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• Data structure for pattern matching.

  - by alvonellos

  Let's say you have an input file with many entries like these: date, ticker, open, high, low, close, <and some other values> And you want to execute a pattern matching routine on the entries(rows) in that file, using a candlestick pattern, for example. (See, Doji) And that pattern can appear on any uniform time interval (let t = 1s, 5s, 10s, 1d, 7d, 2w, 2y, and so on...). Say a pattern matching routine can take an arbitrary number of rows to perform an analysis and contain an arbitrary number of subpatterns. In other words, some patterns may require 4 entries to operate on. Say also that the routine (may) later have to find and classify extrema (local and global maxima and minima as well as inflection points) for the ticker over a closed interval, for example, you could say that a cubic function (x^3) has the extrema on the interval [-1, 1]. (See link) What would be the most natural choice in terms of a data structure? What about an interface that conforms a Ticker object containing one row of data to a collection of Ticker so that an arbitrary pattern can be applied to the data. What's the first thing that comes to mind? I chose a doubly-linked circular linked list that has the following methods: push_front() push_back() pop_front() pop_back() [] //overloaded, can be used with negative parameters But that data structure seems very clumsy, since so much pushing and popping is going on, I have to make a deep copy of the data structure before running an analysis on it. So, I don't know if I made my question very clear -- but the main points are: What kind of data structures should be considered when analyzing sequential data points to conform to a pattern that does NOT require random access? What kind of data structures should be considered when classifying extrema of a set of data points?

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• How does a segment based rendering engine work?

  - by Calmarius

  As far as I know Descent was one of the first games that featured a fully 3D environment, and it used a segment based rendering engine. Its levels are built from cubic segments (these cubes may be deformed as long as it remains convex and sides remain roughly flat). These cubes are connected by their sides. The connected sides are traversable (maybe doors or grids can be placed on these sides), while the unconnected sides are not traversable walls. So the game is played inside of this complex. Descent was software rendered and it had to be very fast, to be playable on those 10-100MHz processors of that age. Some latter levels of the game are huge and contain thousands of segments, but these levels are still rendered reasonably fast. So I think they tried to minimize the amount of cubes rendered somehow. How to choose which cubes to render for a given location? As far as I know they used a kind of portal rendering, but I couldn't find what was the technique used in this particular kind of engine. I think the fact that the levels are built from convex quadrilateral hexahedrons can be exploited.

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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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• How does a segment-based rendering engine (as in Descent) work?

  - by Calmarius

  As far as I know Descent was one of the first games that featured a fully 3D environment, and it used a segment based rendering engine. Its levels are built from cubic segments (these cubes may be deformed as long as it remains convex and sides remain roughly flat). These cubes are connected by their sides. The connected sides are traversable (maybe doors or grids can be placed on these sides), while the unconnected sides are not traversable walls. So the game is played inside of this complex. Descent was software rendered and it had to be very fast, to be playable on those 10-100MHz processors of that age. Some latter levels of the game are huge and contain thousands of segments, but these levels are still rendered reasonably fast. So I think they tried to minimize the amount of cubes rendered somehow. How to choose which cubes to render for a given location? As far as I know they used a kind of portal rendering, but I couldn't find what was the technique used in this particular kind of engine. I think the fact that the levels are built from convex quadrilateral hexahedrons can be exploited.

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• What is the maximum distance from an anchor point to a bezier curve?

  - by drawnonward

  Given a cubic bezier curve P0,P1,P2,P3 with the following properties: • Both P1 and P2 are on the same side of the line formed by P0 and P3. • P2 can be projected onto the line segment formed by P0 and P3 but P1 cannot. What is the T value for the point on the curve farthest from P3? Here is an image with an example curve. The curve bulges on the left, so there is a point on the curve farther from P3 than P0. I found this reference for finding the minimum distance from an arbitrary point to a curve. Is trial and error the only way to solve for maximum distance as well? Does it make any difference that the point is an anchor on the curve? Thanks

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• Designing entire webpages as SVG files

  - by user1311390

  Disclaimer I realize that given the absurdity of the title, this sounds like a troll. However, it's a genuine question. My background involves OpenGL / x86 assembly. I've recently started learning web programming. I really like SVG + CSS, and was wondering -- why do people not design entire webpages in SVG? Context SVG provides beautiful primitive: quadratic + cubic bezier curves; lines + filling -- all as vector graphics SVG provides text SVG provides affine transformations Questions Are there examples of people designing entire websites as a giant SVG file? If not, what the limitations? Are there performance hits when using SVG primitives as opposed to divs/tables?

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• Manage Files Easier With Aero Snap in Windows 7

  - by Mysticgeek

  Before the days of Aero Snap you would need to arrange your Windows in some weird way to see all of your files. Today we show you how to quickly use the Aero Snap feature get it done in few key strokes in Windows 7. You can of course navigate the windows in Explorer to get them so you can see everything side by side, or use a free utility like Cubic Explorer.   Getting Explorer Windows Side by Side The process is actually simple but quite useful when looking for a large amount of data. Right-click the Windows Explorer icon on the taskbar and click Windows Explorer. Our first window opens up and you can certainly drag it over the the right or left side of the screen but the quickest method we’re using is the “Windows Key+Right Arrow” key combo (make sure to hold the Windows key down). Now the Windows is nicely placed on the right side. Next we want to open the other window, simply right-click the Explorer icon again and click Windows Explorer.   Now we have our second window open, and all we need to do this time is use the Windows Key+Left Arrow combination. There we go! Now you should be able to browse your files a lot more simply than relying on the expanding tree method (as much). You can actually use this method to snap a window to all four corners of your screen if you don’t feel like dragging it. Once you play with Aero Snap more you may enjoy it, but if you still despise it, you can disable it too! Similar Articles Productive Geek Tips Multitask Like a Pro with AquaSnapUse Windows Vista Aero through Remote Desktop ConnectionEasily Disable Win 7 or Vista’s Aero Before Running an Application (Such as a Video Game)Understanding Windows Vista Aero Glass RequirementsFree Storage With AOL’s Xdrive (Online Storage Series) TouchFreeze Alternative in AutoHotkey The Icy Undertow Desktop Windows Home Server – Backup to LAN The Clear & Clean Desktop Use This Bookmarklet to Easily Get Albums Use AutoHotkey to Assign a Hotkey to a Specific Window Latest Software Reviews Tinyhacker Random Tips DVDFab 6 Revo Uninstaller Pro Registry Mechanic 9 for Windows PC Tools Internet Security Suite 2010 Awesome Lyrics Finder for Winamp & Windows Media Player Download Videos from Hulu Pixels invade Manhattan Convert PDF files to ePub to read on your iPad Hide Your Confidential Files Inside Images Get Wildlife Photography Tips at BBC’s PhotoMasterClasses

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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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• Texture mapping on gluDisk

  - by Marnix

  I'm trying to map a brick texture on the edge of a fountain and I'm using gluDisk for that. How can I make the right coordinates for the disk? My code looks like this and I have only found a function that takes the texture along with the camera. I want the cubic texture to be alongside of the fountain, but gluDisk does a linear mapping. How do I get a circular mapping? void Fountain::Draw() { glPushMatrix(); // push 1 this->ApplyWorldMatrixGL(); glEnable(GL_TEXTURE_2D); // enable texturing glPushMatrix(); // push 2 glRotatef(90,-1,0,0); // rotate 90 for the quadric // also drawing more here... // stone texture glBindTexture(GL_TEXTURE_2D, texIDs[0]); glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR); glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR); glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT); glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_REPEAT); glPushMatrix(); // push 3 glTranslatef(0,0,height); // spherical texture generation // this piece of code doesn't work as I intended glTexGeni(GL_S, GL_TEXTURE_GEN_MODE, GL_SPHERE_MAP); glTexGeni(GL_T, GL_TEXTURE_GEN_MODE, GL_SPHERE_MAP); glEnable(GL_TEXTURE_GEN_S); glEnable(GL_TEXTURE_GEN_T); GLUquadric *tub = gluNewQuadric(); gluQuadricTexture(tub, GL_TRUE); gluDisk(tub, radius, outerR, nrVertices, nrVertices); gluDeleteQuadric(tub); glDisable(GL_TEXTURE_GEN_S); glDisable(GL_TEXTURE_GEN_T); glPopMatrix(); // pop 3 // more drawing here... glPopMatrix(); // pop 2 // more drawing here... glPopMatrix(); // pop 1 } To refine my question a bit. This is an image of what it is at default (left) and of what I want (right). The texture should fit in the border of the disk, a lot of times. If this is possible with the texture matrix, than that's fine with me as well.

