PCG | Procedural Terrain Generation - Internship and Final Degree | Generator Utils library

This comes down to assigning a separate PRNG for each of your four (or more) stages of generation (in your example, track shape generation, terrain generation, surface generation, and asset picking), and assigning a seed to each one of them. (In your case, one way this can work is to form a hash of the racetrack ID, an ID for each generation stage, and a fixed bitstring, and use that hash as the seed for each PRNG.)

In general, however, your choice of seed may matter, in practice if not in theory.

For example, there are many PRNGs for which a given seeding strategy will produce correlated pseudorandom number sequences. For example, in most versions of PCG, two sequences generated from seeds that differ only in their high bits will be highly correlated ("Subsequences from the same generator").

To reduce the risk of correlated pseudorandom numbers, you can use PRNG algorithms, such as SFC and other so-called "counter-based" PRNGs (Salmon et al., "Parallel Random Numbers: As Easy as 1, 2, 3", 2011), that support independent "streams" of pseudorandom numbers by giving each seed its own independent sequence of pseudorandom numbers. (Note, however, that PCG has a flawed notion of "streams".) There are other strategies as well, and I explain more about this in "Seeding Multiple Processes".

See also:

• Best practices for seeding random and numpy.random in the same program
• Impact of setting random.seed() to recreate a simulated behaviour and choosing the seed

From https://ftdichip.com/wp-content/uploads/2020/08/TN_152_USB_3.0_Compatibility_Issues_Explained.pdf Section 2.1.2 Location ID Returned As 0

LocationIDs are not strictly part of the USB spec in the format provided by FTDI. The feature was added as an additional option to back up identifying and opening ports by index, serial number or product description strings.

When connected to a USB 2.0 port the location is provided on the basis of the USB port that the device is connected to. These values are derived from specific registry keys. As the registry tree for 3rd party USB 3.0 host drivers is different to the Microsoft generic driver the Location ID cannot be calculated.

There is no workaround to this current issue and as such devices should be listed and opened by index, serial number or product description strings.

So this is known behaviour. Btw Win 7 EOL date was january 2020. Changing the OS is strongly adviced.

I will try to answer to myself. To provide an answer, I tried an even more demanding example, with a matrix of size of (N,N) of about half a million by half a million and the corresponding vector (N,1). This, however, is much less sparse (more dense) than the one provided in the question. This matrix stored in ascii is of about 1.7 Gb, compared to the one of the example, which is of about 0.25 Gb (despite its "size" is larger). See its shape here,

Then, I tried to solve Ax=b using again Matlab, Octave and Python using the aforementioned the direct solvers from scipy, the intel MKL wrapper, the UMFPACK from Tim Davis. My first surprise is that both Matlab and Octave could solve the systems using the A\b, which is not for certain that it is a direct solver, since it chooses the best solver based on the characteristics of the matrix, see Matlab's x=A\b. However, the python's linalg.spsolve , the MKL wrapper and the UMFPACK were throwing out-of-memory errors in Windows and Linux. In mac, the linalg.spsolve was somehow computing a solution, and alghouth it was with a very poor performance, it never through memory errors. I wonder if the memory is handled differently depending on the OS. To me, it seems that mac swapped memory to the hard drive rather than using it from the RAM. The performance of the CG solver in Python was rather poor, compared to the matlab. However, to improve the performance in the CG solver in python, one can get a huge improvement in performance if A=0.5(A+A') is computed first (if one obviously, have a symmetric system). Using a preconditioner in Python did not help. I tried using the sp.linalg.spilu method together with sp.linalg.LinearOperator to compute a preconditioner, but the performance was rather poor. In matlab, one can use the incomplete Cholesky decomposition.

For the out-of-memory problem the solution was to use an LU decomposition and solve two nested systems, such as Ax=b, A=LL', y=L\b and x=y\L'.

I put here the min. solution times,

You can use complete to create dates which are missing and fill to fill the NA values from previous non-NA value for each ticker.

What about something like this?

There is a high chance that you are doing nothing wrong within your current approach (at least, I was not able to spot an obvious bug).

A couple of notes:

1. Residual of 29.10655954230801 and 2.5236861383747353 after 500 iterations are effectively the same: your iterative solution has not converged.
2. You seem to request a very high iterative solver tolerance of 1E-12. That would not matter here, as you have a problem that does not converge at all.
3. Factorization (of ILU) should take approximately this time. I am not surprised to see this number for such a system. Not so familiar with this implementation of Cuthill-McKee.

Without knowing where your system comes from, it would be very hard to say anything. However:

1. Check the condition number for your small version of the matrix (if it is somewhat representative of your original problem). High condition number would indicate a problem with the conditioning of the matrix; thus, potential poor convergence or ill-convergence of the iterative solution (or any type of solution in the extreme case).
2. Conjugate gradient is intended for systems that are symmetric and positive-definite. It can converge for other cases; however, it can fail for well-conditioned problems that are not positive-definite.

Let's start small. Say we have a method rng() that generates any random integer in [0, 128). If we map all of its 128 outcomes as follows (where X is one of these outcomes):

Does this code contain any undefined behaviour that would allow GCC to emit the "incorrect" assembly?

The behavior of the code presented in the question is well defined with respect to the C99 and later C language standards. In particular, C permits functions to return structure values without restriction.

One approach would be to use the elipsis (...) operator, so that an option can be repeated zero or more times with square brackets, or one or more times with parenthesis . For example