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  • Extrapolation breaks collision detection

    - by user22241
    Before applying extrapolation to my sprite's movement, my collision worked perfectly. However, after applying extrapolation to my sprite's movement (to smooth things out), the collision no longer works. This is how things worked before extrapolation: However, after I implement my extrapolation, the collision routine breaks. I am assuming this is because it is acting upon the new coordinate that has been produced by the extrapolation routine (which is situated in my render call ). After I apply my extrapolation How to correct this behaviour? I've tried puting an extra collision check just after extrapolation - this does seem to clear up a lot of the problems but I've ruled this out because putting logic into my rendering is out of the question. I've also tried making a copy of the spritesX position, extrapolating that and drawing using that rather than the original, thus leaving the original intact for the logic to pick up on - this seems a better option, but it still produces some weird effects when colliding with walls. I'm pretty sure this also isn't the correct way to deal with this. I've found a couple of similar questions on here but the answers haven't helped me. This is my extrapolation code: public void onDrawFrame(GL10 gl) { //Set/Re-set loop back to 0 to start counting again loops=0; while(System.currentTimeMillis() > nextGameTick && loops < maxFrameskip){ SceneManager.getInstance().getCurrentScene().updateLogic(); nextGameTick+=skipTicks; timeCorrection += (1000d/ticksPerSecond) % 1; nextGameTick+=timeCorrection; timeCorrection %=1; loops++; tics++; } extrapolation = (float)(System.currentTimeMillis() + skipTicks - nextGameTick) / (float)skipTicks; render(extrapolation); } Applying extrapolation render(float extrapolation){ //This example shows extrapolation for X axis only. Y position (spriteScreenY is assumed to be valid) extrapolatedPosX = spriteGridX+(SpriteXVelocity*dt)*extrapolation; spriteScreenPosX = extrapolationPosX * screenWidth; drawSprite(spriteScreenX, spriteScreenY); } Edit As I mentioned above, I have tried making a copy of the sprite's coordinates specifically to draw with.... this has it's own problems. Firstly, regardless of the copying, when the sprite is moving, it's super-smooth, when it stops, it's wobbling slightly left/right - as it's still extrapolating it's position based on the time. Is this normal behavior and can we 'turn it off' when the sprite stops? I've tried having flags for left / right and only extrapolating if either of these is enabled. I've also tried copying the last and current positions to see if there is any difference. However, as far as collision goes, these don't help. If the user is pressing say, the right button and the sprite is moving right, when it hits a wall, if the user continues to hold the right button down, the sprite will keep animating to the right, while being stopped by the wall (therefore not actually moving), however because the right flag is still set and also because the collision routine is constantly moving the sprite out of the wall, it still appear to the code (not the player) that the sprite is still moving, and therefore extrapolation continues. So what the player would see, is the sprite 'static' (yes, it's animating, but it's not actually moving across the screen), and every now and then it shakes violently as the extrapolation attempts to do it's thing....... Hope this help

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  • Handling early/late/dropped packets for interpolation in a 3D multiplayer game

    - by Ben Cracknell
    I'm working on a multiplayer game that for the purposes of this question, is most similar to Team Fortress. Each network data packet will contain the 3D position of the target moving object. (this object could be another player) The packets are sent on a fixed interval, and linear interpolation will be used to smooth the transition between packets. Under normal circumstances, interpolation will occur between the second-to-last packet, and the last packet received. The linear interpolation algorithm is the same as this post: Interpolating positions in a multiplayer game I have the same issue as in that post, but the answers don't seem like they will work in my situation. Consider the following scenario: Normal packet timing, everything is okay The next expected packet is late. That's okay, we'll just extrapolate based on previous positions The late packet eventually arrives with corrections to our extrapolation. Now what do we do with its information? The answers on the above post suggest we should just interpolate to this new packet's position, but that would not work at all. If we have already extrapolated past that point in time, moving back would cause rubber-banding. The issue is similar in the case of an early or dropped packet. So I believe what I am looking for is some way to smoothly deal with new information in an ongoing interpolation/extrapolation process. Since I might be moving on to quadratic or even cubic interpolation, it would be great if the same solutiuon could be applied to those as well.

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  • Interpolation using a sprite's previous frame and current frame

    - by user22241
    Overview I'm currently using a method which has been pointed out to me is extrapolation rather than interolation. As a result, I'm also now looking into the possibility of using another method which is based on a sprite's position at it's last (rendered) frame and it's current one. Assuming an interpolation value of 0.5 this is, (visually), how I understand it should affect my sprite's position.... This is how I'm obtaining an inerpolation value: public void onDrawFrame(GL10 gl) { // Set/re-set loop back to 0 to start counting again loops=0; while(System.currentTimeMillis() > nextGameTick && loops < maxFrameskip) { SceneManager.getInstance().getCurrentScene().updateLogic(); nextGameTick += skipTicks; timeCorrection += (1000d / ticksPerSecond) % 1; nextGameTick += timeCorrection; timeCorrection %= 1; loops++; tics++; } interpolation = (float)(System.currentTimeMillis() + skipTicks - nextGameTick) / (float)skipTicks; render(interpolation); } I am then applying it like so (in my rendering call): render(float interpolation) { spriteScreenX = (spriteScreenX - spritePreviousX) * interpolation + spritePreviousX; spritePreviousX = spriteScreenX; // update and store this for next time } Results This unfortunately does nothing to smooth the movement of my sprite. It's pretty much the same as without the interpolation code. I can't get my head around how this is supposed to work and I honestly can't find any decent resources which explain this in any detail. My understanding of extrapolation is that when we arrive at the rendering call, we calculate the time between the last update call and the render call, and then adjust the sprite's position to reflect this time (moving the sprite forward) - And yet, this (Interpolation) is moving the sprite back, so how can this produce smooth results? Any advise on this would be very much appreciated. Edit I've implemented the code from OriginalDaemon's answer like so: @Override public void onDrawFrame(GL10 gl) { newTime = System.currentTimeMillis()*0.001; frameTime = newTime - currentTime; if ( frameTime > (dt*25)) frameTime = (dt*25); currentTime = newTime; accumulator += frameTime; while ( accumulator >= dt ) { SceneManager.getInstance().getCurrentScene().updateLogic(); previousState = currentState; t += dt; accumulator -= dt; } interpolation = (float) (accumulator / dt); render(); } Interpolation values are now being produced between 0 and 1 as expected (similar to how they were in my original loop) - however, the results are the same as my original loop (my original loop allowed frames to skip if they took too long to draw which I think this loop is also doing). I appear to have made a mistake in my previous logging, it is logging as I would expect it to (interpolated position does appear to be inbetween the previous and current positions) - however, the sprites are most definitely choppy when the render() skipping happens.

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  • How does interpolation actually work to smooth out an object's movement?