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• Application stuck in TCP retransmit

  - by SandeepJ

  I am running Linux kernel 3.13 (Ubuntu 14.04) on two Virtual Machines each of which operates inside two different servers running ESXi 5.1. There is a zeromq client-server application running between the two VMs. After running for about 10-30 minutes, this application consistently hangs due to inability to retransmit a lost packet. When I run the same setup over Ubuntu 12.04 (Linux 3.11), the application never fails If you notice below, "ss" (socket statistics) shows 1 packet lost, sk_wmem_queued of 14110 (i.e. w14110) and a high rto (120000). State Recv-Q Send-Q Local Address:Port Peer Address:Port ESTAB 0 12350 192.168.2.122:41808 192.168.2.172:55550 timer:(on,16sec,10) uid:1000 ino:35042 sk:ffff880035bcb100 <- skmem:(r0,rb648720,t0,tb1164800,f2274,w14110,o0,bl0) ts sack cubic wscale:7,7 rto:120000 rtt:7.5/3 ato:40 mss:8948 cwnd:1 ssthresh:21 send 9.5Mbps unacked:1 retrans:1/10 lost:1 rcv_rtt:1476 rcv_space:37621 Since this has happened so consistently, I was able to capture the TCP log in wireshark. I found that the packet which is lost does get retransmitted and even acknowledged by the TCP in the other OS (the sequence number is seen in the ACK), but the sender doesn't seem to understand this ACK and continues retransmitting. MTU is 9000 on both virtual machines and througout the route. The packets being sent are large in size. As I said earlier, this does not happen on Ubuntu 12.04 (kernel 3.11). So I did a diff on the TCP config options (seen via "sysctl -a |grep tcp ") between 14.04 and 12.04 and found the following differences. I also noticed that net.ipv4.tcp_mtu_probing=0 in both configurations. Left side is 3.11, right side is 3.13 <<net.ipv4.tcp_abc = 0 <<net.ipv4.tcp_cookie_size = 0 <<net.ipv4.tcp_dma_copybreak = 4096 14c11 << net.ipv4.tcp_early_retrans = 2 --- >> net.ipv4.tcp_early_retrans = 3 17c14 << net.ipv4.tcp_fastopen = 0 >> net.ipv4.tcp_fastopen = 1 20d16 << net.ipv4.tcp_frto_response = 0 26,27c22 << net.ipv4.tcp_max_orphans = 16384 << net.ipv4.tcp_max_ssthresh = 0 >> net.ipv4.tcp_max_orphans = 4096 29,30c24,25 << net.ipv4.tcp_max_tw_buckets = 16384 << net.ipv4.tcp_mem = 94377 125837 188754 >> net.ipv4.tcp_max_tw_buckets = 4096 >> net.ipv4.tcp_mem = 23352 31138 46704 34a30 >> net.ipv4.tcp_notsent_lowat = -1 My question to the networking experts on this forum : Are there any other debugging tools or options I can install/enable to dig further into why this TCP retransmit failure is occurring so consistently ? Are there any configuration changes which might account for this weird behaviour.

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• Raytracing (LoS) on 3D hex-like tile maps

  - by herenvardo

  Greetings, I'm working on a game project that uses a 3D variant of hexagonal tile maps. Tiles are actually cubes, not hexes, but are laid out just like hexes (because a square can be turned to a cube to extrapolate from 2D to 3D, but there is no 3D version of a hex). Rather than a verbose description, here goes an example of a 4x4x4 map: (I have highlighted an arbitrary tile (green) and its adjacent tiles (yellow) to help describe how the whole thing is supposed to work; but the adjacency functions are not the issue, that's already solved.) I have a struct type to represent tiles, and maps are represented as a 3D array of tiles (wrapped in a Map class to add some utility methods, but that's not very relevant). Each tile is supposed to represent a perfectly cubic space, and they are all exactly the same size. Also, the offset between adjacent "rows" is exactly half the size of a tile. That's enough context; my question is: Given the coordinates of two points A and B, how can I generate a list of the tiles (or, rather, their coordinates) that a straight line between A and B would cross? That would later be used for a variety of purposes, such as determining Line-of-sight, charge path legality, and so on. BTW, this may be useful: my maps use the (0,0,0) as a reference position. The 'jagging' of the map can be defined as offsetting each tile ((y+z) mod 2) * tileSize/2.0 to the right from the position it'd have on a "sane" cartesian system. For the non-jagged rows, that yields 0; for rows where (y+z) mod 2 is 1, it yields 0.5 tiles. I'm working on C#4 targeting the .Net Framework 4.0; but I don't really need specific code, just the algorithm to solve the weird geometric/mathematical problem. I have been trying for several days to solve this at no avail; and trying to draw the whole thing on paper to "visualize" it didn't help either :( . Thanks in advance for any answer

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• Efficient Context-Free Grammar parser, preferably Python-friendly

  - by Max Shawabkeh

  I am in need of parsing a small subset of English for one of my project, described as a context-free grammar with (1-level) feature structures (example) and I need to do it efficiently . Right now I'm using NLTK's parser which produces the right output but is very slow. For my grammar of ~450 fairly ambiguous non-lexicon rules and half a million lexical entries, parsing simple sentences can take anywhere from 2 to 30 seconds, depending it seems on the number of resulting trees. Lexical entries have little to no effect on performance. Another problem is that loading the (25MB) grammar+lexicon at the beginning can take up to a minute. From what I can find in literature, the running time of the algorithm used to parse such a grammar (Earley or CKY) should be linear to the size of the grammar and cubic to the size of the input token list. My experience with NLTK indicates that ambiguity is what hurts the performance most, not the absolute size of the grammar. So now I'm looking for a CFG parser to replace NLTK. I've been considering PLY but I can't tell whether it supports feature structures in CFGs, which are required in my case, and the examples I've seen seem to be doing a lot of procedural parsing rather than just specifying a grammar. Can anybody show me an example of PLY both supporting feature structs and using a declarative grammar? I'm also fine with any other parser that can do what I need efficiently. A Python interface is preferable but not absolutely necessary.

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• Drawing half of a Bezier path in Raphael

  - by Fibericon

  Let's say I have a cubic Bezier path as follows (formatted for use with the Raphael path function): M55 246S55 247 55 248 Just an example. This was taken from my drawing application, where I use the cursor to draw a line when the user holds the mouse button down, kind of like a pencil or marker. I'm using jquery's mousemove event to draw the line between two points every time the user moves the mouse. There is another (the reference point) that is taken before the line is drawn, so that the Bezier curve can be created. Here's my question: is it possible to make Raphael only draw half of a given path? I'm aware of the getSubpath() function, but if my understanding of Bezier curves is correct, it would be rather difficult to calculate the second argument. The problem with the animate function is that it creates double lines (that is, it creates the curved line that I want, and the boxy line around it which should not be shown, possibly because the mouse is being moved faster than the animation can handle). Of course, if my approach itself is flawed in some way (or my understanding of the possible solutions), I'd like to hear it. Any help would be appreciated.

