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  • In-app paymnt methods

    - by user212228
    I'm interested in developing for Ubuntu (mostly phones) and I can't seem to find the guidelines on app publishing, will apps only work through the ubuntu software center, or can users download and install an app from a website like is possible with an android apk? Also, are there any rules regarding in-app purchase methods, (I hope the minimum price here isn't $2.99 in-app as well or I'm not going to even bother developing for Ubuntu and will just stick with Android) Google for example, requires that in-app purchases go through their servers so that it isn't possible to use other funding methods at least for play store published apps. My main questions here are: Would it be possible to release an app for ubuntu touch that accepted bitcoin, paypal, or other methods for in-app purchases? If not, would it be possible to release apps through a personal website or 3rd party app market that could use alternative payment methods?

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  • Magic Quadrant for x86 Server Virtualization Infrastructure

    - by Cinzia Mascanzoni
    Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} Gartner just published a report showing Oracle having moved into the challengers quadrant. Click here for the report

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  • Ubuntu 14.04 Bluetooth Magic Mouse doesn't pair (No agent available)

    - by Rafael Xavier
    Mouse gets discovered. Although, it doesn't pair. /var/log/syslog: Apr 23 10:05:15 xavier bluetoothd[9873]: No agent available for request type 0 Apr 23 10:05:15 xavier bluetoothd[9873]: btd_event_request_pin: Operation not permitted Apr 23 10:05:15 xavier bluetoothd[9873]: Connection refused (111) It's worth saying that: Keyboard has paired and it's working just fine though; Mouse used to work just fine in Ubuntu 12.04, and 13, and it works when I reboot on Mac; This is the hci device. $ hcitool dev Devices: hci0 E0:F8:47:3A:3F:47 How to get it working?

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  • Image Magic Make Fails - PHP extension

    - by Kyle Adams
    So I was doing the following: sudo apt-get install php-pear php5-dev sudo apt-get install imagemagick libmagickwand-dev sudo pecl install imagick It all works till I get the error: make: *** [imagick_class.lo] Error 1 ERROR: `make' failed Which according to blog posts and forms is because of libmagick9-dev, how ever when trying to install this I get: sudo apt-get install libmagick9-dev Reading package lists... Done Building dependency tree Reading state information... Done Package libmagick9-dev is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source However the following packages replace it: graphicsmagick-libmagick-dev-compat E: Package 'libmagick9-dev' has no installation candidate Thoughts?

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  • Are nullable types preferable to magic numbers?

    - by Matt H
    I have been having a little bit of a debate with a coworker lately. We are specifically using C#, but this could apply to any language with nullable types. Say for example you have a value that represents a maximum. However, this maximum value is optional. I argue that a nullable number would be preferable. My coworker favors the use of zero, citing precedent. Granted, things like network sockets have often used zero to represent an unlimited timeout. If I were to write code dealing with sockets today, I would personally use a nullable value, since I feel it would better represent the fact that there is NO timeout. Which representation is better? Both require a condition checking for the value meaning "none", but I believe that a nullable type conveys the intent a little bit better.

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  • Reuse the data CRUD methods in data access layer, but they are updated too quickly

    - by ValidfroM
    I agree that we should put CRUD methods in a data access layer, However, in my current project I have some issues. It is a legacy system, and there are quite a lot CRUD methods in some concrete manager classes. People including me seem to just add new methods to it, rather than reuse the existing methods. Because We don't know whether the existing method is what we need Even if we have source code, do we really need read other's code then make decision? It is updated too quickly. Do not have time get familiar with the DAO API. Back to the question, how do you solve that in your project? If we say "reuse", it really needs to be reusable rather than just an excuse.

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  • The Magic of Keywords

    When you ask this question of the search engines, there are many definitions all meaning the same thing. The one I liked the best is "Keywords are the words or phrases used in a Web Page that will be noticed and indexed by Search Engines, and guide people to your web site when they type in those words or phrases at the Search Engine." In fact keywords are a very necessary part of an internet marketer's resources, if you want people to find and read what you have written or advertised.

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  • Unconventional Methods of Link Building

    You can find hundreds of link building methods online. Not all methods are suitable for everyone. Whereas the basics of link building are same every time, you can choose entirely different strategy to get the job done. Search engine optimization is a serious matter and you have to check every corner to find the hidden treasure in the form of a top page rank. Here are a few unconventional methods that you can use.

