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  • What does the SEO market look like? [closed]

    - by TheEconomist
    I'm an economist (aspiring economist, if we are being technical) and my curiousity has been recently piqued by search engine optimization services. I had the following questions. 1) What industries most widely use search engine optimization services? 2) Is it small business or big firms that use SEO services typically? 3) What is SEO pricing typically dependent upon and how much is it on average? 4) Do SEO services really increase traffic? Is there a dataset I can get a hold of for this sort of thing? I am not looking for answers to the questions necessarily. Although answers would help, a nudge in the right direction is more than sufficient, and greatly appreciated. Thank you!

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  • How can I tell which page is creating a high-CPU-load httpd process?

    - by Greg
    I have a LAMP server (CentOS-based MediaTemple (DV) Extreme with 2GB RAM) running a customized Wordpress+bbPress combination . At about 30k pageviews per day the server is starting to groan. It stumbled earlier today for about 5 minutes when there was an influx of traffic. Even under normal conditions I can see that the virtual server is sometimes at 90%+ CPU load. Using Top I can often see 5-7 httpd processes that are each using 15-30% (and sometimes even 50%) CPU. Before we do a big optimization pass (our use of MySQL is probably the culprit) I would love to find the pages that are the main offenders and deal with them first. Is there a way that I can find out which specific requests were responsible for the most CPU-hungry httpd processes? I have found a lot of info on optimization in general, but nothing on this specific question. Secondly, I know there are a million variables, but if you have any insight on whether we should be at the boundaries of performance with a single dedicated virtual server with a site of this size, then I would love to hear your opinion. Should we be thinking about moving to a more powerful server, or should we be focused on optimization on the current server?

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  • Apache on CentOS 5.9 VM serves my optimized images corrupted (but my Mac doesn't)

    - by Robert K
    I'm using a Vagrant VM to mirror the client's environment as closely as I can. As part of our build process we do no optimization of assets early on; that comes as we're ready to take a site live. Needless to say, this issue is beginning to worry me as we need to take the site live very soon. I use ImageOptim to automate optimization of image assets, which runs a whole series of tools (Zopfli, PNGOUT, OptiPNG, AdvPNG, PNGCrush). I always set the optimizations to their maximum setting. After optimization, my PNGs start looking like this: What's weird is, if I serve the same file through my Mac's copy of Apache, not through Vagrant, the image loads fine. In fact, the only time it's ever corrupt like this is when the image is served from the Vagrant VM and its install of Drupal. All optimized JPEGs display only the first ~20% of the image. And PNGs, depending on the image, may show either a portion or the "progressive"-style corruption below. The browser itself makes no difference, the same browser will serve an uncorrupted image from my Mac's Apache instance and a corrupt image from the VM. When I disable all PNG optimizations except PNGCrush, and the removal of the PNG metadata, the image is served corrupted. I'm optimizing JPEG images with JPEGmini. The server is running CentOS 5.9, Apache 2.2.3-85, PHP 5.3.3, and Drupal 7. As best as I can tell the error lies somewhere within the VM, either with Apache or with (perhaps) the network stack. Seems like the tools that optimize the compression of the PNGs and JPEGs are what trigger this error. I've already determined that the .htaccess file isn't interfering with how the images load. What should I try to troubleshoot this?

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  • cool project to use a genetic algorithm for?

    - by Ryan
    I'm looking for a practical application to use a genetic algorithm for. Some things that have thought of are: Website interface optimization Vehicle optimization with a physics simulator Genetic programming Automatic test case generation But none have really popped out at me. So if you had some free time (a few months) to spend on a genetic algorithms project, what would you choose to tackle?

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  • How to tell what optimizations bjam is using to build boost

    - by Steve
    I'm building the boost libraries with bjam for both the intel compiler and vs2008, and I can't tell what optimizations are being passed to the compiler from bjam. For one of the compiler's gcc, I can see some optimizations in one of the bjam files, but I can't find the optimization flags for the compilers I care about. So, my questions are - Does anyone know where the default optimization flags are located? If they're declared within bjam, does anyone know how I can override them?

