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  • MATLAB: How do I get 3D coordiantes from a user-click?

    - by Tim
    I'm using Matlab to create a small chess game for one of my courses this semester. The thing I'm having trouble with is having the user be able to select one of the chess pieces. To simplify things, I'm making it so that the user selects a piece by clicking on the square that the chess piece resides on rather than clicking the piece itself (which I assume would be much more difficult). I know how to get the x and y coordinates of the view-port, but how do I transform these coordinates into 3-space coordinates? I know that there are multiple x,y,z coordinates associated with each view-port coordinate, but I'm only interested in the x,y,z coordinate where z = 0 (since the board itself is in the x,y plane that intersects the z axis where z = 0). Thanks!

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  • Requiring clients to solve computational puzzles...

    - by acidzombie24
    Not that I need it, but it was interesting to hear someone speak about their server and protecting it from DOS attack by having a puzzle that the client must solve before the server will do anything (it doesnt do allocations or make a session unless solved). The person also said puzzles can be made to take a quick amount of time or long. And they are easy to check for correct solutions but difficult to solve. What are these puzzles? I never heard of one. Can someone give an example (or a link)?

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  • Reading in MIPS external file so another file can use it?

    - by SkyWookie
    Hey all, I'm working on this final thing for my MIPS project and it's deceptively easy. I need to get a procedure (called feed) and let its main driver program use it by reading it in. I know that I'm supposed to use the call code 14 and .globl sym (I think) in order to feed it into the file and have it read it. I just need a basic tutorial or something, as I CANNOT find it on the Internet or in my book (just lists the call code, real helpful). Here's what I know: I need to use read, but I also need a file descriptor (don't know where to get it). I need to put the buffer in $a1 and the length in $a2. Well, that's about it. If there's any decent tutorial you could whip up or if there is one online that I don't see let me know please :). I just need a push in the right direction, I'm sure it can't be too difficult, just can't find any info on it!

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  • How can I get a set of radio buttons to accept NULL (nothing checked)?

    - by Ethan
    I'm working on a Rails application where I have some a set of two radio buttons where users can click "yes" or "no". The MySQL DB column created by the ActiveRecord migration is a tinyint. If the user doesn't click either radio button I want MySQL to store NULL. (The column allows NULL.) And when they come back to edit the data, neither button should be checked. What's happening is that ActiveRecord is storing 0 and then when I come back the "No" button is checked. Rails 2.3.5 Form code (I'm using Haml): = f.radio_button( :model_attribute, true ) Yes = f.radio_button( :model_attribute, false ) No (In retrospect it probably would have been better to use a single checkbox, but it would be difficult to change that now.)

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  • [C++] which is better, throw an exception or return nonzero value?

    - by xis19
    While you are doing C++ programming, you have two choices of reporting an error. I suppose many teachers would suggest you throw an exception, which is derived from std::exception. Another way, which might be more "C" style, is to return a non-zero value, as zero is "ERROR_SUCCESS". Definitively, return an exception can provide much more information of the error and recovery; while the code will bloat a little bit, and making exception-safe in your mind is a little difficult for me, at least. Other way like returning something else, will make reporting an error much easier; the defect is that managing recovery will be a possibly big problem. So folks, as good programmers, which would be your preference, not considering your boss' opinion? For me, I would like to return some nonzero values.

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  • Entity Framework Security

    - by NYSystemsAnalyst
    In my organization, we are just beginning to use the Entity Framework for some applications. In the past, we have pushed developers to utilize stored procedures for all database access. In addition to helping with SQL injection, we tried to grant logins access to stored procedures only to keep security relatively tight. Although inserting, updating, and deleting are easily done through stored procedures in the EF, it appears to be difficult to use stored procedures to query data with EF. However, using LINQ or Entity SQL and allowing EF to create the queries means giving a user read access to the entire database. How have others handled this dilemma?

