I recently got access to a 12-core Intel MacPro with 64 GB main memory. This motivated me to try parallel programming again, even though in prior years I have never been successfull. The project I am trying to do is particle tracking through a circular accelerator, an embarassingly parallel problem in the sense that you can track n particles in parallel through your machine for many turns and then gather up the results for analysis. The function describing the tracking is a 6-component polynomial function acting on 6-vectors and yielding a 6-Vector as a result. Each accelerator component (magnet, drift section, rf, ...) is described by such a function. I am simplifying this a bit here, but in the problem at hand this is what I am doing. The point is that each particle gets treated independently from the others, hence parallelization should be trivial.

Using an existing package (Lattice, which I published with Maple) as framework I set this up such that the tracking proc for n turns of one particle in the accelerator is a member of a module. This module is in the body of a proc and gets returned when the proc is called, essentially instantiating the tracking object and assigning it to a Vector with as many elements as I have particles to track. The tracking function returns a 6-Vector with the coordinates after all turns are complete. 
A separate proc does the instantiation of all tracking objects, gives each one its particle number (from a Beam object it is being given) and sends it off using Threads:-Create. It then waits until every task is done (using Threads:-Wait) and assembles the result in another Beam object which it returns. Please refer to the enclosed Maple worksheet for how it is done.

This actually all appears to work. MacOS is 15.7.2 (Sequoia); Maple is 2023.2. The results are identical both parallel and serial.

The "interesting" result however, is that usage of the available CPU cores saturates at about 4. In the graph shown below, the green line shows the CPU usage of the mserver process, and it saturates between 400 & 500%, actually going down to 360% as more particles get added. 100% is one core, so I am never getting more than about 4 cores to work for me. Correspondingly, the no. of seconds per particle goes up from about 3 s (particle 1 to 4) up to about 15 s/particle, settling at about 10 s/particle as 12 particles are approached. Below is a graph against no. of particles (n) of running time (red), CPU time (dark blue), CPU usage (yellow) and # or mkernel threads (green). 

Bottom line: I am only getting 4 cores out of the 12. Process limits of MacOS (ulimit -a) do not indicate any limit that would cause this (and I have had build jobs that would merrily use all 12 cores).

Is there a limit in Maple that prevents using all available cores? Am I doing something inefficient that could cause this?? This is the first time I actually got parallel operations in Maple to work, so I am happy about that, but my happiness is tempered by not getting it to work at the level I was aiming for. I did google around a bit and found some prior conversations on MP (mostly involving @acer and @Carl Love) about parallel threads which indicated that (a) environment variable OMP_NUM_THREADS should be set and (b) that numcpus can only be set at the very beginning of a Maple session (which I interpret as "right after firing up Maple"). Did both (and verified the settings were in) but no change in behaviour of this code; I only get four cpu cores to work.

Thanks,

Mac Dude

Parallel_tracking_attempt.mw

Edit: Added graph, fixed up graph.

I just installed Maple 2023 on a MacPro running macOS Sequoia 15.7.2. Update to latest .version and activation worked without a hitch.

When I try to run it from the Finder it immediately puts up a dialog saying something like "Java not found". There is a webpage by Maplesoft addressing this, but it is completely uninformative and unhelpful.

I can get Maple to run using the cli (in Terminal) opening the Maple 2023 .app file, at which point Maple (running the standard GUI) works just as one would expect. So it is not a crisis but I'd like to be able to open it through the Finder as well. The Maple .app folder appears to have all the Java stuff in it, and clearly it is somewhere.

Anyone seen and solved this before?

Thanks,

Mac Dude

I want to write the equation of the line in the form a*x + b*y + c=0, with igcd(a,b,c)=1 of this code

restart;
with(geometry);
point(A, 2, -3);
point(B, -1, 6);
sort(Equation(line(d, [A, B], [x, y])));

I tried by hand

-1/3*sort(Equation(line(d, [A, B], [x, y])))

How can I get the result 3x + y - 3=0 automatically?

PS. I tried and get the answer 3x + y - 3 =0.

restart;
with(geometry);
point(A, 2, -3);
point(B, -1, 6);
eq := sort(Equation(line(AB, [A, B], [x, y])));
k := igcd(coeff(lhs(eq), x), coeff(lhs(eq), y));
sort(eq*sign(coeff(lhs(eq), x))/k);

How Maple 2023 displays new results with old results together

I have a problem calculating integral analytically.

Can anyone help me in this regard?

Thanks

problem_2_integral_&_moshtagh.mw

Dear Maple experts,

is there a possibility/command to get a vizualization of the output of the command FeedbackConnect?

