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  • Efficient Multiple Linear Regression in C# / .Net

    - by mrnye
    Does anyone know of an efficient way to do multiple linear regression in C#, where the number of simultaneous equations may be in the 1000's (with 3 or 4 different inputs). After reading this article on multiple linear regression I tried implementing it with a matrix equation: Matrix y = new Matrix( new double[,]{{745}, {895}, {442}, {440}, {1598}}); Matrix x = new Matrix( new double[,]{{1, 36, 66}, {1, 37, 68}, {1, 47, 64}, {1, 32, 53}, {1, 1, 101}}); Matrix b = (x.Transpose() * x).Inverse() * x.Transpose() * y; for (int i = 0; i < b.Rows; i++) { Trace.WriteLine("INFO: " + b[i, 0].ToDouble()); } However it does not scale well to the scale of 1000's of equations due to the matrix inversion operation. I can call the R language and use that, however I was hoping there would be a pure .Net solution which will scale to these large sets. Any suggestions? EDIT #1: I have settled using R for the time being. By using statconn (downloaded here) I have found it to be both fast & relatively easy to use this method. I.e. here is a small code snippet, it really isn't much code at all to use the R statconn library (note: this is not all the code!). _StatConn.EvaluateNoReturn(string.Format("output <- lm({0})", equation)); object intercept = _StatConn.Evaluate("coefficients(output)['(Intercept)']"); parameters[0] = (double)intercept; for (int i = 0; i < xColCount; i++) { object parameter = _StatConn.Evaluate(string.Format("coefficients(output)['x{0}']", i)); parameters[i + 1] = (double)parameter; }

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  • Attempting my first fortran 95 program, to solve quadratic eqn. Getting weird errors.

    - by Damon
    So, I'm attempting my first program in Fortran, trying to solve quadratic eqn. I have double and triple checked my code and don't see anything wrong. I keep getting "Invalid character in name at (1)" and "Unclassifiable statement at (1)" at various locations. Any help would be greatly appreciated... ! This program solves quadratic equations ! of the form ax^2 + bx + c = 0. ! Record: ! Name: Date: Notes: ! Damon Robles 4/3/10 Original Code PROGRAM quad_solv IMPLICIT NONE ! Variables REAL :: a, b, c REAL :: discrim, root1, root2, COMPLEX :: comp1, comp2 CHARACTER(len=1) :: correct ! Prompt user for coefficients. WRITE(*,*) "This program solves quadratic equations " WRITE(*,*) "of the form ax^2 + bx + c = 0. " WRITE(*,*) "Please enter the coefficients a, b, and " WRITE(*,*) "c, separated by commas:" READ(*,*) a, b, c WRITE(*,*) "Is this correct: a = ", a, " b = ", b WRITE(*,*) " c = ", c, " [Y/N]? " READ(*,*) correct IF correct = N STOP IF correct = Y THEN ! Definition discrim = b**2 - 4*a*c ! Calculations IF discrim > 0 THEN root1 = (-b + sqrt(discrim))/(2*a) root2 = (-b - sqrt(discrim))/(2*a) WRITE(*,*) "This equation has two real roots. " WRITE(*,*) "x1 = ", root1 WRITE(*,*) "x2 = ", root2 IF discrim = 0 THEN root1 = -b/(2*a) WRITE(*,*) "This equation has a double root. " WRITE(*,*) "x1 = ", root1 IF discrim < 0 THEN comp1 = (-b + sqrt(discrim))/(2*a) comp2 = (-b - sqrt(discrim))/(2*a) WRITE(*,*) "x1 = ", comp1 WRITE(*,*) "x2 = ", comp2 PROGRAM END quad_solv Thanks in advance!

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  • Building static (but complicated) lookup table using templates.

    - by MarkD
    I am currently in the process of optimizing a numerical analysis code. Within the code, there is a 200x150 element lookup table (currently a static std::vector < std::vector < double ) that is constructed at the beginning of every run. The construction of the lookup table is actually quite complex- the values in the lookup table are constructed using an iterative secant method on a complicated set of equations. Currently, for a simulation, the construction of the lookup table is 20% of the run time (run times are on the order of 25 second, lookup table construction takes 5 seconds). While 5-seconds might not seem to be a lot, when running our MC simulations, where we are running 50k+ simulations, it suddenly becomes a big chunk of time. Along with some other ideas, one thing that has been floated- can we construct this lookup table using templates at compile time? The table itself never changes. Hard-coding a large array isn't a maintainable solution (the equations that go into generating the table are constantly being tweaked), but it seems that if the table can be generated at compile time, it would give us the best of both worlds (easily maintainable, no overhead during runtime). So, I propose the following (much simplified) scenario. Lets say you wanted to generate a static array (use whatever container suits you best- 2D c array, vector of vectors, etc..) at compile time. You have a function defined- double f(int row, int col); where the return value is the entry in the table, row is the lookup table row, and col is the lookup table column. Is it possible to generate this static array at compile time using templates, and how?