    - by user22241
    I've asked a few similar questions over the past 8 months or so with no real joy, so I am going make the question more general. I have an Android game which is OpenGL ES 2.0. within it I have the following Game Loop: My loop works on a fixed time step principle (dt = 1 / ticksPerSecond) loops=0; while(System.currentTimeMillis() > nextGameTick && loops < maxFrameskip){ updateLogic(dt); nextGameTick+=skipTicks; timeCorrection += (1000d/ticksPerSecond) % 1; nextGameTick+=timeCorrection; timeCorrection %=1; loops++; } render(); My intergration works like this: sprite.posX+=sprite.xVel*dt; sprite.posXDrawAt=sprite.posX*width; Now, everything works pretty much as I would like. I can specify that I would like an object to move across a certain distance (screen width say) in 2.5 seconds and it will do just that. Also because of the frame skipping that I allow in my game loop, I can do this on pretty much any device and it will always take 2.5 seconds. Problem However, the problem is that when a render frame skips, the graphic stutter. It's extremely annoying. If I remove the ability to skip frames, then everything is smooth as you like, but will run at different speeds on different devices. So it's not an option. I'm still not sure why the frame skips, but I would like to point out that this is Nothing to do with poor performance, I've taken the code right back to 1 tiny sprite and no logic (apart from the logic required to move the sprite) and I still get skipped frames. And this is on a Google Nexus 10 tablet (and as mentioned above, I need frame skipping to keep the speed consistent across devices anyway). So, the only other option I have is to use interpolation (or extrapolation), I've read every article there is out there but none have really helped me to understand how it works and all of my attempted implementations have failed. Using one method I was able to get things moving smoothly but it was unworkable because it messed up my collision. I can foresee the same issue with any similar method because the interpolation is passed to (and acted upon within) the rendering method - at render time. So if Collision corrects position (character now standing right next to wall), then the renderer can alter it's position and draw it in the wall. So I'm really confused. People have said that you should never alter an object's position from within the rendering method, but all of the examples online show this. So I'm asking for a push in the right direction, please do not link to the popular game loop articles (deWitters, Fix your timestep, etc) as I've read these multiple times. I'm not asking anyone to write my code for me. Just explain please in simple terms how Interpolation actually works with some examples. I will then go and try to integrate any ideas into my code and will ask more specific questions if need-be further down the line. (I'm sure this is a problem many people struggle with).

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  • Extrapolation using fft in octave

    - by CFP
    Using GNU octave, I'm computing a fft over a piece of signal, then eliminating some frequencies, and finally reconstructing the signal. This give me a nice approximation of the signal ; but it doesn't give me a way to extrapolate the data. Suppose basically that I have plotted three periods and a half of f: x -> sin(x) + 0.5*sin(3*x) + 1.2*sin(5*x) and then added a piece of low amplitude, zero-centered random noise. With fft/ifft, I can easily remove most of the noise ; but then how do I extrapolate 3 more periods of my signal data? (other of course that duplicating the signal). The math way is easy : you have a decomposition of your function as an infinite sum of sines/cosines, and you just need to extract a partial sum and apply it anywhere. But I don't quite get the programmatic way... Thanks!

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  • Frameskipping in Android gameloop causing choppy sprites (Open GL ES 2.0)

    - by user22241
    I have written a simple 2d platform game for Android and am wondering how one deals with frame-skipping? Are there any alternatives? Let me explain further. So, my game loop allows for the rendering to be skipped if game updates and rendering do not fit into my fixed time-slice (16.667ms). This allows my game to run at identically perceived speeds on different devices. And this works great, things do run at the same speed. However, when the gameloop skips a render call for even one frame, the sprite glitches. And thinking about it, why wouldn't it? You're seeing a sprite move say, an average of 10 pixels every 1.6 seconds, then suddenly, there is a pause of 3.2ms, and the sprite then appears to jump 20 pixels. When this happens 3 or 4 times in close succession, the result is very ugly and not something I want in my game. Therfore, my question is how does one deal with these 'pauses' and 'jumps' - I've read every article on game loops I can find (see below) and my loops are even based off of code from these articles. The articles specifically mention frame skipping but they don't make any reference to how to deal with visual glitches that result from it. I've attempted various game-loops. My loop must have a mechanism in-place to allow rendering to be skipped to keep game-speed constant across multiple devices (or alternative, if one exists) I've tried interpolation but this doesn't eliminate this specific problem (although it looks like it may mitigate the issue slightly as when it eventually draws the sprite it 'moves it back' between the old and current positions so the 'jump' isn't so big. I've also tried a form of extrapolation which does seem to keep things smooth considerably, but I find it to be next to completely useless because it plays havoc with my collision detection (even when drawing with a 'display only' coordinate - see extrapolation-breaks-collision-detection) I've tried a loop that uses Thread.sleep when drawing / updating completes with time left over, no frame skipping in this one, again fairly smooth, but runs differently on different devices so no good. And I've tried spawning my own, third thread for logic updates, but this, was extremely messy to deal with and the performance really wasn't good. (upon reading tons of forums, most people seem to agree a 2 thread loops ( so UI and GL threads) is safer / easier). Now if I remove frame skipping, then all seems to run nice and smooth, with or without inter/extrapolation. However, this isn't an option because the game then runs at different speeds on different devices as it falls behind from not being able to render fast enough. I'm running logic at 60 Ticks per second and rendering as fast as I can. I've read, as far as I can see every article out there, I've tried the loops from My Secret Garden and Fix your timestep. I've also read: Against the grain deWITTERS Game Loop Plus various other articles on Game-loops. A lot of the others are derived from the above articles or just copied word for word. These are all great, but they don't touch on the issues I'm experiencing. I really have tried everything I can think of over the course of a year to eliminate these glitches to no avail, so any and all help would be appreciated. A couple of examples of my game loops (Code follows): From My Secret Room public void onDrawFrame(GL10 gl) { //Rre-set loop back to 0 to start counting again loops=0; while(System.currentTimeMillis() > nextGameTick && loops < maxFrameskip) { SceneManager.getInstance().getCurrentScene().updateLogic(); nextGameTick += skipTicks; timeCorrection += (1000d / ticksPerSecond) % 1; nextGameTick += timeCorrection; timeCorrection %= 1; loops++; } extrapolation = (float)(System.currentTimeMillis() + skipTicks - nextGameTick) / (float)skipTicks; render(extrapolation); } And from Fix your timestep double t = 0.0; double dt2 = 0.01; double currentTime = System.currentTimeMillis()*0.001; double accumulator = 0.0; double newTime; double frameTime; @Override public void onDrawFrame(GL10 gl) { newTime = System.currentTimeMillis()*0.001; frameTime = newTime - currentTime; if ( frameTime > (dt*5)) //Allow 5 'skips' frameTime = (dt*5); currentTime = newTime; accumulator += frameTime; while ( accumulator >= dt ) { SceneManager.getInstance().getCurrentScene().updateLogic(); previousState = currentState; accumulator -= dt; } interpolation = (float) (accumulator / dt); render(interpolation); }

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  • A Taxonomy of Numerical Methods v1

    - by JoshReuben
    Numerical Analysis – When, What, (but not how) Once you understand the Math & know C++, Numerical Methods are basically blocks of iterative & conditional math code. I found the real trick was seeing the forest for the trees – knowing which method to use for which situation. Its pretty easy to get lost in the details – so I’ve tried to organize these methods in a way that I can quickly look this up. I’ve included links to detailed explanations and to C++ code examples. I’ve tried to classify Numerical methods in the following broad categories: Solving Systems of Linear Equations Solving Non-Linear Equations Iteratively Interpolation Curve Fitting Optimization Numerical Differentiation & Integration Solving ODEs Boundary Problems Solving EigenValue problems Enjoy – I did ! Solving Systems of Linear Equations Overview Solve sets of algebraic equations with x unknowns The set is commonly in matrix form Gauss-Jordan Elimination http://en.wikipedia.org/wiki/Gauss%E2%80%93Jordan_elimination C++: http://www.codekeep.net/snippets/623f1923-e03c-4636-8c92-c9dc7aa0d3c0.aspx Produces solution of the equations & the coefficient matrix Efficient, stable 2 steps: · Forward Elimination – matrix decomposition: reduce set to triangular form (0s below the diagonal) or row echelon form. If degenerate, then there is no solution · Backward Elimination –write the original matrix as the product of ints inverse matrix & its reduced row-echelon matrix à reduce set to row canonical form & use back-substitution to find the solution to the set Elementary ops for matrix decomposition: · Row multiplication · Row switching · Add multiples of rows to other rows Use pivoting to ensure rows are ordered for achieving triangular form LU Decomposition http://en.wikipedia.org/wiki/LU_decomposition C++: http://ganeshtiwaridotcomdotnp.blogspot.co.il/2009/12/c-c-code-lu-decomposition-for-solving.html Represent the matrix as a product of lower & upper triangular matrices A modified version of GJ Elimination Advantage – can easily apply forward & backward elimination to solve triangular matrices Techniques: · Doolittle Method – sets the L matrix diagonal to unity · Crout Method - sets the U matrix diagonal to unity Note: both the L & U matrices share the same unity diagonal & can be stored compactly in the same matrix Gauss-Seidel Iteration http://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method C++: http://www.nr.com/forum/showthread.php?t=722 Transform the linear set of equations into a single equation & then use numerical integration (as integration formulas have Sums, it is implemented iteratively). an optimization of Gauss-Jacobi: 1.5 times faster, requires 0.25 iterations to achieve the same tolerance Solving Non-Linear Equations Iteratively find roots of polynomials – there may be 0, 1 or n solutions for an n order polynomial use iterative techniques Iterative methods · used when there are no known analytical techniques · Requires set functions to be continuous & differentiable · Requires an initial seed value – choice is critical to convergence à conduct multiple runs with different starting points & then select best result · Systematic - iterate until diminishing returns, tolerance or max iteration conditions are met · bracketing techniques will always yield convergent solutions, non-bracketing methods may fail to converge Incremental method if a nonlinear function has opposite signs at 2 ends of a small interval x1 & x2, then there is likely to be a solution in their interval – solutions are detected by evaluating a function over interval steps, for a change in sign, adjusting the step size dynamically. Limitations – can miss closely spaced solutions in large intervals, cannot detect degenerate (coinciding) solutions, limited to functions that cross the x-axis, gives false positives for singularities Fixed point method http://en.wikipedia.org/wiki/Fixed-point_iteration C++: http://books.google.co.il/books?id=weYj75E_t6MC&pg=PA79&lpg=PA79&dq=fixed+point+method++c%2B%2B&source=bl&ots=LQ-5P_taoC&sig=lENUUIYBK53tZtTwNfHLy5PEWDk&hl=en&sa=X&ei=wezDUPW1J5DptQaMsIHQCw&redir_esc=y#v=onepage&q=fixed%20point%20method%20%20c%2B%2B&f=false Algebraically rearrange a solution to isolate a variable then apply incremental method Bisection method http://en.wikipedia.org/wiki/Bisection_method C++: http://numericalcomputing.wordpress.com/category/algorithms/ Bracketed - Select an initial interval, keep bisecting it ad midpoint into sub-intervals and then apply incremental method on smaller & smaller intervals – zoom in Adv: unaffected by function gradient à reliable Disadv: slow convergence False Position Method http://en.wikipedia.org/wiki/False_position_method C++: http://www.dreamincode.net/forums/topic/126100-bisection-and-false-position-methods/ Bracketed - Select an initial interval , & use the relative value of function at interval end points to select next sub-intervals (estimate how far between the end points the solution might be & subdivide based on this) Newton-Raphson method http://en.wikipedia.org/wiki/Newton's_method C++: http://www-users.cselabs.umn.edu/classes/Summer-2012/csci1113/index.php?page=./newt3 Also known as Newton's method Convenient, efficient Not bracketed – only a single initial guess is required to start iteration – requires an analytical expression for the first derivative of the function as input. Evaluates the function & its derivative at each step. Can be extended to the Newton MutiRoot method for solving multiple roots Can be easily applied to an of n-coupled set of non-linear equations – conduct a Taylor Series expansion of a function, dropping terms of order n, rewrite as a Jacobian matrix of PDs & convert to simultaneous linear equations !!! Secant Method http://en.wikipedia.org/wiki/Secant_method C++: http://forum.vcoderz.com/showthread.php?p=205230 Unlike N-R, can estimate first derivative from an initial interval (does not require root to be bracketed) instead of inputting it Since derivative is approximated, may converge slower. Is fast in practice as it does not have to evaluate the derivative at each step. Similar implementation to False Positive method Birge-Vieta Method http://mat.iitm.ac.in/home/sryedida/public_html/caimna/transcendental/polynomial%20methods/bv%20method.html C++: http://books.google.co.il/books?id=cL1boM2uyQwC&pg=SA3-PA51&lpg=SA3-PA51&dq=Birge-Vieta+Method+c%2B%2B&source=bl&ots=QZmnDTK3rC&sig=BPNcHHbpR_DKVoZXrLi4nVXD-gg&hl=en&sa=X&ei=R-_DUK2iNIjzsgbE5ID4Dg&redir_esc=y#v=onepage&q=Birge-Vieta%20Method%20c%2B%2B&f=false combines Horner's method of polynomial evaluation (transforming into lesser degree polynomials that are more computationally efficient to process) with Newton-Raphson to provide a computational speed-up Interpolation Overview Construct new data points for as close as possible fit within range of a discrete set of known points (that were obtained via sampling, experimentation) Use Taylor Series Expansion of a function f(x) around a specific value for x Linear Interpolation http://en.wikipedia.org/wiki/Linear_interpolation C++: http://www.hamaluik.com/?p=289 Straight line between 2 points à concatenate interpolants between each pair of data points Bilinear Interpolation http://en.wikipedia.org/wiki/Bilinear_interpolation C++: http://supercomputingblog.com/graphics/coding-bilinear-interpolation/2/ Extension of the linear function for interpolating functions of 2 variables – perform linear interpolation first in 1 direction, then in another. Used in image processing – e.g. texture mapping filter. Uses 4 vertices to interpolate a value within a unit cell. Lagrange Interpolation http://en.wikipedia.org/wiki/Lagrange_polynomial C++: http://www.codecogs.com/code/maths/approximation/interpolation/lagrange.php For polynomials Requires recomputation for all terms for each distinct x value – can only be applied for small number of nodes Numerically unstable Barycentric Interpolation http://epubs.siam.org/doi/pdf/10.1137/S0036144502417715 C++: http://www.gamedev.net/topic/621445-barycentric-coordinates-c-code-check/ Rearrange the terms in the equation of the Legrange interpolation by defining weight functions that are independent of the interpolated value of x Newton Divided Difference Interpolation http://en.wikipedia.org/wiki/Newton_polynomial C++: http://jee-appy.blogspot.co.il/2011/12/newton-divided-difference-interpolation.html Hermite Divided Differences: Interpolation polynomial approximation for a given set of data points in the NR form - divided differences are used to approximately calculate the various differences. For a given set of 3 data points , fit a quadratic interpolant through the data Bracketed functions allow Newton divided differences to be calculated recursively Difference table Cubic Spline Interpolation http://en.wikipedia.org/wiki/Spline_interpolation C++: https://www.marcusbannerman.co.uk/index.php/home/latestarticles/42-articles/96-cubic-spline-class.html Spline is a piecewise polynomial Provides smoothness – for interpolations with significantly varying data Use weighted coefficients to bend the function to be smooth & its 1st & 2nd derivatives are continuous through the edge points in the interval Curve Fitting A generalization of interpolating whereby given data points may contain noise à the curve does not necessarily pass through all the points Least Squares Fit http://en.wikipedia.org/wiki/Least_squares C++: http://www.ccas.ru/mmes/educat/lab04k/02/least-squares.c Residual – difference between observed value & expected value Model function is often chosen as a linear combination of the specified functions Determines: A) The model instance in which the sum of squared residuals has the least value B) param values for which model best fits data Straight Line Fit Linear correlation between independent variable and dependent variable Linear Regression http://en.wikipedia.org/wiki/Linear_regression C++: http://www.oocities.org/david_swaim/cpp/linregc.htm Special case of statistically exact extrapolation Leverage least squares Given a basis function, the sum of the residuals is determined and the corresponding gradient equation is expressed as a set of normal linear equations in matrix form that can be solved (e.g. using LU Decomposition) Can be weighted - Drop the assumption that all errors have the same significance –-> confidence of accuracy is different for each data point. Fit the function closer to points with higher weights Polynomial Fit - use a polynomial basis function Moving Average http://en.wikipedia.org/wiki/Moving_average C++: http://www.codeproject.com/Articles/17860/A-Simple-Moving-Average-Algorithm Used for smoothing (cancel fluctuations to highlight longer-term trends & cycles), time series data analysis, signal processing filters Replace each data point with average of neighbors. Can be simple (SMA), weighted (WMA), exponential (EMA). Lags behind latest data points – extra weight can be given to more recent data points. Weights can decrease arithmetically or exponentially according to distance from point. Parameters: smoothing factor, period, weight basis Optimization Overview Given function with multiple variables, find Min (or max by minimizing –f(x)) Iterative approach Efficient, but not necessarily reliable Conditions: noisy data, constraints, non-linear models Detection via sign of first derivative - Derivative of saddle points will be 0 Local minima Bisection method Similar method for finding a root for a non-linear equation Start with an interval that contains a minimum Golden Search method http://en.wikipedia.org/wiki/Golden_section_search C++: http://www.codecogs.com/code/maths/optimization/golden.php Bisect intervals according to golden ratio 0.618.. Achieves reduction by evaluating a single function instead of 2 Newton-Raphson Method Brent method http://en.wikipedia.org/wiki/Brent's_method C++: http://people.sc.fsu.edu/~jburkardt/cpp_src/brent/brent.cpp Based on quadratic or parabolic interpolation – if the function is smooth & parabolic near to the minimum, then a parabola fitted through any 3 points should approximate the minima – fails when the 3 points are collinear , in which case the denominator is 0 Simplex Method http://en.wikipedia.org/wiki/Simplex_algorithm C++: http://www.codeguru.com/cpp/article.php/c17505/Simplex-Optimization-Algorithm-and-Implemetation-in-C-Programming.htm Find the global minima of any multi-variable function Direct search – no derivatives required At each step it maintains a non-degenerative simplex – a convex hull of n+1 vertices. Obtains the minimum for a function with n variables by evaluating the function at n-1 points, iteratively replacing the point of worst result with the point of best result, shrinking the multidimensional simplex around the best point. Point replacement involves expanding & contracting the simplex near the worst value point to determine a better replacement point Oscillation can be avoided by choosing the 2nd worst result Restart if it gets stuck Parameters: contraction & expansion factors Simulated Annealing http://en.wikipedia.org/wiki/Simulated_annealing C++: http://code.google.com/p/cppsimulatedannealing/ Analogy to heating & cooling metal to strengthen its structure Stochastic method – apply random permutation search for global minima - Avoid entrapment in local minima via hill climbing Heating schedule - Annealing schedule params: temperature, iterations at each temp, temperature delta Cooling schedule – can be linear, step-wise or exponential Differential Evolution http://en.wikipedia.org/wiki/Differential_evolution C++: http://www.amichel.com/de/doc/html/ More advanced stochastic methods analogous to biological processes: Genetic algorithms, evolution strategies Parallel direct search method against multiple discrete or continuous variables Initial population of variable vectors chosen randomly – if weighted difference vector of 2 vectors yields a lower objective function value then it replaces the comparison vector Many params: #parents, #variables, step size, crossover constant etc Convergence is slow – many more function evaluations than simulated annealing Numerical Differentiation Overview 2 approaches to finite difference methods: · A) approximate function via polynomial interpolation then differentiate · B) Taylor series approximation – additionally provides error estimate Finite Difference methods http://en.wikipedia.org/wiki/Finite_difference_method C++: http://www.wpi.edu/Pubs/ETD/Available/etd-051807-164436/unrestricted/EAMPADU.pdf Find differences between high order derivative values - Approximate differential equations by finite differences at evenly spaced data points Based on forward & backward Taylor series expansion of f(x) about x plus or minus multiples of delta h. Forward / backward difference - the sums of the series contains even derivatives and the difference of the series contains odd derivatives – coupled equations that can be solved. Provide an approximation of the derivative within a O(h^2) accuracy There is also central difference & extended central difference which has a O(h^4) accuracy Richardson Extrapolation http://en.wikipedia.org/wiki/Richardson_extrapolation C++: http://mathscoding.blogspot.co.il/2012/02/introduction-richardson-extrapolation.html A sequence acceleration method applied to finite differences Fast convergence, high accuracy O(h^4) Derivatives via Interpolation Cannot apply Finite Difference method to discrete data points at uneven intervals – so need to approximate the derivative of f(x) using the derivative of the interpolant via 3 point Lagrange Interpolation Note: the higher the order of the derivative, the lower the approximation precision Numerical Integration Estimate finite & infinite integrals of functions More accurate procedure than numerical differentiation Use when it is not possible to obtain an integral of a function analytically or when the function is not given, only the data points are Newton Cotes Methods http://en.wikipedia.org/wiki/Newton%E2%80%93Cotes_formulas C++: http://www.siafoo.net/snippet/324 For equally spaced data points Computationally easy – based on local interpolation of n rectangular strip areas that is piecewise fitted to a polynomial to get the sum total area Evaluate the integrand at n+1 evenly spaced points – approximate definite integral by Sum Weights are derived from Lagrange Basis polynomials Leverage Trapezoidal Rule for default 2nd formulas, Simpson 1/3 Rule for substituting 3 point formulas, Simpson 3/8 Rule for 4 point formulas. For 4 point formulas use Bodes Rule. Higher orders obtain more accurate results Trapezoidal Rule uses simple area, Simpsons Rule replaces the integrand f(x) with a quadratic polynomial p(x) that uses the same values as f(x) for its end points, but adds a midpoint Romberg Integration http://en.wikipedia.org/wiki/Romberg's_method C++: http://code.google.com/p/romberg-integration/downloads/detail?name=romberg.cpp&can=2&q= Combines trapezoidal rule with Richardson Extrapolation Evaluates the integrand at equally spaced points The integrand must have continuous derivatives Each R(n,m) extrapolation uses a higher order integrand polynomial replacement rule (zeroth starts with trapezoidal) à a lower triangular matrix set of equation coefficients where the bottom right term has the most accurate approximation. The process continues until the difference between 2 successive diagonal terms becomes sufficiently small. Gaussian Quadrature http://en.wikipedia.org/wiki/Gaussian_quadrature C++: http://www.alglib.net/integration/gaussianquadratures.php Data points are chosen to yield best possible accuracy – requires fewer evaluations Ability to handle singularities, functions that are difficult to evaluate The integrand can include a weighting function determined by a set of orthogonal polynomials. Points & weights are selected so that the integrand yields the exact integral if f(x) is a polynomial of degree <= 2n+1 Techniques (basically different weighting functions): · Gauss-Legendre Integration w(x)=1 · Gauss-Laguerre Integration w(x)=e^-x · Gauss-Hermite Integration w(x)=e^-x^2 · Gauss-Chebyshev Integration w(x)= 1 / Sqrt(1-x^2) Solving ODEs Use when high order differential equations cannot be solved analytically Evaluated under boundary conditions RK for systems – a high order differential equation can always be transformed into a coupled first order system of equations Euler method http://en.wikipedia.org/wiki/Euler_method C++: http://rosettacode.org/wiki/Euler_method First order Runge–Kutta method. Simple recursive method – given an initial value, calculate derivative deltas. Unstable & not very accurate (O(h) error) – not used in practice A first-order method - the local error (truncation error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size In evolving solution between data points xn & xn+1, only evaluates derivatives at beginning of interval xn à asymmetric at boundaries Higher order Runge Kutta http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods C++: http://www.dreamincode.net/code/snippet1441.htm 2nd & 4th order RK - Introduces parameterized midpoints for more symmetric solutions à accuracy at higher computational cost Adaptive RK – RK-Fehlberg – estimate the truncation at each integration step & automatically adjust the step size to keep error within prescribed limits. At each step 2 approximations are compared – if in disagreement to a specific accuracy, the step size is reduced Boundary Value Problems Where solution of differential equations are located at 2 different values of the independent variable x à more difficult, because cannot just start at point of initial value – there may not be enough starting conditions available at the end points to produce a unique solution An n-order equation will require n boundary conditions – need to determine the missing n-1 conditions which cause the given conditions at the other boundary to be satisfied Shooting Method http://en.wikipedia.org/wiki/Shooting_method C++: http://ganeshtiwaridotcomdotnp.blogspot.co.il/2009/12/c-c-code-shooting-method-for-solving.html Iteratively guess the missing values for one end & integrate, then inspect the discrepancy with the boundary values of the other end to adjust the estimate Given the starting boundary values u1 & u2 which contain the root u, solve u given the false position method (solving the differential equation as an initial value problem via 4th order RK), then use u to solve the differential equations. Finite Difference Method For linear & non-linear systems Higher order derivatives require more computational steps – some combinations for boundary conditions may not work though Improve the accuracy by increasing the number of mesh points Solving EigenValue Problems An eigenvalue can substitute a matrix when doing matrix multiplication à convert matrix multiplication into a polynomial EigenValue For a given set of equations in matrix form, determine what are the solution eigenvalue & eigenvectors Similar Matrices - have same eigenvalues. Use orthogonal similarity transforms to reduce a matrix to diagonal form from which eigenvalue(s) & eigenvectors can be computed iteratively Jacobi method http://en.wikipedia.org/wiki/Jacobi_method C++: http://people.sc.fsu.edu/~jburkardt/classes/acs2_2008/openmp/jacobi/jacobi.html Robust but Computationally intense – use for small matrices < 10x10 Power Iteration http://en.wikipedia.org/wiki/Power_iteration For any given real symmetric matrix, generate the largest single eigenvalue & its eigenvectors Simplest method – does not compute matrix decomposition à suitable for large, sparse matrices Inverse Iteration Variation of power iteration method – generates the smallest eigenvalue from the inverse matrix Rayleigh Method http://en.wikipedia.org/wiki/Rayleigh's_method_of_dimensional_analysis Variation of power iteration method Rayleigh Quotient Method Variation of inverse iteration method Matrix Tri-diagonalization Method Use householder algorithm to reduce an NxN symmetric matrix to a tridiagonal real symmetric matrix vua N-2 orthogonal transforms     Whats Next Outside of Numerical Methods there are lots of different types of algorithms that I’ve learned over the decades: Data Mining – (I covered this briefly in a previous post: http://geekswithblogs.net/JoshReuben/archive/2007/12/31/ssas-dm-algorithms.aspx ) Search & Sort Routing Problem Solving Logical Theorem Proving Planning Probabilistic Reasoning Machine Learning Solvers (eg MIP) Bioinformatics (Sequence Alignment, Protein Folding) Quant Finance (I read Wilmott’s books – interesting) Sooner or later, I’ll cover the above topics as well.

