Download 10102011.mw

As defined at http://mathworld.wolfram.com/MRBConstant.html the MRB constant is

Hello,

I'm using Maple 7 and got a question:

I've got the function y

y:=x->(x)^0.5; ug:=0; og:=10;

and

xs:=2;

ys:=3;

How do I create a point with the coordinates [xs,ys] and plot it with the function y in one graphic?

I'm using plot(y(x),x=ug..og); to plot the function y.

Thanks for your help!

flash20001

hi,i want my output be a complex number,how do i use the printf command?for example  s=3+4*i be a output.

Hey, I need to write a procedure to calculate the romberg approximation by combining the trapezium rule approximations. The command will be RombInt(f(x),a,b,m,n), where a and b are the 2 limits and m is a number more or equal to 0 which indicates the number of iterations and n is a integer more or equal to m. Also given is that when m=0, this approximation can be called TrapRule(f(x),2^n,a,b). (I have got the procedure for this traprule, if that helps)

So basically...

Hey, I have made this procedure for the trapezium rule but I get an error when I perform this calculation.

Procedure is 

TrapRule:=proc(f,N,a,b)
local k,sum1,h,i:
h:=(b-a)/N:
sum1:=0:
for i from 1 by 1 to n-1 do
sum1:=sum1+f(a+i*h):
end do:
k:=(h/2)*(f(a)+2*sum+f(b)):
return (k):
end proc:

When I try calculating (TrapRule(exp(x),4,-3,1)); I get 

Error, (in TrapRule...

Yesterday I wrote a post that began,

"I realized recently that, while 64bit Maple 15 on Windows (XP64, 7) is now using accelerated BLAS from Intel's MKL, the Operating System environment variable OMP_NUM_THREADS is not being set automatically."

But that first sentence is about where it stopped being correct, as far as how I was interpreting the performance on 64bit Maple on Windows. So I've rewritten the whole post, and this is the revision.

I concluded that, by setting the Windows operating system environment variable OMP_NUM_THREADS to 4, performance would double on a quad core i7. I even showed timings to help establish that. And since I know that memory management and dynamic linking can cause extra overhead, I re-ran all my examples in freshly launched GUI sessions, with the user-interface completely closed between examples. But I got caught out in a mistake, nonetheless. The problem was that there is extra real-time cost to having my machine's Windows operating system dynamically open the MKL dll the very first time after bootup.

So my examples done first after bootup were at a disadvantage. I knew that I could not look just at measured cpu time, since for such threaded applications that reports as some kind of sum of cycles for all threads. But I failed to notice the real-time measurements were being distorted by the cost of loading the dlls the first time. And that penalty is not necessarily paid for each freshly launched, completely new Maple session. So my measurements were not fair.

Here is some illustration of the extra real-time cost, which I was not taking into account. I'll do Matrix-Matrix multiplication for a 1x1 example, to try and show just how much this extra cost is unrelated to the actual computation. In these examples below, I've done a full reboot on Windows 7 where so annotated. The extra time cost for the very first load of the dynamic MKL libraries can be from 1 to over 3 seconds. That's about the same as the cpu time this i7 takes to do the full 3000x3000 Matrix multiplication! Hence the confusion.

Roman brought up hyperthreading in his comment on the original post. So part of redoing all these examples, with full restarts between them, is testing each case both with and without hyperthreading enabled (in the BIOS).

Quad core Intel i7. (four physical cores)

Hyperthreading disabled in BIOS
-------------------------------

> restart: # actual OS reboot
> getenv(OMP_NUM_THREADS);   # NULL, unset in OS

> CodeTools:-Usage( Matrix([[3.]]) . Matrix([[3.]]) ): # initialize external libs
memory used=217.18KiB, alloc change=127.98KiB, cpu time=219.00ms, real time=3.10s

> CodeTools:-Usage( Matrix([[3.]]) . Matrix([[3.]]) ):
memory used=9.46KiB, alloc change=0 bytes, cpu time=0ns, real time=0ns


> restart: # actual OS reboot
> getenv(OMP_NUM_THREADS);
                              "4"

> CodeTools:-Usage( Matrix([[3.]]) . Matrix([[3.]]) ): # initialize external libs
memory used=216.91KiB, alloc change=127.98KiB, cpu time=140.00ms, real time=2.81s

