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  • How do I learn Scheme?

    - by Gautam
    Hey, I'm a relative newbie to programming. I've picked up some very basic Java (File I/O, GUIs, inheritance) and would like to take a look at functional programming - in particular, I would like to learn Scheme. I'm having some trouble finding a Scheme implementation I can understand. Interpreters are weird; I'm not sure how to save my programs and create executables. I've downloaded PLT Scheme, but I would prefer using something less condescending, something similar to NetBeans. Is there a plugin or tool that will allow me to quickly and easily create and manage Scheme programs? All help is appreciated!

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  • What key concepts and nuances in C++ you know?

    - by Narek
    What kind of key points and concepts should a person know from C++ (and from programming in general) to be considered that he/she possesses C++ (and programming, in general) skills good. e.g. //Even if sizeof(T) may not be equal to 1, this code steps over array elements T v[]; for(T *p = v ; *p != 0 ; p++) cout<<*p<<endl; P.S. I hope by exchanging this info we will help each other to know C++ and programing thechnics better by doing explicit our notion that we got from practice.

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  • Should I be using libraries if I'm trying to learn how to program?

    - by CodeJustin.com
    I have been programming "a lot" in the past few months and at first I was trying to find the "easyest" language. Fortunately I realized that it's not about the language, it's about learning HOW to code. I ran into the Stanford lectures online (programming methodology) and I watched them all (around 23 hours total) awhile ago. Then I got into Java ME and programmed about 28.47% of a mobile RPG game (only around 2k lines of code). I feel like I learned a lot from those two experiences compared to previous ones but now that I'm moving into flash/actionscript 3.0 development and I'm finding myself learning like I did when I first started with PHP. I'm not really getting whats under the hood kind of. I'm finding myself using libraries to speed up development time which doesn't seem like a bad thing BUT I personally do not know how to write the libraries myself off hand. So should I be coding everything myself or is it ok to use libraries when you don't even know how to code them?

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  • Where can I find "canonical" sample programs that give quick refreshers for any given language? [on hold]

    - by acheong87
    Note to those close-voting this question: I understand this isn't a conventional programming question and I can agree with the reasoning that it's in the subjective domain (like best-of lists). In other ways though I think it's appropriate because, though it's not a "a specific programming problem," nor concerning "a software algorithm", nor (strictly) concerning "software tools commonly used by programmers", I think it is a "practical, answerable [problem that is] unique to the programming profession," and I think it is "based on an actual [problem I] face." I've been wanting this for some time now, because both approaches of (a) Googling for samples as I write every other line of code and (b) just winging it and seeing what errors crop up, distract me from coding efficiently. This note will be removed if the question gains popularity; this question will be deleted otherwise. I spend most of my time developing in C++, PHP, or Javascript, and every once in a while I have to do something in, say, VBA. In those times, it'd be convenient if I could just put up some sample code on a second monitor, something in between a cheat sheet (often too compact; and doesn't resemble anything that could actually compile/run), and a language reference (often too verbose, or segmented; requires extra steps to search or click through an index), so I can just glance at it and recall things, like how to loop through non-empty cells in a column. I think there's a hidden benefit to seeing formed code, that triggers the right spots in our brains to get back into a language we only need to brush up on. Similar in spirit is how http://ideone.com lets you click "Template" in any given language so you can get started without even doing a search. That template alone tells a lot, sometimes! Case-sensitivity, whitespace conventions, identifier conventions, the spelling of certain types, etc. I couldn't find a resource that pulled together such samples, so if there indeed doesn't exist such a repository, I was hoping this question would inspire professionals and experts to contribute links to the most useful sample code they've used for just this purpose: a keep-on-the-side, form-as-well-as-content, compilable/executable, reminder of a language's basic and oft-used features. Personally I am interested in seeing "samplers" for: VBA, Perl, Python, Java, C# (though for some of these autocompleters in Eclipse, Visual Studio, etc. help enough), awk, and sed. I'm tagging c++, php, and javascript because these are languages for which I'd best be able to evaluate whether proffered sample code matches what I had in mind.