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  • Help Decide between C#/XNA client or Java

    - by Sparkky
    The game runs on a client/server architecture currently setup for TCP, and the client code was built in AS3 to be web based. What we're running into is 3 problems for the client. AS3 has no hardware acceleration so we are having some issues with slowdown when implementing some features TCP is really frustrating for a sidescroller when you're talking with a server. I'm having a heck of a time with the interpolation/extrapolation to make everyone else look smooth while minimizing lag. I would much rather be able to use UDP and throw in something similar to the age old Quake interpolation/extrapolation. No right click I work professionally with C#, and I did all my University (almost 2 years ago) with Java. Java really appeals to me because of the compatability while C# appeals to me because I've heard so much good about XNA and I love visual studio. For a Client/Server based MMOish sidescroller in your opinion should I stick with AS3 and the TCP protocol, or should I abandon some of my audience, ramp up the graphics and hit C#, or journey back to the land of Java. Thanks :D

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  • Movement prediction for non-shooters

    - by ShadowChaser
    I'm working on an isometric 2D game with moderate-scale multiplayer, approximately 20-30 players connected at once to a persistent server. I've had some difficulty getting a good movement prediction implementation in place. Physics/Movement The game doesn't have a true physics implementation, but uses the basic principles to implement movement. Rather than continually polling input, state changes (ie/ mouse down/up/move events) are used to change the state of the character entity the player is controlling. The player's direction (ie/ north-east) is combined with a constant speed and turned into a true 3D vector - the entity's velocity. In the main game loop, "Update" is called before "Draw". The update logic triggers a "physics update task" that tracks all entities with a non-zero velocity uses very basic integration to change the entities position. For example: entity.Position += entity.Velocity.Scale(ElapsedTime.Seconds) (where "Seconds" is a floating point value, but the same approach would work for millisecond integer values). The key point is that no interpolation is used for movement - the rudimentary physics engine has no concept of a "previous state" or "current state", only a position and velocity. State Change and Update Packets When the velocity of the character entity the player is controlling changes, a "move avatar" packet is sent to the server containing the entity's action type (stand, walk, run), direction (north-east), and current position. This is different from how 3D first person games work. In a 3D game the velocity (direction) can change frame to frame as the player moves around. Sending every state change would effectively transmit a packet per frame, which would be too expensive. Instead, 3D games seem to ignore state changes and send "state update" packets on a fixed interval - say, every 80-150ms. Since speed and direction updates occur much less frequently in my game, I can get away with sending every state change. Although all of the physics simulations occur at the same speed and are deterministic, latency is still an issue. For that reason, I send out routine position update packets (similar to a 3D game) but much less frequently - right now every 250ms, but I suspect with good prediction I can easily boost it towards 500ms. The biggest problem is that I've now deviated from the norm - all other documentation, guides, and samples online send routine updates and interpolate between the two states. It seems incompatible with my architecture, and I need to come up with a better movement prediction algorithm that is closer to a (very basic) "networked physics" architecture. The server then receives the packet and determines the players speed from it's movement type based on a script (Is the player able to run? Get the player's running speed). Once it has the speed, it combines it with the direction to get a vector - the entity's velocity. Some cheat detection and basic validation occurs, and the entity on the server side is updated with the current velocity, direction, and position. Basic throttling is also performed to prevent players from flooding the server with movement requests. After updating its own entity, the server broadcasts an "avatar position update" packet to all other players within range. The position update packet is used to update the client side physics simulations (world state) of the remote clients and perform prediction and lag compensation. Prediction and Lag Compensation As mentioned above, clients are authoritative for their own position. Except in cases of cheating or anomalies, the client's avatar will never be repositioned by the server. No extrapolation ("move now and correct later") is required for the client's avatar - what the player sees is correct. However, some sort of extrapolation or interpolation is required for all remote entities that are moving. Some sort of prediction and/or lag-compensation is clearly required within the client's local simulation / physics engine. Problems I've been struggling with various algorithms, and have a number of questions and problems: Should I be extrapolating, interpolating, or both? My "gut feeling" is that I should be using pure extrapolation based on velocity. State change is received by the client, client computes a "predicted" velocity that compensates for lag, and the regular physics system does the rest. However, it feels at odds to all other sample code and articles - they all seem to store a number of states and perform interpolation without a physics engine. When a packet arrives, I've tried interpolating the packet's position with the packet's velocity over a fixed time period (say, 200ms). I then take the difference between the interpolated position and the current "error" position to compute a new vector and place that on the entity instead of the velocity that was sent. However, the assumption is that another packet will arrive in that time interval, and it's incredibly difficult to "guess" when the next packet will arrive - especially since they don't all arrive on fixed intervals (ie/ state changes as well). Is the concept fundamentally flawed, or is it correct but needs some fixes / adjustments? What happens when a remote player stops? I can immediately stop the entity, but it will be positioned in the "wrong" spot until it moves again. If I estimate a vector or try to interpolate, I have an issue because I don't store the previous state - the physics engine has no way to say "you need to stop after you reach position X". It simply understands a velocity, nothing more complex. I'm reluctant to add the "packet movement state" information to the entities or physics engine, since it violates basic design principles and bleeds network code across the rest of the game engine. What should happen when entities collide? There are three scenarios - the controlling player collides locally, two entities collide on the server during a position update, or a remote entity update collides on the local client. In all cases I'm uncertain how to handle the collision - aside from cheating, both states are "correct" but at different time periods. In the case of a remote entity it doesn't make sense to draw it walking through a wall, so I perform collision detection on the local client and cause it to "stop". Based on point #2 above, I might compute a "corrected vector" that continually tries to move the entity "through the wall" which will never succeed - the remote avatar is stuck there until the error gets too high and it "snaps" into position. How do games work around this?

