phi | ports chi | Performance Testing library

I need to give these integers names like ex_number_1, ex_number_2, ex_number_3, etc... These are each going to be saved as a different branch of a tree. So I have done:

I deployed my server on Heroku but when I make any requests it returns a "500 Internal Server" error. It runs fine locally though. Could anyone help figure out what's going on?

When I check my logs this is what I'm getting.

I used barplot3d::barplot3d to visualize my data. I have been trying to assign a color to each row instead of using topcolors = rainbow(100), but I could not figure it out. I appreciate any helps, suggestions, or references.

Here is the code that I have:

I can use \DeclareUnicodeCharacter{0278}{\phi} and then $ɸ$ to display the ɸ symbol in LaTeX. However, when I try to use:

the code below is from the book "Python for Probability, Statistics, and Machine Learning. The clarification needed is for the plotting section. The problem is that "logJ" in the script is not-defined. However, the book provides this as the code to plot the graph. How do you correct (code) the plotting part of the script so it plots the output shown?

I am trying to make a script that prints a set of characters based on their Unicode names (What I mean by 'Unicode name' is that I want to use the character's 'description', not the codepoint).

I understood that the standard way to do it for a single character is to do:

Let's say I have a pytorch-model describing the evolution of some multidimensional system based on its own state x and an external actuator u. So x_(t+1) = f(x_t, u_t) with f being the artificial neural network from pytorch.

Now i want to solve a dynamic optimization problem to find an optimal sequence of u-values to minimize an objective that depends on x. Something like this:

min sum over all timesteps phi(x_t)

s.t.: x_(t+1) = f(x_t, u_t)

Additionally I also have some upper and lower bounds on some of the variables in x.

Is there an easy way to do this using a dynamic optimization toolbox like pyomo or gekko?

I already wrote some code that transforms a feedforward neural network to a numpy-function which can then be passed as a constraint to pyomo. The problem with this approach is, that it requires significant reprogramming-effort every time the structure of the neural network changes, so quick testing becomes difficult. Also integration of recurrent neural networks gets difficult because hidden cell states would have to be added as additional variables to the optimization problem.

I think a good solution could be to do the function evaluations and gradient calculations in torch and somehow pass the results to the dynamic optimizer. I'm just not sure how to do this.

Thanks a lot for your help!

I want to calculate integral of implicit function containing imaginary numbers

where f(iz) is something like:

and g(ix) is something like:

I want to calculate it numerically. Python scipy.quad doesn't calculate integrals of imaginary numbers (explained in Code 1 below). Quadpy isn't efficient also, because it passes entire numpy array instead of single values of integral (explained in code 2 below) and thus needs additional manipulation. So I am thinking about dividing integrals like in the way shown below (where Re is real part and Im is imaginary part):

and expanding above equation:

Can I do that?

And here are codes, where I show two ways to approach the problem.

Code 1:

First approach scipy.quad. According to: Use scipy.integrate.quad to integrate complex numbers I tried dividing into real and imaginary parts and calculating integral values of them separately:

I have a square matrix of some probabilities, call it Phi, stored as a pandas Dataframe. I want to try multiplying this matrix by itself a large number of times to see what happens. I can easily 'square' the matrix with: