f(x+dx, y) - f(x, y))/dx
[df/dy] = (f(x, y+dy) - f(x, y))/dy

https://en.wikipedia.org/wiki/Numerical_differentiation#:~:text=In%20numerical%20analysis%2C%20numerical%20differentiation,other%20knowledge%20about%20the%20function.

Anonymous

Anonymous Tue 10 Nov 2020 17:12:34 No.12326798 Report

Quoted By: >>12326834 >>12327632

>>12325277
>positive random number
so the same x and y can yield different outcomes? That's no even a function.
Example: f(1,3) should always yield the same.

Anonymous

Anonymous Tue 10 Nov 2020 17:20:51 No.12326828 Report

Quoted By: >>12327632

given $f(x,y)$ , find $df(x,y)$ .

The infinitesimal path along which you want construct df is not given.
Therefore assume that $y = g(x)$ where $g(x)$ is linear.
Now, we have $f(x,g(x))$ , where $y = g(x)$ is any linear function of x.
$df(x,g(x)) = f'dx$ or $df(x)/dx = f'(x,g(x))+f'(x,g(x))g'(x)$ which is another expression for $df(x) = f'(x)dx+f'(x)g'(x)dx$ .
This can also be expressed as $df(x) = f'(x,y)dx+f'(x,y)dy$ .

Anonymous

Anonymous Tue 10 Nov 2020 17:23:43 No.12326834 Report

Quoted By: >>12326986 >>12327632

>>12326798
>each time I change the variable x and y, the result becomes somewhat random

I assume what he means is that f(x,y) will always be the same for a given x and y but he can't predict what f is going to be for any given input.

Anonymous

Anonymous Tue 10 Nov 2020 18:08:48 No.12326986 Report

Quoted By:

>>12326834
Well in that case it's an odd use of terminology, he'd have to explain what he means by "random". If he means noisy, but smooth up to noise, it's a completely different thing.

Anonymous

Anonymous Tue 10 Nov 2020 18:14:59 No.12327013 Report

Quoted By: >>12327632

>Blackbox program
Why do CS retards do this?

Anonymous

Anonymous Tue 10 Nov 2020 18:34:29 No.12327077 Report

Quoted By: >>12327632

The thing that you want to do is to find number A, B such that
$f(x+h,y+k)=f(x,y)+Ah+Bk+ R(h,k)$
where R(h,k) is a reminder function such that, $\lim\limits_{(h,k)\to 0} \frac{R(h,k)}{\sqrt{h^2+k^2}}=0.$
If such numbers A,B and function R exists, then
A is the partial derivative of f with respect to x and B is the partial derivative of f with respect to y.

Anonymous

Anonymous Tue 10 Nov 2020 19:29:02 No.12327309 Report

Quoted By: >>12327632

Going on the assumption that by random you mean that you just don't know the mapping from f(x,y) -> z and not that f(x,y) involves sampling a random variable for each (x,y) pair, then you can approximate gradient information by finite difference approximation. Consider for your example you look at f(x + eps, y) - f(x - eps, y)/ 2eps for the approximation of the derivative wrt to x. This is essentially what the slope formula would give you. I would question for what application you need the numerical approximation of the higher-order derivatives of a black-box function.

Anonymous

Anonymous Tue 10 Nov 2020 20:55:51 No.12327632 Report

Quoted By: >>12327857 >>12328744

>>12325734
>It's not quite clear what you want.
>>12327309
>I would question for what application you need the numerical approximation of the higher-order derivatives of a black-box function
I am actually just interested in whether if f(x, y) are increasing, decreasing, will stop or continue on changing, etc. based on their derivatives. Like if their slope at their latest x,y, is positive, I know that f is going up, but if their higher order derivative is negative, I can assume that f is braking, and if its even higher derivative is negative, I can conclude that f is braking hard and will stop very soon.

>>12327013
>Why do CS retards do this?
Sorry.

>>12325851
>run the function a decent number of times
>plot the graph,
Actually I dont have the function, I only have the results.
Here is the example:

F(0, 0) = 100
F(0, 1) = 11
F(0, 2) = 45
F(0, 3) = 743
F(0, 4) = 2
F(0, 5) = 101

F(1, 0) = 7530
F(1, 1) = 272
F(1, 2) = 700
F(1, 3) = 52
F(1, 4) = 21
F(1, 5) = 527

F(2, 0) = 1
F(2, 1) = 975
F(2, 2) = 3
F(2, 3) = 7474
F(2, 4) = 264
F(2, 5) = 12

F(3, 0) = 648
F(3, 1) = 8027
F(3, 2) = 68
F(3, 3) = 17
F(3, 4) = 376
F(3, 5) = 2403

>>12326798
>f(1,3) should always yield the same.
>>12326834
>I assume what he means is that f(x,y) will always be the same for a given x and y but he can't predict what f is going to be for any given input.
Correct. Sorry for the missing info.

