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  • how to determine if a character vector is a valid numeric or integer vector

    - by Andrew Barr
    I am trying to turn a nested list structure into a dataframe. The list looks similar to the following (it is serialized data from parsed JSON read in using the httr package). myList <- list(object1 = list(w=1, x=list(y=0.1, z="cat")), object2 = list(w=2, x=list(y=0.2, z="dog"))) unlist(myList) does a great job of recursively flattening the list, and I can then use lapply to flatten all the objects nicely. flatList <- lapply(myList, FUN= function(object) {return(as.data.frame(rbind(unlist(object))))}) And finally, I can button it up using plyr::rbind.fill myDF <- do.call(plyr::rbind.fill, flatList) str(myDF) #'data.frame': 2 obs. of 3 variables: #$ w : Factor w/ 2 levels "1","2": 1 2 #$ x.y: Factor w/ 2 levels "0.1","0.2": 1 2 #$ x.z: Factor w/ 2 levels "cat","dog": 1 2 The problem is that w and x.y are now being interpreted as character vectors, which by default get parsed as factors in the dataframe. I believe that unlist() is the culprit, but I can't figure out another way to recursively flatten the list structure. A workaround would be to post-process the dataframe, and assign data types then. What is the best way to determine if a vector is a valid numeric or integer vector?

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  • Move camera to fit 3D scene

    - by Burre
    Hi there. I'm looking for an algorithm to fit a bounding box inside a viewport (in my case a DirectX scene). I know about algorithms for centering a bounding sphere in a orthographic camera but would need the same for a bounding box and a perspective camera. I have most of the data: I have the up-vector for the camera I have the center point of the bounding box I have the look-at vector (direction and distance) from the camera point to the box center I have projected the points on a plane perpendicular to the camera and retrieved the coefficients describing how much the max/min X and Y coords are within or outside the viewing plane. Problems I have: Center of the bounding box isn't necessarily in the center of the viewport (that is, it's bounding rectangle after projection). Since the field of view "skew" the projection (see http://en.wikipedia.org/wiki/File:Perspective-foreshortening.svg) I cannot simply use the coefficients as a scale factor to move the camera because it will overshoot/undershoot the desired camera position How do I find the camera position so that it fills the viewport as pixel perfect as possible (exception being if the aspect ratio is far from 1.0, it only needs to fill one of the screen axis)? I've tried some other things: Using a bounding sphere and Tangent to find a scale factor to move the camera. This doesn't work well, because, it doesn't take into account the perspective projection, and secondly spheres are bad bounding volumes for my use because I have a lot of flat and long geometries. Iterating calls to the function to get a smaller and smaller error in the camera position. This has worked somewhat, but I can sometimes run into weird edge cases where the camera position overshoots too much and the error factor increases. Also, when doing this I didn't recenter the model based on the position of the bounding rectangle. I couldn't find a solid, robust way to do that reliably. Help please!

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  • Looping through covariates in regression using R

    - by Kyle Peyton
    I'm trying to run 96 regressions and save the results as 96 different objects. To complicate things, I want the subscript on one of the covariates in the model to also change 96 times. I've almost solved the problem but I've unfortunately hit a wall. The code so far is, for(i in 1:96){ assign(paste("z.out", i,sep=""), lm(rMonExp_EGM~ TE_i+ Month2+Month3+Month4+Month5+Month6+Month7+Month8+Month9+ Month10+Month11+Month12+Yrs_minus_2004 + as.factor(LGA),data=Pokies)) } This works on the object creation side (e.g. I have z.out1 - z.out96) but I can't seem to get the subscript on the covariate to change as well. I have 96 variables called TE_1, TE_2 ... TE_96 in the dataset. As such, the subscript on TE_, the "i" needs to change to correspond to each of the objects I create. That is, z.out1 should hold the results from this model: z.out1 <- lm(rMonExp_EGM~ TE_1 + Month2+Month3+Month4+Month5+Month6+Month7+Month8+Month9+ Month10+Month11+Month12+Yrs_minus_2004 + as.factor(LGA),data=Pokies) And z.out96 should be: z.out96 <- lm(rMonExp_EGM~ TE_96+ Month2+Month3+Month4+Month5+Month6+Month7+Month8+Month9+ Month10+Month11+Month12+Yrs_minus_2004 + as.factor(LGA),data=Pokies) Hopefully this makes sense. I'm grateful for any tips/advice. cheers, kyle

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  • Using Durandal to Create Single Page Apps