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• pylab.savefig() and pylab.show() image difference

  - by Jack1990

  I'm making an script to automatically create plots from .xvg files, but there's a problem when I'm trying to use pylab's savefig() method. Using pylab.show() and saving from there, everything's fine. Using pylab.show() Using pylab.savefig() def producePlot(timestep, energy_values,type_line = 'r', jump = 1,finish = 100): fc = sp.interp1d(timestep[::jump], energy_values[::jump],kind='cubic') xnew = numpy.linspace(0, finish, finish*2) pylab.plot(xnew, fc(xnew),type_line) pylab.xlabel('Time in ps ') pylab.ylabel('kJ/mol') pylab.xlim(xmin=0, xmax=finish) def produceSimplePlot(timestep, energy_values,type_line = 'r', jump = 1,finish = 100): pylab.plot(timestep, energy_values,type_line) pylab.xlabel('Time in ps ') pylab.ylabel('kJ/mol') pylab.xlim(xmin=0, xmax=finish) def linearRegression(timestep, energy_values, type_line = 'g'): #, jump = 1,finish = 100): from scipy import stats import numpy #print 'fuck' timestep = numpy.asarray(timestep) slope, intercept, r_value, p_value, std_err = stats.linregress(timestep,energy_values) line = slope*timestep+intercept pylab.plot(timestep, line, type_line) def plottingTime(Title,file_name, timestep, energy_values ,loc, jump , finish): pylab.title(Title) producePlot(timestep,energy_values, 'b',jump, finish) linearRegression(timestep,energy_values) import numpy Average = numpy.average(energy_values) #print Average pylab.legend(("Average = %.2f" %(Average),'Linear Reg'),loc) #pylab.show() pylab.savefig('%s.jpg' %file_name[:-4], bbox_inches= None, pad_inches=0) #if __name__ == '__main__': #plottingTime(Title,timestep1, energy_values, jump =10, finish = 4800) def specialCase(Title,file_name, timestep, energy_values,loc, jump, finish): #print 'Working here ...?' pylab.title(Title) producePlot(timestep,energy_values, 'b',jump, finish) import numpy from pylab import * Average = numpy.average(energy_values) #print Average pylab.legend(("Average = %.2g" %(Average), Title),loc) locs,labels = yticks() yticks(locs, map(lambda x: "%.3g" % x, locs)) #pylab.show() pylab.savefig('%s.jpg' %file_name[:-4] , bbox_inches= None, pad_inches=0) Thanks in advance, John

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• Help with GetGlyphOutline function(WinAPI)

  - by user146780

  I want to use this function to get contours and within these contours, I want to get cubic bezier. I think I have to call it with GGO_BEZIER. What puzzles me is how the return buffer works. "A glyph outline is returned as a series of one or more contours defined by a TTPOLYGONHEADER structure followed by one or more curves. Each curve in the contour is defined by a TTPOLYCURVE structure followed by a number of POINTFX data points. POINTFX points are absolute positions, not relative moves. The starting point of a contour is given by the pfxStart member of the TTPOLYGONHEADER structure. The starting point of each curve is the last point of the previous curve or the starting point of the contour. The count of data points in a curve is stored in the cpfx member of TTPOLYCURVE structure. The size of each contour in the buffer, in bytes, is stored in the cb member of TTPOLYGONHEADER structure. Additional curve definitions are packed into the buffer following preceding curves and additional contours are packed into the buffer following preceding contours. The buffer contains as many contours as fit within the buffer returned by GetGlyphOutline." I'm really not sure how to access the contours. I know that I can change a pointer another type of pointer but i'm not sure how I go about getting the contours based on this documentation. Thanks

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• Where is rebol fill-pen documented (to get glow effect on a round rectangle) ?

  - by Rebol Tutorial

  There is some discussion here about fill-pen http://www.mail-archive.com/[email protected]/msg02019.html But I can't see documentation about cubic, diamond, etc... effect for fill-pen in rebol's official doc ? I'm trying to draw some round rectangle with glowing effect but don't really understand the parameters I'm playing with so I can't get exactly what I'd like (I'd like the glow effect starting from the center not from the dark left top corner): view layout [ box 278x185 effect [ ; default box face size is 100x100 draw [ anti-alias on ; information for the next draw element (not required) line-width 2.5 ; number of pixels in width of the border pen black ; color of the edge of the next draw element ; fill pen is a little complex: ;fill-pen 10x10 0 90 0 1 1 0.0.0 255.0.0 255.0.255 fill-pen radial 20x20 5 55 5 5 10 0.0.0 55.0.5 55.0.5 ; the draw element box ; another box drawn as an effect 15 ; size of rounding in pixels 0x0 ; upper left corner 278x170 ; lower right corner ] ] ]

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• Is there a way for -webkit-animtion-timing-function to apply to the entire animation instead of each keyframe?

  - by Ken Sykora

  I'm a bit new to animation, so forgive me if I'm missing a huge concept here. I need to animate an arrow that is pointing to a point on a curve, let's just say it's a cubic curve for the sake of this post. The arrow moves along the curve's line, always pointing a few pixels below it. So what I did, is I setup keyframes along the curve's line using CSS3: @-webkit-keyframes ftch { 0% { opacity: 0; left: -10px; bottom: 12px; } 25% { opacity: 0.25; left: 56.5px; bottom: -7px; } 50% { opacity: 0.5; left: 143px; bottom: -20px; } 75% { opacity: 0.75; left: 209.5px; bottom: -24.5px; } 100% { opacity: 1; left: 266px; bottom: -26px; } } However, when I run this animation using -webkit-animation-timing-function: ease-in, it applies that easing to each individual keyframe, which is definitely not what I want. I want the easing to apply to the entire animation. Is there a different way that I should be doing this? Is there some property to apply the easing to the entire sequence rather than each keyframe?

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• Why is -webkit-keyframes not working in my SASS mixin?

  - by Tintin81

  I have this SASS mixin that should make a button flash: @mixin background_animation($color) { -webkit-animation: backgroundAnimation 800ms infinite; @-webkit-keyframes backgroundAnimation { 0% {background-color: $color;} 50% {background-color: red;} 100% {background-color: $color;} } } I am using it like this: @include background_animation(#000000); However, it's not working. The background color of the button won't flash. Can anybody tell me what I'm missing here? P.S. The code works fine when not including it as a mixin. The generated CSS looks like this: -webkit-animation-delay: 0s; -webkit-animation-direction: normal; -webkit-animation-duration: 0.800000011920929s; -webkit-animation-fill-mode: none; -webkit-animation-iteration-count: infinite; -webkit-animation-name: backgroundAnimation; -webkit-animation-timing-function: cubic-bezier(0.25, 0.1, 0.25, 1); ... other rules omitted for brevity

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• Cooling Server Rack with Water? Sensible? Reuse energy for small installation?

  - by TomTom

  First - this is not a shopping question, this is not so much about concrete prices but about general feasibility. Makes no sense to get looking fo ra manufacturer it the approach is bad. I am moving my company to new Offices in September, and among them we will expand and consolidate our number crunch cluster. It is so far in a data center. I have a nice room in the basement prepared now. I think about cooling. We will likely run up a power usage of around 10kw by end of the year. That is a LOT of stuff, and cooling will be expensive. I am located in south Poland, close to the German border. This is an area where water is available for relatively cheap price - "wasting water" is not a concern here. My situation is thus a lot different for example than in Spain ;) Physics tells me that to heat 1 liter of water by 1 degree I use 1 Calorie (1KCal), and a kwh power is (and we can assume 100% efficiency - water heaters are pretty efficient) 750 Calories. That means that 1 KWH is 750 liter by 1 degree. 10kw and a 20 degree heat would mean that per hour I need 375 liters. That is 6.25 liters per minute and not WHAT much ;) We talk 270 cubic meters here. Even in summer, the significant underground pipes really cool down the water a LOT more ;) Question: This such an approach feasible? Anyone done that? We talk of a 10kw installation for now. Is it feasible to reuse that heat? The alternative is a decent cooling system that WILL use around 2.5kwh for running. Dropping the water would basically (a) get me a quite cold input compared to the outside air even in summer (I.e. a lower temperature medium to drop the heat in) and (b) replace the need to actually have the outside cooling (which may b problematic - if the air is 22 degree, that is a LOT to fight off, but OTOH the water will be quite cold). I also would possibly save the investment for the outside part of the cooling circuit. Now, second question - is there a feasible way to heat a house with that? ;) After all, brutally speaking, it is a LOT of energy in that water ;) If it is a bad idea, I stop here - if it is not, I start looking for suppliers. Maybe my math is wrong?

