mm-2389 === Subject: Solving SDE using linear programming I am trying to solve a stochastic differential equation using numerical analysis because a closed-form solution (at first glance) does not seem possible. So, in that vein, I am trying to minimize a particular discretized rendition of a continuous-time problem. By discretizing the state space into (say) 100 intervals, I have, at each interval, a particular 'x'. So, for instance, I have an xmin of 0, an xmax of 10 and say 100 intervals. In this case, x progresses in intervals of (10-0)/100 = 0.1 from 0 to 10 (ie, 0, 0.1, 0.2,...,9.9,10). I then create 100 constraints (one for each 'x') and then run linprog in Matlab (or any other linear programming software) to minimize c^Tv, where c = [1,1,1,...1]' and is a 100 x 1 vector and v is the resulting minimum for the given constraints. The constraints are all linear in v in the continuous-time version and also in the discrete-time version. They involve derivatives of v(x) which can be discretized. So A is a matrix that is 500x100 (if there are five constraints). And b is a 500x1 vector. [More on discretization can be found here (if you're interested): http://clouds.eos.ubc.ca/~phil/numeric/labs/lab1/lab1.pdf] Really, what I'm doing is solving for the optimal value function V(x) numerically in a problem which involves an SDE which is not solvable analytically. This (finally) brings me to my question: I know how to minimize v when it is a function of one variable. But what if V is actually a function of two variables? That is V is V(x,t)? In this case, I obviously have to have two state spaces (ie, xmin, xmax, tmin, tmax, etc). However, when implementing the linear program, my first thought is to have an array that is 500x100x100 (if there are 5 constraints for x and 5 for t). This would be fine if the constraints were separate in t and in x. However, there are constraints in t and x. That is, one of the constraints is something like: V_xx(x,t)*.4 + V_t(x,t) leq 0, where V_xx is the second derivative of V wrt x, and V_t is the first derivative wrt t. The question is: How do I render this problem of a function of two variables into an LP problem which I can solve using linprog in Matlab or any other LP software? Specifically, can anyone tell me how I should create the constraint matrix A and b? I guess the output should be a 3D plot which would be the optimal V(x,t). I hope that I have been clear with my description. I also hope that the answer to this question is trivial to at least someone on the list! starving doctoral candidate with his dissertation. Arnav After a long search, I found this: http://techreport.com/reviews/2005q2/athlon64-x2/index.x?pg=12 (see especially the last two graphs, as well as other pages) precision than on double precision, despite any caching that could benefit the smaller single-precision floats. precision by a factor of about 2. parallel. A laptop I'm thinking of buying has this feature disabled (in BIOS for good reasons or bad) (*) How much of a performance degradation should once expect because of it? It's a $1000+ decision out of my own pocket, so any insights from knowledgeable people are much appreciated. (*) http://zv6000forums.com/viewtopic.php?t=211 Originator: lindahl@pbm.com (Greg Lindahl) >After a long search, I found this: http://techreport.com/reviews/2005q2/athlon64-x2/index.x?pg=12 (see especially the last two graphs, as well as other pages) ... a classic example of bad benchmarking. They say it's an unoptimized matrix multiply; most people either use library routines, or use a compiler that cache-blocks the matrix multiply. >precision than on double precision, That's only interesting in that it sounds like the wrong answer. I would >precision by a factor of about 2. Also the wrong answer. By the way, both Opteron and EM64T get better performance when you specifically schedule for one or the other. Which did the ScienceMark people schedule for? > ... a classic example of bad benchmarking. They say it's an > unoptimized matrix multiply; most people either use library routines, > or use a compiler that cache-blocks the matrix multiply. It's true, I'd like to see ATLAS benchmarked. (And there are some ATLAS timings I posted earlier, which seem to suggest 2.8Ghz P4E is /much/ faster than 1.6Ghz Opteron on DGEMM). However, whether the benchmark is bad depends on how one interprets it. Reference implementation of BLAS (which is what I think they used) is similar to what a normal person would put together (someone who does not have time to fiddle with assembler kernels). In that sense (comparing the code of normal people), naive BLAS makes for a better benchmark. Originator: lindahl@pbm.com (Greg Lindahl) >However, whether the benchmark is bad depends on how one interprets it. Right. And I don't like how you're interpreting it, either. >Reference implementation of BLAS (which is what I think they used) is >similar to what a normal person would put together (someone who does not >have time to fiddle with assembler kernels). BLAS calls in them take the time to link to an optimized library. No need to fiddle with assembler kernels; you just download and install MKL or ACML. Instead, why not use a real application? Or, failing that, toy applications like those found in Polyhedron and SPECcpu? -- greg ... a classic example of bad benchmarking. They say it's an > unoptimized matrix multiply; most people either use library routines, > or use a compiler that cache-blocks the matrix multiply. It's true, I'd like to see ATLAS benchmarked. (And there are some ATLAS > timings I posted earlier, which seem to suggest 2.8Ghz P4E is /much/ faster > than 1.6Ghz Opteron on DGEMM). However, whether the benchmark is bad depends on how one interprets it. > Reference implementation of BLAS (which is what I think they used) is > similar to what a normal person would put together (someone who does not > have time to fiddle with assembler kernels). In that sense (comparing the > code of normal people), naive BLAS makes for a better benchmark. What most people do isn't really relevant to those who actually need good performance badly enough to warrant spending time getting the most from the hardware. -- George White 189 Parklea Dr., Head of St. Margarets Bay, Nova Scotia B3Z 2G6 > After a long search, I found this: http://techreport.com/reviews/2005q2/athlon64-x2/index.x?pg=12 (see especially the last two graphs, as well as other pages) precision than on double precision, despite any caching that could benefit > the smaller single-precision floats. precision by a factor of about 2. parallel. A laptop I'm thinking of buying has this feature disabled (in > BIOS for good reasons or bad) (*) How much of a performance degradation > should once expect because of it? It's a $1000+ decision out of my own pocket, so any insights from > knowledgeable people are much appreciated. reap bleeding-edge performance, you will get very poor battery life indeed -- so much so, it rather misses the whole point of having a laptop. I would go instead for a Pentium M machine; I can get 4+ hours out of mine, *and* it runs quite cool. Of course, on the desktop, things are different; all of my workstations cheers, Rich Alex - the performance will depend strongly on what compiler you use. If, like me, you're using the ocamlopt OCaml compiler then it does a much This is evident from the results of my mini ray tracer: http://www.ffconsultancy.com/free/ray_tracer/languages.html Although I have no Intel benchmark results for comparison. If you are using Intel's Fortran compiler, for example, I'd expect Intel > reap bleeding-edge performance, you will get very poor battery life > indeed -- so much so, it rather misses the whole point of having a > laptop. I would go instead for a Pentium M machine; I can get 4+ hours > out of mine, *and* it runs quite cool. I've got to disagree with that. (Centrion). Naturally, I couldn't resist fiddling with her laptop. runs similarly cool. > Of course, on the desktop, things are different; all of my workstations Agreed. I was under the impression that there hasn't been a contest here for quite some time (when price is included). -- Dr Jon D Harrop, Flying Frog Consultancy http://www.ffconsultancy.com > (Centrion). Naturally, I couldn't resist fiddling with her laptop. > runs similarly cool. about as fast as my Pentium M laptop (Acer Travelmate), but her battery experiences with a previous laptop, battery life is the #1 issue for me, so I don't mind if I don't have the fastest machine possible. After all, how fast is a 200 THz CPU when there is no power to run it? cheers, Rich > about as fast as my Pentium M laptop (Acer Travelmate), but her battery > life is c. 1.5 hours, as compared to c. 4.5 hours on mine. Do you downclock the Sempron? > experiences with a previous laptop, battery life is the #1 issue for me, > so I don't mind if I don't have the fastest machine possible. After all, > how fast is a 200 THz CPU when there is no power to run it? How much computation can be done in half the time on a machine that is 4x faster? :-) I chose the Athlon64 Acer Aspire primarily because it has decent graphics (nVidia GeForce FX 5700Go) whereas the Pentium M (Medion Sim 2000) laptop lacks decent OpenGL support (SiS M661MX). -- Dr Jon D Harrop, Flying Frog Consultancy http://www.ffconsultancy.com Originator: lindahl@pbm.com (Greg Lindahl) >If you are using Intel's Fortran compiler, for example, I'd expect Intel chip slightly beats Intel's compiler on Intel's best x86 chip. :-) Use -- greg (working for, not speaking for, PathScale.) > Of course, on the desktop, things are different; all of my workstations BTW, if you tried switching between single and double precision, how does >> Of course, on the desktop, things are different; all of my workstations >BTW, if you tried switching between single and double precision, how does On many machines, single precision arithmetic effectively does not exist; operations are done in double precision and converted back to single. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 > reap bleeding-edge performance, you will get very poor battery life > indeed -- so much so, it rather misses the whole point of having a > laptop. I would go instead for a Pentium M machine; I can get 4+ hours > out of mine, and it runs quite cool. Battery life isn't especially important to me, and in zv6000forums.com everyone claims the laptops (HP zv6000 or Compaq R4000) are cooler than anything they've owned. === Subject: Humans Becoming Genetically Less Intelligent http://www.neoeugenics.com/ 1. Human intelligence is largely hereditary. 2. Civilization depends totally upon innate intelligence. Without innate intelligence, civilization would never have been created. When intelligence declines, so does civilization. 3. The higher the level of civilization, the better off the population. Civilization is not an either-or proposition. Rather, it's a matter of degree, and each degree, up or down, affects the well-being of every citizen. 4. At the present time, we are evolving to become less intelligent with each new generation. Why is this happening? Simple: the least-intelligent people are having the most children. 5. Unless we halt or reverse this trend, our civilization will invariably decline. Any decline in civilization produces a commensurate increase in the collective misery quotient. Logic and scientific evidence stand behind each statement listed above. So, what are your thoughts? === Subject: Re: Humans Becoming Genetically Less Intelligent > 4. At the present time, we are evolving to become less intelligent with > each new generation. You are a living proof of this. I bet your grandfather was a genius. === Subject: calculating sin(exp(a)) I would like to calculate sin(exp(a)) as accurately as possible where a >1e400 Is there any literature about this? === Subject: Re: calculating sin(exp(a)) First of all : suppose that yourt PC accepts/works with positive real numbers X , .with X < 10^{p} , and with positive integers m where m=< NMAX:= 2^{Q} -1 , e.g. Q in {32,64 } . In order to find sin(Z) for Z large we need the integer part /floor function/ of 2*p i / Z . However as a condiion we must impose | 2*pi/z | =< NMAX . The most usual algorihms use an approximatin for exp(a) , like (*) exp(a) :=2^{m} * e^{Z} with m= [a / Q] , Z= {a/Q}*Q in [0,0.7) with Q=ln(2.) =0.69314718055994530942...,.. I have denoted by [ . ] the integral part and by { . } the fractional part. My opinmion = it's very ,,dangerous to compute sin (exp(a)) for a ,,large , e.g . a> 300 . === Subject: Re: calculating sin(exp(a)) >I would like to calculate sin(exp(a)) as >accurately as possible where >a >1e400 As others have noted, this is hopeless in general. However, for certain values of a (given exactly) it is easy: e.g. if a = ln(2 pi r) where r is a rational number. Of course r will be enormous, so the issue of how to represent it is nontrivial, but if it is represented in such a way that frac(r) can be computed, then of course sin(exp(a)) = sin(2 pi frac(r)). Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: calculating sin(exp(a)) I would like to calculate sin(exp(a)) as > accurately as possible where a >1e400 Besides the responses you already got - why & and for what do you want that? === Subject: Re: calculating sin(exp(a)) >I would like to calculate sin(exp(a)) as >accurately as possible where >a >1e400 >Is there any literature about this? I doubt that you have a to enough accuracy to get any accuracy in the result; the record precision of pi to some billions of digits is an infinitesimal amount compared to the number of digits in exp(a), which is greater than any estimate I have seen of the number when divided by pi. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: calculating sin(exp(a)) >I would like to calculate sin(exp(a)) as >accurately as possible where > >a >1e400 > >Is there any literature about this? > there is little help thinkable: because of the periodicity of the sin you need exactly a lot of digits of the fractional part of exp(a)/(2*pi) but exp(a) with a>1e400 will need already more than 1e400/ln(10) decimal digits more than can be stored on any computer system and there is of course no theory which tells you what the zzz-th digit of exp(x) will be : there are methods to compute it with a given arbitrary precision i.e. with all digits up to the zzz-th.. === Subject: Re: calculating sin(exp(a)) >I would like to calculate sin(exp(a)) as >accurately as possible where >a >1e400 >there is little help thinkable: because of the periodicity of the sin you >need exactly a lot of digits of the fractional part of exp(a)/(2*pi) >but exp(a) with a>1e400 will need already more than 1e400/ln(10) decimal digits >more than can be stored on any computer system and there is of course no theory >which tells you what the zzz-th digit of exp(x) will be Well, in principle this need not be true. We do have algorithms which can tell us