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  • question about Littles Law

    - by davit-datuashvili
    I know that Little's Law states (paraphrased): the average number of things in a system is the product of the average rate at which things leave the system and the average time each one spends in the system, or: n=x*(r+z); x-throughput r-response time z-think time r+z - average response time now i have question about a problem from programming pearls: Suppose that system makes 100 disk accesses to process a transaction (although some systems require fewer, some systems will require several hundred disk access per transaction). How many transactions per hour per disk can the system handle? please help

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  • Should I use C(99) booleans ? ( also c++ booleans in c++ ?)

    - by Roman A. Taycher
    I haven't done much c programming but when I do when I need a false I put 0 when I want true I put 1, (ex. while(1)), in other cases I use things like "while(ptr)" or "if(x)". Should I try using C99 booleans, should I recommend them to others if I'm helping people new to programming learn c basics(thinking of cs 1?? students)? I'm pretty sure the Visual Studio compiler supports c99 bools, but do a lot of projects (open source and c apps in industry) compile for c89? If I don't use C bools should I at least do something like #define TRUE 1 #define FALSE 0? Also what about c++ Booleans (for c++)?

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  • Fastest way to convert a binary file to SQLite database

    - by chown
    I've some binary files and I'm looking for a way to convert each of those files to a SQLite database. I've already tried C# but the performance is too slow. I'm seeking an advice on how and what programming language should be the best to perform this kind of conversion. Though I prefer any Object Oriented Language more (like C#, Java etc), I'm open for any programming language that boosts up the conversion. I don't need a GUI frontend for the conversion, running the script/program from console is okay. Thanks in advance

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  • What are some good practice assignments for learning Java?

    - by HW
    Hello, I am a computer science in my Student Second year. I already know a good deal about C++, Data Structures, File Structures, OOP, etc. I decided to learn Java. I have read couple of books but I know that it takes practice to master any Programming language. I was wondering if anyone knew of some assignments or problems that helped them become good at programming. I am looking for something more challenging than "hello world"s and "3+2=5"s exercises. Thanks, ~HW

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  • Pass, edit and return variable in C

    - by Supertecnoboff
    I am new to C programming and recently I have been playing around with functions in C programming. But I have a simple problem: Basically I want to pass an integer to a function, have the function edit it and then pass back the integer to the main function. I am working on this but it isn't working..... Here is my code: int update_SEG_values(int DIGIT_1, int DIGIT_2) { // How many tens in the "TEMP_COUNT". DIGIT_2 = ((TEMP_COUNT) / 10); // How much is left for us to display. TEMP_COUNT = TEMP_COUNT - ((DIGIT_2) * 10); // How many ones. DIGIT_1 = ((TEMP_COUNT) / 1); return(DIGIT_1, DIGIT_2); } What am I doing wrong here?

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  • Language Prejudices

    - by paranoid_pedlar
    I've been researching programming languages, in hopes of learning to program. Since I've heard a lot of good things about Ruby, I went ahead and purchased The Pragmatic guide to Ruby. I understand that there is a lot of hype about Ruby on Rails. Because ruby lets you program scripts, applications, and internet helped me to decide on learning Ruby vs other languages. Today I watched a talk about google go, and it's really caught my attention. Coincidently I stumbled on a talk about jruby. I've been under the impression that java applications are bloated an slow. However the speaker made a point of what is wrong with Ruby, and how Jruby diagnosed Ruby's shortcomings. All that said. I would like to hear peoples opinions on Jruby vs Ruby, and if Ruby is working on fixing these "short comings". Also, how do you, the programming community feel about "go" and if I'm making a mistake learning Ruby instead of go, or Jruby. Appreciate your advice and opinions Thanks,

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  • How to keep your self up to date? [closed]

    - by nimo
    Possible Duplicate: Staying Relevant As a Programmer As you all know in our line of work it is important to keep your self up to date with all of the technical progress that is being made out there. As a developer you have to be quick to grasp new programming languages and programming concepts as well as completely new technologies. I read about a guy who got fired at 50 years of age with tons of experience in some ancient technology and he now couldn't get a job anywhere because his experience wasn't in OOP or some other more modern concept. I don't what to end up in that situation. How do you keep your self up to date? How do you train your self and make sure that you keep your self at the forefront?