    - by Stephen.Walther
    A few days ago, I gave a talk on building Single Page Apps on the Microsoft Stack. In that talk, I recommended that people use Knockout, Sammy, and RequireJS to build their presentation layer and use the ASP.NET Web API to expose data from their server. After I gave the talk, several people contacted me and suggested that I investigate a new open-source JavaScript library named Durandal. Durandal stitches together Knockout, Sammy, and RequireJS to make it easier to use these technologies together. In this blog entry, I want to provide a brief walkthrough of using Durandal to create a simple Single Page App. I am going to demonstrate how you can create a simple Movies App which contains (virtual) pages for viewing a list of movies, adding new movies, and viewing movie details. The goal of this blog entry is to give you a sense of what it is like to build apps with Durandal. Installing Durandal First things first. How do you get Durandal? The GitHub project for Durandal is located here: https://github.com/BlueSpire/Durandal The Wiki — located at the GitHub project — contains all of the current documentation for Durandal. Currently, the documentation is a little sparse, but it is enough to get you started. Instead of downloading the Durandal source from GitHub, a better option for getting started with Durandal is to install one of the Durandal NuGet packages. I built the Movies App described in this blog entry by first creating a new ASP.NET MVC 4 Web Application with the Basic Template. Next, I executed the following command from the Package Manager Console: Install-Package Durandal.StarterKit As you can see from the screenshot of the Package Manager Console above, the Durandal Starter Kit package has several dependencies including: · jQuery · Knockout · Sammy · Twitter Bootstrap The Durandal Starter Kit package includes a sample Durandal application. You can get to the Starter Kit app by navigating to the Durandal controller. Unfortunately, when I first tried to run the Starter Kit app, I got an error because the Starter Kit is hard-coded to use a particular version of jQuery which is already out of date. You can fix this issue by modifying the App_Start\DurandalBundleConfig.cs file so it is jQuery version agnostic like this: bundles.Add( new ScriptBundle("~/scripts/vendor") .Include("~/Scripts/jquery-{version}.js") .Include("~/Scripts/knockout-{version}.js") .Include("~/Scripts/sammy-{version}.js") // .Include("~/Scripts/jquery-1.9.0.min.js") // .Include("~/Scripts/knockout-2.2.1.js") // .Include("~/Scripts/sammy-0.7.4.min.js") .Include("~/Scripts/bootstrap.min.js") ); The recommendation is that you create a Durandal app in a folder off your project root named App. The App folder in the Starter Kit contains the following subfolders and files: · durandal – This folder contains the actual durandal JavaScript library. · viewmodels – This folder contains all of your application’s view models. · views – This folder contains all of your application’s views. · main.js — This file contains all of the JavaScript startup code for your app including the client-side routing configuration. · main-built.js – This file contains an optimized version of your application. You need to build this file by using the RequireJS optimizer (unfortunately, before you can run the optimizer, you must first install NodeJS). For the purpose of this blog entry, I wanted to start from scratch when building the Movies app, so I deleted all of these files and folders except for the durandal folder which contains the durandal library. Creating the ASP.NET MVC Controller and View A Durandal app is built using a single server-side ASP.NET MVC controller and ASP.NET MVC view. A Durandal app is a Single Page App. When you navigate between pages, you are not navigating to new pages on the server. Instead, you are loading new virtual pages into the one-and-only-one server-side view. For the Movies app, I created the following ASP.NET MVC Home controller: public class HomeController : Controller { public ActionResult Index() { return View(); } } There is nothing special about the Home controller – it is as basic as it gets. Next, I created the following server-side ASP.NET view. This is the one-and-only server-side view used by the Movies app: @{ Layout = null; } <!DOCTYPE html> <html> <head> <title>Index</title> </head> <body> <div id="applicationHost"> Loading app.... </div> @Scripts.Render("~/scripts/vendor") <script type="text/javascript" src="~/App/durandal/amd/require.js" data-main="/App/main"></script> </body> </html> Notice that I set the Layout property for the view to the value null. If you neglect to do this, then the default ASP.NET MVC layout will be applied to the view and you will get the <!DOCTYPE> and opening and closing <html> tags twice. Next, notice that the view contains a DIV element with the Id applicationHost. This marks the area where virtual pages are loaded. When you navigate from page to page in a Durandal app, HTML page fragments are retrieved from the server and stuck in the applicationHost DIV element. Inside the applicationHost element, you can place any content which you want to display when a Durandal app is starting up. For example, you can create a fancy splash screen. I opted for simply displaying the text “Loading app…”: Next, notice the view above includes a call to the Scripts.Render() helper. This helper renders out all of the JavaScript files required by the Durandal library such as jQuery and Knockout. Remember to fix the App_Start\DurandalBundleConfig.cs as described above or Durandal will attempt to load an old version of jQuery and throw a JavaScript exception and stop working. Your application JavaScript code is not included in the scripts rendered by the Scripts.Render helper. Your application code is loaded dynamically by RequireJS with the help of the following SCRIPT element located at the bottom of the view: <script type="text/javascript" src="~/App/durandal/amd/require.js" data-main="/App/main"></script> The data-main attribute on the SCRIPT element causes RequireJS to load your /app/main.js JavaScript file to kick-off your Durandal app. Creating the Durandal Main.js File The Durandal Main.js JavaScript file, located in your App folder, contains all of the code required to configure the behavior of Durandal. Here’s what the Main.js file looks like in the case of the Movies app: require.config({ paths: { 'text': 'durandal/amd/text' } }); define(function (require) { var app = require('durandal/app'), viewLocator = require('durandal/viewLocator'), system = require('durandal/system'), router = require('durandal/plugins/router'); //>>excludeStart("build", true); system.debug(true); //>>excludeEnd("build"); app.start().then(function () { //Replace 'viewmodels' in the moduleId with 'views' to locate the view. //Look for partial views in a 'views' folder in the root. viewLocator.useConvention(); //configure routing router.useConvention(); router.mapNav("movies/show"); router.mapNav("movies/add"); router.mapNav("movies/details/:id"); app.adaptToDevice(); //Show the app by setting the root view model for our application with a transition. app.setRoot('viewmodels/shell', 'entrance'); }); }); There are three important things to notice about the main.js file above. First, notice that it contains a section which enables debugging which looks like this: //>>excludeStart(“build”, true); system.debug(true); //>>excludeEnd(“build”); This code enables debugging for your Durandal app which is very useful when things go wrong. When you call system.debug(true), Durandal writes out debugging information to your browser JavaScript console. For example, you can use the debugging information to diagnose issues with your client-side routes: (The funny looking //> symbols around the system.debug() call are RequireJS optimizer pragmas). The main.js file is also the place where you configure your client-side routes. In the case of the Movies app, the main.js file is used to configure routes for three page: the movies show, add, and details pages. //configure routing router.useConvention(); router.mapNav("movies/show"); router.mapNav("movies/add"); router.mapNav("movies/details/:id");   The route for movie details includes a route parameter named id. Later, we will use the id parameter to lookup and display the details for the right movie. Finally, the main.js file above contains the following line of code: //Show the app by setting the root view model for our application with a transition. app.setRoot('viewmodels/shell', 'entrance'); This line of code causes Durandal to load up a JavaScript file named shell.js and an HTML fragment named shell.html. I’ll discuss the shell in the next section. Creating the Durandal Shell You can think of the Durandal shell as the layout or master page for a Durandal app. The shell is where you put all of the content which you want to remain constant as a user navigates from virtual page to virtual page. For example, the shell is a great place to put your website logo and navigation links. The Durandal shell is composed from two parts: a JavaScript file and an HTML file. Here’s what the HTML file looks like for the Movies app: <h1>Movies App</h1> <div class="container-fluid page-host"> <!--ko compose: { model: router.activeItem, //wiring the router afterCompose: router.afterCompose, //wiring the router transition:'entrance', //use the 'entrance' transition when switching views cacheViews:true //telling composition to keep views in the dom, and reuse them (only a good idea with singleton view models) }--><!--/ko--> </div> And here is what the JavaScript file looks like: define(function (require) { var router = require('durandal/plugins/router'); return { router: router, activate: function () { return router.activate('movies/show'); } }; }); The JavaScript file contains the view model for the shell. This view model returns the Durandal router so you can access the list of configured routes from your shell. Notice that the JavaScript file includes a function named activate(). This function loads the movies/show page as the first page in the Movies app. If you want to create a different default Durandal page, then pass the name of a different age to the router.activate() method. Creating the Movies Show Page Durandal pages are created out of a view model and a view. The view model contains all of the data and view logic required for the view. The view contains all of the HTML markup for rendering the view model. Let’s start with the movies show page. The movies show page displays a list of movies. The view model for the show page looks like this: define(function (require) { var moviesRepository = require("repositories/moviesRepository"); return { movies: ko.observable(), activate: function() { this.movies(moviesRepository.listMovies()); } }; }); You create a view model by defining a new RequireJS module (see http://requirejs.org). You create a RequireJS module by placing all of your JavaScript code into an anonymous function passed to the RequireJS define() method. A RequireJS module has two parts. You retrieve all of the modules which your module requires at the top of your module. The code above depends on another RequireJS module named repositories/moviesRepository. Next, you return the implementation of your module. The code above returns a JavaScript object which contains a property named movies and a method named activate. The activate() method is a magic method which Durandal calls whenever it activates your view model. Your view model is activated whenever you navigate to a page which uses it. In the code above, the activate() method is used to get the list of movies from the movies repository and assign the list to the view model movies property. The HTML for the movies show page looks like this: <table> <thead> <tr> <th>Title</th><th>Director</th> </tr> </thead> <tbody data-bind="foreach:movies"> <tr> <td data-bind="text:title"></td> <td data-bind="text:director"></td> <td><a data-bind="attr:{href:'#/movies/details/'+id}">Details</a></td> </tr> </tbody> </table> <a href="#/movies/add">Add Movie</a> Notice that this is an HTML fragment. This fragment will be stuffed into the page-host DIV element in the shell.html file which is stuffed, in turn, into the applicationHost DIV element in the server-side MVC view. The HTML markup above contains data-bind attributes used by Knockout to display the list of movies (To learn more about Knockout, visit http://knockoutjs.com). The list of movies from the view model is displayed in an HTML table. Notice that the page includes a link to a page for adding a new movie. The link uses the following URL which starts with a hash: #/movies/add. Because the link starts with a hash, clicking the link does not cause a request back to the server. Instead, you navigate to the movies/add page virtually. Creating the Movies Add Page The movies add page also consists of a view model and view. The add page enables you to add a new movie to the movie database. Here’s the view model for the add page: define(function (require) { var app = require('durandal/app'); var router = require('durandal/plugins/router'); var moviesRepository = require("repositories/moviesRepository"); return { movieToAdd: { title: ko.observable(), director: ko.observable() }, activate: function () { this.movieToAdd.title(""); this.movieToAdd.director(""); this._movieAdded = false; }, canDeactivate: function () { if (this._movieAdded == false) { return app.showMessage('Are you sure you want to leave this page?', 'Navigate', ['Yes', 'No']); } else { return true; } }, addMovie: function () { // Add movie to db moviesRepository.addMovie(ko.toJS(this.movieToAdd)); // flag new movie this._movieAdded = true; // return to list of movies router.navigateTo("#/movies/show"); } }; }); The view model contains one property named movieToAdd which is bound to the add movie form. The view model also has the following three methods: 1. activate() – This method is called by Durandal when you navigate to the add movie page. The activate() method resets the add movie form by clearing out the movie title and director properties. 2. canDeactivate() – This method is called by Durandal when you attempt to navigate away from the add movie page. If you return false then navigation is cancelled. 3. addMovie() – This method executes when the add movie form is submitted. This code adds the new movie to the movie repository. I really like the Durandal canDeactivate() method. In the code above, I use the canDeactivate() method to show a warning to a user if they navigate away from the add movie page – either by clicking the Cancel button or by hitting the browser back button – before submitting the add movie form: The view for the add movie page looks like this: <form data-bind="submit:addMovie"> <fieldset> <legend>Add Movie</legend> <div> <label> Title: <input data-bind="value:movieToAdd.title" required /> </label> </div> <div> <label> Director: <input data-bind="value:movieToAdd.director" required /> </label> </div> <div> <input type="submit" value="Add" /> <a href="#/movies/show">Cancel</a> </div> </fieldset> </form> I am using Knockout to bind the movieToAdd property from the view model to the INPUT elements of the HTML form. Notice that the FORM element includes a data-bind attribute which invokes the addMovie() method from the view model when the HTML form is submitted. Creating the Movies Details Page You navigate to the movies details Page by clicking the Details link which appears next to each movie in the movies show page: The Details links pass the movie ids to the details page: #/movies/details/0 #/movies/details/1 #/movies/details/2 Here’s what the view model for the movies details page looks like: define(function (require) { var router = require('durandal/plugins/router'); var moviesRepository = require("repositories/moviesRepository"); return { movieToShow: { title: ko.observable(), director: ko.observable() }, activate: function (context) { // Grab movie from repository var movie = moviesRepository.getMovie(context.id); // Add to view model this.movieToShow.title(movie.title); this.movieToShow.director(movie.director); } }; }); Notice that the view model activate() method accepts a parameter named context. You can take advantage of the context parameter to retrieve route parameters such as the movie Id. In the code above, the context.id property is used to retrieve the correct movie from the movie repository and the movie is assigned to a property named movieToShow exposed by the view model. The movie details view displays the movieToShow property by taking advantage of Knockout bindings: <div> <h2 data-bind="text:movieToShow.title"></h2> directed by <span data-bind="text:movieToShow.director"></span> </div> Summary The goal of this blog entry was to walkthrough building a simple Single Page App using Durandal and to get a feel for what it is like to use this library. I really like how Durandal stitches together Knockout, Sammy, and RequireJS and establishes patterns for using these libraries to build Single Page Apps. Having a standard pattern which developers on a team can use to build new pages is super valuable. Once you get the hang of it, using Durandal to create new virtual pages is dead simple. Just define a new route, view model, and view and you are done. I also appreciate the fact that Durandal did not attempt to re-invent the wheel and that Durandal leverages existing JavaScript libraries such as Knockout, RequireJS, and Sammy. These existing libraries are powerful libraries and I have already invested a considerable amount of time in learning how to use them. Durandal makes it easier to use these libraries together without losing any of their power. Durandal has some additional interesting features which I have not had a chance to play with yet. For example, you can use the RequireJS optimizer to combine and minify all of a Durandal app’s code. Also, Durandal supports a way to create custom widgets (client-side controls) by composing widgets from a controller and view. You can download the code for the Movies app by clicking the following link (this is a Visual Studio 2012 project): Durandal Movie App