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  • How to arrange a weekly schedule in org-mode?

    - by mbork
    I'd like to put my schedule into org-mode, so that I can see my classes in the agenda. I have different classes, repeated every week, all of them taking 90 minutes. I was thinking about something like this: * My schedule ** Differential equations <2012-10-04 Thu 11:45 +1w>--<2012-10-04 Thu 13:15 +1w> However, there are two problems: I can see only the next instance in the agenda, and I can't see the ending time. Any ideas?

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  • How to change the style of a source reference in Word ?

    - by ldigas
    I have a number of references in Word 2007; there is several way of referencing them and the one I find the most fitting is purely numeric, e.g. (3) for reference number 3 in the list. But since I reference equations by round parenthesis, I'd like to change the literature references to square brackets. How can I do that ?

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  • Encoding / Error Correction Challenge

    - by emi1faber
    Is it mathematically feasible to encode and initial 4 byte message into 8 bytes and if one of the 8 bytes is completely dropped and another is wrong to reconstruct the initial 4 byte message? There would be no way to retransmit nor would the location of the dropped byte be known. If one uses Reed Solomon error correction with 4 "parity" bytes tacked on to the end of the 4 "data" bytes, such as DDDDPPPP, and you end up with DDDEPPP (where E is an error) and a parity byte has been dropped, I don't believe there's a way to reconstruct the initial message (although correct me if I am wrong)... What about multiplying (or performing another mathematical operation) the initial 4 byte message by a constant, then utilizing properties of an inverse mathematical operation to determine what byte was dropped. Or, impose some constraints on the structure of the message so every other byte needs to be odd and the others need to be even. Alternatively, instead of bytes, it could also be 4 decimal digits encoded in some fashion into 8 decimal digits where errors could be detected & corrected under the same circumstances mentioned above - no retransmission and the location of the dropped byte is not known. I'm looking for any crazy ideas anyone might have... Any ideas out there?

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  • Project Euler: Programmatic Optimization for Problem 7?

    - by bmucklow
    So I would call myself a fairly novice programmer as I focused mostly on hardware in my schooling and not a lot of Computer Science courses. So I solved Problem 7 of Project Euler: By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the 10001st prime number? I managed to solve this without problem in Java, but when I ran my solution it took 8 and change seconds to run. I was wondering how this could be optimized from a programming standpoint, not a mathematical standpoint. Is the array looping and while statements the main things eating up processing time? And how could this be optimized? Again not looking for a fancy mathematical equation..there are plenty of those in the solution thread. SPOILER My solution is listed below. public class PrimeNumberList { private ArrayList<BigInteger> primesList = new ArrayList<BigInteger>(); public void fillList(int numberOfPrimes) { primesList.add(new BigInteger("2")); primesList.add(new BigInteger("3")); while (primesList.size() < numberOfPrimes){ getNextPrime(); } } private void getNextPrime() { BigInteger lastPrime = primesList.get(primesList.size()-1); BigInteger currentTestNumber = lastPrime; BigInteger modulusResult; boolean prime = false; while(!prime){ prime = true; currentTestNumber = currentTestNumber.add(new BigInteger("2")); for (BigInteger bi : primesList){ modulusResult = currentTestNumber.mod(bi); if (modulusResult.equals(BigInteger.ZERO)){ prime = false; break; } } if(prime){ primesList.add(currentTestNumber); } } } public BigInteger get(int primeTerm) { return primesList.get(primeTerm - 1); } }

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  • writing a web service with dynamically determined web methods

    - by quillbreaker
    Let's say I have a text file of basic mathematical functions. I want to make a web service that answers these mathematical functions. Say the first one is y=x*x. If I wanted to turn this into a web service, I could simply do this: [WebMethod] public int A(int x) { return x*x; } However, I've extracted the function from the list by hand and coded it into a function by hand. That's not what I want to do. I want the wsdl for the service to be generated at call time directly from the text file, and I want the web method calls to the service to go to a specific method that also parses the text file at run time. How much heavy lifting is this? I've found a sample on how to generate WSDLs dynamically at this link, but there's a lot more to do beyond that and I don't want to bark up this tree if there are parts of the project that arn't feasible. Does anyone have any links, guides, books, or positive experiences trying this kind of thing?