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  • Can I rent exclusive time on a powerful server running linux? [closed]

    - by Mark Borgerding
    My company is involved in a proposal that requires speed estimates of our software on a server with the latest & greatest processors. This is not the first time we've been in this situation. The servers themselves are too expensive to buy a new one every time, so we end up extrapolating from what we have. There are so many variables: processor generation & speed, memory speed, memory channels, cache configurations; it makes extrapolation difficult and error-prone. Is there a business that rents time on the newest servers? At least part of the time we'd need exclusive access to an otherwise quiescent system either via ssh shell access or unattended batch jobs. I am not looking for general cloud computing services. I don't need much time on the server, but it needs to be exclusive. And the server needs to be pretty cutting edge for a solid basis of estimate.

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  • 1D Function into 2D Function Interpolation

    - by Drazick
    Hello. I have a 1D function which I want to interpolate into 2D function. I know the function should have "Polar Symmetry". Hence I use the following code (Matlab Syntax): Assuming the 1D function is LSF of the length 15. [x, y] = meshgrid([-7:7]); r = sqrt(x.^2 + y.^2); PSF = interp1([-7:7], LSF, r(:)); % Sometimes using 'spline' option, same results. PSF = reshape(PSF, [7, 7]); I have few problems: 1. Got some overshoot at the edges (As there some Extrapolation). 2. Can't enforce some assumptions (Monotonic, Non Negative). Is there a better Interpolation method for those circumstances? I couldn't find "Lanczos" based interpolation I can use the same way as interp1 (For a certain vector of points, in "imresize" you can only set the length). Is there such function anywhere? Has anyone encountered a function which allows enforcing some assumptions (Monotonically Decreasing, Non Negative, etc..). Thanks.

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  • How to get the best LINPACK result and conquer the Top500?

    - by knweiss
    Given a large Linux HPC cluster with hundreds/thousands of nodes. What are your best practices to get the best possible LINPACK benchmark (HPL) result to submit for the Top500 supercomputer list? To give you an idea what kind of answers I would appreciate here are some sub-questions (with links): How to you tune the parameters (N, NB, P, Q, memory-alignment, etc) for the HPL.dat file (without spending too much time trying each possible permutation - esp with large problem sizes N)? Are there any Top500 submission rules to be aware of? What is allowed, what isn't? Which MPI product, which version? Does it make a difference? Any special host order in your MPI machine file? Do you use CPU pinning? How to you configure your interconnect? Which interconnect? Which BLAS package do you use for which CPU model? (Intel MKL, AMD ACML, GotoBLAS2, etc.) How do you prepare for the big run (on all nodes)? Start with small runs on a subset of nodes and then scale up? Is it really necessary to run LINPACK with a big run on all of the nodes (or is extrapolation allowed)? How do you optimize for the latest Intel/AMD CPUs? Hyperthreading? NUMA? Is it worth it to recompile the software stack or do you use precompiled binaries? Which settings? Which compiler optimizations, which compiler? (What about profile-based compilation?) How to get the best result given only a limited amount of time to do the benchmark run? (You can block a huge cluster forever) How do you prepare the individual nodes (stopping system daemons, freeing memory, etc)? How do you deal with hardware faults (ruining a huge run)? Are there any must-read documents or websites about this topic? E.g. I would love to hear about some background stories of some of the current Top500 systems and how they did their LINPACK benchmark. I deliberately don't want to mention concrete hardware details or discuss hardware recommendations because I don't want to limit the answers. However, feel free to mention hints e.g. for specific CPU models.

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  • Partitioned Repository for WebCenter Content using Oracle Database 11g