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  • procedure that swaps the bytes (low/high) of a Word variable

    - by Altar
    Hi. I have this procedure that swaps the bytes (low/high) of a Word variable (It does the same stuff as System.Swap function). The procedure works when the compiler optimization is OFF but not when it is ON. Can anybody help me with this? { UNSAFE! IT IS NOW WORKING WHEN COMPILER OPTIMIZATION IS ON ! } procedure SwapWord_NotWorking(VAR TwoBytes: word); asm Mov EBX, TwoBytes Mov AX, [EBX] XCHG AL,AH Mov [EBX], AX end;

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  • Largest triangle from a set of points

    - by Faken
    I have a set of random points from which i want to find the largest triangle by area who's verticies are each on one of those points. So far I have figured out that the largest triangle's verticies will only lie on the outside points of the cloud of points (or the convex hull) so i have programmed a function to do just that (using Graham scan in nlogn time). However that's where I'm stuck. The only way I can figure out how to find the largest triangle from these points is to use brute force at n^3 time which is still acceptable in an average case as the convex hull algorithm usually kicks out the vast majority of points. However in a worst case scenario where points are on a circle, this method would fail miserably. Dose anyone know an algorithm to do this more efficiently? Note: I know that CGAL has this algorithm there but they do not go into any details on how its done. I don't want to use libraries, i want to learn this and program it myself (and also allow me to tweak it to exactly the way i want it to operate, just like the graham scan in which other implementations pick up collinear points that i don't want).

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  • Qt C++ signals and slots did not fire