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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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  • Identifier for the “completed” stage of a process: 0, 99, something else?

    - by Arnold Sakhnov
    Say, that you are handling a multi-step process (like a complex registration form, with a number of steps the user has go through in order). You need to be able to save the current state of the process (e.g. so the user can come back to that registration form later and continue form the step where they were left off). Obviously, you’ll probably want to give each “step” an identifier you can refer to: 1, 2, 3, 4, etc. You logic will check for this step_id (or whatever you call it) to render the appropriate data. The question: how would you identify the stage after the final step, like the completed registration state (say, that you have to give that last “step” its own id, that’s how your logic is structured). Would it be a 0, 999, a non-integer value, something else entirely?

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  • How to deploy Document Set using CAML in SharePoint2010 solution package

    - by ybbest
    In my last post, I showed you how to use Document Set using SharePoint UI in the browser. In this post, I’d like to show you how to create the same Document Set using CAML and SharePoint solution package. You can download the complete solution here. 1. Create the Application Number site column using the SharePoint empty element item template in VS2010 <?xml version="1.0" encoding="utf-8"?> <Elements xmlns="http://schemas.microsoft.com/sharepoint/"> <Field Type="Text" DisplayName="ApplicationNumber" Required="FALSE" EnforceUniqueValues="FALSE" Indexed="FALSE" MaxLength="255" Group="YBBEST" ID="{916bf3af-5ec1-4441-acd8-88ff62ab1b7e}" Name="ApplicationNumber" ></Field> </Elements> 2. Create the Loan Application Form and Loan Contract Form content types. <?xml version="1.0" encoding="utf-8"?> <Elements xmlns="http://schemas.microsoft.com/sharepoint/"> <!-- Parent ContentType: Document (0x0101) --> <ContentType ID="0x0101005dfbf820ce3c49f69c73a00e0e0e53f6" Name="Loan Contract Form" Group="YBBEST" Description="Loan Contract Form" Inherits="TRUE" Version="0"> <FieldRefs> <FieldRef ID="916bf3af-5ec1-4441-acd8-88ff62ab1b7e" Name="ApplicationNumber" DisplayName="ApplicationNumber" /> </FieldRefs> </ContentType> <!-- Parent ContentType: Document (0x0101) --> <ContentType ID="0x010100f3016e3d03454b93bc4d6ab63941c0d2" Name="Loan Application Form" Group="YBBEST" Description="Loan Application Form" Inherits="TRUE" Version="0"> <FieldRefs> <FieldRef ID="916bf3af-5ec1-4441-acd8-88ff62ab1b7e" Name="ApplicationNumber" DisplayName="ApplicationNumber" /> </FieldRefs> </ContentType> </Elements> 3. Create the Loan Application Document Set. 4. Create the Document Set Welcome Page using the SharePoint Module item template. Notes: 1.When creating document set content type , you need to set the  Inherits=”FALSE”  or remove the  Inherits=”TRUE” from the content type definition (default is  Inherits=”FALSE”) . This is the Document Set limitation in the current version of SharePoint2010. Because of this , you also need to manually  attach the event receiver and  Document Set welcome page to your custom Document Set Content Type. 2. Shared Fields are push down only: 3. Not available in SharePoint foundation (only SharePoint Server 2010). 4. You can’t have folders within document sets (you can place document sets in folders though). For a complete limitation and considerations , you can see the references for details. References: Document Set Limitations and Considerations in SharePoint 2010 1 Document Set Limitations and Considerations in SharePoint 2010 2 Document Sets planning (SharePoint Server 2010) Import Document Sets Issue http://msdn.microsoft.com/en-us/library/gg581064.aspx http://channel9.msdn.com/Events/TechEd/NorthAmerica/2010/OSP305 DocumentSet Class

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  • How to deploy Document Set using CAML in SharePoint2010 solution package

    - by ybbest
    In my last post, I showed you how to use Document Set using SharePoint UI in the browser. In this post, I’d like to show you how to create the same Document Set using CAML and SharePoint solution package. You can download the complete solution here. 1. Create the Application Number site column using the SharePoint empty element item template in VS2010 <?xml version="1.0" encoding="utf-8"?> <Elements xmlns="http://schemas.microsoft.com/sharepoint/"> <Field Type="Text" DisplayName="ApplicationNumber" Required="FALSE" EnforceUniqueValues="FALSE" Indexed="FALSE" MaxLength="255" Group="YBBEST" ID="{916bf3af-5ec1-4441-acd8-88ff62ab1b7e}" Name="ApplicationNumber" ></Field> </Elements> 2. Create the Loan Application Form and Loan Contract Form content types. <?xml version="1.0" encoding="utf-8"?> <Elements xmlns="http://schemas.microsoft.com/sharepoint/"> <!-- Parent ContentType: Document (0x0101) --> <ContentType ID="0x0101005dfbf820ce3c49f69c73a00e0e0e53f6" Name="Loan Contract Form" Group="YBBEST" Description="Loan Contract Form" Inherits="TRUE" Version="0"> <FieldRefs> <FieldRef ID="916bf3af-5ec1-4441-acd8-88ff62ab1b7e" Name="ApplicationNumber" DisplayName="ApplicationNumber" /> </FieldRefs> </ContentType> <!-- Parent ContentType: Document (0x0101) --> <ContentType ID="0x010100f3016e3d03454b93bc4d6ab63941c0d2" Name="Loan Application Form" Group="YBBEST" Description="Loan Application Form" Inherits="TRUE" Version="0"> <FieldRefs> <FieldRef ID="916bf3af-5ec1-4441-acd8-88ff62ab1b7e" Name="ApplicationNumber" DisplayName="ApplicationNumber" /> </FieldRefs> </ContentType> </Elements> 3. Create the Loan Application Document Set. 4. Create the Document Set Welcome Page using the SharePoint Module item template. Notes: 1.When creating document set content type , you need to set the  Inherits=”FALSE”  or remove the  Inherits=”TRUE” from the content type definition (default is  Inherits=”FALSE”) . This is the Document Set limitation in the current version of SharePoint2010. Because of this , you also need to manually  attach the event receiver and  Document Set welcome page to your custom Document Set Content Type. 2. Shared Fields are push down only: 3. Not available in SharePoint foundation (only SharePoint Server 2010). 4. You can’t have folders within document sets (you can place document sets in folders though). For a complete limitation and considerations , you can see the references for details. References: Document Set Limitations and Considerations in SharePoint 2010 1 Document Set Limitations and Considerations in SharePoint 2010 2 Document Sets planning (SharePoint Server 2010) Import Document Sets Issue http://msdn.microsoft.com/en-us/library/gg581064.aspx http://channel9.msdn.com/Events/TechEd/NorthAmerica/2010/OSP305 DocumentSet Class

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  • Task-It Webinar - Source Code