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  • is it possible to create a multi-project template that references n number of existing projects and

    - by jcollum
    The situation: I need to create about 40+ solutions that all reference 3 projects and have one project that is unique to each one. I'd like to create a multi-project template that does this, but from what I've read it looks like it's very difficult or impossible (related SO question, but doesn't answer). I want my solution to look like this (names changed of course): These three are used by all solutions created under this "family": MyCompany.Extensions MyCompany.MyProject.Tests.Shared MyCompany.MyProject.Scripts This one is the one that makes the solution unique, 123, 124, 125 etc: MyCompany.MyProject.Tests.Unit123 Is it possible to set up a multi-project template that will generate this structure? References: MSDN Create Multi Project Templates

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  • Language D compared to C++?

    - by Henrik
    Anyone here with experience of the language D? I was just reading through its presentation at http://www.d-programming-language.org/ and at Wikipedia and it seems like a good (better) alternative to C++. With good/better I mean that it seem simpler yet it has all the good stuff within C/C++. But without some of the difficulties that make C++ more difficult to learn and use in a good and efficient way. So anyone with comments/experience with the language D? Performance?

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  • Would you tell your prospective boss your SO username?

    - by Sebi
    Today I met a friend who is also using stackoverflow. He had a job interview today at a small business and during the interview, the prospective boss asked him how he assures that he's alawys up-to-date concerning technical questions and what he's doing to seek for a solution for a problem he can't solve by its own. Besides some magazines, journals, books and blogs my friend also mentioned stackoverflow. The prospective boss seems very interested about that and asked him if he could tell him his username. It appears that was the most difficult during the whole interview ;) Would you tell your prospective boss your username? An the pro side one can mention that the boss sees that you're very involved in your business and community but on the other hand it is a really private thing and you cant post anymore in thread like "what was the worst working environment?" My friend circumnaviagted this question by a rather lame answer (more or less: i use autologin, thats why i have to check the username later at home, ill maybe send you an email)

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  • The pImpl idiom and Testability

    - by Rimo
    The pImpl idiom in c++ aims to hide the implementation details (=private members) of a class from the users of that class. However it also hides some of the dependencies of that class which is usually regarded bad from a testing point of view. For example if class A hides its implementation details in Class AImpl which is only accessible from A.cpp and AImpl depends on a lot of other classes, it becomes very difficult to unit test class A since the testing framework has no access to the methods of AImpl and also no way to inject dependency into AImpl. This has been a problem for me lately and I am beginning to think that the pImpl idiom and writing testable code don't mix well. Has anyone come across this problem before? and have you found a solution?

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  • number of methods in an interface.

    - by Jeow
    I know this might seem a controversial question but it really is not meant to be. is there an optimal number of methods in an interface. For example, I personally hate an interface with 20 methods. It is just difficult to implement. The contract seems to hard to maintain. Similarly if the number of methods is just 1. It makes me wonder if it is really a good abstraction. Any thoughts ?

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  • Elegant ways of displaying a GridView with lots of columns (ASP.NET)

    - by Chris
    Hi, just a general design question that I'd like to hear some of your opinions on. I am designing a system for a client, and I'm using GridView' a lot. They need a lot of columns to be displayed in some of these, and I've had to resort to using a panel with a horizontal scrollbar. This presents some issues - keeping track of which row is which is difficult, even with alternating row colours, and it's generally pretty ugly. How have you dealt with these issues before? Are there any sort of AJAX controls that could help, so some data could be only displayed on hover or such? Or any other general ideas.

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  • Possible to use Javascript to access the client side's network(knowingly)

    - by Earlz
    I recently found an exploit in my router to basically give me root access. The catch? There is a nonce hidden form value that is randomly generated and must be sent in for it to work that makes it difficult to do "easily" So basically I'm wanting to do something like this in javascript: get http://192.168.1.254/blah use a regex or similar to extract the nonce value put the nonce value into a hidden field in the current page submit the form by POST to http://192.168.1.254/blah complete with the nonce value and other form values I want to send in. Is this at all possible using only HTML and Javascript? I'm open to things like "must save HTML file locally and then open", which I'm thinking is one way around the cross domain policy. But anyway, is this at all possible? I'm hoping for this to be able to run from at least Firefox and Chrome. The audience for this is those with some technical know how.