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  • How to create a NSPredicate to find entries with leading numerical value?

    - by Toastor
    Hello, I'm using NSPredicates to fetch entities based on a name attribute. Creating a predicate for names beginning with letters was easy (@"name BEGINSWITH %@", searchLetter), however now I'd like to fetch all entities with a name that begins with a numerical value, or rather a non-alphabetical number. What would be the appropriate predicate expression here? Right now I don't want to get too deep into predicate programming, as this is all I need right now and time flies. So, please, don't point me to the Predicate Programming Guide, I just need that expression.. :) Thanks alot guys!

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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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  • creating a heirarchy of terminals or workspaces

    - by intuited
    <rant This question occurred to me ('occurred' meaning 'whispered seductively in my ear for the 100th time') while using GNU-screen, so I'll make that my example. However this is a much more general question about user interfaces and what I perceive as a flawmissing feature in every implementation I've yet seen. I'm wondering if there is some way to create a heirarchy/tree of terminals in a screen session. EG I'd like to have something like 1 bash 1.1 bash 1.2 bash 2 bash 3 bash 3.1 bash 3.1.1 bash 3.1.2 bash It would be good if the terminals could be labelled instead of having to be navigated to via some arrangement that I suspect doesn't exist. So then you could jump to one using eg ^A:goto happydays or ^A:goto dykstra.angry. So to generalize that: Firefox, Chrome, Internet Explorer, gnome-terminal, roxterm, konsole, yakuake, OpenOffice, Microsoft Office, Mr. Snuffaluppagus's Funtime Carousel™, and Your Mom's Jam Browser™ all offer the ability to create a flat set of tabs containing documents of an identical nature: web pages, terminals, documents, fun rideable animals, and jams. GNU-screen implements the same functionality without using tabs. Linux and OS/X window managers provide the ability to organize windows into an array of workspaces, which amounts to again, the same deal. Over the past few years, this has become a more or less ubiquitous concept which has been righteously welcomed into the far reaches of the computer interface funfest. Heavy users of these systems quickly encounter a problem with it: the set of entities is flat. In the case of workspaces, an option may be available to create a 2d array. However none of these applications furnish their users with the ability to create heirarchies, similar to filesystem directory structures, containing instances of their particular contained type. I for one am consistently bothered by this, and am wondering if the community can offer some wisdom as to why this has not happened in any of the foremost collections of computational functionality our culture has yet produced. Or if perhaps it has and I'm just an ignorant savage. I'd like to be able to not only group things into a tree structure, but also to create references (aka symbolic links, aka pointers) from one part of the structure to another, as well as apply properties (eg default directory, colorscheme, ...) recursively downward from a given node. I see no reason why we shouldn't be able to save these structures as known sessions, and apply tags to particular instances. So then you can sort through them by tag, find them by name, or just use the arrow keys (with an appropriate modifier) to move left or right and in or out of a given level. Another key combo would serve to create a branch in the place of the current terminal/webpage/lifelike statue/spreadsheet/spreadsheet sheet/presentation/jam and move that entity into the new branch, then create a fresh one as a sibling to it: a second leaf node within the same branch node. They would get along well. I find it a bit astonishing that this hasn't happened yet, and the only reason I can venture as a guess is that the creators of these fine systems do not consider such functionality to be useful to a significant portion of their userbase. I posit that the probability that that such an assumption would be correct is pretty low. On the other hand, given the relative ease with which such structures can be implemented using modern libraries/languages, it doesn't seem likely that difficulty of implementation would be a major roadblock. If it could be done in 1972 or whenever within the constraints of a filesystem driver, it should be relatively painless to implement in 2010 in a fullblown application. Given that all of these systems are capable of maintaining a set of equivalent entities, it seems unlikely that a major infrastructure overhaul would be necessary in order to enable a navigable heirarchy of them. </rant Mostly I'm just looking to start up a discussion and/or brainstorming on this topic. Any ideas, examples, criticism, or analysis are quite welcome. * Mr. Snuffaluppagus's Funtime Carousel is a registered trademark of Children's Television Workshop Inc. * Your Mom's Jam Browser is a registered trademark of Your Mom Inc.