> CodeTools:-Usage( Matrix([[3.]]) . Matrix([[3.]]) ):
memory used=9.46KiB, alloc change=0 bytes, cpu time=0ns, real time=0ns


Hyperthreading enabled in BIOS
------------------------------

> restart: # actual OS reboot
> getenv(OMP_NUM_THREADS);    # NULL, unset in OS

> CodeTools:-Usage( Matrix([[3.]]) . Matrix([[3.]]) ): # initialize external libs
memory used=217.00KiB, alloc change=127.98KiB, cpu time=202.00ms, real time=2.84s

> CodeTools:-Usage( Matrix([[3.]]) . Matrix([[3.]]) ):
memory used=9.46KiB, alloc change=0 bytes, cpu time=0ns, real time=0ns


> restart: # actual OS reboot
> getenv(OMP_NUM_THREADS);
                              "4"

> CodeTools:-Usage( Matrix([[3.]]) . Matrix([[3.]]) ): # initialize external libs
memory used=215.56KiB, alloc change=127.98KiB, cpu time=187.00ms, real time=1.12s

> CodeTools:-Usage( Matrix([[3.]]) . Matrix([[3.]]) ):
memory used=9.46KiB, alloc change=0 bytes, cpu time=0ns, real time=0ns

Having established that the first use after reboot was incurring a real time penalty of a few seconds, I redid the timings in order to gauge the benefit of having OMP_NUM_THREADS set appropriately. These too were done with and without hyperthreading enabled. The timings below appear to indicate that slightly bettern performance can be had for this example in the case that hyperthreading is disabled. The timings also appear to indicate that having OMP_NUM_THREADS unset results in performance competitive with having it set to the number of physical cores.

Hyperthreading disabled in BIOS
-------------------------------

> restart:
> CodeTools:-Usage( Matrix([[3.]]) . Matrix([[3.]]) ): # initialize external libs
memory used=217.84KiB, alloc change=127.98KiB, cpu time=141.00ms, real time=142.00ms

> getenv(OMP_NUM_THREADS);  # NULL, unset in OS

> M:=LinearAlgebra:-RandomMatrix(3000,datatype=float[8]):
> CodeTools:-Usage( M . M ):
memory used=68.67MiB, alloc change=68.74MiB, cpu time=7.50s, real time=1.92s


> restart:
> CodeTools:-Usage( Matrix([[3.]]) . Matrix([[3.]]) ): # initialize external libs
memory used=217.84KiB, alloc change=127.98KiB, cpu time=141.00ms, real time=141.00ms

> getenv(OMP_NUM_THREADS);
                              "1"

> M:=LinearAlgebra:-RandomMatrix(3000,datatype=float[8]):
> CodeTools:-Usage( M . M ):
memory used=68.67MiB, alloc change=68.74MiB, cpu time=7.38s, real time=7.38s


> restart:
> CodeTools:-Usage( Matrix([[3.]]) . Matrix([[3.]]) ): # initialize external libs
memory used=217.11KiB, alloc change=127.98KiB, cpu time=125.00ms, real time=125.00ms

> getenv(OMP_NUM_THREADS);
                              "4"

> M:=LinearAlgebra:-RandomMatrix(3000,datatype=float[8]):
> CodeTools:-Usage( M . M ):
memory used=68.67MiB, alloc change=68.74MiB, cpu time=7.57s, real time=1.94s



Hyperthreading enabled in BIOS
------------------------------

> restart:
> CodeTools:-Usage( Matrix([[3.]]) . Matrix([[3.]]) ): # initialize external libs
memory used=216.57KiB, alloc change=127.98KiB, cpu time=125.00ms, real time=125.00ms

> getenv(OMP_NUM_THREADS);  # NULL, unset in OS

> M:=LinearAlgebra:-RandomMatrix(3000,datatype=float[8]):
> CodeTools:-Usage( M . M ):
memory used=68.67MiB, alloc change=68.74MiB, cpu time=8.46s, real time=2.15s


> restart:
> CodeTools:-Usage( Matrix([[3.]]) . Matrix([[3.]]) ): # initialize external libs
memory used=216.80KiB, alloc change=127.98KiB, cpu time=125.00ms, real time=125.00ms