>>12327077
>>12326828
>>12325893
Thank you but I already know how to do partial/total differential. What I don't know is that can I use the method based on only the result of f(x, y).

To all, I am very sorry for burdening you with my stupidity...

Anonymous

Anonymous Tue 10 Nov 2020 21:22:16 No.12327772 Report

Quoted By: >>12327859

So for example, my total derivative for latest data point (x -> inf, y -> inf), equals to dfdx/dx + dfdy/dy which will be

= [f(3, 5) - f(2, 5)] + [f(3, 5) - f(3, 4)]
= (2403 - 12) + (2403 - 376)

Am I understanding these correctly?

Anonymous

Anonymous Tue 10 Nov 2020 21:45:38 No.12327857 Report

Quoted By: >>12327880

>>12327632
Can you generate as much as you want

Anonymous

Anonymous Tue 10 Nov 2020 21:45:49 No.12327859 Report

Quoted By: >>12327880

>>12327772
yes

Anonymous

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Anonymous Tue 10 Nov 2020 21:53:51 No.12327880 Report

Quoted By: >>12327895

>>12327859
THANK YOU

>>12327857
Yes!

Anonymous

Anonymous Tue 10 Nov 2020 21:57:07 No.12327895 Report

Quoted By: >>12327904

>>12327880
since its 2D you can make a grid. Then you can plot it and see if it is noisy but generally "smooth" or not.

Anonymous

Anonymous Tue 10 Nov 2020 21:59:20 No.12327904 Report

Quoted By: >>12327929

>>12327895
Eh? I thought it is 3d?

x on x-axis, y on y-axis, and f(x,y) on z-axis?

Anonymous

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Anonymous Tue 10 Nov 2020 22:06:07 No.12327929 Report

Quoted By: >>12328173 >>12328190

>>12327904
yes, and? You need a 2D gird of (x,y) values and compute f(x,y). The result is a graph in 3D space.

Anonymous

Anonymous Tue 10 Nov 2020 23:24:02 No.12328173 Report

Quoted By: >>12328190

>>12327929
This is what I (>>12325851) told you to do.
See the pattern and try to choose a data fitting method that yields a differentiable function.
Could this function be related to something where local partial derivatives are more important than the whole thing?

Anonymous

Anonymous Tue 10 Nov 2020 23:27:49 No.12328190 Report

Quoted By: >>12328250 >>12328439

>>12327929
I see. Anon, now I know how to find the differential with respect to the x axis, and y axis. But how to find the differential with respect to the diagonal of x axis and y-axis such as between f(2, 4) and f(3, 5)? Is it impossible or against the law?

>>12328173
>try to choose a data fitting method that yields a differentiable function.
I wont like that to happen, to me the real value is very important.

>Could this function be related to something where local partial derivatives are more important than the whole thing?
What do you mean by "the whole thing"?

Anonymous

Anonymous Tue 10 Nov 2020 23:51:00 No.12328250 Report

Quoted By: >>12328744

>>12328190
That's just a directional derivative, and defined as the scalar product of the gradient with the direction vector (normalized)

Anonymous

Anonymous Wed 11 Nov 2020 00:36:36 No.12328439 Report

Quoted By: >>12328744

>>12328190
Nevermind, I was talking about come constrained systems where local partial derivatives can be wildly different depending on location on no one equation could represent those disparities.
I'm still trying to wrap my head in what do you want to get, is it the diff eq of the blackbox so you can try to solve it?
Also, that the slope you want is 3d

Anonymous

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Anonymous Wed 11 Nov 2020 02:21:27 No.12328744 Report

Quoted By: >>12329795 >>12329809 >>12329862 >>12329984

>>12328250
>direction vector (normalized)
So my u is (1, 1) since I want to go from (2, 4) to (3, 5)? What does directional derivative can tell me tho if my output's behaviour is like above post: >>12327632

>>12328439
>I'm still trying to wrap my head in what do you want to get, is it the diff eq of the blackbox so you can try to solve it?
No, I don't want to solve the equation or trying to predict the future value. I just want to be able to tell what is going on with the output.

