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  • Evaluating a function at a particular value in parallel

    - by Gaurav Kalra
    Hi. The question may seem vague, but let me explain it. Suppose we have a function f(x,y,z ....) and we need to find its value at the point (x1,y1,z1 .....). The most trivial approach is to just replace (x,y,z ...) with (x1,y1,z1 .....). Now suppose that the function is taking a lot of time in evaluation and I want to parallelize the algorithm to evaluate it. Obviously it will depend on the nature of function, too. So my question is: what are the constraints that I have to look for while "thinking" to parallelize f(x,y,z...)? If possible, please share links to study.

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  • What's a good matrix manipulation library available for C ?

    - by banister
    Hi, I am doing a lot of image processing in C and I need a good, reasonably lightweight, and above all FAST matrix manipulation library. I am mostly focussing on affine transformations and matrix inversions, so i do not need anything too sophisticated or bloated. Primarily I would like something that is very fast (using SSE perhaps?), with a clean API and (hopefully) prepackaged by many of the unix package management systems. Note this is for C not for C++. Thanks :)

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  • Is there any sense in performing binary AND with a number where all bits are set to 1

    - by n535
    Greetings everybody. I have seen examples of such operations for so many times that I begin to think that I am getting something wrong with binary arithmetic. Is there any sense to perform the following: byte value = someAnotherByteValue & 0xFF; I don't really understand this, because it does not change anything anyway. Thanks for help. P.S. I was trying to search for information both elsewhere and here, but unsuccessfully. EDIT: Well, off course i assume that someAnotherByteValue is 8 bits long, the problem is that i don't get why so many people ( i mean professionals ) use such things in their code. For example in Jon Skeet's MiscUtil there is: uint s1 = (uint)(initial & 0xffff); where initial is int.

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  • An algorithm for converting a base-10 number to a base-N number.

    - by roja
    Guys, I am looking for a way to convert a base-10 number into a base-N number where N can be large. Specifically i am looking at converting to base-85 and back again. Does anyone know a simple algorithm to perform the conversion? Ideally it would provide something like: to_radix(83992, 85) - [11, 53, 12] Any ideas are appreciated! Roja

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  • Code computing the cross-product

    - by WizardOfOdds
    This is not a dupe of my question: http://stackoverflow.com/questions/2532810/detecting-one-points-location-compared-to-two-other-points If I have the following piece of pseudo-C/Java/C# code: int a[]= { 30, 20 }; int b[] = { 40, 50 }; int c[] = {12, 12}; How do I compute the sign of the cross-product ABxAC? I'm only interested in the sign, so I have: boolean signABxAC = ? Now concretely what do I write to get the sign of the cross-product ABxAC?

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  • Fastest primality test

    - by Grigory Javadyan
    Hi. Could you suggest a fast, deterministic method that is usable in practice, for testing if a large number is prime or not? Also, I would like to know how to use non-deterministic primality tests correctly. For example, if I'm using such a method, I can be sure that a number is not prime if the output is "no", but what about the other case, when the output is "probably"? Do I have to test for primality manually in this case? Thanks in advance.

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  • Java Polynomial Multiplication with ArrayList

    - by user1506919
    I am having a problem with one of my methods in my program. The method is designed to take 2 arraylists and the perform multiplication between the two like a polynomial. For example, if I was to say list1={3,2,1} and list2={5,6,7}; I am trying to get a return value of 15,28,38,20,7. However, all I can get is an error message that says: Exception in thread "main" java.lang.IndexOutOfBoundsException: Index: 0, Size: 0. I have provided the method below: private static ArrayList<Integer> multiply(ArrayList<Integer> list1,ArrayList<Integer> list2) { ArrayList<Integer> array =new ArrayList<Integer>(list1.size()+list2.size()); for (int i=0;i<array.size();i++) array.add(i, 0); for (int i = 0; i < list1.size(); i++) for (int j = 0; j < list2.size(); j++) array.set(i+j, ((list1.get(i) * list2.get(j))+array.get(i+j))); return array; } Any help with solving this problem is greatly appreciated.