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• NET Math Libraries

  - by JoshReuben

  NET Mathematical Libraries   .NET Builder for Matlab The MathWorks Inc. - http://www.mathworks.com/products/netbuilder/ MATLAB Builder NE generates MATLAB based .NET and COM components royalty-free deployment creates the components by encrypting MATLAB functions and generating either a .NET or COM wrapper around them. .NET/Link for Mathematica www.wolfram.com a product that 2-way integrates Mathematica and Microsoft's .NET platform call .NET from Mathematica - use arbitrary .NET types directly from the Mathematica language. use and control the Mathematica kernel from a .NET program. turns Mathematica into a scripting shell to leverage the computational services of Mathematica. write custom front ends for Mathematica or use Mathematica as a computational engine for another program comes with full source code. Leverages MathLink - a Wolfram Research's protocol for sending data and commands back and forth between Mathematica and other programs. .NET/Link abstracts the low-level details of the MathLink C API. Extreme Optimization http://www.extremeoptimization.com/ a collection of general-purpose mathematical and statistical classes built for the.NET framework. It combines a math library, a vector and matrix library, and a statistics library in one package. download the trial of version 4.0 to try it out. Multi-core ready - Full support for Task Parallel Library features including cancellation. Broad base of algorithms covering a wide range of numerical techniques, including: linear algebra (BLAS and LAPACK routines), numerical analysis (integration and differentiation), equation solvers. Mathematics leverages parallelism using .NET 4.0's Task Parallel Library. Basic math: Complex numbers, 'special functions' like Gamma and Bessel functions, numerical differentiation. Solving equations: Solve equations in one variable, or solve systems of linear or nonlinear equations. Curve fitting: Linear and nonlinear curve fitting, cubic splines, polynomials, orthogonal polynomials. Optimization: find the minimum or maximum of a function in one or more variables, linear programming and mixed integer programming. Numerical integration: Compute integrals over finite or infinite intervals, over 2D and higher dimensional regions. Integrate systems of ordinary differential equations (ODE's). Fast Fourier Transforms: 1D and 2D FFT's using managed or fast native code (32 and 64 bit) BigInteger, BigRational, and BigFloat: Perform operations with arbitrary precision. Vector and Matrix Library Real and complex vectors and matrices. Single and double precision for elements. Structured matrix types: including triangular, symmetrical and band matrices. Sparse matrices. Matrix factorizations: LU decomposition, QR decomposition, singular value decomposition, Cholesky decomposition, eigenvalue decomposition. Portability and performance: Calculations can be done in 100% managed code, or in hand-optimized processor-specific native code (32 and 64 bit). Statistics Data manipulation: Sort and filter data, process missing values, remove outliers, etc. Supports .NET data binding. Statistical Models: Simple, multiple, nonlinear, logistic, Poisson regression. Generalized Linear Models. One and two-way ANOVA. Hypothesis Tests: 12 14 hypothesis tests, including the z-test, t-test, F-test, runs test, and more advanced tests, such as the Anderson-Darling test for normality, one and two-sample Kolmogorov-Smirnov test, and Levene's test for homogeneity of variances. Multivariate Statistics: K-means cluster analysis, hierarchical cluster analysis, principal component analysis (PCA), multivariate probability distributions. Statistical Distributions: 25 29 continuous and discrete statistical distributions, including uniform, Poisson, normal, lognormal, Weibull and Gumbel (extreme value) distributions. Random numbers: Random variates from any distribution, 4 high-quality random number generators, low discrepancy sequences, shufflers. New in version 4.0 (November, 2010) Support for .NET Framework Version 4.0 and Visual Studio 2010 TPL Parallellized – multicore ready sparse linear program solver - can solve problems with more than 1 million variables. Mixed integer linear programming using a branch and bound algorithm. special functions: hypergeometric, Riemann zeta, elliptic integrals, Frensel functions, Dawson's integral. Full set of window functions for FFT's. Product  Price Update subscription Single Developer License $999  $399  Team License (3 developers) $1999  $799  Department License (8 developers) $3999  $1599  Site License (Unlimited developers in one physical location) $7999  $3199    NMath http://www.centerspace.net .NET math and statistics libraries matrix and vector classes random number generators Fast Fourier Transforms (FFTs) numerical integration linear programming linear regression curve and surface fitting optimization hypothesis tests analysis of variance (ANOVA) probability distributions principal component analysis cluster analysis built on the Intel Math Kernel Library (MKL), which contains highly-optimized, extensively-threaded versions of BLAS (Basic Linear Algebra Subroutines) and LAPACK (Linear Algebra PACKage). Product  Price Update subscription Single Developer License $1295 $388 Team License (5 developers) $5180 $1554   DotNumerics http://www.dotnumerics.com/NumericalLibraries/Default.aspx free DotNumerics is a website dedicated to numerical computing for .NET that includes a C# Numerical Library for .NET containing algorithms for Linear Algebra, Differential Equations and Optimization problems. The Linear Algebra library includes CSLapack, CSBlas and CSEispack, ports from Fortran to C# of LAPACK, BLAS and EISPACK, respectively. Linear Algebra (CSLapack, CSBlas and CSEispack). Systems of linear equations, eigenvalue problems, least-squares solutions of linear systems and singular value problems. Differential Equations. Initial-value problem for nonstiff and stiff ordinary differential equations ODEs (explicit Runge-Kutta, implicit Runge-Kutta, Gear's BDF and Adams-Moulton). Optimization. Unconstrained and bounded constrained optimization of multivariate functions (L-BFGS-B, Truncated Newton and Simplex methods).   Math.NET Numerics http://numerics.mathdotnet.com/ free an open source numerical library - includes special functions, linear algebra, probability models, random numbers, interpolation, integral transforms. A merger of dnAnalytics with Math.NET Iridium in addition to a purely managed implementation will also support native hardware optimization. constants & special functions complex type support real and complex, dense and sparse linear algebra (with LU, QR, eigenvalues, ... decompositions) non-uniform probability distributions, multivariate distributions, sample generation alternative uniform random number generators descriptive statistics, including order statistics various interpolation methods, including barycentric approaches and splines numerical function integration (quadrature) routines integral transforms, like fourier transform (FFT) with arbitrary lengths support, and hartley spectral-space aware sequence manipulation (signal processing) combinatorics, polynomials, quaternions, basic number theory. parallelized where appropriate, to leverage multi-core and multi-processor systems fully managed or (if available) using native libraries (Intel MKL, ACMS, CUDA, FFTW) provides a native facade for F# developers

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• Using scipy.interpolate.splrep function