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  • C#.Net window application EXE and SQL SERVER 2000 Database at Client Machine

    - by user1397931
    Friends I have install a .net window application exe at client machine and its database in sql server 2000. For Exe I install .net framework and other support software and for DB i install sql server 2000 and Create Database over there and connect it. Working Properly But now client change Xp to window7. I search for installation of SQL Server 2000 , but its not working over there. So what i did, i send the MDF file of database with exe application and make connection string and its also working. Now i change something in DB , and trying to update .mdf file but its not reflecting the new one mdf its getting the old one. i am Stuck...... am i did any wrong ? because its difficult for me to fix. OR i want to know what is the efficient way of use of SQL Server 2000 database on window7 or any else solution is there? Please help me...

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  • What is the purpose of @ as part of a member name in C#?

    - by thelaughingdm
    As you can imagine, Googling or Binging for any phrase containing an '@' is difficult. In creating a new web service, one of the members of the imported C# proxy class is prefixed with the @. For example: plan.@event = new Insurance.Event(); I assume that it is Visual Studio's way resolving potential conflicts with reserved words because 'event' is a reserved word. Changing the property in the web service interface to something other than 'event' (i.e. 'healthevent') removes the @ from the property. Is this a correct assumption?

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  • Way to store dates with missing days/months in mysql (php)

    - by Paul M
    I want to store dates in mysql so I set the table to be of type 'Date', which is fine but mysql requires that the full date is provided YYYY-MM-DD. However some of my data does not include day and some is missing the month. Now I could just use a varchar(10) field, but then its difficult to run date based queries on the data. Is there another date format which is not as strong and would allow me to use ?? or 00 where the day/month is not known?

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  • How can I make the small icon(16x16)?

    - by Cora
    Hi All, I found it difficult to make small icons look clear and clean. For instance, I made the 16x16 size icons, they looked ok in PS or AI, but after saved them as some other image types, they are not that clear at all. Is that because i used wrong color or wrong tools? I wonder if there are some special tools for making extremely small icons. So any options? How i can make them look more clear and clean? Thanks a lot!

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  • (Python) Extracting Text from Source Code?

    - by zhuyxn
    Currently have a large webpage whose source code is ~200,000 lines of almost all (if not all) HTML. More specifically, it is a webpage whose content is a few thousand blocks of paragraphs separated by line breaks (though a line break does not specifically mean there is a separation in content) My main objective is to extract text from the source code as if I were copying/pasting the webpage into a text editor. There is another parsing function I would like to use, which originally took in copied/pasted text rather than the source code. To do this, I'm currently using urllib2, and calling .get_text() in Beautiful Soup. The problem is, Beautiful Soup is leaving tremendous amounts of white space in my code, and it is difficult to pass the result into the second "text" parser. I have done quite a bit of research on parsing HTMLs, but I'm frankly not sure how to solve this problem easily. Furthermore, I'm a bit confused on how to use imports like lxml to extract text as if I were to simply copy and paste?

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  • JQuery or Javascript solution for selecting default value in drop down

    - by user1446843
    I have a calender list in a webpart page, this webpart page has a version number in it's title e.g. "WebPart 1.62". What I need to do is when a New item is created in the calender list on a webpart page, the New Item form has a dropdown menu 'SystemID' which gets it's values from the title column of a 'Systems' list, which is pre-populated with all versions of webpart forms. This dropdown menu 'SystemID' should select the version of the webpart page it is in as the default value. I need a JQuery solution for this, or even Javascript. I am finding it difficult as I am new to both JQuery and Sharepoint. I am using SP2007. I'll appreciate any guidance in solving this. At the moment the Create New Item form of the Calender list has the 'SystemID' drop down list pre-populated with the versions from the Systems list. If anyhthing is unclear pls let me know and I'll explain in more detail.

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  • How to make my JavaScript code unusable by anyone else? [closed]

    - by egasimus
    Heh, that's something that many plugin authors do without needing help, isn't it? :) Here's the rub -- I'm coding a jQuery plugin which I have the intent to sell. I want to provide a live demo of it; of course, I don't want anyone just using the demo code. I know it's dumb, and it certainly doesn't bring any good karma, but what are some naughty things I can do in the demo script that would make life reasonably difficult for anyone trying to use it? Setting undefined = true comes to mind, as well as overriding jQuery methods. Any suggestions beyond that?

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  • Debug Mode for CodeIgniter?