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  • Animation with Initial Velocity

    - by abustin
    I've been trying to solve this problem for a number of days now but I must be missing something. Known Variables: vi = Initial Velocity t = Animation Duration d = Distance The function I'm trying to create: D(t) = the current distance for a given time Using this information I want to be able to create a smooth animation curve with varying velocity (ease-in/ease-out). The animation must be able ease-in from an initial velocity. The animation must be exactly t seconds and must be travel exactly d units. The curve should lean towards the average velocity with acceleration occurring at the beginning and the end portions of the curve. I'm open to extra configuration variables. The best I've been able to come up with is something that doesn't factor in the initial velocity. I'm hoping someone smarter can help me out. ;) Thank you! p.s. I'm working with an ECMAScript variant

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  • Using JavaCC to infer semantics from a Composite tree

    - by Skice
    Hi all, I am programming (in Java) a very limited symbolic calculus library that manages polynomials, exponentials and expolinomials (sums of elements like "x^n * e^(c x)"). I want the library to be extensible in the sense of new analytic forms (trigonometric, etc.) or new kinds of operations (logarithm, domain transformations, etc.), so a Composite pattern that represent the syntactic structure of an expression, together with a bunch of Visitors for the operations, does the job quite well. My problem arise when I try to implement operations that depends on the semantics more than on the syntax of the Expression (like integrals, for instance: there are a lot of resolution methods for specific classes of functions, but these same classes can be represented with more than a single syntax). So I thought I need something to "parse" the Composite tree to infer its semantics in order to invoke the right integration method (if any). Someone pointed me to JavaCC, but all the examples I've seen deal only with string parsing; so, I don't know if I'm digging in the right direction. Some suggestions? (I hope to have been clear enough!)

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  • Can my loop be optimized any more? (C++)

    - by Sagekilla
    Below is one of my inner loops that's run several thousand times, with input sizes of 20 - 1000 or more. Is there anything I can do to help squeeze any more performance out of this? I'm not looking to move this code to something like using tree codes (Barnes-Hut), but towards optimizing the actual calculations happening inside, since the same calculations occur in the Barnes-Hut algorithm. Any help is appreciated! typedef double real; struct Particle { Vector pos, vel, acc, jerk; Vector oldPos, oldVel, oldAcc, oldJerk; real mass; }; class Vector { private: real vec[3]; public: // Operators defined here }; real Gravity::interact(Particle *p, size_t numParticles) { PROFILE_FUNC(); real tau_q = 1e300; for (size_t i = 0; i < numParticles; i++) { p[i].jerk = 0; p[i].acc = 0; } for (size_t i = 0; i < numParticles; i++) { for (size_t j = i+1; j < numParticles; j++) { Vector r = p[j].pos - p[i].pos; Vector v = p[j].vel - p[i].vel; real r2 = lengthsq(r); real v2 = lengthsq(v); // Calculate inverse of |r|^3 real r3i = Constants::G * pow(r2, -1.5); // da = r / |r|^3 // dj = (v / |r|^3 - 3 * (r . v) * r / |r|^5 Vector da = r * r3i; Vector dj = (v - r * (3 * dot(r, v) / r2)) * r3i; // Calculate new acceleration and jerk p[i].acc += da * p[j].mass; p[i].jerk += dj * p[j].mass; p[j].acc -= da * p[i].mass; p[j].jerk -= dj * p[i].mass; // Collision estimation // Metric 1) tau = |r|^2 / |a(j) - a(i)| // Metric 2) tau = |r|^4 / |v|^4 real mij = p[i].mass + p[j].mass; real tau_est_q1 = r2 / (lengthsq(da) * mij * mij); real tau_est_q2 = (r2*r2) / (v2*v2); if (tau_est_q1 < tau_q) tau_q = tau_est_q1; if (tau_est_q2 < tau_q) tau_q = tau_est_q2; } } return sqrt(sqrt(tau_q)); }

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  • Linear regression confidence intervals in SQL

    - by Matt Howells
    I'm using some fairly straight-forward SQL code to calculate the coefficients of regression (intercept and slope) of some (x,y) data points, using least-squares. This gives me a nice best-fit line through the data. However we would like to be able to see the 95% and 5% confidence intervals for the line of best-fit (the curves below). What these mean is that the true line has 95% probability of being below the upper curve and 95% probability of being above the lower curve. How can I calculate these curves? I have already read wikipedia etc. and done some googling but I haven't found understandable mathematical equations to be able to calculate this. Edit: here is the essence of what I have right now. --sample data create table #lr (x real not null, y real not null) insert into #lr values (0,1) insert into #lr values (4,9) insert into #lr values (2,5) insert into #lr values (3,7) declare @slope real declare @intercept real --calculate slope and intercept select @slope = ((count(*) * sum(x*y)) - (sum(x)*sum(y)))/ ((count(*) * sum(Power(x,2)))-Power(Sum(x),2)), @intercept = avg(y) - ((count(*) * sum(x*y)) - (sum(x)*sum(y)))/ ((count(*) * sum(Power(x,2)))-Power(Sum(x),2)) * avg(x) from #lr Thank you in advance.