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  • Did a recent WinXP update break CD/DVD read speeds? SP2/SP3

    - by quack quixote
    I have two systems with fresh installations of Windows XP Pro SP3 (SP3 slipstreamed into the installer; fully updated after install). One's a refurbished 2.4GHz Pentium4 system; the other is a new 1.6GHz Atom330 build. Both have brand-new dual-layer CD/DVD burners (one's a LiteOn IDE, the other an LG SATA). Both take a really looooong time to read a single-layer DVD in Windows with Cygwin tools. Specifically, 40 minutes or more. I burn backup data to single-layer DVD+/-R and use MD5 hashes for data verification (made with the standard md5sum tool in Unix or Cygwin). The hashes are burned to disc with the data files, and I use this command to verify: $ cd /path/to/disc/mountpoint ; time md5sum -c < md5.txt Here's how long that takes to run on a full single-layer DVD+/-R disc: Old system (WinXP SP2, 1.8GHz Athlon 2500+, last summer): ~10 minutes Old system (Ubuntu 9.04, 1.8GHz Athlon 2500+): ~10 minutes Old system (Debian 5, dual 550MHz P3): ~10 minutes New Pentium4 system (running Ubuntu 9.04): ~5 minutes New Pentium4 system (running WinXP SP3, file copy from Win Explorer): ~6 minutes New Atom330 system (running WinXP SP3, file copy from Win Explorer): ~6 minutes Now the weird stuff: Old system (WinXP SP2, 1.8GHz Athlon 2500+, today): ~25 minutes New Pentium4 system (running WinXP SP3, read from Cygwin): ~40-50 minutes (?!!) New Atom330 system (running WinXP SP3, read from Cygwin): ~40 minutes (can do it in ~30 minutes ...if i have another program spin up the drive first) Since both systems will copy files in 6 minutes using Windows Explorer, I know it's not a hardware problem. Windows just never spins up the drive during the Cygwin read, so it stays super-slow the whole time. Other programs like EAC and DVD Decrypter seem to spin up the disc just fine during their processing. DMA is enabled on both systems. (Can confirm in Windows' Device Manager on the Atom330, not on the P4.) Nero's DriveSpeed tool doesn't seem to have any effect. Copy times are comparable from commandline with Windows' xcopy. Copying with Cygwin's cp looks more like the problem state -- it will spin up the drive for a short time, never reaches full speed, and lets it spin back down again for most of the copy. What I need is to get full read speeds from Cygwin. Is this a known issue with SP3 or some other recent Windows update? Any other ideas? Update: More testing; Windows will spin up the drive when data is copied with Windows tools, but not when read in place or copied with Cygwin tools. It doesn't make sense to me that Windows spins up the drive for copying, but not for other reads. Might be more of a Cygwin problem? Update 2: GUI activity is sluggish during the problem state -- during the Cygwin verifies, there's a slight but noticable delay when dragging windows or icons around on the desktop, switching windows, Alt-Tabbing through open applications, opening new windows, etc. It reminds me of the delay when opening a Windows Explorer window on My Computer just after inserting a DVD. I've tried updating Cygwin (from 1.5.x to 1.7.x), but no change in the problem behavior. I've also noticed this issue occurs on WinXP SP2, but it's not exactly the same -- some spin-up occurs, so the read happens in ~25-30 minutes instead of 40+. The SP2 system used to run the verifies in ~10 minutes, and when it first changed (not sure exactly when, maybe in late November or early December 2009) I thought it was dying hardware. This is why I suspect an official update of breaking this functionality; this has worked for years on that SP2 box.