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  • Mathematics for Computer Science Students

    - by Ender
    To cut a long story short, I am a CS student that has received no formal Post-16 Maths education for years. Right now even my Algebra is extremely rusty and I have a couple of months to shape up my skills. I've got a couple of video lectures in my bookmarks, consisting of: Pre-Calculus Algebra Calculus Probability Introduction to Statistics Differential Equations Linear Algebra My aim as of today is to be able to read the CLRS book Introduction to Algorithms and be able to follow the Mathematical notation in that, as well as being able to confidently read and back-up any arguments written in Mathematical notation. Aside from these video lectures, can anyone recommend any good books to help teach someone wishing to go from a low-foundation level to a more advanced level of Mathematics? Just as a note, I've taken a first-year module in Analytical Modelling, so I understand some of the basic concepts of Discrete Mathematics. EDIT: Just a note to those that are looking to learn Linear Algebra using the Video Lectures I have posted up. Peteris Krumins' Blog contains a run-through of these lecture notes as well as his own commentary and lecture notes, an invaluable resource for those looking to follow the lectures too.

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  • MKL Accelerated Math Libraries for Java...

    - by Kaopua
    I've looked at the related threads on StackOverflow and Googled with not much luck. I'm also very new to Java (I'm coming from a C# and .NET background) so please bear with me. There is so much available in the Java world it's pretty overwhelming. I'm starting on a new Java-on-Linux project that requires some heavy and highly repetitious numerical calculations (i.e. statistics, FFT, Linear Algebra, Matrices, etc.). So maximizing the performance of the mathematical operations is a requirement, as is ensuring the math is correct. So hence I have an interest in finding a Java library that perhaps leverages native acceleration such as MKL, and is proven (so commercial options are definitely a possibility here). In the .NET space there are highly optimized and MKL accelerated commercial Mathematical libraries such as Centerspace NMath and Extreme Optimization. Is there anything comparable in Java? Most of the math libraries I have found for Java either do not seem to be actively maintained (such as Colt) or do not appear to leverage MKL or other native acceleration (such as Apache Commons Math). I have considered trying to leverage MKL directly from Java myself (e.g. JNI), but me being new to Java (let alone interoperating between Java and native libraries) it seemed smarter finding a Java library that has already done this correctly, efficiently, and is proven. Again I apologize if I am mistaken or misguided (even in regarding any libraries I've mentioned) and my ignorance of the Java offerings. It's a whole new world for me coming from the heavily commercialized Microsoft stock so I could easily be mistaken on where to look and regarding the Java libraries I've mentioned. I would greatly appreciate any help or advice.

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  • What is the the relation between programming and mathematics?

    - by Math Grad
    Programmers seem to think that their work is quite mathematical. I understand this when you try to optimize something in performance, find the most efficient alogithm, etc.. But it patently seems false when you look at a billing application for a shop, or a systems software riddled with I/O calls. So what is it exactly? Is computation and associated programming really mathematical? Here I have in mind particularly the words of the philosopher Schopenhauer in mind: That arithmetic is the basest of all mental activities is proved by the fact that it is the only one that can be accomplished by means of a machine. Take, for instance, the reckoning machines that are so commonly used in England at the present time, and solely for the sake of convenience. But all analysis finitorum et infinitorum is fundamentally based on calculation. Therefore we may gauge the “profound sense of the mathematician,” of whom Lichtenberg has made fun, in that he says: “These so-called professors of mathematics have taken advantage of the ingenuousness of other people, have attained the credit of possessing profound sense, which strongly resembles the theologians’ profound sense of their own holiness.” I lifted the above quote from here. It seems that programmers are doing precisely the sort of mechanized base mental activity the grand old man is contemptuous about. So what exactly is the deal? Is programming really the "good" kind of mathematics, or just the baser type, or altogether something else just meant for business not to be confused with a pure discipline?

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  • Are there real world applications where the use of prefix versus postfix operators matters?

