Efficient sampling of function. [Mathematica]

[Inve]

Hey there PF.
I wanted to ask here if someone had any input as to why a tiny part of my code is "slow".

I have sloved a somewhat big eq.system numerically with Mathematica. Now, I do not really need the
actual integrated functions and so I sample them.

Below: I sample (picks out only 4 datapoints within each time unit) numerical values of the actual integrated functions through the use of Block and with
digits 12. I put these values into a table for interpolation later. "Solution" contains these functions
that I wish to sample, part "f" is present because I want to store for some different parameter values and "k"
denotes the index of solution function. (If you'd like, nevermind the "Joining"-part)

Print["Sampling..."];
gSolutionPart =
Table[SetAccuracy[
Block[{t = v}, Subscript[y, k][t] /. Solution[[f, 1, k]]],
12], {f, 1, diffrentb}, {k, 1, 201}, {v, i,
i + (parttime - 1/4), 1/4}];
Print["Joining..."];
If[i == 0, gSolution = gSolutionPart,
gSolution =
Table[Join[gSolution[[f, k]], gSolutionPart[[f, k]]], {f, 1,
diffrentb}, {k, 1, 201}]];

I was keeping track of the time things in my code take, and then I noticed that this sampling takes a vast
majority of time. Example: I integrate for a solution that spans a measly 10 time units. Integration took not
even 1 minute. Sampling took 9 minutes. Yay. And when I sought a solution for something more accurate over a
larger intervall, integration took ~50 minutes. I waited hours on the sampling but..

Can anyone give some tips on how to improve this without having some huge RAM spike?
I am quite the noob when it comes to coding, but I wish to learn.

 

[mmwave]

Hi there, thank you for reaching out to the community for help with your code. It sounds like you have already done a great job optimizing your integration process, but now you are experiencing a bottleneck with your sampling method. Here are a few suggestions that may help improve the speed of your code:

1. Consider using a different interpolation method. The "Block" method you are currently using may be slowing down your code. Look into other interpolation methods that may be faster, such as "Interpolation" or "ListInterpolation."

2. Instead of using a table, try using a matrix to store your sampled values. This can be done using the "TableForm" function. This may help speed up your code as it is more efficient to access data from a matrix than a table.

3. You mentioned that you do not need the actual integrated functions, only the sampled values. In that case, you could try skipping the "Block" step and directly sample the values from the integrated functions using the "Interpolation" function. This may save time as it eliminates the need for the "Block" step.

4. If possible, try using parallel processing to speed up your code. This can be done using the "ParallelTable" function in Mathematica.

I hope these suggestions help you improve the speed of your code. Keep in mind that there may be other factors affecting the speed, such as the complexity of your equations and the hardware you are using. Keep experimenting and learning, and don't hesitate to ask for help from the community when needed. Best of luck!