  - by Koustav Ghosal

  I am trying to fit a cubic spline to a given set of points. My points are not ordered. I CANNOT sort or reorder the points, since I need that information. But since the function scipy.interpolate.splrep works only on non-duplicate and monotonically increasing points I have defined a function that maps the x-coordinates to a monotonically increasing space. My old points are: xpoints=[4913.0, 4912.0, 4914.0, 4913.0, 4913.0, 4913.0, 4914.0, 4915.0, 4918.0, 4921.0, 4925.0, 4932.0, 4938.0, 4945.0, 4950.0, 4954.0, 4955.0, 4957.0, 4956.0, 4953.0, 4949.0, 4943.0, 4933.0, 4921.0, 4911.0, 4898.0, 4886.0, 4874.0, 4865.0, 4858.0, 4853.0, 4849.0, 4848.0, 4849.0, 4851.0, 4858.0, 4864.0, 4869.0, 4877.0, 4884.0, 4893.0, 4903.0, 4913.0, 4923.0, 4935.0, 4947.0, 4959.0, 4970.0, 4981.0, 4991.0, 5000.0, 5005.0, 5010.0, 5015.0, 5019.0, 5020.0, 5021.0, 5023.0, 5025.0, 5027.0, 5027.0, 5028.0, 5028.0, 5030.0, 5031.0, 5033.0, 5035.0, 5037.0, 5040.0, 5043.0] ypoints=[10557.0, 10563.0, 10567.0, 10571.0, 10575.0, 10577.0, 10578.0, 10581.0, 10582.0, 10582.0, 10582.0, 10581.0, 10578.0, 10576.0, 10572.0, 10567.0, 10560.0, 10550.0, 10541.0, 10531.0, 10520.0, 10511.0, 10503.0, 10496.0, 10490.0, 10487.0, 10488.0, 10488.0, 10490.0, 10495.0, 10504.0, 10513.0, 10523.0, 10533.0, 10542.0, 10550.0, 10556.0, 10559.0, 10560.0, 10559.0, 10555.0, 10550.0, 10543.0, 10533.0, 10522.0, 10514.0, 10505.0, 10496.0, 10490.0, 10486.0, 10482.0, 10481.0, 10482.0, 10486.0, 10491.0, 10497.0, 10506.0, 10516.0, 10524.0, 10534.0, 10544.0, 10552.0, 10558.0, 10564.0, 10569.0, 10573.0, 10576.0, 10578.0, 10581.0, 10582.0] Plots: The code for the mapping function and interpolation is: xnew=[] ynew=ypoints for c3,i in enumerate(xpoints): if np.isfinite(np.log(i*pow(2,c3))): xnew.append(np.log(i*pow(2,c3))) else: if c==0: xnew.append(np.random.random_sample()) else: xnew.append(xnew[c3-1]+np.random.random_sample()) xnew=np.asarray(xnew) ynew=np.asarray(ynew) constant1=10.0 nknots=len(xnew)/constant1 idx_knots = (np.arange(1,len(xnew)-1,(len(xnew)-2)/np.double(nknots))).astype('int') knots = [xnew[i] for i in idx_knots] knots = np.asarray(knots) int_range=np.linspace(min(xnew),max(xnew),len(xnew)) tck = interpolate.splrep(xnew,ynew,k=3,task=-1,t=knots) y1= interpolate.splev(int_range,tck,der=0) The code is throwing an error at the function interpolate.splrep() for some set of points like the above one. The error is: File "/home/neeraj/Desktop/koustav/res/BOS5/fit_spline3.py", line 58, in save_spline_f tck = interpolate.splrep(xnew,ynew,k=3,task=-1,t=knots) File "/usr/lib/python2.7/dist-packages/scipy/interpolate/fitpack.py", line 465, in splrep raise _iermessier(_iermess[ier][0]) ValueError: Error on input data But for other set of points it works fine. For example for the following set of points. xpoints=[1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1630.0, 1630.0, 1630.0, 1631.0, 1631.0, 1631.0, 1631.0, 1630.0, 1629.0, 1629.0, 1629.0, 1628.0, 1627.0, 1627.0, 1625.0, 1624.0, 1624.0, 1623.0, 1620.0, 1618.0, 1617.0, 1616.0, 1615.0, 1614.0, 1614.0, 1612.0, 1612.0, 1612.0, 1611.0, 1610.0, 1609.0, 1608.0, 1607.0, 1607.0, 1603.0, 1602.0, 1602.0, 1601.0, 1601.0, 1600.0, 1599.0, 1598.0] ypoints=[10570.0, 10572.0, 10572.0, 10573.0, 10572.0, 10572.0, 10571.0, 10570.0, 10569.0, 10565.0, 10564.0, 10563.0, 10562.0, 10560.0, 10558.0, 10556.0, 10554.0, 10551.0, 10548.0, 10547.0, 10544.0, 10542.0, 10541.0, 10538.0, 10534.0, 10532.0, 10531.0, 10528.0, 10525.0, 10522.0, 10519.0, 10517.0, 10516.0, 10512.0, 10509.0, 10509.0, 10507.0, 10504.0, 10502.0, 10500.0, 10501.0, 10499.0, 10498.0, 10496.0, 10491.0, 10492.0, 10488.0, 10488.0, 10488.0, 10486.0, 10486.0, 10485.0, 10485.0, 10486.0, 10483.0, 10483.0, 10482.0, 10480.0] Plots: Can anybody suggest what's happening ?? Thanks in advance......

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• Diagnosing packet loss / high latency in Ubuntu

  - by Sam Gammon

  We have a Linux box (Ubuntu 12.04) running Nginx (1.5.2), which acts as a reverse proxy/load balancer to some Tornado and Apache hosts. The upstream servers are physically and logically close (same DC, sometimes same-rack) and show sub-millisecond latency between them: PING appserver (10.xx.xx.112) 56(84) bytes of data. 64 bytes from appserver (10.xx.xx.112): icmp_req=1 ttl=64 time=0.180 ms 64 bytes from appserver (10.xx.xx.112): icmp_req=2 ttl=64 time=0.165 ms 64 bytes from appserver (10.xx.xx.112): icmp_req=3 ttl=64 time=0.153 ms We receive a sustained load of about 500 requests per second, and are currently seeing regular packet loss / latency spikes from the Internet, even from basic pings: sam@AM-KEEN ~> ping -c 1000 loadbalancer PING 50.xx.xx.16 (50.xx.xx.16): 56 data bytes 64 bytes from loadbalancer: icmp_seq=0 ttl=56 time=11.624 ms 64 bytes from loadbalancer: icmp_seq=1 ttl=56 time=10.494 ms ... many packets later ... Request timeout for icmp_seq 2 64 bytes from loadbalancer: icmp_seq=2 ttl=56 time=1536.516 ms 64 bytes from loadbalancer: icmp_seq=3 ttl=56 time=536.907 ms 64 bytes from loadbalancer: icmp_seq=4 ttl=56 time=9.389 ms ... many packets later ... Request timeout for icmp_seq 919 64 bytes from loadbalancer: icmp_seq=918 ttl=56 time=2932.571 ms 64 bytes from loadbalancer: icmp_seq=919 ttl=56 time=1932.174 ms 64 bytes from loadbalancer: icmp_seq=920 ttl=56 time=932.018 ms 64 bytes from loadbalancer: icmp_seq=921 ttl=56 time=6.157 ms --- 50.xx.xx.16 ping statistics --- 1000 packets transmitted, 997 packets received, 0.3% packet loss round-trip min/avg/max/stddev = 5.119/52.712/2932.571/224.629 ms The pattern is always the same: things operate fine for a while (<20ms), then a ping drops completely, then three or four high-latency pings (1000ms), then it settles down again. Traffic comes in through a bonded public interface (we will call it bond0) configured as such: bond0 Link encap:Ethernet HWaddr 00:xx:xx:xx:xx:5d inet addr:50.xx.xx.16 Bcast:50.xx.xx.31 Mask:255.255.255.224 inet6 addr: <ipv6 address> Scope:Global inet6 addr: <ipv6 address> Scope:Link UP BROADCAST RUNNING MASTER MULTICAST MTU:1500 Metric:1 RX packets:527181270 errors:1 dropped:4 overruns:0 frame:1 TX packets:413335045 errors:0 dropped:0 overruns:0 carrier:0 collisions:0 txqueuelen:0 RX bytes:240016223540 (240.0 GB) TX bytes:104301759647 (104.3 GB) Requests are then submitted via HTTP to upstream servers on the private network (we can call it bond1), which is configured like so: bond1 Link encap:Ethernet HWaddr 00:xx:xx:xx:xx:5c inet addr:10.xx.xx.70 Bcast:10.xx.xx.127 Mask:255.255.255.192 inet6 addr: <ipv6 address> Scope:Link UP BROADCAST RUNNING MASTER MULTICAST MTU:1500 Metric:1 RX packets:430293342 errors:1 dropped:2 overruns:0 frame:1 TX packets:466983986 errors:0 dropped:0 overruns:0 carrier:0 collisions:0 txqueuelen:0 RX bytes:77714410892 (77.7 GB) TX bytes:227349392334 (227.3 GB) Output of uname -a: Linux <hostname> 3.5.0-42-generic #65~precise1-Ubuntu SMP Wed Oct 2 20:57:18 UTC 2013 x86_64 GNU/Linux We have customized sysctl.conf in an attempt to fix the problem, with no success. Output of /etc/sysctl.conf (with irrelevant configs omitted): # net: core net.core.netdev_max_backlog = 10000 # net: ipv4 stack net.ipv4.tcp_ecn = 2 net.ipv4.tcp_sack = 1 net.ipv4.tcp_fack = 1 net.ipv4.tcp_tw_reuse = 1 net.ipv4.tcp_tw_recycle = 0 net.ipv4.tcp_timestamps = 1 net.ipv4.tcp_window_scaling = 1 net.ipv4.tcp_no_metrics_save = 1 net.ipv4.tcp_max_syn_backlog = 10000 net.ipv4.tcp_congestion_control = cubic net.ipv4.ip_local_port_range = 8000 65535 net.ipv4.tcp_syncookies = 1 net.ipv4.tcp_synack_retries = 2 net.ipv4.tcp_thin_dupack = 1 net.ipv4.tcp_thin_linear_timeouts = 1 net.netfilter.nf_conntrack_max = 99999999 net.netfilter.nf_conntrack_tcp_timeout_established = 300 Output of dmesg -d, with non-ICMP UFW messages suppressed: [508315.349295 < 19.852453>] [UFW BLOCK] IN=bond1 OUT= MAC=<mac addresses> SRC=118.xx.xx.143 DST=50.xx.xx.16 LEN=68 TOS=0x00 PREC=0x00 TTL=51 ID=43221 PROTO=ICMP TYPE=3 CODE=1 [SRC=50.xx.xx.16 DST=118.xx.xx.143 LEN=40 TOS=0x00 PREC=0x00 TTL=249 ID=10220 DF PROTO=TCP SPT=80 DPT=53817 WINDOW=8190 RES=0x00 ACK FIN URGP=0 ] [517787.732242 < 0.443127>] Peer 190.xx.xx.131:59705/80 unexpectedly shrunk window 1155488866:1155489425 (repaired) How can I go about diagnosing the cause of this problem, on a Debian-family Linux box?