    Last week I presented a webinar called "Building a real-world application with RadControls for Silverlight 4". For those that didn't get to see the webinar, you can view it here: Building a read-world application with RadControls for Silverlight 4 Since the webinar I've received several requests asking if I could post the source code for the simple application I showed demonstrating some of the techniques used in the development of Task-It, such as MVVM, Commands and Internationalization. This source code is now available for downloadhere. After downloading the source: Extract it to the location of your choice on your hard-drive Open the solution Right-click ModuleProject.Web and selecte 'Set as StartUp Project'. Right-click ProjectTestPage.aspx and selected 'Set as Start Page' Create a database in SQL Server called WebinarProject. Navigate to the Database folder under the WebinarProject directory and run the .sql script against your WebinarProject database. The last two steps are necessary only for the Tasks page to work properly (using WCF RIA Services). Now some notes about each page: Code-behind This is not the way I recommend coding a line-of-business application in Silverlight, but simply wanted to show how the code-behind approach would look. Command This page introduces MVVM and Commands. You'll notice in the XAML that the Command property of theRadMenuItem and the Button are both bound to a SaveCommand. That comes from the view model. If you look in the code- behind of the user control you'll see that an instance of a CommandViewModel is instantiated and set as the DataContext of the UserControl.There is also a listener for the view model's SaveCompleted event. When this is fired, it tells the view (UserControl) to display the MessageBox. Internationalization This sample is similar to the previous one, but instead of using hard-coded strings in the UI, the strings are obtained via binding toview model properties. The view model gets the strings from the .resx files (Strings.resx or Strings.de.resx) under Assets/Resources. If you uncomment the call to ShowGerman() in App.xaml.cs's Application_Startup method and re-run the application, you will see the UI in German. Note that this code, which sets the CurrentCulture and CurrentUICulture on the current thread to "de" (German) is for testing purposes only. RadWindow Once again, very similar to the previous example.The difference is that we are now using a RadWindow to display the 'Saved' message instead of a MessageBox. The advantage here is that we do not have to hold on to a reference to the view model in our code behind so that we can get the 'Saved' message from it. The RadWindow's DataContext is now also bound to the view model, so within its XAML we can bind directly to properties in the view model. Much nicer, and cleaner. One other thing I introduced in this example is the use of spacer Rectangles. Rather than setting a width and/or height on the rectangles for spacing, I am now referencing a style in my ResourceDictionary called StandardSpacerStyle. I like doing this better than using margins or padding because now I have a reusable way to create space between elements, the Rectangle does not show (because I have not set its Fill color), and I can change my spacing throughout the user interface in one place if I'd like. Tasks This page is quite a bit different than the other four. It is a very simple, stripped-down version of the Tasks page in the Task-It application. The Tasks.xaml UserControl has a ContentControl, and the Content of that control is set based on whether we are looking at the list of tasks or editing a task. So it displays one of two child UserControls, which are called List and Details. List has the RadGridView, Details has the form. In the code-behind of the Tasks UserControl I am once again setting its DataContext to a view model class. The nice thing is, whichever child UserControl is being displayed (List or Details) inherits its DataContext from its parent control (Tasks), so I do not have to explicitly set it. The List UserControl simply displays a RadGridView whose ItemsSource is bound to a property in the view model called Tasks, and its SelectedItem property is bound to a property in the view model called SelectedItem. The SelectedItem binding must be TwoWay so that the view is notified when the SelectedItem changes in the view model, and the view model is notified when something changes in the view (like when a user changes the Name and/or DueDate in the form). You'll also notice that the form's TextBox and RadDatePicker are also TwoWay bound to the SelectedItem property in the view model. You can experiment with the binding by removing TwoWay and see how changes in the form do not show up in the RadGridView. So here we have an example of two different views (List and Details) that are both bound to the same view model...and actually, so is the Tasks UserControl, so it is really three views. WCF RIA Services By the way, I am using WCF RIA Services to retrieve data for the RadGridView and save the data when the user clicks the Save button in the form. I created a really simple ADO.NET Entity Data Model in WebinarProject.Web called DataModel.edmx. I also created a simple Domain Data Service called DataService that has methods for retrieving data, inserting, updating and deleting. However I am only using the retrieval and update methods in this sample. Note that I do not currently have any validation in place on the form, as I wanted to keep the sample as simple as possible. Wrap up Technically, I should move the calls to WCF RIA Services out of the view model and put them into a separate layer, but this works for now, and that is a topic for another day! Did you know that DotNetSlackers also publishes .net articles written by top known .net Authors? We already have over 80 articles in several categories including Silverlight. Take a look: here.

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  • Do backlinks to blocked content add value?

    - by David Fisher
    We've been debating the following SEO question at our office: If you block bot access to a page either via robots.txt or on-page noindex metadata, does that negate the value of any backlinks to that page? We have a client who wants to block some event booking form pages from being indexed as each booking form page has a unique URL parameter and the pages are "clogging up" the Google index; however lots of websites link to those booking form pages and we wouldn't want to lose the value of those links. Any opinions welcomed.

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  • Regarding Microsoft MVC framework and usage [closed]

    - by Thomas
    it will be better if some one tell me that what type of web application should develop using Microsoft MVC framework. i am familiar with web form but not familiar with MS MVC framework. i feel any type of web application can be developed with web form. i search google lot to know the specific reason for using MS MVC framework. i am keen interested to know when i should develop web apps using MS MVC framework and when i should use web form. i will be happy if some one discuss this issue in detail. thanks

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  • Ball bouncing at a certain angle and efficiency computations