    - by user350814
    Does CodeIgniter provide a Debug Mode, for example, when accessing an Invalid URL? Ruby on Rails does show debugging Messages when a incorrect URL has been given, and the controller is unable to resolve it using the routes map. How would I enable such debugging messages in CodeIgniter? The profiler ... $this->output->enable_profiler(TRUE); ... only affects single classes, but not all routes. So debugging without an actual debugger mode is a little... difficult. :-)

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  • A puzzle coded in ASCII [closed]

    - by user1905398
    I'm asking this question again because it is valid: "How do I convert this: M D Y z M D Y w M D Y z M D Y x M D Y z M D Y w M D Y z M D Y w M D Y z M D Y w M D Y z M D Y x M D Y z M D Y x M D Y z M D Y w into a letter? I have 272 constructed just like this one that I need to convert to form the message in a mystery I'm trying to solve. Thanks!" It is very difficult to include all 272 strings with each one having 16 sets of 4! There wouldn't be enough room in this post for that, so I just put the first of the 272 strings. To hopefully clarify, this is a puzzle. The puzzler put his 272 word message in ASCII. Since there is no online converter, I put the question out hoping to get some help.

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  • Integrating JavaScript Unit Tests with Visual Studio

    - by Stephen Walther
    Modern ASP.NET web applications take full advantage of client-side JavaScript to provide better interactivity and responsiveness. If you are building an ASP.NET application in the right way, you quickly end up with lots and lots of JavaScript code. When writing server code, you should be writing unit tests. One big advantage of unit tests is that they provide you with a safety net that enable you to safely modify your existing code – for example, fix bugs, add new features, and make performance enhancements -- without breaking your existing code. Every time you modify your code, you can execute your unit tests to verify that you have not broken anything. For the same reason that you should write unit tests for your server code, you should write unit tests for your client code. JavaScript is just as susceptible to bugs as C#. There is no shortage of unit testing frameworks for JavaScript. Each of the major JavaScript libraries has its own unit testing framework. For example, jQuery has QUnit, Prototype has UnitTestJS, YUI has YUI Test, and Dojo has Dojo Objective Harness (DOH). The challenge is integrating a JavaScript unit testing framework with Visual Studio. Visual Studio and Visual Studio ALM provide fantastic support for server-side unit tests. You can easily view the results of running your unit tests in the Visual Studio Test Results window. You can set up a check-in policy which requires that all unit tests pass before your source code can be committed to the source code repository. In addition, you can set up Team Build to execute your unit tests automatically. Unfortunately, Visual Studio does not provide “out-of-the-box” support for JavaScript unit tests. MS Test, the unit testing framework included in Visual Studio, does not support JavaScript unit tests. As soon as you leave the server world, you are left on your own. The goal of this blog entry is to describe one approach to integrating JavaScript unit tests with MS Test so that you can execute your JavaScript unit tests side-by-side with your C# unit tests. The goal is to enable you to execute JavaScript unit tests in exactly the same way as server-side unit tests. You can download the source code described by this project by scrolling to the end of this blog entry. Rejected Approach: Browser Launchers One popular approach to executing JavaScript unit tests is to use a browser as a test-driver. When you use a browser as a test-driver, you open up a browser window to execute and view the results of executing your JavaScript unit tests. For example, QUnit – the unit testing framework for jQuery – takes this approach. The following HTML page illustrates how you can use QUnit to create a unit test for a function named addNumbers(). <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> <html> <head> <title>Using QUnit</title> <link rel="stylesheet" href="http://github.com/jquery/qunit/raw/master/qunit/qunit.css" type="text/css" /> </head> <body> <h1 id="qunit-header">QUnit example</h1> <h2 id="qunit-banner"></h2> <div id="qunit-testrunner-toolbar"></div> <h2 id="qunit-userAgent"></h2> <ol id="qunit-tests"></ol> <div id="qunit-fixture">test markup, will be hidden</div> <script type="text/javascript" src="http://code.jquery.com/jquery-latest.js"></script> <script type="text/javascript" src="http://github.com/jquery/qunit/raw/master/qunit/qunit.js"></script> <script type="text/javascript"> // The function to test function addNumbers(a, b) { return a+b; } // The unit test test("Test of addNumbers", function () { equals(4, addNumbers(1,3), "1+3 should be 4"); }); </script> </body> </html> This test verifies that calling addNumbers(1,3) returns the expected value 4. When you open this page in a browser, you can see that this test does, in fact, pass. The idea is that you can quickly refresh this QUnit HTML JavaScript test driver page in your