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  • Extension methods on a null object instance – something you did not know

    - by nmarun
    Extension methods gave developers with a lot of bandwidth to do interesting (read ‘cool’) things. But there are a couple of things that we need to be aware of while using these extension methods. I have a StringUtil class that defines two extension methods: 1: public static class StringUtils 2: { 3: public static string Left( this string arg, int leftCharCount) 4: { 5: if (arg == null ) 6: { 7: throw new ArgumentNullException( "arg" ); 8: } 9: return arg.Substring(0, leftCharCount); 10...(read more)

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  • Magic Quadrant for x86 Server Virtualization Infrastructure

    - by Cinzia Mascanzoni
    The 2012 Gartner MQ for x86 Server Virtualization has just published.  KEY TAKEAWAYS - Oracle is in the “Challengers” quadrant. - This is a significant “jump” above the x-axis (from the “Niche” quadrant) during previous years - The move into the “Challengers” quadrant was possible for 3 primary reasons - 1) strength of the Oracle VM 3.0 release - 2) integrated management capabilities - 3) solid customer momentum during past year - Gartner even specifically states that Oracle VM use is growing amongst VMware customers Read the full report here.

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  • Why would I need a using statement to Libary B extn methods, if they're used in Library A & it's Li

    - by Greg
    Hi, I have: Main Program Class - uses Library A Library A - has partial classes which mix in methods from Library B Library B - mix in methods & interfaces Why would I need a using statement to LibaryB just to get their extension methods working in the main class? That is given that it's Library B that defines the classes that will be extended. EDIT - Except from code // *** PROGRAM *** using TopologyDAL; using Topology; // *** THIS WAS NEEDED TO GET EXTN METHODS APPEARING *** class Program { static void Main(string[] args) { var context = new Model1Container(); Node myNode; // ** trying to get myNode mixin methods to appear seems to need using line to point to Library B *** } } // ** LIBRARY A namespace TopologyDAL { public partial class Node { // Auto generated from EF } public partial class Node : INode<int> // to add extension methods from Library B { public int Key } } // ** LIBRARY B namespace ToplogyLibrary { public static class NodeExtns { public static void FromNodeMixin<T>(this INode<T> node) { // XXXX } } public interface INode<T> { // Properties T Key { get; } // Methods } }

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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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  • C#: Adding Functionality to 3rd Party Libraries With Extension Methods