I was thinking of something like this:


as it is given on the maple-help page for that command (but not generated via a maple command as far as I understood)

Thanks in advance !

I have plotted a 3D figure by maple 2023. but all numbers and units on axes are seen a black boxes. How can fix this problem?

Hi,

Experiencing the following problem.  One of our servers was cloned, the GUID was replaced and then rejoined to the domain.  All applications are working exept Maple.  The application launches but then closes right away.  No error messages provided so not sure where else to look for possible fixes to this problem.  The application is runing on Server 2022.

Thank you.

I have a system of 4 nonlinear equations in 4 lambda variables. I cannot obtain a solution using solve():

4_nonlinear_equations.mw

I can sometimes simplify similar systems by rescaling equations to reduce parameters. With only 3 parameters (sigma_v, sigma_d, sigma_d3) in this case, complexity arises from the interactions of the 4 lambdas in the 4 equations. Upon examining the equations (highlighted in yellow), I suspect hidden symmetries. Is it possible to solve the system by rewriting the equations in terms of each other to find an equivalent system? I am exploring if a smarter and simpler reformulation could lead to a solution. Thank you.

Recently a new configuration of a computer, with a better cpu - AMD Ryzen 7 8700G w/ Radeon 780M Graphics, but maple computation is particularly slow, cpu call special less computation is particularly slow, is there any way to improve?

How to use maple to compute the solution of two coupling equations that both have higher order derivatives? I used dsolve and couldn't solve it.

question928.mw

Executing the code in ?InvertedPendulum produces an error when

sysLin := Linearize(convert(sysEqs, list), [u(t)], [x(t), theta(t)], lin_point)

is executed. The problem is the line where EQ4 is assigned a value.

Something is wrong with the line where EQ4 is assigned a value. It is not executed.
It is like the mode changes to text for that line????

can someone help me curve fitting these parameeters...i only got 1 for all of this 90As4.mw

Download 90As4.mw

How do I stop truncation in Maple 2023?  Everything was working fine yesterday but today all of a sudden all assignments are truncated to only 10 digits.

If:

with(Units) :

a_Terra := 149598023.*Unit(km) :
A_Luna := 0.136 :
L_Sol := 3.75E28*Unit(lm) :
S_sphere := r -> 4*Pi*r^2 :

J_Luna := A_Luna*L_Sol/S_sphere(a_Terra) :

Then:

"" gives ""

but

"" gives ""

"" without "evalf" also provides a truncated number instead of showing the "Pi" for an exact value.  So something is wrong in the assignment settings.

Somehow the settings must have changed for how assignments are stored. The answer is irrational with a factor of "1/Pi" and so should not be truncated for calculations.  "a_Terra" is assigned with 9 significant digits ("" km) which I am wondering if maybe why "evalf" is truncating to 10 digits (though it should round and not truncate in that case) but it wasn't doing this before.

"Tools --> Options --> Precision" hasn't changed is set globally to round screen display to 32 decimal places and to round calculation to 64 significant digits.

Is there a way to reassign the arcsecant function "arcsec()" as "asec()" so that "arcsec" can be assigned to the arcsecond unit "Unit(arcsec)"?

Ideally, I would like all of the inverse trigonometric functions to use the shorter notation "asec()" instead of "arcsec()".  I usually do this as aliases, i.e. "alias(asin = arcsin) : alias(asec = arcsec) :" but this won't allow reusing "arcsec" for a unit instead.

Example error for Maple 2023:

alias(asec = arcsec) :
AddUnit(astronomical_unit, context = astronomy, default = true, prefix = SI, conversion = 149597870700*m) : # https://en.wikipedia.org/wiki/astronomical_unit
AddUnit(second, context = angle, spelling = arcsecond, plural = arcseconds, symbol = arcsec, prefix = SI_negative) :

AddUnit(parsec, context = astronomy, default = true, prefix = SI, conversion = AU/tan(arcsec)) ; # https://en.wikipedia.org/wiki/Parsec#Calculating_the_value_of_a_parsec

"Pi/648000" has to be used instead of "arcsec" here when defining the parsec since "arcsec" is already reserved for the arcsecant function, even with "alias(asec = arcsec) ;".

Correction: it looks like the parsec was redefined by the IAU in 2012 as exactly "648000*AU/Pi" without any tangents (or sines) in the definition (so the angle subtended by 1 AU at 1 PC is actually 0.999999999992" not 1").  Both "astronomical_unit" and "parsec" have the wrong values in Maple 2023 which need to be corrected manually.  But the conflict between arcseconds and arcsecants remains the same.

https://iau.org/static/resolutions/IAU2015_English.pdf

https://iopscience.iop.org/article/10.3847/0004-6256/152/2/41