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  • Lustre - issues with simple setup

    - by ethrbunny
    Issue: I'm trying to assess the (possible) use of Lustre for our group. To this end I've been trying to create a simple system to explore the nuances. I can't seem to get past the 'llmount.sh' test with any degree of success. What I've done: Each system (throwaway PCs with 70Gb HD, 2Gb RAM) is formatted with CentOS 6.2. I then update everything and install the Lustre kernel from downloads.whamcloud.com and add on the various (appropriate) lustre and e2fs RPM files. Systems are rebooted and tested with 'llmount.sh' (and then cleared with 'llmountcleanup.sh'). All is well to this point. First I create an MDS/MDT system via: /usr/sbin/mkfs.lustre --mgs --mdt --fsname=lustre --device-size=200000 --param sys.timeout=20 --mountfsoptions=errors=remount-ro,user_xattr,acl --param lov.stripesize=1048576 --param lov.stripecount=0 --param mdt.identity_upcall=/usr/sbin/l_getidentity --backfstype ldiskfs --reformat /tmp/lustre-mdt1 and then mkdir -p /mnt/mds1 mount -t lustre -o loop,user_xattr,acl /tmp/lustre-mdt1 /mnt/mds1 Next I take 3 systems and create a 2Gb loop mount via: /usr/sbin/mkfs.lustre --ost --fsname=lustre --device-size=200000 --param sys.timeout=20 --mgsnode=lustre_MDS0@tcp --backfstype ldiskfs --reformat /tmp/lustre-ost1 mkdir -p /mnt/ost1 mount -t lustre -o loop /tmp/lustre-ost1 /mnt/ost1 The logs on the MDT box show the OSS boxes connecting up. All appears ok. Last I create a client and attach to the MDT box: mkdir -p /mnt/lustre mount -t lustre -o user_xattr,acl,flock luster_MDS0@tcp:/lustre /mnt/lustre Again, the log on the MDT box shows the client connection. Appears to be successful. Here's where the issues (appear to) start. If I do a 'df -h' on the client it hangs after showing the system drives. If I attempt to create files (via 'dd') on the lustre mount the session hangs and the job can't be killed. Rebooting the client is the only solution. If I do a 'lctl dl' from the client it shows that only 2/3 OST boxes are found and 'UP'. [root@lfsclient0 etc]# lctl dl 0 UP mgc MGC10.127.24.42@tcp 282d249f-fcb2-b90f-8c4e-2f1415485410 5 1 UP lov lustre-clilov-ffff880037e4d400 00fc176e-3156-0490-44e1-da911be9f9df 4 2 UP lmv lustre-clilmv-ffff880037e4d400 00fc176e-3156-0490-44e1-da911be9f9df 4 3 UP mdc lustre-MDT0000-mdc-ffff880037e4d400 00fc176e-3156-0490-44e1-da911be9f9df 5 4 UP osc lustre-OST0000-osc-ffff880037e4d400 00fc176e-3156-0490-44e1-da911be9f9df 5 5 UP osc lustre-OST0003-osc-ffff880037e4d400 00fc176e-3156-0490-44e1-da911be9f9df 5 Doing a 'lfs df' from the client shows: [root@lfsclient0 etc]# lfs df UUID 1K-blocks Used Available Use% Mounted on lustre-MDT0000_UUID 149944 16900 123044 12% /mnt/lustre[MDT:0] OST0000 : inactive device OST0001 : Resource temporarily unavailable OST0002 : Resource temporarily unavailable lustre-OST0003_UUID 187464 24764 152636 14% /mnt/lustre[OST:3] filesystem summary: 187464 24764 152636 14% /mnt/lustre Given that each OSS box has a 2Gb (loop) mount I would expect to see this reflected in available size. There are no errors on the MDS/MDT box to indicate that multiple OSS/OST boxes have been lost. EDIT: each system has all other systems defined in /etc/hosts and entries in iptables to provide access. SO: I'm clearly making several mistakes. Any pointers as to where to start correcting them?