    - by James Michael Hare
    Ever have one of those third party libraries that you love but it's missing that one feature or one piece of syntactical candy that would make it so much more useful?  This, I truly think, is one of the best uses of extension methods.  I began discussing extension methods in my last post (which you find here) where I expounded upon what I thought were some rules of thumb for using extension methods correctly.  As long as you keep in line with those (or similar) rules, they can often be useful for adding that little extra functionality or syntactical simplification for a library that you have little or no control over. Oh sure, you could take an open source project, download the source and add the methods you want, but then every time the library is updated you have to re-add your changes, which can be cumbersome and error prone.  And yes, you could possibly extend a class in a third party library and override features, but that's only if the class is not sealed, static, or constructed via factories. This is the perfect place to use an extension method!  And the best part is, you and your development team don't need to change anything!  Simply add the using for the namespace the extensions are in! So let's consider this example.  I love log4net!  Of all the logging libraries I've played with, it, to me, is one of the most flexible and configurable logging libraries and it performs great.  But this isn't about log4net, well, not directly.  So why would I want to add functionality?  Well, it's missing one thing I really want in the ILog interface: ability to specify logging level at runtime. For example, let's say I declare my ILog instance like so:     using log4net;     public class LoggingTest     {         private static readonly ILog _log = LogManager.GetLogger(typeof(LoggingTest));         ...     }     If you don't know log4net, the details aren't important, just to show that the field _log is the logger I have gotten from log4net. So now that I have that, I can log to it like so:     _log.Debug("This is the lowest level of logging and just for debugging output.");     _log.Info("This is an informational message.  Usual normal operation events.");     _log.Warn("This is a warning, something suspect but not necessarily wrong.");     _log.Error("This is an error, some sort of processing problem has happened.");     _log.Fatal("Fatals usually indicate the program is dying hideously."); And there's many flavors of each of these to log using string formatting, to log exceptions, etc.  But one thing there isn't: the ability to easily choose the logging level at runtime.  Notice, the logging levels above are chosen at compile time.  Of course, you could do some fun stuff with lambdas and wrap it, but that would obscure the simplicity of the interface.  And yes there is a Logger property you can dive down into where you can specify a Level, but the Level properties don't really match the ILog interface exactly and then you have to manually build a LogEvent and... well, it gets messy.  I want something simple and sexy so I can say:     _log.Log(someLevel, "This will be logged at whatever level I choose at runtime!");     Now, some purists out there might say you should always know what level you want to log at, and for the most part I agree with them.  For the most party the ILog interface satisfies 99% of my needs.  In fact, for most application logging yes you do always know the level you will be logging at, but when writing a utility class, you may not always know what level your user wants. I'll tell you, one of my favorite things is to write reusable components.  If I had my druthers I'd write framework libraries and shared components all day!  And being able to easily log at a runtime-chosen level is a big need for me.  After all, if I want my code to really be re-usable, I shouldn't force a user to deal with the logging level I choose. One of my favorite uses for this is in Interceptors -- I'll describe Interceptors in my next post and some of my favorites -- for now just know that an Interceptor wraps a class and allows you to add functionality to an existing method without changing it's signature.  At the risk of over-simplifying, it's a very generic implementation of the Decorator design pattern. So, say for example that you were writing an Interceptor that would time method calls and emit a log message if the method call execution time took beyond a certain threshold of time.  For instance, maybe if your database calls take more than 5,000 ms, you want to log a warning.  Or if a web method call takes over 1,000 ms, you want to log an informational message.  This would be an excellent use of logging at a generic level. So here was my personal wish-list of requirements for my task: Be able to determine if a runtime-specified logging level is enabled. Be able to log generically at a runtime-specified logging level. Have the same look-and-feel of the existing Debug, Info, Warn, Error, and Fatal calls.    Having the ability to also determine if logging for a level is on at runtime is also important so you don't spend time building a potentially expensive logging message if that level is off.  Consider an Interceptor that may log parameters on entrance to the method.  If you choose to log those parameter at DEBUG level and if DEBUG is not on, you don't want to spend the time serializing those parameters. Now, mine may not be the most elegant solution, but it performs really well since the enum I provide all uses contiguous values -- while it's never guaranteed, contiguous switch values usually get compiled into a jump table in IL which is VERY performant - O(1) - but even if it doesn't, it's still so fast you'd never need to worry about it. So first, I need a way to let users pass in logging levels.  Sure, log4net has a Level class, but it's a class with static members and plus it provides way too many options compared to ILog interface itself -- and wouldn't perform as well in my level-check -- so I define an enum like below.     namespace Shared.Logging.Extensions     {         // enum to specify available logging levels.         public enum LoggingLevel         {             Debug,             Informational,             Warning,             Error,             Fatal         }     } Now, once I have this, writing the extension methods I need is trivial.  Once again, I would typically /// comment fully, but I'm eliminating for blogging brevity:     namespace Shared.Logging.Extensions     {         // the extension methods to add functionality to the ILog interface         public static class LogExtensions         {             // Determines if logging is enabled at a given level.             public static bool IsLogEnabled(this ILog logger, LoggingLevel level)             {                 switch (level)                 {                     case LoggingLevel.Debug:                         return logger.IsDebugEnabled;                     case LoggingLevel.Informational:                         return logger.IsInfoEnabled;                     case LoggingLevel.Warning:                         return logger.IsWarnEnabled;                     case LoggingLevel.Error:                         return logger.IsErrorEnabled;                     case LoggingLevel.Fatal:                         return logger.IsFatalEnabled;                 }                                 return false;             }             // Logs a simple message - uses same signature except adds LoggingLevel             public static void Log(this ILog logger, LoggingLevel level, object message)             {                 switch (level)                 {                     case LoggingLevel.Debug:                         logger.Debug(message);                         break;                     case LoggingLevel.Informational:                         logger.Info(message);                         break;                     case LoggingLevel.Warning:                         logger.Warn(message);                         break;                     case LoggingLevel.Error:                         logger.Error(message);                         break;                     case LoggingLevel.Fatal:                         logger.Fatal(message);                         break;                 }             }             // Logs a message and exception to the log at specified level.             public static void Log(this ILog logger, LoggingLevel level, object message, Exception exception)             {                 switch (level)                 {                     case LoggingLevel.Debug:                         logger.Debug(message, exception);                         break;                     case LoggingLevel.Informational:                         logger.Info(message, exception);                         break;                     case LoggingLevel.Warning:                         logger.Warn(message, exception);                         break;                     case LoggingLevel.Error:                         logger.Error(message, exception);                         break;                     case LoggingLevel.Fatal:                         logger.Fatal(message, exception);                         break;                 }             }             // Logs a formatted message to the log at the specified level.              public static void LogFormat(this ILog logger, LoggingLevel level, string format,                                          params object[] args)             {                 switch (level)                 {                     case LoggingLevel.Debug:                         logger.DebugFormat(format, args);                         break;                     case LoggingLevel.Informational:                         logger.InfoFormat(format, args);                         break;                     case LoggingLevel.Warning:                         logger.WarnFormat(format, args);                         break;                     case LoggingLevel.Error:                         logger.ErrorFormat(format, args);                         break;                     case LoggingLevel.Fatal:                         logger.FatalFormat(format, args);                         break;                 }             }         }     } So there it is!  I didn't have to modify the log4net source code, so if a new version comes out, i can just add the new assembly with no changes.  I didn't have to subclass and worry about developers not calling my sub-class instead of the original.  I simply provide the extension methods and it's as if the long lost extension methods were always a part of the ILog interface! Consider a very contrived example using the original interface:     // using the original ILog interface     public class DatabaseUtility     {         private static readonly ILog _log = LogManager.Create(typeof(DatabaseUtility));                 // some theoretical method to time         IDataReader Execute(string statement)         {             var timer = new System.Diagnostics.Stopwatch();                         // do DB magic                                    // this is hard-coded to warn, if want to change at runtime tough luck!             if (timer.ElapsedMilliseconds > 5000 && _log.IsWarnEnabled)             {                 _log.WarnFormat("Statement {0} took too long to execute.", statement);             }             ...         }     }     Now consider this alternate call where the logging level could be perhaps a property of the class          // using the original ILog interface     public class DatabaseUtility     {         private static readonly ILog _log = LogManager.Create(typeof(DatabaseUtility));                 // allow logging level to be specified by user of class instead         public LoggingLevel ThresholdLogLevel { get; set; }                 // some theoretical method to time         IDataReader Execute(string statement)         {             var timer = new System.Diagnostics.Stopwatch();                         // do DB magic                                    // this is hard-coded to warn, if want to change at runtime tough luck!             if (timer.ElapsedMilliseconds > 5000 && _log.IsLogEnabled(ThresholdLogLevel))             {                 _log.LogFormat(ThresholdLogLevel, "Statement {0} took too long to execute.",                     statement);             }             ...         }     } Next time, I'll show one of my favorite uses for these extension methods in an Interceptor.