the 1e400-th digit of pi without collecting all the previous digits. I suppose it is conceivable that such an algorithm could likewise produce the just the units digit of 10*(exp(a)/(2pi)). IIRC a similar calculation is part of a tale told of Feynmann(?) who boasted that he could estimate the value of any number that could be described in a just a few words; but of course tan(10^10^10^10) is essentially unknowable. dave === Subject: geodesics on quadrics I have a quadric x'Qx = 1 (homogeneous cooridates in 3d) I have two points on the quadric p,q. I would like to calculate the geodesic between p and q. Is there a way analytically to calculate this curve? Numerically? Any hints? --j === Subject: geodesics on quadrics I have a quadric x'Qx + Rx + 1 = 0 (in homogeneous coordiantes). I have two points on this quadric, p,q. Is there an easy way to define the geodesic between p and q? Analytically? Numerically? Any hints? === Subject: Re: Help with Fourier coefficients > Setting A = (m/v)^2 we see that it is > sufficient to be able to evaluate quantities like int(sqrt( A +sin(x)^2)*cos(18*x),x=0..2*Pi); Maple can do this, although the answer is obtained > more quickly > with the addendum assuming(A>0). (Curiously, the > answer thus obtained > is very long, though a pass through simplify(%); > makes it much better. > Without the assuming part, the answer appears > already simplified > but would invoke complex arguments needlessly.) Writing the integral in the form > int(sqrt( (B^2 - 1) > - 1) +sin(x)^2)*cos(18*x),x=0..2*Pi) assuming(B>1); > shows that the answer can be expressed as > B ( P(B) EllipticE(1/B) + Q(B) EllipticK(1/B) ) > where P and Q are polynomials of degree 9 in B^2 > . I didn't bother expanding the cos(k*x) term but it > should prove what > is found experimentally: that a similar expansion > will hold for other k, > with a recurrence relation (k+1) P_k(B) = (2 B^2 - 1) (2k-4) P_{k-2} - (k-5) > k-5) P_{k-4} and exactly the same recurrence for the Q's. (This > makes (k+1)!! P_k > an integer polynomial, by the way.) dave > I was probably not so clear. I actually need an estimate (or better, an exact expression) for k--> infinity. Your recursion formula is interesting but not so useful to me as it stands. Besides it is difficult to grasp from it the correct asymptotic that, as I said is c_k sim exp(-k*ix) ix=arcsinh(m/v) using saddle point one can get an expansion like c_k = exp(-k*ix)/(k^(3/2)) * ( A + B/k +C/k^2 +O(k^-3)) and obtain explicit expressions for A,B,C.. But this series, besides being only an asymptotic one (i.e. does not converge in 1/k) has a most dangereous property: some coefficients (B,C..) start diverging when (m/v)->0. This is quite wrong as |c_k| < M < infinity for some M, for all k. Lorenzo > That's only for DGEM. > It's called DGEMM Grow up. Once I start carrying a signature this post guaranteed not typos then you can start nitpicking. > Run Stream and you'll get other results. Too generic a name to mean anything to me. Btw, you can also try the HPC Challenge. V. -- email: lastname at cs utk edu homepage: www cs utk edu tilde lastname > That's only for DGEM. > It's called DGEMM Grow up. Once I start carrying a signature this post guaranteed not > typos then you can start nitpicking. > Run Stream and you'll get other results. >> Too generic a name to mean anything to me. > Btw, you can also try the HPC Challenge. You know what I think? You aren't very familiar with BLAS, hence DGEM instead of DGEMM, and you aren't much of a computer scientist, and didn't know stream meant delayed list. So you thought it's OK to throw the word around unqualified, and others would understand you. Now that your shortcomings have been pointed out to you, you grasp at straws Do I want to keep talking to you? No. That's only for DGEM. > It's called DGEMM >> Grow up. Once I start carrying a signature this post guaranteed not >> typos then you can start nitpicking. > Run Stream and you'll get other results. Too generic a name to mean anything to me. >> Btw, you can also try the HPC Challenge. You know what I think? You aren't very familiar with BLAS, hence > DGEM instead of DGEMM, and you aren't much of a computer > scientist, and didn't know stream meant delayed list. So you > thought it's OK to throw the word around unqualified, and others would > understand you. Now that your shortcomings have been pointed out to you, you grasp at Do I want to keep talking to you? No. Tee hee. I'm reminded of a story of, I believe, Bernard Shaw who once asked a woman if she would sleep with him for a million pounds. When, after some consideration, she said yes, he asked if she would sleep with him for ten shillings. Indignantly she expostulated Certainly not, what sort of a woman do you think I am? Shaw replied Madam, I have ascertained what you are, now I am merely trying to discover the price. You, young man, are a troll, and not a very good one at that. john > Tee hee. I'm reminded of a story of, I believe, Bernard Shaw who