Replace x with height, h and y with time, t. Then I can compare the df/dt when h=0 with the df/dt when h=3 (top), as t:0->5, if it is bigger then I can conclude that f is more active when h is 0 more than when h is 4. I can also compare the df/dh when t=5 with the df/dh when t=4, as h:0 -> 3, if it is bigger, then f wants to be active on a higher unit of height. Am I correct to conclude the data like this? Am I retarded?

Anonymous

Anonymous Wed 11 Nov 2020 11:36:13 No.12329795 Report

Quoted By: >>12329809

>>12328744
in your case,
$u=\sqrt{\frac{1}{2}}\begin{pmatrix}1\\1\end{pmatrix},$ like I said, normalized.
A directional derivative only gives you a 1D slope in a given direction. Honestly I don't see what you'd want with it, unless you have a good reason to look at that direction.

On a sidenote, you've only provided integer examples. So I assume whatever you're looking at only accepts integer values?

Anonymous

Anonymous Wed 11 Nov 2020 11:41:48 No.12329809 Report

Quoted By: >>12329823

>>12329795
I think I wont be using directional differential then. I cannot think how I can make use of the values.

>So I assume whatever you're looking at only accepts integer values?
Correct. Anon, can you answer my question in this post
>>12328744
>Am I correct to conclude the data like this?

Thank you for your time!

Anonymous

Anonymous Wed 11 Nov 2020 11:51:49 No.12329823 Report

Quoted By: >>12329833

>>12329809
Do you mean by h the offset you use for an approximate derivative?

Anonymous

Anonymous Wed 11 Nov 2020 11:59:51 No.12329833 Report

Quoted By: >>12329867

>>12329823
Eeh, no.. h is height. I will be using dx or dy if I was talking about the variable offset or timestep.

Anonymous

Anonymous Wed 11 Nov 2020 12:15:50 No.12329862 Report

Quoted By: >>12329984

>>12328744
>Am I correct to conclude the data like this? Am I retarded?

If the blackbox a pure pseudo random function why would you assume assume the slopes from the partial derivative would allow you to predict future values? Good RNG functions would in fact be designed against this.

Anonymous

Anonymous Wed 11 Nov 2020 12:18:23 No.12329867 Report

Quoted By: >>12329984

>>12329833
>height
height of what? the graph at a given point? So you mean the value f(x,y)?

Anonymous

Anonymous Wed 11 Nov 2020 13:28:33 No.12329984 Report

Quoted By: >>12330287 >>12331980 >>12332126

>>12329867
In my earlier post, 3rd para, >>12328744 I wrote
>Replace x with height, h and y with time, t

>>12329862
I see. It is not a random function actually. I might've lied in the OP. The f(h, t) is actually the number of clicks to my workplace new landing page based on the position of the hyperlink that I put at different height of the old landing page.

I am just trying to figure out what is the best height and what is the best time to display the hyperlink/popup to the workplace's new page. People have been complaining that the popup is distracting their work so I have to remove them for now, but thankfully I managed to perform the test and gathered the necessary data for each time interval and varied height of the popup.

Sorry for lying.

Anonymous

Anonymous Wed 11 Nov 2020 15:47:09 No.12330287 Report

Quoted By: >>12331677

>>12329984
Ah, misread, so f(h,t), and you wanna know how much f(h,t) changes as a function of t with h being more of a parameter, so you're more looking at something like $f_{h}(t)$ . If I were you I would REALLY visualize that data first. You can even make 1D plots if h is more of a parameter. Also, df/dt is not necessarily the best metric for rapid change.

Anonymous

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Anonymous Wed 11 Nov 2020 22:05:56 No.12331677 Report

Quoted By:

>>12330287
Thank you fren

Anonymous

Anonymous Wed 11 Nov 2020 23:18:41 No.12331957 Report

Quoted By: >>12332126

this thread smells of the classic 'retard thinks their middle-school math trick is going to beat the stock market'

Anonymous

Anonymous Wed 11 Nov 2020 23:22:25 No.12331980 Report

Quoted By: >>12332126

>>12329984
why don't you just plot clicks (z, or color ) vs time and position and fucking look at it

Anonymous

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Anonymous Wed 11 Nov 2020 23:58:14 No.12332126 Report

Quoted By:

>>12331957
Refer to 3rd para of this post >>12329984.

>>12331980
I don't want to eyeball, if possible i want to extract some numbers.

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