    - by Kenneth
    In college it is taught how you can do math problems which use the ++ or -- operators on some variable referenced in the equation such that the result of the equation would yield different results if you switched the operator from postfix to prefix or vice versa. Are there any real world applications of using postfix or prefix operator where it makes a difference as to which you use? It doesn't seem to me (maybe I just don't have enough experience yet in programming) that there really is much use to having the different operators if it only applies in math equations. EDIT: Suggestions so far include: function calls //f(++x) != f(x++) loop comparison //while (++i < MAX) != while (i++ < MAX)

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  • How can I write only to the stencil buffer in OpenGL ES 2.0?

    - by stephelton
    I'd like to write to the stencil buffer without incurring the cost of my expensive shaders. As I understand it, I write to the stencil buffer as a 'side effect' of rendering something. In this first pass where I write to the stencil buffer, I don't want to write anything to the color or depth buffer, and I definitely don't want to run through my lighting equations in my shaders. Do I need to create no-op shaders for this (and can I just discard fragments), or is there a better way to do this? As the title says, I'm using OpenGL ES 2.0. I haven't used the stencil buffer before, so if I seem to be misunderstanding something, feel free to be verbose.

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  • Does XNA 4 support 3D affine transformations for 2D images?

    - by Paul Baker Salt Shaker
    Looooong story short I'm essentially trying to code Mode 7 in XNA. Before I continue bashing my brains out in research and various failed matrix math equations; I just want to make sure that XNA supports this just out-of-the-box (so to speak). I'd prefer not to have to import other libraries, because I want to learn how it works myself that way I understand the whole thing better. However that's all for naught if it won't work at all. So no opengl, directx, etc if possible (will eventually do it just to optimize everything, but not for now). tl;dr: Can I has Mode 7 in XNA?

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  • Homemaking a 2d soft body physics engine

    - by Griffin
    hey so I've decided to Code my own 2D soft-body physics engine in C++ since apparently none exist and I'm starting only with a general idea/understanding on how physics work and could be simulated: by giving points and connections between points properties such as elasticity, density, mass, shape retention, friction, stickiness, etc. What I want is a starting point: resources and helpful examples/sites that could give me the specifics needed to actually make this such as equations and required physics knowledge. It would be great if anyone out there also would give me their attempts or ideas. finally I was wondering if it was possible to... use the source code of an existing 3D engine such as Bullet and transform it to be 2D based? use the source code of a 2D Rigid body physics engine such as box2d as a starting point?

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  • Doing an SNES Mode 7 (affine transform) effect in pygame

    - by 2D_Guy
    Is there such a thing as a short answer on how to do a Mode 7 / mario kart type effect in pygame? I have googled extensively, all the docs I can come up with are dozens of pages in other languages (asm, c) with lots of strange-looking equations and such. Ideally, I would like to find something explained more in English than in mathematical terms. I can use PIL or pygame to manipulate the image/texture, or whatever else is necessary. I would really like to achieve a mode 7 effect in pygame, but I seem close to my wit's end. Help would be greatly appreciated. Any and all resources or explanations you can provide would be fantastic, even if they're not as simple as I'd like them to be. If I can figure it out, I'll write a definitive how to do mode 7 for newbies page. edit: mode 7 doc: http://www.coranac.com/tonc/text/mode7.htm

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  • Homemaking a 2d soft body physics engine

    - by Griffin
    hey so I've decided to Code my own 2D soft-body physics engine in C++ since apparently none exist and I'm starting only with a general idea/understanding on how physics work and could be simulated: by giving points and connections between points properties such as elasticity, density, mass, shape retention, friction, stickiness, etc. What I want is a starting point: resources and helpful examples/sites that could give me the specifics needed to actually make this such as equations and required physics knowledge. It would be great if anyone out there also would give me their attempts or ideas. finally I was wondering if it was possible to... use the source code of an existing 3D engine such as Bullet and transform it to be 2D based? use the source code of a 2D Rigid body physics engine such as box2d as a starting point?

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  • Good book or tutorial for learning how to apply integration methods

    - by Cumatru
    I'm looking to animate a graph layout using edges as springs and nodes as weights ( a node with more links will have a bigger weight ). I'm not capable of wrapping my head around the usage of mathematical and physics relations in my application. As far as i read, Runge Kutta 4 ( preferably ) or Verlet will be a good choice, but i have problems with understanding how they really work, and what physics equations should i apply. If i can't understand them, i can't use them. I'm looking for a book or a tutorial which describe the things that i need.