    - by Adao Junior
    One of the biggest challenges for content management solutions is related to the storage management due the high volumes of the unstoppable growing of information. Even if you have storage appliances and a lot of terabytes, thinks like backup, compression, deduplication, storage relocation, encryption, availability could be a nightmare. One standard option that you have with the Oracle WebCenter Content is to store data to the database. And the Oracle Database allows you leverage features like compression, deduplication, encryption and seamless backup. But with a huge volume, the challenge is passed to the DBA to keep the WebCenter Content Database up and running. One solution is the use of DB partitions for your content repository, but what are the implications of this? Can I fit this with my business requirements? Well, yes. It’s up to you how you will manage that, you just need a good plan. During you “storage brainstorm plan” take in your mind what you need, such as storage petabytes of documents? You need everything on-line? There’s a way to logically separate the “good content” from the “legacy content”? The first thing that comes to my mind is to use the creation date of the document, but you need to remember that this document could receive a lot of revisions and maybe you can consider the revision creation date. Your plan can have also complex rules like per Document Type or per a custom metadata like department or an hybrid per date, per DocType and an specific virtual folder. Extrapolation the use, you can have your repository distributed in different servers, different disks, different disk types (Such as ssds, sas, sata, tape,…), separated accordingly your business requirements, separating the “hot” content from the legacy and easily matching your compliance requirements. If you think to use by revision, the simple way is to consider the dId, that is the sequential unique id for every content created using the WebCenter Content or the dLastModified that is the date field of the FileStorage table that contains the date of inclusion of the content to the DB Table using SecureFiles. Using the scenario of partitioned repository using an hierarchical separation by date, we will transform the FileStorage table in an partitioned table using  “Partition by Range” of the dLastModified column (You can use the dId or a join with other tables for other metadata such as dDocType, Security, etc…). The test scenario bellow covers: Previous existent data on the JDBC Storage to be migrated to the new partitioned JDBC Storage Partition by Date Automatically generation of new partitions based on a pre-defined interval (Available only with Oracle Database 11g+) Deduplication and Compression for legacy data Oracle WebCenter Content 11g PS5 (Could present some customizations that do not affect the test scenario) For the test case you need some data stored using JDBC Storage to be the “legacy” data. If you do not have done before, just create an Storage rule pointed to the JDBC Storage: Enable the metadata StorageRule in the UI and upload some documents using this rule. For this test case you can run using the schema owner or an dba user. We will use the schema owner TESTS_OCS. I can’t forgot to tell that this is just a test and you should do a proper backup of your environment. When you use the schema owner, you need some privileges, using the dba user grant the privileges needed: REM Grant privileges required for online redefinition. GRANT EXECUTE ON DBMS_REDEFINITION TO TESTS_OCS; GRANT ALTER ANY TABLE TO TESTS_OCS; GRANT DROP ANY TABLE TO TESTS_OCS; GRANT LOCK ANY TABLE TO TESTS_OCS; GRANT CREATE ANY TABLE TO TESTS_OCS; GRANT SELECT ANY TABLE TO TESTS_OCS; REM Privileges required to perform cloning of dependent objects. GRANT CREATE ANY TRIGGER TO TESTS_OCS; GRANT CREATE ANY INDEX TO TESTS_OCS; In our test scenario we will separate the content as Legacy, Day1, Day2, Day3 and Future. This last one will partitioned automatically using 3 tablespaces in a round robin mode. In a real scenario the partition rule could be per month, per year or any rule that you choose. Table spaces for the test scenario: CREATE TABLESPACE TESTS_OCS_PART_LEGACY DATAFILE 'tests_ocs_part_legacy.dat' SIZE 500K AUTOEXTEND ON NEXT 500K MAXSIZE UNLIMITED; CREATE TABLESPACE TESTS_OCS_PART_DAY1 DATAFILE 'tests_ocs_part_day1.dat' SIZE 500K AUTOEXTEND ON NEXT 500K MAXSIZE UNLIMITED; CREATE TABLESPACE TESTS_OCS_PART_DAY2 DATAFILE 'tests_ocs_part_day2.dat' SIZE 500K AUTOEXTEND ON NEXT 500K MAXSIZE UNLIMITED; CREATE TABLESPACE TESTS_OCS_PART_DAY3 DATAFILE 'tests_ocs_part_day3.dat' SIZE 500K AUTOEXTEND ON NEXT 500K MAXSIZE UNLIMITED; CREATE TABLESPACE TESTS_OCS_PART_ROUND_ROBIN_A 'tests_ocs_part_round_robin_a.dat' DATAFILE SIZE 500K AUTOEXTEND ON NEXT 500K MAXSIZE UNLIMITED; CREATE TABLESPACE TESTS_OCS_PART_ROUND_ROBIN_B 'tests_ocs_part_round_robin_b.dat' DATAFILE SIZE 500K AUTOEXTEND ON NEXT 500K MAXSIZE UNLIMITED; CREATE TABLESPACE TESTS_OCS_PART_ROUND_ROBIN_C 'tests_ocs_part_round_robin_c.dat' DATAFILE SIZE 500K AUTOEXTEND ON NEXT 500K MAXSIZE UNLIMITED; Before start, gather optimizer statistics on the actual FileStorage table: EXEC DBMS_STATS.GATHER_TABLE_STATS(USER, 'FileStorage', cascade => TRUE); Now check if is possible execute the redefinition process: EXEC DBMS_REDEFINITION.CAN_REDEF_TABLE('TESTS_OCS', 'FileStorage',DBMS_REDEFINITION.CONS_USE_PK); If no errors messages, you are good to go. Create a Partitioned Interim FileStorage table. You need to create a new table with the partition information to act as an interim table: CREATE TABLE FILESTORAGE_Part ( DID NUMBER(*,0) NOT NULL ENABLE, DRENDITIONID VARCHAR2(30 CHAR) NOT NULL ENABLE, DLASTMODIFIED TIMESTAMP (6), DFILESIZE NUMBER(*,0), DISDELETED VARCHAR2(1 CHAR), BFILEDATA BLOB ) LOB (BFILEDATA) STORE AS SECUREFILE ( ENABLE STORAGE IN ROW NOCACHE LOGGING KEEP_DUPLICATES NOCOMPRESS ) PARTITION BY RANGE (DLASTMODIFIED) INTERVAL (NUMTODSINTERVAL(1,'DAY')) STORE IN (TESTS_OCS_PART_ROUND_ROBIN_A, TESTS_OCS_PART_ROUND_ROBIN_B, TESTS_OCS_PART_ROUND_ROBIN_C) ( PARTITION FILESTORAGE_PART_LEGACY VALUES LESS THAN (TO_DATE('05-APR-2012 12.00.00 AM', 'DD-MON-YYYY HH.MI.SS AM')) TABLESPACE TESTS_OCS_PART_LEGACY LOB (BFILEDATA) STORE AS SECUREFILE ( TABLESPACE TESTS_OCS_PART_LEGACY RETENTION NONE DEDUPLICATE COMPRESS HIGH ), PARTITION FILESTORAGE_PART_DAY1 VALUES LESS THAN (TO_DATE('06-APR-2012 07.25.00 PM', 'DD-MON-YYYY HH.MI.SS AM')) TABLESPACE TESTS_OCS_PART_DAY1 LOB (BFILEDATA) STORE AS SECUREFILE ( TABLESPACE TESTS_OCS_PART_DAY1 RETENTION AUTO KEEP_DUPLICATES COMPRESS ), PARTITION FILESTORAGE_PART_DAY2 VALUES LESS THAN (TO_DATE('06-APR-2012 07.55.00 PM', 'DD-MON-YYYY HH.MI.SS AM')) TABLESPACE TESTS_OCS_PART_DAY2 LOB (BFILEDATA) STORE AS SECUREFILE ( TABLESPACE TESTS_OCS_PART_DAY2 RETENTION AUTO KEEP_DUPLICATES NOCOMPRESS ), PARTITION FILESTORAGE_PART_DAY3 VALUES LESS THAN (TO_DATE('06-APR-2012 07.58.00 PM', 'DD-MON-YYYY HH.MI.SS AM')) TABLESPACE TESTS_OCS_PART_DAY3 LOB (BFILEDATA) STORE AS SECUREFILE ( TABLESPACE TESTS_OCS_PART_DAY3 RETENTION AUTO KEEP_DUPLICATES NOCOMPRESS ) ); After the creation you should see your partitions defined. Note that only the fixed range partitions have been created, none of the interval partition have been created. Start the redefinition process: BEGIN DBMS_REDEFINITION.START_REDEF_TABLE( uname => 'TESTS_OCS' ,orig_table => 'FileStorage' ,int_table => 'FileStorage_PART' ,col_mapping => NULL ,options_flag => DBMS_REDEFINITION.CONS_USE_PK ); END; This operation can take some time to complete, depending how many contents that you have and on the size of the table. Using the DBA user you can check the progress with this command: SELECT * FROM v$sesstat WHERE sid = 1; Copy dependent objects: DECLARE redefinition_errors PLS_INTEGER := 0; BEGIN DBMS_REDEFINITION.COPY_TABLE_DEPENDENTS( uname => 'TESTS_OCS' ,orig_table => 'FileStorage' ,int_table => 'FileStorage_PART' ,copy_indexes => DBMS_REDEFINITION.CONS_ORIG_PARAMS ,copy_triggers => TRUE ,copy_constraints => TRUE ,copy_privileges => TRUE ,ignore_errors => TRUE ,num_errors => redefinition_errors ,copy_statistics => FALSE ,copy_mvlog => FALSE ); IF (redefinition_errors > 0) THEN DBMS_OUTPUT.PUT_LINE('>>> FileStorage to FileStorage_PART temp copy Errors: ' || TO_CHAR(redefinition_errors)); END IF; END; With the DBA user, verify that there's no errors: SELECT object_name, base_table_name, ddl_txt FROM DBA_REDEFINITION_ERRORS; *Note that will show 2 lines related to the constrains, this is expected. Synchronize the interim table FileStorage_PART: BEGIN DBMS_REDEFINITION.SYNC_INTERIM_TABLE( uname => 'TESTS_OCS', orig_table => 'FileStorage', int_table => 'FileStorage_PART'); END; Gather statistics on the new table: EXEC DBMS_STATS.GATHER_TABLE_STATS(USER, 'FileStorage_PART', cascade => TRUE); Complete the redefinition: BEGIN DBMS_REDEFINITION.FINISH_REDEF_TABLE( uname => 'TESTS_OCS', orig_table => 'FileStorage', int_table => 'FileStorage_PART'); END; During the execution the FileStorage table is locked in exclusive mode until finish the operation. After the last command the FileStorage table is partitioned. If you have contents out of the range partition, you should see the new partitions created automatically, not generating an error if you “forgot” to create all the future ranges. You will see something like: You now can drop the FileStorage_PART table: border-bottom-width: 1px; border-bottom-style: solid; text-align: left; border-left-color: silver; border-left-width: 1px; border-left-style: solid; padding-bottom: 4px; line-height: 12pt; background-color: #f4f4f4; margin-top: 20px; margin-right: 0px; margin-bottom: 10px; margin-left: 0px; padding-left: 4px; width: 97.5%; padding-right: 4px; font-family: 'Courier New', Courier, monospace; direction: ltr; max-height: 200px; font-size: 8pt; overflow-x: auto; overflow-y: auto; border-top-color: silver; border-top-width: 1px; border-top-style: solid; cursor: text; border-right-color: silver; border-right-width: 1px; border-right-style: solid; padding-top: 4px; " id="codeSnippetWrapper"> DROP TABLE FileStorage_PART PURGE; To check the FileStorage table is valid and is partitioned, use the command: SELECT num_rows,partitioned FROM user_tables WHERE table_name = 'FILESTORAGE'; You can list the contents of the FileStorage table in a specific partition, per example: SELECT * FROM FileStorage PARTITION (FILESTORAGE_PART_LEGACY) Some useful commands that you can use to check the partitions, note that you need to run using a DBA user: SELECT * FROM DBA_TAB_PARTITIONS WHERE table_name = 'FILESTORAGE';   SELECT * FROM DBA_TABLESPACES WHERE tablespace_name like 'TESTS_OCS%'; After the redefinition process complete you have a new FileStorage table storing all content that has the Storage rule pointed to the JDBC Storage and partitioned using the rule set during the creation of the temporary interim FileStorage_PART table. At this point you can test the WebCenter Content downloading the documents (Original and Renditions). Note that the content could be already in the cache area, take a look in the weblayout directory to see if a file with the same id is there, then click on the web rendition of your test file and see if have created the file and you can open, this means that is all working. The redefinition process can be repeated many times, this allow you test what the better layout, over and over again. Now some interesting maintenance actions related to the partitions: Make an tablespace read only. No issues viewing, the WebCenter Content do not alter the revisions When try to delete an content that is part of an read only tablespace, an error will occurs and the document will not be deleted The only way to prevent errors today is creating an custom component that checks the partitions and if you have an document in an “Read Only” repository, execute the deletion process of the metadata and mark the document to be deleted on the next db maintenance, like a new redefinition. Take an tablespace off-line for archiving purposes or any other reason. When you try open an document that is included in this tablespace will receive an error that was unable to retrieve the content, but the others online tablespaces are not affected. Same behavior when deleting documents. Again, an custom component is the solution. If you have an document “out of range”, the component can show an message that the repository for that document is offline. This can be extended to a option to the user to request to put online again. Moving some legacy content to an offline repository (table) using the Exchange option to move the content from one partition to a empty nonpartitioned table like FileStorage_LEGACY. Note that this option will remove the registers from the FileStorage and will not be able to open the stored content. You always need to keep in mind the indexes and constrains. An redefinition separating the original content (vault) from the renditions and separate by date ate the same time. This could be an option for DAM environments that want to have an special place for the renditions and put the original files in a storage with less performance. The process will be the same, you just need to change the script of the interim table to use composite partitioning. Will be something like: CREATE TABLE FILESTORAGE_RenditionPart ( DID NUMBER(*,0) NOT NULL ENABLE, DRENDITIONID VARCHAR2(30 CHAR) NOT NULL ENABLE, DLASTMODIFIED TIMESTAMP (6), DFILESIZE NUMBER(*,0), DISDELETED VARCHAR2(1 CHAR), BFILEDATA BLOB ) LOB (BFILEDATA) STORE AS SECUREFILE ( ENABLE STORAGE IN ROW NOCACHE LOGGING KEEP_DUPLICATES NOCOMPRESS ) PARTITION BY LIST (DRENDITIONID) SUBPARTITION BY RANGE (DLASTMODIFIED) ( PARTITION Vault VALUES ('primaryFile') ( SUBPARTITION FILESTORAGE_VAULT_LEGACY VALUES LESS THAN (TO_DATE('05-APR-2012 12.00.00 AM', 'DD-MON-YYYY HH.MI.SS AM')) LOB (BFILEDATA) STORE AS SECUREFILE , SUBPARTITION FILESTORAGE_VAULT_DAY1 VALUES LESS THAN (TO_DATE('06-APR-2012 07.25.00 PM', 'DD-MON-YYYY HH.MI.SS AM')) LOB (BFILEDATA) STORE AS SECUREFILE , SUBPARTITION FILESTORAGE_VAULT_DAY2 VALUES LESS THAN (TO_DATE('06-APR-2012 07.55.00 PM', 'DD-MON-YYYY HH.MI.SS AM')) LOB (BFILEDATA) STORE AS SECUREFILE , SUBPARTITION FILESTORAGE_VAULT_DAY3 VALUES LESS THAN (TO_DATE('06-APR-2012 07.58.00 PM', 'DD-MON-YYYY HH.MI.SS AM')) LOB (BFILEDATA) STORE AS SECUREFILE , SUBPARTITION FILESTORAGE_VAULT_FUTURE VALUES LESS THAN (MAXVALUE) ) ,PARTITION WebLayout VALUES ('webViewableFile') ( SUBPARTITION FILESTORAGE_WEBLAYOUT_LEGACY VALUES LESS THAN (TO_DATE('05-APR-2012 12.00.00 AM', 'DD-MON-YYYY HH.MI.SS AM')) LOB (BFILEDATA) STORE AS SECUREFILE , SUBPARTITION FILESTORAGE_WEBLAYOUT_DAY1 VALUES LESS THAN (TO_DATE('06-APR-2012 07.25.00 PM', 'DD-MON-YYYY HH.MI.SS AM')) LOB (BFILEDATA) STORE AS SECUREFILE , SUBPARTITION FILESTORAGE_WEBLAYOUT_DAY2 VALUES LESS THAN (TO_DATE('06-APR-2012 07.55.00 PM', 'DD-MON-YYYY HH.MI.SS AM')) LOB (BFILEDATA) STORE AS SECUREFILE , SUBPARTITION FILESTORAGE_WEBLAYOUT_DAY3 VALUES LESS THAN (TO_DATE('06-APR-2012 07.58.00 PM', 'DD-MON-YYYY HH.MI.SS AM')) LOB (BFILEDATA) STORE AS SECUREFILE , SUBPARTITION FILESTORAGE_WEBLAYOUT_FUTURE VALUES LESS THAN (MAXVALUE) ) ,PARTITION Special VALUES ('Special') ( SUBPARTITION FILESTORAGE_SPECIAL_LEGACY VALUES LESS THAN (TO_DATE('05-APR-2012 12.00.00 AM', 'DD-MON-YYYY HH.MI.SS AM')) LOB (BFILEDATA) STORE AS SECUREFILE , SUBPARTITION FILESTORAGE_SPECIAL_DAY1 VALUES LESS THAN (TO_DATE('06-APR-2012 07.25.00 PM', 'DD-MON-YYYY HH.MI.SS AM')) LOB (BFILEDATA) STORE AS SECUREFILE , SUBPARTITION FILESTORAGE_SPECIAL_DAY2 VALUES LESS THAN (TO_DATE('06-APR-2012 07.55.00 PM', 'DD-MON-YYYY HH.MI.SS AM')) LOB (BFILEDATA) STORE AS SECUREFILE , SUBPARTITION FILESTORAGE_SPECIAL_DAY3 VALUES LESS THAN (TO_DATE('06-APR-2012 07.58.00 PM', 'DD-MON-YYYY HH.MI.SS AM')) LOB (BFILEDATA) STORE AS SECUREFILE , SUBPARTITION FILESTORAGE_SPECIAL_FUTURE VALUES LESS THAN (MAXVALUE) ) )ENABLE ROW MOVEMENT; The next post related to partitioned repository will come with an sample component to handle the possible exceptions when you need to take off line an tablespace/partition or move to another place. Also, we can include some integration to the Retention Management and Records Management. Another subject related to partitioning is the ability to create an FileStore Provider pointed to a different database, raising the level of the distributed storage vs. performance. Let us know if this is important to you or you have an use case not listed, leave a comment. Cross-posted on the blog.ContentrA.com

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