browser whenever you modify your JavaScript code. In other words, you can keep a browser window open and keep refreshing it over and over while you are developing your application. That way, you can know very quickly whenever you have broken your JavaScript code. While easy to setup, there are several big disadvantages to this approach to executing JavaScript unit tests: You must view your JavaScript unit test results in a different location than your server unit test results. The JavaScript unit test results appear in the browser and the server unit test results appear in the Visual Studio Test Results window. Because all of your unit test results don’t appear in a single location, you are more likely to introduce bugs into your code without noticing it. Because your unit tests are not integrated with Visual Studio – in particular, MS Test -- you cannot easily include your JavaScript unit tests when setting up check-in policies or when performing automated builds with Team Build. A more sophisticated approach to using a browser as a test-driver is to automate the web browser. Instead of launching the browser and loading the test code yourself, you use a framework to automate this process. There are several different testing frameworks that support this approach: · Selenium – Selenium is a very powerful framework for automating browser tests. You can create your tests by recording a Firefox session or by writing the test driver code in server code such as C#. You can learn more about Selenium at http://seleniumhq.org/. LTAF – The ASP.NET team uses the Lightweight Test Automation Framework to test JavaScript code in the ASP.NET framework. You can learn more about LTAF by visiting the project home at CodePlex: http://aspnet.codeplex.com/releases/view/35501 jsTestDriver – This framework uses Java to automate the browser. jsTestDriver creates a server which can be used to automate multiple browsers simultaneously. This project is located at http://code.google.com/p/js-test-driver/ TestSwam – This framework, created by John Resig, uses PHP to automate the browser. Like jsTestDriver, the framework creates a test server. You can open multiple browsers that are automated by the test server. Learn more about TestSwarm by visiting the following address: https://github.com/jeresig/testswarm/wiki Yeti – This is the framework introduced by Yahoo for automating browser tests. Yeti uses server-side JavaScript and depends on Node.js. Learn more about Yeti at http://www.yuiblog.com/blog/2010/08/25/introducing-yeti-the-yui-easy-testing-interface/ All of these frameworks are great for integration tests – however, they are not the best frameworks to use for unit tests. In one way or another, all of these frameworks depend on executing tests within the context of a “living and breathing” browser. If you create an ASP.NET Unit Test then Visual Studio will launch a web server before executing the unit test. Why is launching a web server so bad? It is not the worst thing in the world. However, it does introduce dependencies that prevent your code from being tested in isolation. One of the defining features of a unit test -- versus an integration test – is that a unit test tests code in isolation. Another problem with launching a web server when performing unit tests is that launching a web server can be slow. If you cannot execute your unit tests quickly, you are less likely to execute your unit tests each and every time you make a code change. You are much more likely to fall into the pit of failure. Launching a browser when performing a JavaScript unit test has all of the same disadvantages as launching a web server when performing an ASP.NET unit test. Instead of testing a unit of JavaScript code in isolation, you are testing JavaScript code within the context of a particular browser. Using the frameworks listed above for integration tests makes perfect sense. However, I want to consider a different approach for creating unit tests for JavaScript code. Using Server-Side JavaScript for JavaScript Unit Tests A completely different approach to executing JavaScript unit tests is to perform the tests outside of any browser. If you really want to test JavaScript then you should test JavaScript and leave the browser out of the testing process. There are several ways that you can execute JavaScript on the server outside the context of any browser: Rhino – Rhino is an implementation of JavaScript written in Java. The Rhino project is maintained by the Mozilla project. Learn more about Rhino at http://www.mozilla.org/rhino/ V8 – V8 is the open-source Google JavaScript engine written in C++. This is the JavaScript engine used by the Chrome web browser. You can download V8 and embed it in your project by visiting http://code.google.com/p/v8/ JScript – JScript is the JavaScript Script Engine used by Internet Explorer (up to but not including Internet Explorer 9), Windows Script Host, and Active Server Pages. Internet Explorer is still the most popular web browser. Therefore, I decided to focus on using the JScript Script Engine to execute JavaScript unit tests. Using the Microsoft Script Control There are two basic ways that you can pass JavaScript to the JScript Script Engine and execute the code: use the Microsoft Windows Script Interfaces or use the