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  • Kepler orbit : get position on the orbit over time

    - by Artefact2
    I'm developing a space-simulation related game, and I am having some trouble implementing the movement of binary stars, like this: The two stars orbit their centroid, and their trajectories are ellipses. I basically know how to determine the angular velocity at any position, but not the angular velocity over time. So, for a given angle, I can very easily compute the stars position (cf. http://en.wikipedia.org/wiki/Orbit_equation). I'd want to get the stars position over time. The parametric equations of the ellipse works but doesn't give the correct speed : { X(t) = a×cos(t) ; Y(t) = b×sin(t) }. Is it possible, and how can it be done?

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  • Circular motion on low powered hardware

    - by Akroy
    I was thinking about platforms and enemies moving in circles in old 2D games, and I was wondering how that was done. I understand parametric equations, and it's trivial to use sin and cos to do it, but could an NES or SNES make real time trig calls? I admit heavy ignorance, but I thought those were expensive operations. Is there some clever way to calculate that motion more cheaply? I've been working on deriving an algorithm from trig sum identities that would only use precalculated trig, but that seems convoluted.

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  • Would a professional, self taught programmer benefit from reading an algorithms book?

    - by user65483
    I'm a 100% self taught, professional programmer (I've worked at a few web startups and made a few independent games). I've read quite a few of the "essential" books (Clean Code, The Pragmatic Programmer, Code Complete, SICP, K&R). I'm considering reading Introduction to Algorithms. I've asked a few colleagues if reading it will improve my programming skills, and I got very mixed answers. A few said yes, a few said no, and a one said "only if you spend a lot of time implementing these algorithms" (I don't). So, I figured I'd ask Stack Exchange. Is it worth the time to read about algorithms if you're a professional programmer who seldom needs to use complex algorithms? For what it's worth, I have a strong mathematical background (have a 2 year degree in Mathematics; took Linear Algebra, Differential Equations, Calc I-III).

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  • How can I simulate objects floating on water without a physics engine?

    - by user1075940
    In my game the water movement is done in a shader using Gerstner equations. The water movement looks realistic enough for a school project but I encounter serious problem when I wanted to do sailing on waves (similar to this). I managed to do collision with land by calculating quad's vertices and normals beneath ship, however same method can not be applied to water because XZ are displaced and Y is calculated in a shader :( How to approach this problem ? Is it possible to retrieve transformed grid from shader? Unfortunately no external physics libraries can be used.

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  • How do I find the closest points(thereby forming a polygon) enclosing a particular point?(see image)

    - by nilspin
    I am working with a game engine, and my task is to add code for simulating fracture of rigid meshes. Right now I'm only working on breaking a cube. I am using Voronoi's algorithm to make a (realistic)fractured shard and I am using the half-plane method to generate a voronoi cell. Now the way I do this is for every seed point, I make planes that are perpendicular bisector planes(the straight black lines in the image) with rest of the seed points and I calculate the intersections of all these planes to give me distinct points(all the orange dots). I've gotten this far. Out of all these calculated intersection points, I only need the ones that are closest and enclosing the seed point(the points encircled in red) and I need to discard all the rest. Information that I have : 1) Plane equations of all planes(defined by normalized normal vectors and their distance from origin) 2) Points of intersection(that I've calculated) Can anybody help me find out how I can find the points encircled in red? Thanks.

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  • Need the co-ordinates of innerPolygon

    - by user960567
    Let say I have this diagram, Given that i have all the co-ordinates of outer polygon and the distance between inner and outer polygon is d is also given. How to calculate the inner polygon co-ordinates? Edit: I was able to solved the issue by getting the mid-points of all lines. From these mid-points I can move d distance, So I can get three points. No I have 3 points and 3 slopes. From this, I can get three new equations. Simultaneously, solving the equation get the 3 points.

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  • Setting density for Android game

    - by Asghar
    I am developing an Android game, in which a ball (bitmap) translates( is in motion). So I have provided motion equations for the ball. I have checked my app on Samsung galaxy S2 whose actual density is roundly 252 dpi, and It works fine on that. So my question is that Does these motions of bitmaps in surfaceView, depends on actual density of phone( i.e 252 dpi for S2) or generalized density(i.e 240 dpi). I am confused whether if I run this app on 235 dpi smartphone, So will it have the same performance of motion as it is on Galaxy S2( with 252 dpi) or it would be little slow ? Any help will be appreciated.

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