once asked a > woman if she would sleep with him for a million pounds. It sounds to me like you are high on something. More sex, less crack, more fresh air, less coffee. Try to experiment along those lines. You'll find your local extremum. > You know what I think? You aren't very familiar with BLAS, hence DGEM > instead of DGEMM, and you aren't much of a computer scientist, and didn't > know stream meant delayed list. So you thought it's OK to throw the > word around unqualified, and others would understand you. Yes, well done you are a very clever computer scientist. > Now that your shortcomings have been pointed out to you, you grasp at straws What kind of straw? Define please or stop throwing words around qualified. > Do I want to keep talking to you? No. Fuck off then. >>Run Stream and you'll get other results. > Too generic a name to mean anything to me. Tut, tut. Ill-informed _and_ foul-mannered? Just typing stream into Google will give you the proper hit at number 5 - that surprised even me. Add McCalpin to it and you'll have it in first place. Not knowing the Stream benchmark and discussing processor performance is like discussing music and being deaf - it can be done, but it won't get you very far. >>Run some sparse benchmark and you'll get other other results. You have >>to pick a benchmark that has some relation to your application. Otherwise >>there's no point. > Have you read the message you are replying to? I picked what I could find. > Incidentally, ATLAS is very much related to my application. So? ATLAS surely contains both code suited to dense and to sparse matrices. They behave quite differently on modern processors. Have you read the message you are replying to? Jan <1gz8h8m.l7vgam14y0sjkN%see.sig@for.addy> <1461325.4EiY8fxVgj@yahoo.com> <3j1d8vFnq7pbU1@individual.net Not knowing the Stream benchmark and discussing processor performance is > like discussing music and being deaf - it can be done, but it won't get you > very far. ask L. van Beethoven about opus 111 ! Joost >>Not knowing the Stream benchmark and discussing processor performance is >>like discussing music and being deaf - it can be done, but it won't get you >>very far. > ask L. van Beethoven about opus 111 ! Indeed 8-)...but at least he wasn't congenitally deaf... Jan >Run Stream and you'll get other results. >> Too generic a name to mean anything to me. Tut, tut. Ill-informed _and_ foul-mannered? Speaking of yourself, obviously. > Just typing stream into Google will give you the proper hit at number 5 > - that surprised even me. This is what I get at #5: http://www.apple.com/quicktime/qtv/wwdc05/ Does not seem to be remotely relevant, since Apple software does not, nor When someone uses stream in the context of computer science, I think of http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-24.html >Run Stream and you'll get other results. > Too generic a name to mean anything to me. >> Tut, tut. Ill-informed _and_ foul-mannered? Speaking of yourself, obviously. > Just typing stream into Google will give you the proper hit at >> number 5 - that surprised even me. This is what I get at #5: http://www.apple.com/quicktime/qtv/wwdc05/ > do that I do indeed get the stream benchmark at number 5. Using my parochialism, but you are guilty of not using your brain as well. john > but you are guilty of not using your brain as well. I think I've made it abundantly clear why I don't feel like running for > but you are guilty of not using your brain as well. I think I've made it abundantly clear why I don't feel like running And yet the information was there for you, and easily retrievable. And as far as I can see from your posts, you still don't have it. Whose loss? john but you are guilty of not using your brain as well. >> I think I've made it abundantly clear why I don't feel like running And yet the information was there for you, and easily retrievable. And > as far as I can see from your posts, you still don't have it. Whose > loss? Last I checked, the royalists lost. Germans too. That's not the point though, is it? It's just sophistry if even that. I had $1000 that I would have paypaled you, had you written empty hollow thud in your message, but you didn't. Whose loss? >> but you are guilty of not using your brain as well. I think I've made it abundantly clear why I don't feel like running >> And yet the information was there for you, and easily retrievable. >> And as far as I can see from your posts, you still don't have it. >> Whose loss? Last I checked, the royalists lost. Germans too. That's not the point though, is it? It's just sophistry if even that. I had $1000 that I would have paypaled you, had you written empty > hollow thud in your message, but you didn't. Whose loss? a) No you didn't. b) You couldn't have. c) I don't think you know what sophistry means, despite deploying it above. john (nice try with the follow-up) >>> but you are guilty of not using your brain as well. >> I think I've made it abundantly clear why I