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  • Ajax Control Toolkit and Superexpert

    - by Stephen Walther
    Microsoft has asked my company, Superexpert Consulting, to take ownership of the development and maintenance of the Ajax Control Toolkit moving forward. In this blog entry, I discuss our strategy for improving the Ajax Control Toolkit. Why the Ajax Control Toolkit? The Ajax Control Toolkit is one of the most popular projects on CodePlex. In fact, some have argued that it is among the most successful open-source projects of all time. It consistently receives over 3,500 downloads a day (not weekends -- workdays). A mind-boggling number of developers use the Ajax Control Toolkit in their ASP.NET Web Forms applications. Why does the Ajax Control Toolkit continue to be such a popular project? The Ajax Control Toolkit fills a strong need in the ASP.NET Web Forms world. The Toolkit enables Web Forms developers to build richly interactive JavaScript applications without writing any JavaScript. For example, by taking advantage of the Ajax Control Toolkit, a Web Forms developer can add modal dialogs, popup calendars, and client tabs to a web application simply by dragging web controls onto a page. The Ajax Control Toolkit is not for everyone. If you are comfortable writing JavaScript then I recommend that you investigate using jQuery plugins instead of the Ajax Control Toolkit. However, if you are a Web Forms developer and you don’t want to get your hands dirty writing JavaScript, then the Ajax Control Toolkit is a great solution. The Ajax Control Toolkit is Vast The Ajax Control Toolkit consists of 40 controls. That’s a lot of controls (For the sake of comparison, jQuery UI consists of only 8 controls – those slackers J). Furthermore, developers expect the Ajax Control Toolkit to work on browsers both old and new. For example, people expect the Ajax Control Toolkit to work with Internet Explorer 6 and Internet Explorer 9 and every version of Internet Explorer in between. People also expect the Ajax Control Toolkit to work on the latest versions of Mozilla Firefox, Apple Safari, and Google Chrome. And, people expect the Ajax Control Toolkit to work with different operating systems. Yikes, that is a lot of combinations. The biggest challenge which my company faces in supporting the Ajax Control Toolkit is ensuring that the Ajax Control Toolkit works across all of these different browsers and operating systems. Testing, Testing, Testing Because we wanted to ensure that we could easily test the Ajax Control Toolkit with different browsers, the very first thing that we did was to set up a dedicated testing server. The dedicated server -- named Schizo -- hosts 4 virtual machines so that we can run Internet Explorer 6, Internet Explorer 7, Internet Explorer 8, and Internet Explorer 9 at the same time (We also use the virtual machines to host the latest versions of Firefox, Chrome, Opera, and Safari). The five developers on our team (plus me) can each publish to a separate FTP website on the testing server. That way, we can quickly test how changes to the Ajax Control Toolkit affect different browsers. QUnit Tests for the Ajax Control Toolkit Introducing regressions – introducing new bugs when trying to fix existing bugs – is the concern which prevents me from sleeping well at night. There are so many people using the Ajax Control Toolkit in so many unique scenarios, that it is difficult to make improvements to the Ajax Control Toolkit without introducing regressions. In order to avoid regressions, we decided early on that it was extremely important to build good test coverage for the 40 controls in the Ajax Control Toolkit. We’ve been focusing a lot of energy on building automated JavaScript unit tests which we can use to help us discover regressions. We decided to write the unit tests with the QUnit test framework. We picked QUnit because it is quickly becoming the standard unit testing framework in the JavaScript world. For example, it is the unit testing framework used by the jQuery team, the jQuery UI team, and many jQuery UI plugin developers. We had to make several enhancements to the QUnit framework in order to test the Ajax Control Toolkit. For example, QUnit does not support tests which include postbacks. We modified the QUnit framework so that it works with IFrames so we could perform postbacks in our automated tests. At this point, we have written hundreds of QUnit tests. For example, we have written 135 QUnit tests for the Accordion control. The QUnit tests are included with the Ajax Control Toolkit source code in a project named AjaxControlToolkit.Tests. You can run all of the QUnit tests contained in the project by opening the Default.aspx page. Automating the QUnit Tests across Multiple Browsers Automated tests are useless if no one ever runs them. In order for the QUnit tests to be useful, we needed an easy way to run the tests automatically against a matrix of browsers. We wanted to run the unit tests against Internet Explorer 6, Internet Explorer 7, Internet Explorer 8, Internet Explorer 9, Firefox, Chrome, and Safari automatically. Expecting a developer to run QUnit tests against every browser after every check-in is just too much to expect. It takes 20 seconds to run the Accordion QUnit tests. We are testing against 8 browsers. That would require the developer to open 8 browsers and wait for the results after each change in code. Too much work. Therefore, we built a JavaScript Test Server. Our JavaScript Test Server project was inspired by John Resig’s TestSwarm project. The JavaScript Test Server runs our QUnit tests in a swarm of browsers (running on different operating systems) automatically. Here’s how the JavaScript Test Server works: 1. We created an ASP.NET page named RunTest.aspx that constantly polls the JavaScript Test Server for a new set of QUnit tests to run. After the RunTest.aspx page runs the QUnit tests, the RunTest.aspx records the test results back to the JavaScript Test Server. 2. We opened the RunTest.aspx page on instances of Internet Explorer 6, Internet Explorer 7, Internet Explorer 8, Internet Explorer 9, FireFox, Chrome, Opera, Google, and Safari. Now that we have the JavaScript Test Server setup, we can run all of our QUnit tests against all of the browsers which we need to support with a single click of a button. A New Release of the Ajax Control Toolkit Each Month The Ajax Control Toolkit Issue Tracker contains over one thousand five hundred open issues and feature requests. So we have plenty of work on our plates J At CodePlex, anyone can vote for an issue to be fixed. Originally, we planned to fix issues in order of their votes. However, we quickly discovered that this approach was inefficient. Constantly switching back and forth between different controls was too time-consuming. It takes time to re-familiarize yourself with a control. Instead, we decided to focus on two or three controls each month and really focus on fixing the issues with those controls. This way, we can fix sets of related issues and avoid the randomization caused by context switching. Our team works in monthly sprints. We plan to do another release of the Ajax Control Toolkit each and every month. So far, we have competed one release of the Ajax Control Toolkit which was released on April 1, 2011. We plan to release a new version in early May. Conclusion Fortunately, I work with a team of smart developers. We currently have 5 developers working on the Ajax Control Toolkit (not full-time, they are also building two very cool ASP.NET MVC applications). All the developers who work on our team are required to have strong JavaScript, jQuery, and ASP.NET MVC skills. In the interest of being as transparent as possible about our work on the Ajax Control Toolkit, I plan to blog frequently about our team’s ongoing work. In my next blog entry, I plan to write about the two Ajax Control Toolkit controls which are the focus of our work for next release.