    - by X Y
    I would like to make a pong game with a small twist (for now). Every time the ball bounces off one of the paddles i want it to be under a certain angle (between a min and a max). I simply can't wrap my head around how to actually do it (i have some thoughts and such but i simply cannot implement them properly - i feel i'm overcomplicating things). Here's an image with a small explanation . One other problem would be that the conditions for bouncing have to be different for every edge. For example, in the picture, on the two small horizontal edges i do not want a perfectly vertical bounce when in the middle of the edge but rather a constant angle (pi/4 maybe) in either direction depending on the collision point (before the middle of the edge, or after). All of my collisions are done with the Separating Axes Theorem (and seem to work fine). I'm looking for something efficient because i want to add a lot of things later on (maybe polygons with many edges and such). So i need to keep to a minimum the amount of checking done every frame. The collision algorithm begins testing whenever the bounding boxes of the paddle and the ball intersect. Is there something better to test for possible collisions every frame? (more efficient in the long run,with many more objects etc, not necessarily easy to code). I'm going to post the code for my game: Paddle Class public class Paddle : Microsoft.Xna.Framework.DrawableGameComponent { #region Private Members private SpriteBatch spriteBatch; private ContentManager contentManager; private bool keybEnabled; private bool isLeftPaddle; private Texture2D paddleSprite; private Vector2 paddlePosition; private float paddleSpeedY; private Vector2 paddleScale = new Vector2(1f, 1f); private const float DEFAULT_Y_SPEED = 150; private Vector2[] Normals2Edges; private Vector2[] Vertices = new Vector2[4]; private List<Vector2> lst = new List<Vector2>(); private Vector2 Edge; #endregion #region Properties public float Speed { get {return paddleSpeedY; } set { paddleSpeedY = value; } } public Vector2[] Normal2EdgesVector { get { NormalsToEdges(this.isLeftPaddle); return Normals2Edges; } } public Vector2[] VertexVector { get { return Vertices; } } public Vector2 Scale { get { return paddleScale; } set { paddleScale = value; NormalsToEdges(this.isLeftPaddle); } } public float X { get { return paddlePosition.X; } set { paddlePosition.X = value; } } public float Y { get { return paddlePosition.Y; } set { paddlePosition.Y = value; } } public float Width { get { return (Scale.X == 1f ? (float)paddleSprite.Width : paddleSprite.Width * Scale.X); } } public float Height { get { return ( Scale.Y==1f ? (float)paddleSprite.Height : paddleSprite.Height*Scale.Y ); } } public Texture2D GetSprite { get { return paddleSprite; } } public Rectangle Boundary { get { return new Rectangle((int)paddlePosition.X, (int)paddlePosition.Y, (int)this.Width, (int)this.Height); } } public bool KeyboardEnabled { get { return keybEnabled; } } #endregion private void NormalsToEdges(bool isLeftPaddle) { Normals2Edges = null; Edge = Vector2.Zero; lst.Clear(); for (int i = 0; i < Vertices.Length; i++) { Edge = Vertices[i + 1 == Vertices.Length ? 0 : i + 1] - Vertices[i]; if (Edge != Vector2.Zero) { Edge.Normalize(); //outer normal to edge !! (origin in top-left) lst.Add(new Vector2(Edge.Y, -Edge.X)); } } Normals2Edges = lst.ToArray(); } public float[] ProjectPaddle(Vector2 axis) { if (Vertices.Length == 0 || axis == Vector2.Zero) return (new float[2] { 0, 0 }); float min, max; min = Vector2.Dot(axis, Vertices[0]); max = min; for (int i = 1; i < Vertices.Length; i++) { float p = Vector2.Dot(axis, Vertices[i]); if (p < min) min = p; else if (p > max) max = p; } return (new float[2] { min, max }); } public Paddle(Game game, bool isLeftPaddle, bool enableKeyboard = true) : base(game) { contentManager = new ContentManager(game.Services); keybEnabled = enableKeyboard; this.isLeftPaddle = isLeftPaddle; } public void setPosition(Vector2 newPos) { X = newPos.X; Y = newPos.Y; } public override void Initialize() { base.Initialize(); this.Speed = DEFAULT_Y_SPEED; X = 0; Y = 0; NormalsToEdges(this.isLeftPaddle); } protected override void LoadContent() { spriteBatch = new SpriteBatch(GraphicsDevice); paddleSprite = contentManager.Load<Texture2D>(@"Content\pongBar"); } public override void Update(GameTime gameTime) { //vertices array Vertices[0] = this.paddlePosition; Vertices[1] = this.paddlePosition + new Vector2(this.Width, 0); Vertices[2] = this.paddlePosition + new Vector2(this.Width, this.Height); Vertices[3] = this.paddlePosition + new Vector2(0, this.Height); // Move paddle, but don't allow movement off the screen if (KeyboardEnabled) { float moveDistance = Speed * (float)gameTime.ElapsedGameTime.TotalSeconds; KeyboardState newKeyState = Keyboard.GetState(); if (newKeyState.IsKeyDown(Keys.Down) && Y + paddleSprite.Height + moveDistance <= Game.GraphicsDevice.Viewport.Height) { Y += moveDistance; } else if (newKeyState.IsKeyDown(Keys.Up) && Y - moveDistance >= 0) { Y -= moveDistance; } } else { if (this.Y + this.Height > this.GraphicsDevice.Viewport.Height) { this.Y = this.Game.GraphicsDevice.Viewport.Height - this.Height - 1; } } base.Update(gameTime); } public override void Draw(GameTime gameTime) { spriteBatch.Begin(SpriteSortMode.Texture,null); spriteBatch.Draw(paddleSprite, paddlePosition, null, Color.White, 0f, Vector2.Zero, Scale, SpriteEffects.None, 0); spriteBatch.End(); base.Draw(gameTime); } } Ball Class public class Ball : Microsoft.Xna.Framework.DrawableGameComponent { #region Private Members private SpriteBatch spriteBatch; private ContentManager contentManager; private const float DEFAULT_SPEED = 50; private float speedIncrement = 0; private Vector2 ballScale = new Vector2(1f, 1f); private const float INCREASE_SPEED = 50; private Texture2D ballSprite; //initial texture private Vector2 ballPosition; //position private Vector2 centerOfBall; //center coords private Vector2 ballSpeed = new Vector2(DEFAULT_SPEED, DEFAULT_SPEED); //speed #endregion #region Properties public float DEFAULTSPEED { get { return DEFAULT_SPEED; } } public Vector2 ballCenter { get { return centerOfBall; } } public Vector2 Scale { get { return ballScale; } set { ballScale = value; } } public float SpeedX { get { return ballSpeed.X; } set { ballSpeed.X = value; } } public float SpeedY { get { return ballSpeed.Y; } set { ballSpeed.Y = value; } } public float X { get { return ballPosition.X; } set { ballPosition.X = value; } } public float Y { get { return ballPosition.Y; } set { ballPosition.Y = value; } } public Texture2D GetSprite { get { return ballSprite; } } public float Width { get { return (Scale.X == 1f ? (float)ballSprite.Width : ballSprite.Width * Scale.X); } } public float Height { get { return (Scale.Y == 1f ? (float)ballSprite.Height : ballSprite.Height * Scale.Y); } } public float SpeedIncreaseIncrement { get { return speedIncrement; } set { speedIncrement = value; } } public Rectangle Boundary { get { return new Rectangle((int)ballPosition.X, (int)ballPosition.Y, (int)this.Width, (int)this.Height); } } #endregion public Ball(Game game) : base(game) { contentManager = new ContentManager(game.Services); } public void Reset() { ballSpeed.X = DEFAULT_SPEED; ballSpeed.Y = DEFAULT_SPEED; ballPosition.X = Game.GraphicsDevice.Viewport.Width / 2 - ballSprite.Width / 2; ballPosition.Y = Game.GraphicsDevice.Viewport.Height / 2 - ballSprite.Height / 2; } public void SpeedUp() { if (ballSpeed.Y < 0) ballSpeed.Y -= (INCREASE_SPEED + speedIncrement); else ballSpeed.Y += (INCREASE_SPEED + speedIncrement); if (ballSpeed.X < 0) ballSpeed.X -= (INCREASE_SPEED + speedIncrement); else ballSpeed.X += (INCREASE_SPEED + speedIncrement); } public float[] ProjectBall(Vector2 axis) { if (axis == Vector2.Zero) return (new float[2] { 0, 0 }); float min, max; min = Vector2.Dot(axis, this.ballCenter) - this.Width/2; //center - radius max = min + this.Width; //center + radius return (new float[2] { min, max }); } public void ChangeHorzDirection() { ballSpeed.X *= -1; } public void ChangeVertDirection() { ballSpeed.Y *= -1; } public override void