> getenv(OMP_NUM_THREADS);
                              "1"

> M:=LinearAlgebra:-RandomMatrix(3000,datatype=float[8]):
> CodeTools:-Usage( M . M ):
memory used=68.67MiB, alloc change=68.74MiB, cpu time=7.35s, real time=7.35s


> restart:
> CodeTools:-Usage( Matrix([[3.]]) . Matrix([[3.]]) ): # initialize external libs
memory used=216.80KiB, alloc change=127.98KiB, cpu time=125.00ms, real time=125.00ms

> getenv(OMP_NUM_THREADS);  # NULL, unset in OS
                              "4"

> M:=LinearAlgebra:-RandomMatrix(3000,datatype=float[8]):
> CodeTools:-Usage( M . M ):
memory used=68.67MiB, alloc change=68.74MiB, cpu time=8.56s, real time=2.15s


> restart:
> CodeTools:-Usage( Matrix([[3.]]) . Matrix([[3.]]) ): # initialize external libs
memory used=216.80KiB, alloc change=127.98KiB, cpu time=125.00ms, real time=125.00ms

> getenv(OMP_NUM_THREADS);
                              "8"

> M:=LinearAlgebra:-RandomMatrix(3000,datatype=float[8]):
> CodeTools:-Usage( M . M ):
memory used=68.67MiB, alloc change=68.74MiB, cpu time=8.69s, real time=2.23s

With all those new timing measurements it appears that having to set the global environment variable OMP_NUM_THREADS to the number of physical cores may not be necessary. The performance is comparable, when that variable is left unset. So, while this post is now a non-story, it's interesting to know.

And the lesson about comparitive timings is also useful. Sometimes, even complete GUI/kernel relaunch is not enough to get a level and fair field for comparison.

Simple question:

Solve y''(x)-y'(x)+2y(x)=10e^(-x)sin(x)

Mathematica answer:

which is correct.

Maple 15 can get the homogeneous solution (the first two terms) but the particular solution? Not as we know it.

y(x) = exp((1/2)*x)*sin((1/2)*sqrt(7)*x)*_C2+exp((1/2...

I am evaluating a difficult integral of an oscillating function.

f:=k->evalhf(piecewise(k=0,1,k>0,cos(k*(dz))*BK0(k*rho1)/BK0(k*a)));

evalf(Int(f, kmin..kmax, method = _d01akc,epsilon=eps,maxintervals=1000000))

with dz>0 and possibly very large
kmin is Pi/(2*dz)
the number of cycles is nc = ceil((1/2)*kl*dz/Pi) with kl = 91.563
kmax=  kmin+nc*2*Pi/dz

Each evaluation of this integral using a call to the NAG routine (_d01akc ) eats up 

As we look ahead to our next Maple release, I wanted to let you know of some changes that we are making  to the platforms and operating systems that will be supported by Maple 16.

With Maple 16 we will be adding support for Linux Ubuntu 11.10 and Macintosh OS X 10.7 while dropping support for Linux Ubuntu 10.10 and Macintosh OS X 10.5.  As a result, we will no longer support Maple on the PPC platform (Apple stopped PPC support as of OS X 10.5).

If...

hi;

when run file , maple give wrong result, plz help me

my file is attached

thx

 EKM3-cylindrical_pan.mw

If we have a matrix with n rows and 1 column of n-variable function  how to use the subs?

Recently posted onto Wolfram's Blog is a set of 10 tips for how to write fast Mathematica code.  It is a very amusing read -- go read it now, because below I am going to make some comments on it, assuming that you have read it.

1. Use floating-point numbers if you can, and use them early.
   Basically: if you're using Mathematica as a...

How to implement in maple, the differentiation matrix of second order ?
Is it possible to implement it with the command LinearAlgebra[BandMatrix]?

I can not get the matrix:



Lets look at an example using the following set of 8 discrete points (x,y)

(2,5),(4,15),(6,35),(8,65),(10,100),(12,145),(14,195), and (16,255).

Hi,

I need to extract the extremes of a cyclical function, actually I have all the data (x,y) and I was wondering whether extracting these extremes as I have shown in the attached figure will be easy with Maple or not? NOTICE that the attached figure is actually 2 series of data overlaid, you just consider the blue one and ignore the red one

TIA