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  • How can I transform latitude and longitude to x,y in Java?

    - by hory.incpp
    Hello, I am working on a geographic project in Java. The input are coordinates : 24.4444 N etc Output: a PLAIN map (not round) showing the point of the coordinates. I don't know the algorithm to transform from coordinates to x,y on a JComponent, can somebody help me? The map looks like this: http://upload.wikimedia.org/wikipedia/commons/7/74/Mercator-projection.jpg Thank you

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  • mod,prime -> inverse possible

    - by Piet
    Hi all. I was wondering if one can do the following: We have: X is a product of N-primes, thus I assume unique. C is a constant. We can assure that C is a number that is part of the N-primes or not. Whichever will work best. Thus: X mod C = Z We have Z and C and we know that X was a product of N-primes, where N is restricted lets say first 100 primes. Is there anyway we can get back X?

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  • PHP Code to Generate Simple Flowchart

    - by revbackup
    I am making a flowchart out the subjects in the curriculum of our school. a flowchart is generated through its preRequisite.... for example FIRST YEAR FIRST SEMESTER SUBJECTS ---- PREREQUISITE MATH 1 ---- NONE MATH 2 ---- NONE ENGL 1 ---- NONE SOCIO 1 ----- NONE POLSCI 1 ----- NONE FIRSTE YEAR SECOND SEMESTER SUBJECTS ---- PREREQUISITE MATH 3 ----- MATH 1 MATH 4 ----- MATH 2, MATH 1 ENGL 2 ----- ENGL 1 POLSCI 2 ----- POLSCI 1 So, I must print it this way, just using simple PHP but difficult Logic.: MATH1 -----> MATH3 -----> MATH4 MATH 2 ----->MATH 4 ENGL1 -----> ENGL 2 SOCIO 1 POLSCI 1 -----> POLSCI 2 Can anyone give me a good algorithm for this, because this is really difficult. I am planning to echo the results in an HTML table, and it makes it more complicated. Do you have suggestions how to solve this problem properly and display the results also properly???? Thank you in advance!

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  • Mapping Hilbert values to 3D points

    - by Alexander Gladysh
    I have a set of Hilbert values (length from the start of the Hilbert curve to the given point). What is the best way to convert these values to 3D points? Original Hilbert curve was not in 3D, so I guess I have to pick by myself the Hilbert curve rank I need. I do have total curve length though (that is, the maximum value in the set). Perhaps there is an existing implementation? Some library that would allow me to work with Hilbert curve / values? Language does not matter much.

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  • Divide and conquer method to compute roots [SOLVED]

    - by hellsoul153
    Hello, Knowing that we can use Divide-and-Conquer algorithm to compute large exponents, for exemple 2 exp 100 = 2 exp(50) * 2 exp(50), which is quite more efficient, is this method efficient using roots ? For exemple 2 exp (1/100) = (2 exp(1/50)) exp(1/50) ? In other words, I'm wondering if (n exp(1/x)) is more efficient to (n exp(1/y)) for x < y and where x and y are integers.

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  • Counting problem: possible sudoko tables?

    - by Sorush Rabiee
    Hi, I'm working on a sudoko solver. my method is using a game tree and explore possible permutations for each set of digits by DFS Algorithm. in order to analyzing problem, i want to know what is the count of possible valid and invalid sudoko tables? - a 9*9 table that have 9 one, 9 two, ... , 9 nine. (this isn't exact duplicate by this question) my solution is: 1- First select 9 cells for 1s: (*) 2- and like (1) for other digits (each time, 9 cells will be deleted from remaining available cells): C(81-9,9) , C(81-9*2,9) .... = 3- finally multiply the result by 9! (permutation of 123456789 in (*)) this is not equal to accepted answer of this question but problems are equivalent. what did i do wrong?

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