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• Improving TCP performance over a gigabit network with lots of connections and high traffic of small packets

  - by MinimeDJ

  I’m trying to improve my TCP throughput over a “gigabit network with lots of connections and high traffic of small packets”. My server OS is Ubuntu 11.10 Server 64bit. There are about 50.000 (and growing) clients connected to my server through TCP Sockets (all on the same port). 95% of of my packets have size of 1-150 bytes (TCP header and payload). The rest 5% vary from 150 up to 4096+ bytes. With the config below my server can handle traffic up to 30 Mbps (full duplex). Can you please advice best practice to tune OS for my needs? My /etc/sysctl.cong looks like this: kernel.pid_max = 1000000 net.ipv4.ip_local_port_range = 2500 65000 fs.file-max = 1000000 # net.core.netdev_max_backlog=3000 net.ipv4.tcp_sack=0 # net.core.rmem_max = 16777216 net.core.wmem_max = 16777216 net.core.somaxconn = 2048 # net.ipv4.tcp_rmem = 4096 87380 16777216 net.ipv4.tcp_wmem = 4096 65536 16777216 # net.ipv4.tcp_synack_retries = 2 net.ipv4.tcp_syncookies = 1 net.ipv4.tcp_mem = 50576 64768 98152 # net.core.wmem_default = 65536 net.core.rmem_default = 65536 net.ipv4.tcp_window_scaling=1 # net.ipv4.tcp_mem= 98304 131072 196608 # net.ipv4.tcp_timestamps = 0 net.ipv4.tcp_rfc1337 = 1 net.ipv4.ip_forward = 0 net.ipv4.tcp_congestion_control=cubic net.ipv4.tcp_tw_recycle = 0 net.ipv4.tcp_tw_reuse = 0 # net.ipv4.tcp_orphan_retries = 1 net.ipv4.tcp_fin_timeout = 25 net.ipv4.tcp_max_orphans = 8192 Here are my limits: $ ulimit -a core file size (blocks, -c) 0 data seg size (kbytes, -d) unlimited scheduling priority (-e) 0 file size (blocks, -f) unlimited pending signals (-i) 193045 max locked memory (kbytes, -l) 64 max memory size (kbytes, -m) unlimited open files (-n) 1000000 pipe size (512 bytes, -p) 8 POSIX message queues (bytes, -q) 819200 real-time priority (-r) 0 stack size (kbytes, -s) 8192 cpu time (seconds, -t) unlimited max user processes (-u) 1000000 [ADDED] My NICs are the following: $ dmesg | grep Broad [ 2.473081] Broadcom NetXtreme II 5771x 10Gigabit Ethernet Driver bnx2x 1.62.12-0 (2011/03/20) [ 2.477808] bnx2x 0000:02:00.0: eth0: Broadcom NetXtreme II BCM57711E XGb (A0) PCI-E x4 5GHz (Gen2) found at mem fb000000, IRQ 28, node addr d8:d3:85:bd:23:08 [ 2.482556] bnx2x 0000:02:00.1: eth1: Broadcom NetXtreme II BCM57711E XGb (A0) PCI-E x4 5GHz (Gen2) found at mem fa000000, IRQ 40, node addr d8:d3:85:bd:23:0c [ADDED 2] ethtool -k eth0 Offload parameters for eth0: rx-checksumming: on tx-checksumming: on scatter-gather: on tcp-segmentation-offload: on udp-fragmentation-offload: off generic-segmentation-offload: on generic-receive-offload: on large-receive-offload: on rx-vlan-offload: on tx-vlan-offload: on ntuple-filters: off receive-hashing: off [ADDED 3] sudo ethtool -S eth0|grep -vw 0 NIC statistics: [1]: rx_bytes: 17521104292 [1]: rx_ucast_packets: 118326392 [1]: tx_bytes: 35351475694 [1]: tx_ucast_packets: 191723897 [2]: rx_bytes: 16569945203 [2]: rx_ucast_packets: 114055437 [2]: tx_bytes: 36748975961 [2]: tx_ucast_packets: 194800859 [3]: rx_bytes: 16222309010 [3]: rx_ucast_packets: 109397802 [3]: tx_bytes: 36034786682 [3]: tx_ucast_packets: 198238209 [4]: rx_bytes: 14884911384 [4]: rx_ucast_packets: 104081414 [4]: rx_discards: 5828 [4]: rx_csum_offload_errors: 1 [4]: tx_bytes: 35663361789 [4]: tx_ucast_packets: 194024824 [5]: rx_bytes: 16465075461 [5]: rx_ucast_packets: 110637200 [5]: tx_bytes: 43720432434 [5]: tx_ucast_packets: 202041894 [6]: rx_bytes: 16788706505 [6]: rx_ucast_packets: 113123182 [6]: tx_bytes: 38443961940 [6]: tx_ucast_packets: 202415075 [7]: rx_bytes: 16287423304 [7]: rx_ucast_packets: 110369475 [7]: rx_csum_offload_errors: 1 [7]: tx_bytes: 35104168638 [7]: tx_ucast_packets: 184905201 [8]: rx_bytes: 12689721791 [8]: rx_ucast_packets: 87616037 [8]: rx_discards: 2638 [8]: tx_bytes: 36133395431 [8]: tx_ucast_packets: 196547264 [9]: rx_bytes: 15007548011 [9]: rx_ucast_packets: 98183525 [9]: rx_csum_offload_errors: 1 [9]: tx_bytes: 34871314517 [9]: tx_ucast_packets: 188532637 [9]: tx_mcast_packets: 12 [10]: rx_bytes: 12112044826 [10]: rx_ucast_packets: 84335465 [10]: rx_discards: 2494 [10]: tx_bytes: 36562151913 [10]: tx_ucast_packets: 195658548 [11]: rx_bytes: 12873153712 [11]: rx_ucast_packets: 89305791 [11]: rx_discards: 2990 [11]: tx_bytes: 36348541675 [11]: tx_ucast_packets: 194155226 [12]: rx_bytes: 12768100958 [12]: rx_ucast_packets: 89350917 [12]: rx_discards: 2667 [12]: tx_bytes: 35730240389 [12]: tx_ucast_packets: 192254480 [13]: rx_bytes: 14533227468 [13]: rx_ucast_packets: 98139795 [13]: tx_bytes: 35954232494 [13]: tx_ucast_packets: 194573612 [13]: tx_bcast_packets: 2 [14]: rx_bytes: 13258647069 [14]: rx_ucast_packets: 92856762 [14]: rx_discards: 3509 [14]: rx_csum_offload_errors: 1 [14]: tx_bytes: 35663586641 [14]: tx_ucast_packets: 189661305 rx_bytes: 226125043936 rx_ucast_packets: 1536428109 rx_bcast_packets: 351 rx_discards: 20126 rx_filtered_packets: 8694 rx_csum_offload_errors: 11 tx_bytes: 548442367057 tx_ucast_packets: 2915571846 tx_mcast_packets: 12 tx_bcast_packets: 2 tx_64_byte_packets: 35417154 tx_65_to_127_byte_packets: 2006984660 tx_128_to_255_byte_packets: 373733514 tx_256_to_511_byte_packets: 378121090 tx_512_to_1023_byte_packets: 77643490 tx_1024_to_1522_byte_packets: 43669214 tx_pause_frames: 228 Some info about SACK: When to turn TCP SACK off?