    - by Xegara
    I have programmed Qt a couple of times already and I really like the signals and slots feature. But now, I guess I'm having a problem when a signal is emitted from one thread, the corresponding slot from another thread is not fired. The connection was made in the main program. This is also my first time to use Qt for ROS which uses CMake. The signal fired by the QThread triggered their corresponding slots but the emitted signal of my class UserInput did not trigger the slot in tflistener where it supposed to. I have tried everything I can. Any help? The code is provided below. Main.cpp #include <QCoreApplication> #include <QThread> #include "userinput.h" #include "tfcompleter.h" int main(int argc, char** argv) { QCoreApplication app(argc, argv); QThread *thread1 = new QThread(); QThread *thread2 = new QThread(); UserInput *input1 = new UserInput(); TfCompleter *completer = new TfCompleter(); QObject::connect(input1, SIGNAL(togglePause2()), completer, SLOT(toggle())); QObject::connect(thread1, SIGNAL(started()), completer, SLOT(startCounting())); QObject::connect(thread2, SIGNAL(started()), input1, SLOT(start())); completer->moveToThread(thread1); input1->moveToThread(thread2); thread1->start(); thread2->start(); app.exec(); return 0; } What I want to do is.. There are two seperate threads. One thread is for the user input. When the user enters [space], the thread emits a signal to toggle the boolean member field of the other thread. The other thread 's task is to just continue its process if the user wants it to run, otherwise, the user does not want it to run. I wanted to grant the user to toggle the processing anytime that he wants, that's why I decided to bring them into seperate threads. The following codes are the tflistener and userinput. tfcompleter.h #ifndef TFCOMPLETER_H #define TFCOMPLETER_H #include <QObject> #include <QtCore> class TfCompleter : public QObject { Q_OBJECT private: bool isCount; public Q_SLOTS: void toggle(); void startCounting(); }; #endif tflistener.cpp #include "tfcompleter.h" #include <iostream> void TfCompleter::startCounting() { static uint i = 0; while(true) { if(isCount) std::cout << i++ << std::endl; } } void TfCompleter::toggle() { // isCount = ~isCount; std::cout << "isCount " << std::endl; } UserInput.h #ifndef USERINPUT_H #define USERINPUT_H #include <QObject> #include <QtCore> class UserInput : public QObject { Q_OBJECT public Q_SLOTS: void start(); // Waits for the keypress from the user and emits the corresponding signal. public: Q_SIGNALS: void togglePause2(); }; #endif UserInput.cpp #include "userinput.h" #include <iostream> #include <cstdio> // Implementation of getch #include <termios.h> #include <unistd.h> /* reads from keypress, doesn't echo */ int getch(void) { struct termios oldattr, newattr; int ch; tcgetattr( STDIN_FILENO, &oldattr ); newattr = oldattr; newattr.c_lflag &= ~( ICANON | ECHO ); tcsetattr( STDIN_FILENO, TCSANOW, &newattr ); ch = getchar(); tcsetattr( STDIN_FILENO, TCSANOW, &oldattr ); return ch; } void UserInput::start() { char c = 0; while (true) { c = getch(); if (c == ' ') { Q_EMIT togglePause2(); std::cout << "SPACE" << std::endl; } c = 0; } } Here is the CMakeLists.txt. I just placed it here also since I don't know maybe the CMake has also a factor here. CMakeLists.txt ############################################################################## # CMake ############################################################################## cmake_minimum_required(VERSION 2.4.6) ############################################################################## # Ros Initialisation ############################################################################## include($ENV{ROS_ROOT}/core/rosbuild/rosbuild.cmake) rosbuild_init() set(CMAKE_AUTOMOC ON) #set the default path for built executables to the "bin" directory set(EXECUTABLE_OUTPUT_PATH ${PROJECT_SOURCE_DIR}/bin) #set the default path for built libraries to the "lib" directory set(LIBRARY_OUTPUT_PATH ${PROJECT_SOURCE_DIR}/lib) # Set the build type. Options are: # Coverage : w/ debug symbols, w/o optimization, w/ code-coverage # Debug : w/ debug symbols, w/o optimization # Release : w/o debug symbols, w/ optimization # RelWithDebInfo : w/ debug symbols, w/ optimization # MinSizeRel : w/o debug symbols, w/ optimization, stripped binaries #set(ROS_BUILD_TYPE Debug) ############################################################################## # Qt Environment ############################################################################## # Could use this, but qt-ros would need an updated deb, instead we'll move to catkin # rosbuild_include(qt_build qt-ros) rosbuild_find_ros_package(qt_build) include(${qt_build_PACKAGE_PATH}/qt-ros.cmake) rosbuild_prepare_qt4(QtCore) # Add the appropriate components to the component list here ADD_DEFINITIONS(-DQT_NO_KEYWORDS) ############################################################################## # Sections ############################################################################## #file(GLOB QT_FORMS RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} ui/*.ui) #file(GLOB QT_RESOURCES RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} resources/*.qrc) file(GLOB_RECURSE QT_MOC RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} FOLLOW_SYMLINKS include/rgbdslam_client/*.hpp) #QT4_ADD_RESOURCES(QT_RESOURCES_CPP ${QT_RESOURCES}) #QT4_WRAP_UI(QT_FORMS_HPP ${QT_FORMS}) QT4_WRAP_CPP(QT_MOC_HPP ${QT_MOC}) ############################################################################## # Sources ############################################################################## file(GLOB_RECURSE QT_SOURCES RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} FOLLOW_SYMLINKS src/*.cpp) ############################################################################## # Binaries ############################################################################## rosbuild_add_executable(rgbdslam_client ${QT_SOURCES} ${QT_MOC_HPP}) #rosbuild_add_executable(rgbdslam_client ${QT_SOURCES} ${QT_RESOURCES_CPP} ${QT_FORMS_HPP} ${QT_MOC_HPP}) target_link_libraries(rgbdslam_client ${QT_LIBRARIES})

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  • Thinktecture.IdentityModel: Comparing Strings without leaking Timinig Information