Microsoft Script Control. The difficult and proper way to execute JavaScript using the JScript Script Engine is to use the Microsoft Windows Script Interfaces. You can learn more about the Script Interfaces by visiting http://msdn.microsoft.com/en-us/library/t9d4xf28(VS.85).aspx The main disadvantage of using the Script Interfaces is that they are difficult to use from .NET. There is a great series of articles on using the Script Interfaces from C# located at http://www.drdobbs.com/184406028. I picked the easier alternative and used the Microsoft Script Control. The Microsoft Script Control is an ActiveX control that provides a higher level abstraction over the Window Script Interfaces. You can download the Microsoft Script Control from here: http://www.microsoft.com/downloads/en/details.aspx?FamilyID=d7e31492-2595-49e6-8c02-1426fec693ac After you download the Microsoft Script Control, you need to add a reference to it to your project. Select the Visual Studio menu option Project, Add Reference to open the Add Reference dialog. Select the COM tab and add the Microsoft Script Control 1.0. Using the Script Control is easy. You call the Script Control AddCode() method to add JavaScript code to the Script Engine. Next, you call the Script Control Run() method to run a particular JavaScript function. The reference documentation for the Microsoft Script Control is located at the MSDN website: http://msdn.microsoft.com/en-us/library/aa227633%28v=vs.60%29.aspx Creating the JavaScript Code to Test To keep things simple, let’s imagine that you want to test the following JavaScript function named addNumbers() which simply adds two numbers together: MvcApplication1\Scripts\Math.js function addNumbers(a, b) { return 5; } Notice that the addNumbers() method always returns the value 5. Right-now, it will not pass a good unit test. Create this file and save it in your project with the name Math.js in your MVC project’s Scripts folder (Save the file in your actual MVC application and not your MVC test application). Creating the JavaScript Test Helper Class To make it easier to use the Microsoft Script Control in unit tests, we can create a helper class. This class contains two methods: LoadFile() – Loads a JavaScript file. Use this method to load the JavaScript file being tested or the JavaScript file containing the unit tests. ExecuteTest() – Executes the JavaScript code. Use this method to execute a JavaScript unit test. Here’s the code for the JavaScriptTestHelper class: JavaScriptTestHelper.cs   using System; using System.IO; using Microsoft.VisualStudio.TestTools.UnitTesting; using MSScriptControl; namespace MvcApplication1.Tests { public class JavaScriptTestHelper : IDisposable { private ScriptControl _sc; private TestContext _context; /// <summary> /// You need to use this helper with Unit Tests and not /// Basic Unit Tests because you need a Test Context /// </summary> /// <param name="testContext">Unit Test Test Context</param> public JavaScriptTestHelper(TestContext testContext) { if (testContext == null) { throw new ArgumentNullException("TestContext"); } _context = testContext; _sc = new ScriptControl(); _sc.Language = "JScript"; _sc.AllowUI = false; } /// <summary> /// Load the contents of a JavaScript file into the /// Script Engine. /// </summary> /// <param name="path">Path to JavaScript file</param> public void LoadFile(string path) { var fileContents = File.ReadAllText(path); _sc.AddCode(fileContents); } /// <summary> /// Pass the path of the test that you want to execute. /// </summary> /// <param name="testMethodName">JavaScript function name</param> public void ExecuteTest(string testMethodName) { dynamic result = null; try { result = _sc.Run(testMethodName, new object[] { }); } catch { var error = ((IScriptControl)_sc).Error; if (error != null) { var description = error.Description; var line = error.Line; var column = error.Column; var text = error.Text; var source = error.Source; if (_context != null) { var details = String.Format("{0} \r\nLine: {1} Column: {2}", source, line, column); _context.WriteLine(details); } } throw new AssertFailedException(error.Description); } } public void Dispose() { _sc = null; } } }     Notice that the JavaScriptTestHelper class requires a Test Context to be instantiated. For this reason, you can use the JavaScriptTestHelper only with a Visual Studio Unit Test and not a Basic Unit Test (These are two different types of Visual Studio project items). Add the JavaScriptTestHelper file to your MVC test application (for example, MvcApplication1.Tests). Creating the JavaScript Unit Test Next, we need to create the JavaScript unit test function that we will use to test the addNumbers() function. Create a folder in your MVC test project named JavaScriptTests and add the following JavaScript file to this folder: MvcApplication1.Tests\JavaScriptTests\MathTest.js /// <reference path="JavaScriptUnitTestFramework.js"/> function testAddNumbers() { // Act var result = addNumbers(1, 3); // Assert assert.areEqual(4, result, "addNumbers did not return right value!"); }   The testAddNumbers() function takes advantage of another JavaScript library named JavaScriptUnitTestFramework.js. This library contains all of the code necessary to make assertions. Add the following JavaScriptnitTestFramework.js to the same folder as the MathTest.js file: MvcApplication1.Tests\JavaScriptTests\JavaScriptUnitTestFramework.js var assert = { areEqual: function (expected, actual, message) { if (expected !