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• CodePlex Daily Summary for Tuesday, June 18, 2013

  CodePlex Daily Summary for Tuesday, June 18, 2013Popular ReleasesCODE Framework: 4.0.30618.0: See change notes in the documentation section for details on what's new. Note: If you download the class reference help file with, you have to right-click the file, pick "Properties", and then unblock the file, as many browsers flag the file as blocked during download (for security reasons) and thus hides all content.Toolbox for Dynamics CRM 2011: XrmToolBox (v1.2013.6.18): XrmToolbox improvement Use new connection controls (use of Microsoft.Xrm.Client.dll) New display capabilities for tools (size, image and colors) Added prerequisites check Added Most Used Tools feature Tools improvementNew toolSolution Transfer Tool (v1.0.0.0) developed by DamSim Updated toolView Layout Replicator (v1.2013.6.17) Double click on source view to display its layoutXml All tools list Access Checker (v1.2013.6.17) Attribute Bulk Updater (v1.2013.6.18) FetchXml Tester (v1.2013.6.1...Media Companion: Media Companion MC3.570b: New* Movie - using XBMC TMDB - now renames movies if option selected. * Movie - using Xbmc Tmdb - Actor images saved from TMDb if option selected. Fixed* Movie - Checks for poster.jpg against missing poster filter * Movie - Fixed continual scraping of vob movie file (not DVD structure) * Both - Correctly display audio channels * Both - Correctly populate audio info in nfo's if multiple audio tracks. * Both - added icons and checked for DTS ES and Dolby TrueHD audio tracks. * Both - Stream d...LINQ Extensions Library: 1.0.4.2: New to release 1.0.4.2 Custom sorting extensions that perform up to 50% better than LINQ OrderBy, ThenBy extensions... Extensions allow for fine tuning of the sort by controlling the algorithm each sort uses.ExtJS based ASP.NET Controls: FineUI v3.3.0: ??FineUI ?? ExtJS ??? ASP.NET ???。 FineUI??? ?? No JavaScript，No CSS，No UpdatePanel，No ViewState，No WebServices ???????。 ?????? IE 7.0、Firefox 3.6、Chrome 3.0、Opera 10.5、Safari 3.0+ ???? Apache License v2.0 ?：ExtJS ?? GPL v3 ?????(http://www.sencha.com/license)。 ???? ??：http://fineui.com/bbs/ ??：http://fineui.com/demo/ ??：http://fineui.com/doc/ ??：http://fineui.codeplex.com/ FineUI???? ExtJS ?????????，???? ExtJS ?。 ????? FineUI ? ExtJS ?：http://fineui.com/bbs/forum.php?mod=viewthrea...BarbaTunnel: BarbaTunnel 8.0: Check Version History for more information about this release.ExpressProfiler: ExpressProfiler v1.5: [+] added Start time, End time event columns [+] added SP:StmtStarting, SP:StmtCompleted events [*] fixed bug with Audit:Logout eventpatterns & practices: Data Access Guidance: Data Access Guidance Drop4 2013.06.17: Drop 4Microsoft Ajax Minifier: Microsoft Ajax Minifier 4.94: add dstLine and dstCol attributes to the -Analyze output in XML mode. un-combine leftover comma-separates expression statements after optimizations are complete so downstream tools don't stack-overflow on really deep comma trees. add support for using a single source map generator instance with multiple runs of MinifyJavaScript, assuming that the results are concatenated to the same output file.Kooboo CMS: Kooboo CMS 4.1.1: The stable release of Kooboo CMS 4.1.0 with fixed the following issues: https://github.com/Kooboo/CMS/issues/1 https://github.com/Kooboo/CMS/issues/11 https://github.com/Kooboo/CMS/issues/13 https://github.com/Kooboo/CMS/issues/15 https://github.com/Kooboo/CMS/issues/19 https://github.com/Kooboo/CMS/issues/20 https://github.com/Kooboo/CMS/issues/24 https://github.com/Kooboo/CMS/issues/43 https://github.com/Kooboo/CMS/issues/45 https://github.com/Kooboo/CMS/issues/46 https://github....VidCoder: 1.5.0 Beta: The betas have started up again! If you were previously on the beta track you will need to install this to get back on it. That's because you can now run both the Beta and Stable version of VidCoder side-by-side! Note that the OpenCL and Intel QuickSync changes being tested by HandBrake are not in the betas yet. They will appear when HandBrake integrates them into the main branch. Updated HandBrake core to SVN 5590. This adds a new FDK AAC encoder. The FAAC encoder has been removed and now...Employee Info Starter Kit: v6.0 - ASP.NET MVC Edition: Release Home - Getting Started - Hands on Coding Walkthrough – Technology Stack - Design & Architecture EISK v6.0 – ASP.NET MVC edition bundles most of the greatest and successful platforms, frameworks and technologies together, to enable web developers to learn and build manageable and high performance web applications with rich user experience effectively and quickly. User End SpecificationsCreating a new employee record Read existing employee records Update an existing employee reco...OLAP PivotTable Extensions: Release 0.8.1: Use the 32-bit download for... Excel 2007 Excel 2010 32-bit (even Excel 2010 32-bit on a 64-bit operating system) Excel 2013 32-bit (even Excel 2013 32-bit on a 64-bit operating system) Use the 64-bit download for... Excel 2010 64-bit Excel 2013 64-bit Just download and run the EXE. There is no need to uninstall the previous release. If you have problems getting the add-in to work, see the Troubleshooting Installation wiki page. The new features in this release are: View #VALUE! Err...DirectXTex texture processing library: June 2013: June 15, 2013 Custom filtering implementation for Resize & GenerateMipMaps(3D) - Point, Box, Linear, Cubic, and Triangle TEX_FILTER_TRIANGLE finite low-pass triangle filter TEX_FILTER_WRAP, TEX_FILTER_MIRROR texture semantics for custom filtering TEX_FILTER_BOX alias for TEX_FILTER_FANT WIC Ordered and error diffusion dithering for non-WIC conversion sRGB gamma correct custom filtering and conversion DDS_FLAGS_EXPAND_LUMINANCE - Reader conversion option for L8, L16, and A8L8 legacy ...WPF Application Framework (WAF): WPF Application Framework (WAF) 3.0.0.440: Version: 3.0.0.440 (Release Candidate): This release contains the source code of the WPF Application Framework (WAF) and the sample applications. Please build the whole solution before you start one of the sample applications. Requirements .NET Framework 4.5 (The package contains a solution file for Visual Studio 2012) Changelog Legend: [B] Breaking change; [O] Marked member as obsolete Samples: Use ValueConverters via StaticResource instead of x:Static. Other Downloads Downloads OverviewBlackJumboDog: Ver5.9.1: 2013.06.13 Ver5.9.1 (1) Web??????SSI?#include???、CGI?????????????????????? (2) ???????????????????????????Lakana - WPF Framework: Lakana V2.1 RTM: - Dynamic text localization - A new application wide message busFree language translator and file converter: Free Language Translator 3.3: some bug fixes and a new link to video tutorials on Youtube.Pokemon Battle Online: ETV: ETV???2012?12??????，????，???????$/PBO/branches/PrivateBeta??。 ???????bug???????。 ???? Server??????，?????。 ?????????，?????????????，?????????。 ????????，????，?????????，???????????（??）??。 ???? ????????????。 ???????。 ???PP????，????????????????????PP????，??3。 ?????????????，??????????。 ???????? ??? ?? ???? ??? ???? ?? ?????????? ?? ??? ??? ??? ???????? ???? ???? ???????????????、???????????，??“???????”??。 ???bug ???Modern UI for WPF: Modern UI 1.0.4: The ModernUI assembly including a demo app demonstrating the various features of Modern UI for WPF. Related downloads NuGet ModernUI for WPF is also available as NuGet package in the NuGet gallery, id: ModernUI.WPF Download Modern UI for WPF Templates A Visual Studio 2012 extension containing a collection of project and item templates for Modern UI for WPF. The extension includes the ModernUI.WPF NuGet package. DownloadNew ProjectsAux Browser: This browser is secured by system level sandbox technology, and it helps you get where you want to go in the shortest possible time. Best solution to convert Outlook OST to PST files: Convert OST to PST without fearing for data loss. An immaculate converter by Recover Data gives user a privilege to perform OST file recovery with no data loss.Bitbucket.NET: A high-performance .NET library for developing applications that use the Bitbucket service.caosu: aaaChartApp: Chart App for SharePoint 2013Custom Membership Provider SQL + LDAP with one login page: Custom membership provider to allow users to login to there portal from one login page whether its custom SQLDB or the current Active Directory.DroidBrowse: Web browser for Android 1.6 or later.haseebtestProject: This project is created to add random files and for testing purposesHiveSense: Hive monitoring system.JQuery File Upload Plugin with Backload server side component (Demo/Examples): Backload is a professional, full featured ASP.NET MVC 4 file upload controller and handler (server side). JSLocator: Locate javascript functions in the sourceMoonCMS: This is a trivial thing. It doesn't make any sense!MyLabs: MyLabs is Private Labpcvvpes: pcvvpesPrism Model Factory Extensions: Micro framework for model cloning, equality check and mergingSharePoint 2007 Solution and Packaging Guidance: WSPSolution is a standard for building SP 2007 solutions in Visual Studio, namespace planning, deployment planning, WSP creation, and build automation.Windows Phone Wi-Fi Launcher: Wi-Fi settings page launcher for Windows Phone 8.0