    - by Your DisplayName here!
    Paul Hill commented on a recent post where I was comparing HMACSHA256 signatures. In a nutshell his complaint was that I am leaking timing information while doing so – or in other words, my code returned faster with wrong (or partially wrong) signatures than with the correct signature. This can be potentially used for timing attacks like this one. I think he got a point here, especially in the era of cloud computing where you can potentially run attack code on the same physical machine as your target to do high resolution timing analysis (see here for an example). It turns out that it is not that easy to write a time-constant string comparer due to all sort of (unexpected) clever optimization mechanisms in the CLR. With the help and feedback of Paul and Shawn I came up with this: Structure the code in a way that the CLR will not try to optimize it In addition turn off optimization (just in case a future version will come up with new optimization methods) Add a random sleep when the comparison fails (using Shawn’s and Stephen’s nice Random wrapper for RNGCryptoServiceProvider). You can find the full code in the Thinktecture.IdentityModel download. [MethodImpl(MethodImplOptions.NoOptimization)] public static bool IsEqual(string s1, string s2) {     if (s1 == null && s2 == null)     {         return true;     }       if (s1 == null || s2 == null)     {         return false;     }       if (s1.Length != s2.Length)     {         return false;     }       var s1chars = s1.ToCharArray();     var s2chars = s2.ToCharArray();       int hits = 0;     for (int i = 0; i < s1.Length; i++)     {         if (s1chars[i].Equals(s2chars[i]))         {             hits += 2;         }         else         {             hits += 1;         }     }       bool same = (hits == s1.Length * 2);       if (!same)     {         var rnd = new CryptoRandom();         Thread.Sleep(rnd.Next(0, 10));     }       return same; }

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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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  • How can I make an object's hitbox rotate with its texture?

    - by Matthew Optional Meehan
    In XNA, when you have a rectangular sprite that doesnt rotate, it's easy to get its four corners to make a hitbox. However, when you do a rotation, the points get moved and I assume there is some kind of math that I can use to aquire them. I am using the four points to draw a rectangle that visually represents the hitboxes. I have seen some per-pixel collision examples, but I can forsee they would be hard to draw a box/'convex hull' around. I have also seen physics like farseer but I'm not sure if there is a quick tutorial to do what I want.

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  • How can I locate empty space next to polygon regions?

    - by Stephen
    Let's say I have the following area in a top-down map: The circle is the player, the black square is an obstacle, and the grey polygons with red borders are walk-able areas that will be used as a navigation mesh for enemies. Obstacles and grey polygons are always convex. The grey regions were defined using an algorithm when the world was generated at runtime. Notice the little white column. I need to figure out where any empty space like this is, if at all, after the algorithm builds the grey regions, so that I can fill the space with another region. Basically what I'm hoping for is an algorithm that can detect empty space next to a polygon.

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  • Implementing 2D CSG (for collision shapes)?

    - by bluescrn
    Are there any simple (or well documented) algorithms for basic CSG operations on 2D polygons? I'm looking for a way to 'add' a number of overlapping 2D collision shapes. These may be convex or concave, but will be closed shapes, defined as a set of line segments, with no self-intersections. The use of this would be to construct a clean set of collision edges, for use with a 2D physics engine, from a scene consisting of many arbitrarily placed (and frequently overlapping) objects, each with their own collision shape. To begin with, I only need to 'add' shapes, but the ability to 'subtract', to create holes, may also be useful.

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  • Can SpriteBatch be used to fill a polygon with a texture?

    - by can poyrazoglu
    I basically need to fill a texture into a polygon using the SpriteBatch. I've done some research but couldn't find anything useful except polygon triangulation method, which works well only with convex polygons (without diving into super math which is definitely not something I'm pretty good at). Are there any solutions for filling in a polygon in a basic way? I of course need something dynamic (I'll have a map editor that you can define polygons, and the game will render them (and collision detection will also use them but that's off topic), basically I can't accept solutions like "pre-calculated" bitmaps or anything like that. I need to draw a polygon with the segments provided, to the screen, using the SpriteBatch.

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  • Drawing an outline around an arbitrary group of hexagons

    - by Perky
    Is there an algorithm for drawing an outline around around an arbitrary group of hexagons? The polygon outline drawn may be concave. See the images below, the green line is what I am trying to achieve. The hexagons are stored as vertices and drawn as polygons. Edit: I've uploaded images that should explain more. I want to favour convex hulls because it's conveys an area of control more quickly. Each hexagon is stored in a multidimensional array so they all have x and y coordinates, I can easily find adjacent hexagons and the opposite vertex, i.e. adjacentHexagon = getAdjacentHexagon( someHexagon, NORTHWEST ) if there isn't a hexagon immediately adjacent it will continue to search in that direction until it finds one or hits the map edges.

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  • Continuous Collision Detection Techniques

    - by Griffin
    I know there are quite a few continuous collision detection algorithms out there , but I can't find a list or summary of different 2D techniques; only tutorials on specific algorithms. What techniques are out there for calculating when different 2D bodies will collide and what are the advantages / disadvantages of each? I say techniques and not algorithms because I have not yet decided on how I will store different polygons which might be concave or even have holes. I plan to make a decision on this based on what the algorithm requires (for instance if an algorithm breaks down a polygon into triangles or convex shapes I will simply store the polygon data in this form).

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  • what is the easiest way to make a hitbox that rotates with it's texture

    - by Matthew Optional Meehan
    In xna when you have a sprite that doesnt rotate it's very easy to get the four corner of a sprite to make a hitbox, but when you do a rotation the points get moved and I assume there is some kind of math that I can use to aquire them. I am using the four points to draw a rectangle that visually represents the hitboxes. I have seen some per-pixel collission examples but I can forsee they would be hard to draw a box/'convex hull' around. I have also seen physics like farseer but I'm not sure if there is a quick tutorial to do what I want. What do you guys think is the best approach becuase I am looking to complete this work by the end of the week.

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  • Drawing Shape in DebugView (Farseer)

    - by keyvan kazemi
    As the title says, I need to draw a shape/polygon in Farseer using debugview. I have this piece of code which converts a Texture to polygon: //load texture that will represent the tray trayTexture = Content.Load<Texture2D>("tray"); //Create an array to hold the data from the texture uint[] data = new uint[trayTexture.Width * trayTexture.Height]; //Transfer the texture data to the array trayTexture.GetData(data); //Find the vertices that makes up the outline of the shape in the texture Vertices verts = PolygonTools.CreatePolygon(data, trayTexture.Width, false); //Since it is a concave polygon, we need to partition it into several smaller convex polygons _list = BayazitDecomposer.ConvexPartition(verts); Vector2 vertScale = new Vector2(ConvertUnits.ToSimUnits(1)); foreach (Vertices verti in _list) { verti.Scale(ref vertScale); } tray = BodyFactory.CreateCompoundPolygon(MyWorld, _list, 10); Now in DebugView I guess I have to use "DrawShape" method which requires: DrawShape(Fixture fixture, Transform xf, Color color) My question is how can I get the variables needed for this method, namely Fixture and Transform?

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  • Full-text indexing? You must read this

    - by Kyle Hatlestad
    For those of you who may have missed it, Peter Flies, Principal Technical Support Engineer for WebCenter Content, gave an excellent webcast on database searching and indexing in WebCenter Content.  It's available for replay along with a download of the slidedeck.  Look for the one titled 'WebCenter Content: Database Searching and Indexing'. One of the items he led with...and concluded with...was a recommendation on optimizing your search collection if you are using full-text searching with the Oracle database.  This can greatly improve your search performance.  And this would apply to both Oracle Text Search and DATABASE.FULLTEXT search methods.  Peter describes how a collection can become fragmented over time as content is added, updated, and deleted.  Just like you should defragment your hard drive from time to time to get your files placed on the disk in the most optimal way, you should do the same for the search collection. And optimizing the collection is just a simple procedure call that can be scheduled to be run automatically.   beginctx_ddl.optimize_index('FT_IDCTEXT1','FULL', parallel_degree =>'1');end; When I checked my own test instance, I found my collection had a row fragmentation of about 80% After running the optimization procedure, it went down to 0% The knowledgebase article On Index Fragmentation and Optimization When Using OracleTextSearch or DATABASE.FULLTEXT [ID 1087777.1] goes into detail on how to check your current index fragmentation, how to run the procedure, and then how to schedule the procedure to run automatically.  While the article mentions scheduling the job weekly, Peter says he now is recommending this be run daily, especially on more active systems. And just as a reminder, be sure to involve your DBA with your WebCenter Content implementation as you go to production and over time.  We recently had a customer complain of slow performance of the application when it was discovered the database was starving for memory.  So it's always helpful to keep a watchful eye on your database.