don't feel like running And yet the information was there for you, and easily retrievable. > And as far as I can see from your posts, you still don't have it. > Whose loss? >> Last I checked, the royalists lost. Germans too. >> That's not the point though, is it? It's just sophistry if even that. >> I had $1000 that I would have paypaled you, had you written empty >> hollow thud in your message, but you didn't. Whose loss? I don't think Of course you don't. You can't follow a simple argument or detect sarcasm. <15354939.ChbRSgUcfa@yahoo.com> Yes? The source code is available. > Yes? The source code is available. Besides, if I had access to all sorts of systems to benchmark stuff on myself, why would I want to run someone else's benchmarks instead of my own programs? Sorry, but that wasn't helpful at all. <15354939.ChbRSgUcfa@yahoo.com> <1998257.qHXaAKoWUq@yahoo.com> I am not sure I am wise to continue this thread but I am having my morning coffee. measure what is representative of what you will do with the machine. You declined to answer this when I asked earlier. In my case I want to measure numerical performance for the range of numerically intensive research codes that would be run on the machine over its lifetime. These are C/Fortran codes which tend not to call a large proportion of low level hand coded routines. The NAS Parallel Benchmarks not only provide this information but allow us to investigate when we see interesting/anomolous behaviour in one or two figures (almost always). Yes it takes an hour or two to gather the information but it is informative and reliable in the sense it correlates pretty well with what we get on the machines with our range of codes. In my experience, manufacturers are prepared to supply the figures to guide purchasing decisions and many of the engineering/scientific computers run these tests as part of the commissioning process if you talk to them. They tend not to be used for promotional purposes because they are a set of numbers rather than a single number. Like you I initially believed the best benchmark was to take one of our codes and get the manufacturers to run it on their machines. In the 80s I did this with a real code and was assured that the code had been deleted afterwards. A year later when we are buying the next machine not only does the original manufacturer immediately come up with performance numbers for this code but one of their competitors I had not dealt with in the previous round also produced numbers for it! After that I supplied cut down benchmark code which contained routines I was sure of the copyright. With hindsight this was probably too much effort for too little information. I really wanted to measure the performance for the range of codes we used at the time and the codes we would write in the future. The NAS tests are almost certainly a better measure of this than running one of our existing codes. > Like you I initially believed the best benchmark was to take one of our > codes and get the manufacturers to run it on their machines. That's not the point. There is obviously a communication problem here in the form of your preferring typing to reading. I'm thinking of which laptop to buy - I don't have the negotiating power to have the manufacturers run the benchmarks of my choice on the hardware they are offering. I can only look up existing benchmarks and results, and draw conclusions from that. <15354939.ChbRSgUcfa@yahoo.com> <1998257.qHXaAKoWUq@yahoo.com> <3464142.4uIhyiyOEA@yahoo.com> I am curious why you maintain an offensive tone in your dialogue? Do you find it helps extract the information you seek? I can see it would help keep a thread going but would expect the discussion to wander somewhat. Running numerically intensive code on a laptop would seem rather odd and I think you are correct that manufacturers are unlikely to have much interest in providing you with performance information beyond what is used for marketing. The NAS tests are widely known and used in scientific computing and so manufacturers have often run them internally. If you talk to them they are often prepared to provide the numbers or point you at groups that have already run the tests. It is not really to do with clout but certainly prepared to provide such numbers when the Opteron came out and, as far as I can recall, they did not know me from Adam. However, I was interested in the numerical performance of their microprocessor in motherboards suitable for clusters and not laptops which may have helped get a response. > I am curious why you maintain an offensive tone in your dialogue? My tone in talking to you is no more offensive than your earlier I'm not sure I'm wise to continue ... remark, so please save your high-and-mighty act for someone else. <15354939.ChbRSgUcfa@yahoo.com> <1998257.qHXaAKoWUq@yahoo.com> <3464142.4uIhyiyOEA@yahoo.com> I guess I will have to draw my own conclusions about why the tone. It does not seem to be happening in this branch of the thread.