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• Class member functions instantiated by traits

  - by Jive Dadson

  I am reluctant to say I can't figure this out, but I can't figure this out. I've googled and searched Stack Overflow, and come up empty. The abstract, and possibly overly vague form of the question is, how can I use the traits-pattern to instantiate non-virtual member functions? The question came up while modernizing a set of multivariate function optimizers that I wrote more than 10 years ago. The optimizers all operate by selecting a straight-line path through the parameter space away from the current best point (the "update"), then finding a better point on that line (the "line search"), then testing for the "done" condition, and if not done, iterating. There are different methods for doing the update, the line-search, and conceivably for the done test, and other things. Mix and match. Different update formulae require different state-variable data. For example, the LMQN update requires a vector, and the BFGS update requires a matrix. If evaluating gradients is cheap, the line-search should do so. If not, it should use function evaluations only. Some methods require more accurate line-searches than others. Those are just some examples. The original version instantiates several of the combinations by means of virtual functions. Some traits are selected by setting mode bits that are tested at runtime. Yuck. It would be trivial to define the traits with #define's and the member functions with #ifdef's and macros. But that's so twenty years ago. It bugs me that I cannot figure out a whiz-bang modern way. If there were only one trait that varied, I could use the curiously recurring template pattern. But I see no way to extend that to arbitrary combinations of traits. I tried doing it using boost::enable_if, etc.. The specialized state information was easy. I managed to get the functions done, but only by resorting to non-friend external functions that have the this-pointer as a parameter. I never even figured out how to make the functions friends, much less member functions. The compiler (VC++ 2008) always complained that things didn't match. I would yell, "SFINAE, you moron!" but the moron is probably me. Perhaps tag-dispatch is the key. I haven't gotten very deeply into that. Surely it's possible, right? If so, what is best practice? UPDATE: Here's another try at explaining it. I want the user to be able to fill out an order (manifest) for a custom optimizer, something like ordering off of a Chinese menu - one from column A, one from column B, etc.. Waiter, from column A (updaters), I'll have the BFGS update with Cholesky-decompositon sauce. From column B (line-searchers), I'll have the cubic interpolation line-search with an eta of 0.4 and a rho of 1e-4, please. Etc... UPDATE: Okay, okay. Here's the playing-around that I've done. I offer it reluctantly, because I suspect it's a completely wrong-headed approach. It runs okay under vc++ 2008. #include <boost/utility.hpp> #include <boost/type_traits/integral_constant.hpp> namespace dj { struct CBFGS { void bar() {printf("CBFGS::bar %d\n", data);} CBFGS(): data(1234){} int data; }; template<class T> struct is_CBFGS: boost::false_type{}; template<> struct is_CBFGS<CBFGS>: boost::true_type{}; struct LMQN {LMQN(): data(54.321){} void bar() {printf("LMQN::bar %lf\n", data);} double data; }; template<class T> struct is_LMQN: boost::false_type{}; template<> struct is_LMQN<LMQN> : boost::true_type{}; struct default_optimizer_traits { typedef CBFGS update_type; }; template<class traits> class Optimizer; template<class traits> void foo(typename boost::enable_if<is_LMQN<typename traits::update_type>, Optimizer<traits> >::type& self) { printf(" LMQN %lf\n", self.data); } template<class traits> void foo(typename boost::enable_if<is_CBFGS<typename traits::update_type>, Optimizer<traits> >::type& self) { printf("CBFGS %d\n", self.data); } template<class traits = default_optimizer_traits> class Optimizer{ friend typename traits::update_type; //friend void dj::foo<traits>(typename Optimizer<traits> & self); // How? public: //void foo(void); // How??? void foo() { dj::foo<traits>(*this); } void bar() { data.bar(); } //protected: // How? typedef typename traits::update_type update_type; update_type data; }; } // namespace dj int main_() { dj::Optimizer<> opt; opt.foo(); opt.bar(); std::getchar(); return 0; }

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