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  • A Technical Perspective On Rapid Planning

    - by Robert Story
    Upcoming WebcastTitle: A Technical Perspective On Rapid PlanningDate: April 14, 2010 Time: 11:00 am EDT, 9:00 am MDT, 8:00 am PDT, 16:00 GMT Product Family: Value Chain PlanningSummary Oracle's Strategic Network Optimization (SNO) product is a powerful supply chain design and tactical planning tool.  This one-hour session is recommended for functional users who want to gain a better understanding of how Oracle's SNO solution can help you solve complex supply chain issues, including supply chain design, risk management, logistics planning, sustainability planning, and a whole lot in between! Find out how SNO can be used to solve many different types of real-world business issues. Topics will include: Risk/Disaster Management Carbon Emissions Management Global Sourcing Labor/Workforce Planning Product Mix Optimization A short, live demonstration (only if applicable) and question and answer period will be included. Click here to register for this session....... ....... ....... ....... ....... ....... .......The above webcast is a service of the E-Business Suite Communities in My Oracle Support.For more information on other webcasts, please reference the Oracle Advisor Webcast Schedule.Click here to visit the E-Business Communities in My Oracle Support Note that all links require access to My Oracle Support.

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  • ArchBeat Link-o-Rama for November 30, 2012

    - by Bob Rhubart
    Oracle SOA Database Adapter Polling in a Cluster: A Handy Logical Delete Pattern | Carlo Arteaga "Using the SOA database adapter usually becomes easier when the adapter is simply viewed and treated as a gateway between the Oracle SOA composite world and the database world," says Carlo Arteaga. "When viewing the adapter in this light one should come to understand that the adapter is not the ultimate all-in-one solution for database access and database logic needs." OIM 11g : Multi-thread approach for writing custom scheduled job | Saravanan V S Saravanan shares insight and expertise relevant to "designing and developing an OIM schedule job that uses multi threaded approach for updating data in OIM using APIs." When Premature Optimization Isn't | Dustin Marx "Perhaps the most common situations in which I have seen developers make bad decisions under the pretense of 'avoiding premature optimization' is making bad architecture or design choices," says Dustin Marx. Protecting Intranet and Extranet Applications with a Single OAM 11g Deployment | Brian Eidelman Oracle Fusion Middleware A-Team member Brian Eideleman's post, part of the Oracle Access Manager Academy series, explores issues and soluions around setting up a single OAM deployment to protect both intranet and extranet apps. Thought for the Day "Never make a technical decision based upon the politics of the situation, and never make a political decision based upon technical issues." — Geoffrey James Source: SoftwareQuotes.com

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  • Spotlight: How Scandinavia's Largest Nuclear Power Plant Increased Productivity and Reduced Costs wi

    - by [email protected]
    Ringhals nuclear power plant, which is part of the Vattenfall Group, is located about 60 km south-west of the beautiful coastal city of Gothenburg in Sweden. A deep concern to reduce environmental impact coupled with an effort to increase plant safety and operational efficiency have led to a recent surge in investments and initiatives around plant modification and plant optimization at Ringhals. A multitude of challenges were faced by the users in various groups that were involved in these projects. First, it was very difficult for users to easily access complex and layered asset and engineering information, which was critical to increased productivity and completing projects on time. Moreover, the 20 or so different solutions that were being used to view various document formats, not only resulted in collaboration complexity but also escalated IT administration costs and woes. Finally, there was a considerable non-engineering community comprising non-CAD specialists that needed easy access to plant data in an effort to minimize engineering disruption. Oracle's AutoVue significantly simplified the ability to efficiently view and use digital asset information by providing a standardized visualization solution for the enterprise. The key benefits achieved by Ringhals include: Increased productivity of plant optimization and plant modification by 3% Saved around $ 500 K annually Cut IT maintenance costs by 50% by using a single solution Reduced engineering disruption by allowing non-CAD users easy access to digital plant data The complete case-study can be found here

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