parfor | A package to mimic the use of parfor as done in Matlab

I want to generate same normal random numbers for loop and parfor loop. Following MATLAB documentation I tried three different method:

Method 1: Using rng(seed, 'twister')

I need some help with parallel programming in MATLAB. To be clear, I have never implemented parallelization techniques in any of my codes before. I have a video compression engine, developed as part of my university project. It is a basic verion of H.264 video compression engine. I have to implement the parallel proceesing techniques available in MATALB to this engine. Basically, I have a function which divides an image frame into a number of blocks (predtermined by the size of the block). I'm trying to partially or fully parallelize this block of the code. I have used "parfor" when there was no dependency between the blocks, and this worked out well. I have uploaded this implementation. Now I'm trying to parallalize a case were there are dependencies between blocks.

I am currently running a compute-intensive financial trading test; the test has 503 independent loops. I have two PCs in my office, one has 10-core Intel i9-10900k @ 3.7GHz with 128GB DDR4; the other one has 18-core Intel i9-7980XE @ 3.4GHz with 128GB DDR4 as well.

In order to speed up the whole processing, the first 10-core PC runs loop 1-to-189 in parfor; the second 18-core PC runs loop 190-to-503 in parfor.

After one-day running, I found the 10-core PC finished 25 loops, the 18-core PC only finished 4 loops. I found very curious, can anyone know the reason of this problem?

P.S. 10-core PC running MATLAB 2020b with latest updates with MOSEK 9.2.35 18-core PC running MATLAB 2021a with latest updates with MOSEK 9.2.36

I also checked the taskmgr.exe, unlike the 10-core PC, I found in 18-core PC, 10 matlab tasks are in one group, the other 10 tasks are seperated....

I'm running a parallel Matlab job on a single node of a remote cluster. Each node of the cluster has 2 processors with 24 cores each, for a total of 48 cores per node. The job contains some sequential code followed by a single parfor loop. I run it using a slurm bash script.

The bash script test.sh is:

I am using Matlab to work on my project, and I want to use "parfor" as a part of my code that returns an array of structures in each its iteration, But when I run my code I got some errors. I just tried to bring an example of my problem in the simplest way. Will be appreciated any helps! Here is the example:

I have huge dynamically created tables/matrices in MATLAB of varying first dimension, whose rows represent (sorted) combinations of integers in the range 1-50 of order 6.

I would like to assign to each combination a unique value (hash, ranking), so that I can check if the same combinations appear in different tables. Different combinations are not allowed to have same value assigned, i.e. no collisions. I have to make a lot of such comparisons between a lot of such tables. So, for performance reasons, I would like to accomplish this by vectorization of uint32 operations to make it suitable for GPU acceleration in MATLAB.

Things I have thought of so far:

1. Lexicographic ranking: no idea how to vectorize the standard fast recursive algorithms well, and the only option seems to be to parfor it through the rows, which is slower than other options. IIRC, the direct explicit formula, though vectorizable, requires computation of binomials, which in turn requires log Gamma function in order to avoid huge factorials + double type to avoid collision if I am not mistaken, i.e. is slower because it's 'very numerical'.
2. Cantor pairing function: one can successively apply Cantor's pairing, which is nice because it's a polynomial expression, but it produces huge numbers well beyond uint32 and is definitely slower than other options.
3. Base 51 (no pun intended) integers: sends a combination/row vector (x_1,...,x_6) to x_1 + x_2 * 51 + ... + x_6 * 51^5. This is the fastest I currently have. It's easily vectorizable, but unfortunately still requires uint64 or double for rank-6 combinations of 50 elements, which is slower than uint32 or single type operations would be.

So, I guess, I am looking for a 'clever' injective function on these combinations that computes within the uint32 range and is also well vectorizable (in MATLAB).

Any help would be much appreciated!

EDIT: Here is a routine that benchmarks both ranking and searching in uint32, single, and double. I have used MATLAB's gputimeit to produce accurate results.

I am using 'fminsearch' in Matlab to solve the value function iteration problem.

I have an assignment to implement a parallel version of the longest common subsequence algorithm (just calculating the LCS length). The program must use threads in order to complete the task as quickly as possible (at least, faster than a sequential implementation). Ideally, it should also utilize TLS in the threads. We had a similar assignment that implemented a template within a .hpp file and I want to use the same template, but it does not seem like I can use a .hpp file in this assignment. My problem lies in passing the template function to my threads. Below is the code:

I am using Pari/GP to test (pseudo)primality of a sequence of numbers f(n), where f(n) is some function. I have parallelized the code as