asymptote | 2D & 3D TeX-Aware Vector Graphics Language | Graphics library

I am trying to write a script that will take an input array of x and y values and fit them to a 5-PL curve (defined by the equation F(x) = D+(A-D)/((1+(x/C)^B)^E)). I then want to be able to use the predicted curve to take a given y value and extrapolate an x value from the curve, given by the equation F(y) = C(((A-D)/(-D+y))^(1/E)-1)^(1/B).

The answer below fixed the previous error, but the fit is still really bad. I've introduced a print function with a handful of y values across the range fed into curve_fit, and it yields almost the exact same x value across the range. Any ideas what may be going on here?

Edit: For anyone looking now, the problem appears to have been my estimate for B. The hill slope should be between -1 and 1 in most cases, not in the thousands. That made it too far to estimate.

I have a hyperbolic function and i need to find the 0 of it. I have tried various classical methods (bisection, newton and so on).

Second derivatives are continuous but not accessible analytically, so i have to exclude methods using them.

For the purpose of my application Newton method is the only one providing sufficient speed but it's relatively unstable if I'm not close enough to the actual zero. Here is a simple screenshot:

The zero is somewhere around 0.05. and since the function diverges at 0, if i take a initial guess value greater then the minimum location of a certain extent, then i obviously have problems with the asymptote.

Is there a more stable method in this case that would eventually offer speeds comparable to Newton?

I also thought of transforming the function in an equivalent better function with the same zero and only then applying Newton but I don't really know which transformations I can do.

Any help would be appreciated.

This is the correct graph of x^(1/3):

However, when trying to plot x**(1./3) on gnuplot, this is what I get:

How can I fix this?

Additionally, it is not the first time that gnuplot doesn't plot values around zero in other functions (when it is supposed to, of course: I'm not talking about asymptotes etc.). What can I do?

I finally understood why my car in unity can't drift/powerslide like cars do in other racing games. Feel free to skip the boring part and only read the question down below if you know this issue.

problem: Not realistic car grip/drift happens because tire slip value (from which the tire grip is evaluated) is separately measured for forward and sideways friction of wheel. This means that when you are in a turn with RWD car and you give car more throttle, rear tires lose forward grip and start to slip forward but car won't start to drift sideways like in reality because even though rear tires started slipping forward, sideways slip is still the same thus there will be no change on sideways friction curve and car will not lose any sideways grip. For the same reason cars with unity wheel colliders can't do handbrake turns because rear wheels will start to slip forward but that only influences forward grip not sideways.

real tire physics: From a physics standpoint it's obviously not realistic because when tire starts to slip it goes from static friction where it sits on road to kinetic friction where it is doing lots of little jumps and this "jumping state" of kinetic friction affects tire grip in all directions not just forward or sideways separately.

my theoretical solution: So the obvious solution would be that we can keep separated friction curves (because of different tire tread designs) but the slip value for these friction curves must be only one, evaluated as magnitude of vector2 of sideways and forward tire movement (slip). Unfortunately we can't modify slip value only extremum, asymptote and stiffness of friction curve.

finally the question: Is there something that I am missing with separated forward and sideways slips to make car drift realistically and if not, is there any workaround with friction curve parameters to fix this issue or can you suggest me some alternative wheel colliders which doesn't have this issue?

THX in advance :)

I am trying to visualize the graph of this function with matplotlib.

f(x) = (x*x*x) / (x*x - 3*x + 2)

This function has a pretty interesting properties and graph.

It has as vertical asymptotes the lines x=1 and x=2.
Also, it has another asymptote y=x+3 which f(x) approaches
as x tends to plus and to minus infinity.

It has a local maximum at 3-sqrt(3) and local min at 3+sqrt(3).

But the graph looks very ugly because the scale on the Y axis
is produced way larger than the scale on X axis. I guess that is
because the function is not defined for x=1 and x=2.

See a (slightly) better graph here:
https://www.wolframalpha.com/input/?i=x*x*x+%2F+%28x*x+-+3*x%2B2%29+

How can I make this graph look nicer with matplotlib?
Or... is this not possible and I should use some other library instead?

Here is my code.

Use R to plot the hyperbola x² - y²/3 = 1, as in Figure 4.3:

I'm trying to make a little game where the user can click on a place on the page, the circle will follow to the pointer's position, and from there, the user can drag their mouse to make the circle move like a slingshot. I want the circle to be able to bounce off the walls.

However, it seems that on the circle's collision with a wall, the circle seems to 'stick' to the wall instead of bouncing right off. I think it might be because of the circle changing directions too quickly due to a rounding error? Also the top wall's collision hasn't been implemented yet because I don't think I declared the top wall div object properly.

I have a multi-label classification in which each target is a vector of ones and zeros not mutually exclusive (for the sake of clarity, my target is something like [0, 1, 0, 0, 1, 1, ... ]).

My understanding so far is:

• I should use a binary cross-entropy function. (as explained in this answer)

• Also, I understood that tf.keras.losses.BinaryCrossentropy() is a wrapper around tensorflow's sigmoid_cross_entropy_with_logits. This can be used either with from_logits True or False. (as explained in this question)

• Since sigmoid_cross_entropy_with_logits performs itself the sigmoid, it expects the input to be in the [-inf,+inf] range.

• tf.keras.losses.BinaryCrossentropy(), when the network implements itself a sigmoid activation of the last layer, must be used with from_logits=False. It will then infert the sigmoid function and pass the output to sigmoid_cross_entropy_with_logits that will do the sigmoid again. This however can cause numerical issues due to the asymptotes of the sigmoid/logit function.

• To improve the numerical stability, we can avoid the last sigmoid layer and use tf.keras.losses.BinaryCrossentropy(from_logits=False)

Question:

If we use tf.keras.losses.BinaryCrossentropy(from_logits=False), what target should I use? Do I need to change my target for the one-hot vector?

I suppose that I should apply then a sigmoid activation to the network output at inference time. Is there a way to add a sigmoid layer active only in inference mode and not in training mode?

I have made a rarefaction curves using the iNEXT package in R and added two horizontal lines for the asymptotes of both curves manually (the package does not do that, so I tried to utilize ggplot functions and it seemed to work), furthermore I extended the x/y axis. Unfortunately, my skills are apparently too limited to figure out how to add the asymptotes in the legend of the graph under, labelled as "Asymptotes: North and South" (or something like that). I would very much appreciate the help. I added my code below and the graph as a picture, if something is missing, let me know!

Best wishes and stay healthy!