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  • How can I make a career in Formal Methods programming in USA?

    - by A5al Andy
    I've found that my (USA) professors recoil with a near-disgust when I ask them about how to pursue a career in Formal Methods programming. They say, "Oh, that stuff! That stuff is anal. You don't need that European POS to get a job." I'm sure I'll get a job without it, but Formal Methods interests me so much that I bet I'd like to make a career of it. I'd like to learn about Formal Methods at an American University and then work in that field here. I've found that even professors at more important universities than mine don't seem to welcome Formal Methods. Almost all FM research project webpages are semi-abandoned and moldering. Europe is where the action seems to be for this. Can anyone suggest a plan of attack, and along the way explain the antipathy to Formal Methods in the US? I'm a sophomore at a public university in the South.

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  • Creating Asynchronous Methods in EJB 3.1

    - by cindo
    Normal 0 false false false EN-US X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} OBE of the Month: Creating Asynchronous Methods in EJB 3.1 This OBE covers creating an EJB 3.1 application that demonstrates the use of the @Asynchronous annotation in an Enterprise Java Bean (EJB) class or specific method. In this tutorial, you will create a Java EE 6 Web Application and add the following components to it - a Stateless Session Bean with two asynchronous methods. You define a Servlet to call the asynchronous methods and to keep track of the invocation and completion times to demonstrate the asynchronous nature of the method calls. The index.jsp will contain a form with a submit button, Run allowing you to execute the application. The form will submit to the Servlet which invokes the asynchronous methods defined in the session bean and the response is re-directed to response.jsp. Information about the asynchronous handling procedure is displayed to users. From this information, users will notice that the invoker thread and the called asynchronous thread are working concurrently. Check out this new OBE on the Oracle Learning Library: Creating Asynchronous Methods in EJB 3.1. This OBE is part of the new EJB 3.1 New Features Series. Related OBE’s that might interest you: Creating a No-Interface View Session Bean and Packaging in a WAR File Creating and Accessing a Session Bean in a  Web Application

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