Initialize() { base.Initialize(); ballPosition.X = Game.GraphicsDevice.Viewport.Width / 2 - ballSprite.Width / 2; ballPosition.Y = Game.GraphicsDevice.Viewport.Height / 2 - ballSprite.Height / 2; } protected override void LoadContent() { spriteBatch = new SpriteBatch(GraphicsDevice); ballSprite = contentManager.Load<Texture2D>(@"Content\ball"); } public override void Update(GameTime gameTime) { if (this.Y < 1 || this.Y > GraphicsDevice.Viewport.Height - this.Height - 1) this.ChangeVertDirection(); centerOfBall = new Vector2(ballPosition.X + this.Width / 2, ballPosition.Y + this.Height / 2); base.Update(gameTime); } public override void Draw(GameTime gameTime) { spriteBatch.Begin(); spriteBatch.Draw(ballSprite, ballPosition, null, Color.White, 0f, Vector2.Zero, Scale, SpriteEffects.None, 0); spriteBatch.End(); base.Draw(gameTime); } } Main game class public class gameStart : Microsoft.Xna.Framework.Game { GraphicsDeviceManager graphics; SpriteBatch spriteBatch; public gameStart() { graphics = new GraphicsDeviceManager(this); Content.RootDirectory = "Content"; this.Window.Title = "Pong game"; } protected override void Initialize() { ball = new Ball(this); paddleLeft = new Paddle(this,true,false); paddleRight = new Paddle(this,false,true); Components.Add(ball); Components.Add(paddleLeft); Components.Add(paddleRight); this.Window.AllowUserResizing = false; this.IsMouseVisible = true; this.IsFixedTimeStep = false; this.isColliding = false; base.Initialize(); } #region MyPrivateStuff private Ball ball; private Paddle paddleLeft, paddleRight; private int[] bit = { -1, 1 }; private Random rnd = new Random(); private int updates = 0; enum nrPaddle { None, Left, Right }; private nrPaddle PongBar = nrPaddle.None; private ArrayList Axes = new ArrayList(); private Vector2 MTV; //minimum translation vector private bool isColliding; private float overlap; //smallest distance after projections private Vector2 overlapAxis; //axis of overlap #endregion protected override void LoadContent() { spriteBatch = new SpriteBatch(GraphicsDevice); paddleLeft.setPosition(new Vector2(0, this.GraphicsDevice.Viewport.Height / 2 - paddleLeft.Height / 2)); paddleRight.setPosition(new Vector2(this.GraphicsDevice.Viewport.Width - paddleRight.Width, this.GraphicsDevice.Viewport.Height / 2 - paddleRight.Height / 2)); paddleLeft.Scale = new Vector2(1f, 2f); //scale left paddle } private bool ShapesIntersect(Paddle paddle, Ball ball) { overlap = 1000000f; //large value overlapAxis = Vector2.Zero; MTV = Vector2.Zero; foreach (Vector2 ax in Axes) { float[] pad = paddle.ProjectPaddle(ax); //pad0 = min, pad1 = max float[] circle = ball.ProjectBall(ax); //circle0 = min, circle1 = max if (pad[1] <= circle[0] || circle[1] <= pad[0]) { return false; } if (pad[1] - circle[0] < circle[1] - pad[0]) { if (Math.Abs(overlap) > Math.Abs(-pad[1] + circle[0])) { overlap = -pad[1] + circle[0]; overlapAxis = ax; } } else { if (Math.Abs(overlap) > Math.Abs(circle[1] - pad[0])) { overlap = circle[1] - pad[0]; overlapAxis = ax; } } } if (overlapAxis != Vector2.Zero) { MTV = overlapAxis * overlap; } return true; } protected override void Update(GameTime gameTime) { updates += 1; float ftime = 5 * (float)gameTime.ElapsedGameTime.TotalSeconds; if (updates == 1) { isColliding = false; int Xrnd = bit[Convert.ToInt32(rnd.Next(0, 2))]; int Yrnd = bit[Convert.ToInt32(rnd.Next(0, 2))]; ball.SpeedX = Xrnd * ball.SpeedX; ball.SpeedY = Yrnd * ball.SpeedY; ball.X += ftime * ball.SpeedX; ball.Y += ftime * ball.SpeedY; } else { updates = 100; ball.X += ftime * ball.SpeedX; ball.Y += ftime * ball.SpeedY; } //autorun :) paddleLeft.Y = ball.Y; //collision detection PongBar = nrPaddle.None; if (ball.Boundary.Intersects(paddleLeft.Boundary)) { PongBar = nrPaddle.Left; if (!isColliding) { Axes.Clear(); Axes.AddRange(paddleLeft.Normal2EdgesVector); //axis from nearest vertex to ball's center Axes.Add(FORMULAS.NormAxisFromCircle2ClosestVertex(paddleLeft.VertexVector, ball.ballCenter)); } } else if (ball.Boundary.Intersects(paddleRight.Boundary)) { PongBar = nrPaddle.Right; if (!isColliding) { Axes.Clear(); Axes.AddRange(paddleRight.Normal2EdgesVector); //axis from nearest vertex to ball's center Axes.Add(FORMULAS.NormAxisFromCircle2ClosestVertex(paddleRight.VertexVector, ball.ballCenter)); } } if (PongBar != nrPaddle.None && !isColliding) switch (PongBar) { case nrPaddle.Left: if (ShapesIntersect(paddleLeft, ball)) { isColliding = true; if (MTV != Vector2.Zero) ball.X += MTV.X; ball.Y += MTV.Y; ball.ChangeHorzDirection(); } break; case nrPaddle.Right: if (ShapesIntersect(paddleRight, ball)) { isColliding = true; if (MTV != Vector2.Zero) ball.X += MTV.X; ball.Y += MTV.Y; ball.ChangeHorzDirection(); } break; default: break; } if (!ShapesIntersect(paddleRight, ball) && !ShapesIntersect(paddleLeft, ball)) isColliding = false; ball.X += ftime * ball.SpeedX; ball.Y += ftime * ball.SpeedY; //check ball movement if (ball.X > paddleRight.X + paddleRight.Width + 2) { //IncreaseScore(Left); ball.Reset(); updates = 0; return; } else if (ball.X < paddleLeft.X - 2) { //IncreaseScore(Right); ball.Reset(); updates = 0; return; } base.Update(gameTime); } protected override void Draw(GameTime gameTime) { GraphicsDevice.Clear(Color.Aquamarine); spriteBatch.Begin(SpriteSortMode.BackToFront, BlendState.AlphaBlend); spriteBatch.End(); base.Draw(gameTime); } } And one method i've used: public static Vector2 NormAxisFromCircle2ClosestVertex(Vector2[] vertices, Vector2 circle) { Vector2 temp = Vector2.Zero; if (vertices.Length > 0) { float dist = (circle.X - vertices[0].X) * (circle.X - vertices[0].X) + (circle.Y - vertices[0].Y) * (circle.Y - vertices[0].Y); for (int i = 1; i < vertices.Length;i++) { if (dist > (circle.X - vertices[i].X) * (circle.X - vertices[i].X) + (circle.Y - vertices[i].Y) * (circle.Y - vertices[i].Y)) { temp = vertices[i]; //memorize the closest vertex dist = (circle.X - vertices[i].X) * (circle.X - vertices[i].X) + (circle.Y - vertices[i].Y) * (circle.Y - vertices[i].Y); } } temp = circle - temp; temp.Normalize(); } return temp; } Thanks in advance for any tips on the 4 issues. EDIT1: Something isn't working properly. The collision axis doesn't come out right and the interpolation also seems to have no effect. I've changed the code a bit: private bool ShapesIntersect(Paddle paddle, Ball ball) { overlap = 1000000f; //large value overlapAxis = Vector2.Zero; MTV = Vector2.Zero; foreach (Vector2 ax in Axes) { float[] pad = paddle.ProjectPaddle(ax); //pad0 = min, pad1 = max float[] circle = ball.ProjectBall(ax); //circle0 = min, circle1 = max if (pad[1] < circle[0] || circle[1] < pad[0]) { return false; } if (Math.Abs(pad[1] - circle[0]) < Math.Abs(circle[1] - pad[0])) { if (Math.Abs(overlap) > Math.Abs(-pad[1] + circle[0])) { overlap = -pad[1] + circle[0]; overlapAxis = ax * (-1); } //to get the proper axis } else { if (Math.Abs(overlap) > Math.Abs(circle[1] - pad[0])) { overlap = circle[1] - pad[0]; overlapAxis = ax; } } } if (overlapAxis != Vector2.Zero) { MTV = overlapAxis * Math.Abs(overlap); } return true; } And part of the Update method: if (ShapesIntersect(paddleRight, ball)) { isColliding = true; if (MTV != Vector2.Zero) { ball.X += MTV.X; ball.Y += MTV.Y; } //test if (overlapAxis.X == 0) //collision with horizontal edge { } else if (overlapAxis.Y == 0) //collision with vertical edge { float factor = Math.Abs(ball.ballCenter.Y - paddleRight.Y) / paddleRight.Height; if (factor > 1) factor = 1f; if (overlapAxis.X < 0) //left edge? ball.Speed = ball.DEFAULTSPEED * Vector2.Normalize(Vector2.Reflect(ball.Speed, (Vector2.Lerp(new Vector2(-1, -3), new Vector2(-1, 3), factor)))); else //right edge? ball.Speed = ball.DEFAULTSPEED * Vector2.Normalize(Vector2.Reflect(ball.Speed, (Vector2.Lerp(new Vector2(1, -3), new Vector2(1, 3), factor)))); } else //vertex collision??? { ball.Speed = -ball.Speed; } } What seems to happen is that "overlapAxis" doesn't always return the right one. 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    - by ConcernedOfTunbridgeWells
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  • Generic socket 940 CPU fan for HP XW9300 interchangeable with HP part number 411454-001