== actual) { throw new Error("Expected value " + expected + " is not equal to " + actual + ". " + message); } } }; There is only one type of assertion supported by this file: the areEqual() assertion. Most likely, you would want to add additional types of assertions to this file to make it easier to write your JavaScript unit tests. Deploying the JavaScript Test Files This step is non-intuitive. When you use Visual Studio to run unit tests, Visual Studio creates a new folder and executes a copy of the files in your project. After you run your unit tests, your Visual Studio Solution will contain a new folder named TestResults that includes a subfolder for each test run. You need to configure Visual Studio to deploy your JavaScript files to the test run folder or Visual Studio won’t be able to find your JavaScript files when you execute your unit tests. You will get an error that looks something like this when you attempt to execute your unit tests: You can configure Visual Studio to deploy your JavaScript files by adding a Test Settings file to your Visual Studio Solution. It is important to understand that you need to add this file to your Visual Studio Solution and not a particular Visual Studio project. Right-click your Solution in the Solution Explorer window and select the menu option Add, New Item. Select the Test Settings item and click the Add button. After you create a Test Settings file for your solution, you can indicate that you want a particular folder to be deployed whenever you perform a test run. Select the menu option Test, Edit Test Settings to edit your test configuration file. Select the Deployment tab and select your MVC test project’s JavaScriptTest folder to deploy. Click the Apply button and the Close button to save the changes and close the dialog. Creating the Visual Studio Unit Test The very last step is to create the Visual Studio unit test (the MS Test unit test). Add a new unit test to your MVC test project by selecting the menu option Add New Item and selecting the Unit Test project item (Do not select the Basic Unit Test project item): The difference between a Basic Unit Test and a Unit Test is that a Unit Test includes a Test Context. We need this Test Context to use the JavaScriptTestHelper class that we created earlier. Enter the following test method for the new unit test: [TestMethod] public void TestAddNumbers() { var jsHelper = new JavaScriptTestHelper(this.TestContext); // Load JavaScript files jsHelper.LoadFile("JavaScriptUnitTestFramework.js"); jsHelper.LoadFile(@"..\..\..\MvcApplication1\Scripts\Math.js"); jsHelper.LoadFile("MathTest.js"); // Execute JavaScript Test jsHelper.ExecuteTest("testAddNumbers"); } This code uses the JavaScriptTestHelper to load three files: JavaScripUnitTestFramework.js – Contains the assert functions. Math.js – Contains the addNumbers() function from your MVC application which is being tested. MathTest.js – Contains the JavaScript unit test function. Next, the test method calls the JavaScriptTestHelper ExecuteTest() method to execute the testAddNumbers() JavaScript function. Running the Visual Studio JavaScript Unit Test After you complete all of the steps described above, you can execute the JavaScript unit test just like any other unit test. You can use the keyboard combination CTRL-R, CTRL-A to run all of the tests in the current Visual Studio Solution. Alternatively, you can use the buttons in the Visual Studio toolbar to run the tests: (Unfortunately, the Run All Impacted Tests button won’t work correctly because Visual Studio won’t detect that your JavaScript code has changed. Therefore, you should use either the Run Tests in Current Context or Run All Tests in Solution options instead.) The results of running the JavaScript tests appear side-by-side with the results of running the server tests in the Test Results window. For example, if you Run All Tests in Solution then you will get the following results: Notice that the TestAddNumbers() JavaScript test has failed. That is good because our addNumbers() function is hard-coded to always return the value 5. If you double-click the failing JavaScript test, you can view additional details such as the JavaScript error message and the line number of the JavaScript code that failed: Summary The goal of this blog entry was to explain an approach to creating JavaScript unit tests that can be easily integrated with Visual Studio and Visual Studio ALM. I described how you can use the Microsoft Script Control to execute JavaScript on the server. By taking advantage of the Microsoft Script Control, we were able to execute our JavaScript unit tests side-by-side with all of our other unit tests and view the results in the standard Visual Studio Test Results window. You can download the code discussed in this blog entry from here: http://StephenWalther.com/downloads/Blog/JavaScriptUnitTesting/JavaScriptUnitTests.zip Before running this code, you need to first install the Microsoft Script Control which you can download from here: http://www.microsoft.com/downloads/en/details.aspx?FamilyID=d7e31492-2595-49e6-8c02-1426fec693ac