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  • Ask the Readers: Do You Use the Command Line?

    - by Asian Angel
    Most people have heard of it but not everyone is familiar or comfortable with how to use this bastion of geekdom. This week we would like to know if you use the command line or not. The command line…the bastion of ultimate geekery in many peoples’ eyes. You often hear people referring to doing things using the command line, so there must be something to it, right? For some people using the command line is the best, most efficient, and easiest way to do things on their systems. These are the people that many of us wish we were like. Next you have those who are proficient at using the command line but do not rely on it for everything they do on their systems. Then there are people who know how to perform some tasks or hacks using the command line but may not be as comfortable or knowledgeable as they wish to be using it. Moving on you find those who are interested in learning how to use the command line and just need a small push to get started.  Perhaps you feel too intimidated to learn it and just need the right opportunity to come along. And maybe you do not care one way or the other so long as you get done what you want to do on your system. Or you may prefer to simply use a graphical interface since that is quicker and easier for you (along with being familiar). You can find the whole range of people when it comes to using the command line… This week we would like to know if you use the command line or not. What command line category do you fit into? Power user? Casual usage? Totally lost? Let us know in the comments! How-To Geek Polls require Javascript. Please Click Here to View the Poll. Latest Features How-To Geek ETC The How-To Geek Holiday Gift Guide (Geeky Stuff We Like) LCD? LED? Plasma? The How-To Geek Guide to HDTV Technology The How-To Geek Guide to Learning Photoshop, Part 8: Filters Improve Digital Photography by Calibrating Your Monitor Our Favorite Tech: What We’re Thankful For at How-To Geek The How-To Geek Guide to Learning Photoshop, Part 7: Design and Typography Fun and Colorful Firefox Theme for Windows 7 Happy Snow Bears Theme for Chrome and Iron [Holiday] Download Full Command and Conquer: Tiberian Sun Game for Free Scorched Cometary Planet Wallpaper Quick Fix: Add the RSS Button Back to the Firefox Awesome Bar Dropbox Desktop Client 1.0.0 RC for Windows, Linux, and Mac Released