    - by ConcernedOfTunbridgeWells
    Hi, I'm trying to find a generic Socket 940 CPU fan that will fit the air duct in an XW9300. Note that two different CPU fan mounting schemes have been used on this machine. One has two grommets in the motherboard that the CPU fan screws into and the other has a plastic collar and base plate. The form factor I'm looking for is the former (see the picture below). Two HP part numbers for fans in this form factor are 411454-001 (shown below) and 416055-001. Note that the dimensions are important as the machine has an air duct that fits over the fan. Can anyone tell me the manufacturer and model of an equivalent generic part? Better yet, do you know somewhere (preferrably in the UK) from which such an item can be obtained?

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  • Why would a PCI scan fail because of components that are not even installed?

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  • New Technical Articles on SOA, Mobile, IDM, WebLogic, Coherence

    - by OTN ArchBeat
    For your reading pleasure... In October the following items of techie goodness from members of the architect community were added to the ever-growing library of OTN technical articles. SOA in Real Life: Mobile Solutions by Jürgen Kress, Berthold Maier, Hajo Normann, Danilo Schmeidel, Guido Schmutz, Bernd Trops, Clemens Utschig-Utschig, Torsten Winterberg Consumers are no longer content to be chained to a desktop or laptop computer. This article, teh ninth chapter in the Industrial SOA series, describes ways companies can take SOA to go. [More SOA Articles] SOA and User Interfaces by Juergen Kress, Hajo Normann, Danilo Schmiedel, Guido Schmutz, Clemens Utschig-Utschig, Torsten Winterberg, and Bernd Trops The eighth chapter in the Industrial SOA series addresses the challenges of developing user interfaces in a service oriented architecture, and describes a practical application of Thomas Erl's UI Mediator pattern.[More SOA Articles] Enterprise Grade Deployment Considerations for Oracle Identity Manager AD Connector by Firdaus Fraz Oracle Fusion Middleware solution architect Firdaus Fraz illustrates provides best practice recommendations for setting up an enterprise deployment environment for the OIM connector for Microsoft Active Directory. [More Identity Management Articles] Coherence*Web: Sharing an httpSession Among Applications in Different Oracle WebLogic Clusters by Jordi Villena SOA solution architect Jordi Villena shows how easy it is to extend Coherence*Web to enable session sharing. [More SOA Articles] Multi-Factor Authentication in Oracle WebLogic by Shailesh K. Mishra Using multi-factor authentication to protect web applications deployed on Oracle WebLogic.[More Identity Management Articles] You'll find many more articles on many more topics here.

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  • Numerous Unexpected Obstacles Ruining any Project Plans

    - by Libor
    I am working as software developer and struggling with this problem time and time again for almost thirteen years. There seems not to be any way out of the following problem. And it happens with small projects as well. For example, I plan to write an extension for Microsoft Visual Studio. I dowload learning materials, get some book on the topic and allocate time for learning and development. However, during the development, many seemingly trivial problems arise, for example: Why the script refuses to delete the file? Why Visual Studio does not register the extension? (after two days) OK, it registers it, but now it got broken. How to fix it? each of these "small" obstacles usually take 1-5 days to resolve and the project finally consumes several times more man-hours than planned. Maybe it happens only because I am working on Microsoft platform and many of their Frameworks and architectures are bit confusing and badly documented. I would like to have most problems resolved by finding answer in a book or official documentation (MSDN), but the only answer I usually find is on some weird forum or personal blog googled after desperately searching for any relevant information on the topic. Do you have the same struggles? Do you have techniques on how to prevent these problems? I was thinking of simply multiplying projected time for a given project by some factor, but this does not help. Some projects get done briskly and some take months and the guiding factor here are these small "glitches" which take programmers whole weeks to resolve. I have to admit that lots of these obstacles demoralizes me and drains me of focus and joy of work (who likes to get back to work when he have to resolve some stupid registry problem or weird framework bug instead of doing creative work?) After the project is finally done, I am feeling like dying from thousand cuts.

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