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  • How to Add Proprietary Drivers to Ubuntu 10.04

    - by Matthew Guay
    Does the hardware on your Ubuntu system need proprietary drivers work at peak performance?  Today we take a look how easy version 10.04 makes it to install them. Ubuntu 10.04 finally automatically recognizes and installs drivers for most hardware today, it even recognized and configured Wi-Fi drivers correctly every time in our tests.  This is in contrast to the past, when it was often difficult to get hardware to work in Linux.  However, most video cards still need proprietary drivers from their manufacturer to get full hardware video acceleration. Even though Ubuntu doesn’t include any non-open source components, it still makes it easy to install proprietary drivers if you wish.  When you first install and boot into Ubuntu, you may see a popup informing you that “restricted” drivers are available. You may see a notification asking you if you’d like to install optional drivers from your graphics card manufacturer when you try to enable advanced desktop effects.  Click Enable to directly install the drivers right there. Or, you can select the tray icon from the first popup, and click Install drivers. Alternately, if the tray icon has disappeared, click System, then Administration, and select Hardware Drivers.   This will open a dialog showing all the proprietary drivers available for your system, which may include drivers for your video card and other hardware depending on your computer.  Select the driver you wish to install, and click Activate. Enter your password, and then Ubuntu will download and install the driver without any more input.  After installation you may be prompted to reboot your system. Now, you should be able to take full advantage of your hardware, including fancy desktop effects with hardware acceleration. If you ever wish to remove these drivers, simply re-open the drivers dialog as above, select the driver, and click Remove.  Once again, a reboot may be required to finish the process. Conclusion Ubuntu has definitely made it easier to use Linux on your desktop computer, no matter what hardware you have.  If your video card or other hardware require proprietary drivers, it makes them available and simple to install.  And, best of all, all of your drivers stay updated with your software updates, so you can be sure you’re always running the latest. Similar Articles Productive Geek Tips Adding extra Repositories on UbuntuBackup and Restore Hardware Drivers the Easy Way with Double DriverCopy Windows Drivers From One Machine to AnotherInstalling PHP4 and Apache on UbuntuInstalling PHP5 and Apache on Ubuntu TouchFreeze Alternative in AutoHotkey The Icy Undertow Desktop Windows Home Server – Backup to LAN The Clear & Clean Desktop Use This Bookmarklet to Easily Get Albums Use AutoHotkey to Assign a Hotkey to a Specific Window Latest Software Reviews Tinyhacker Random Tips CloudBerry Online Backup 1.5 for Windows Home Server Snagit 10 VMware Workstation 7 Acronis Online Backup Gmail Button Addon (Firefox) Hyperwords addon (Firefox) Backup Outlook 2010 Daily Motivator (Firefox) FetchMp3 Can Download Videos & Convert Them to Mp3 Use Flixtime To Create Video Slideshows

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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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