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  • Parallelism in .NET – Part 6, Declarative Data Parallelism

    - by Reed
    When working with a problem that can be decomposed by data, we have a collection, and some operation being performed upon the collection.  I’ve demonstrated how this can be parallelized using the Task Parallel Library and imperative programming using imperative data parallelism via the Parallel class.  While this provides a huge step forward in terms of power and capabilities, in many cases, special care must still be given for relative common scenarios. C# 3.0 and Visual Basic 9.0 introduced a new, declarative programming model to .NET via the LINQ Project.  When working with collections, we can now write software that describes what we want to occur without having to explicitly state how the program should accomplish the task.  By taking advantage of LINQ, many operations become much shorter, more elegant, and easier to understand and maintain.  Version 4.0 of the .NET framework extends this concept into the parallel computation space by introducing Parallel LINQ. Before we delve into PLINQ, let’s begin with a short discussion of LINQ.  LINQ, the extensions to the .NET Framework which implement language integrated query, set, and transform operations, is implemented in many flavors.  For our purposes, we are interested in LINQ to Objects.  When dealing with parallelizing a routine, we typically are dealing with in-memory data storage.  More data-access oriented LINQ variants, such as LINQ to SQL and LINQ to Entities in the Entity Framework fall outside of our concern, since the parallelism there is the concern of the data base engine processing the query itself. LINQ (LINQ to Objects in particular) works by implementing a series of extension methods, most of which work on IEnumerable<T>.  The language enhancements use these extension methods to create a very concise, readable alternative to using traditional foreach statement.  For example, let’s revisit our minimum aggregation routine we wrote in Part 4: double min = double.MaxValue; foreach(var item in collection) { double value = item.PerformComputation(); min = System.Math.Min(min, value); } .csharpcode, .csharpcode pre { font-size: small; color: black; font-family: consolas, "Courier New", courier, monospace; background-color: #ffffff; /*white-space: pre;*/ } .csharpcode pre { margin: 0em; } .csharpcode .rem { color: #008000; } .csharpcode .kwrd { color: #0000ff; } .csharpcode .str { color: #006080; } .csharpcode .op { color: #0000c0; } .csharpcode .preproc { color: #cc6633; } .csharpcode .asp { background-color: #ffff00; } .csharpcode .html { color: #800000; } .csharpcode .attr { color: #ff0000; } .csharpcode .alt { background-color: #f4f4f4; width: 100%; margin: 0em; } .csharpcode .lnum { color: #606060; } Here, we’re doing a very simple computation, but writing this in an imperative style.  This can be loosely translated to English as: Create a very large number, and save it in min Loop through each item in the collection. For every item: Perform some computation, and save the result If the computation is less than min, set min to the computation Although this is fairly easy to follow, it’s quite a few lines of code, and it requires us to read through the code, step by step, line by line, in order to understand the intention of the developer. We can rework this same statement, using LINQ: double min = collection.Min(item => item.PerformComputation()); Here, we’re after the same information.  However, this is written using a declarative programming style.  When we see this code, we’d naturally translate this to English as: Save the Min value of collection, determined via calling item.PerformComputation() That’s it – instead of multiple logical steps, we have one single, declarative request.  This makes the developer’s intentions very clear, and very easy to follow.  The system is free to implement this using whatever method required. Parallel LINQ (PLINQ) extends LINQ to Objects to support parallel operations.  This is a perfect fit in many cases when you have a problem that can be decomposed by data.  To show this, let’s again refer to our minimum aggregation routine from Part 4, but this time, let’s review our final, parallelized version: // Safe, and fast! double min = double.MaxValue; // Make a "lock" object object syncObject = new object(); Parallel.ForEach( collection, // First, we provide a local state initialization delegate. () => double.MaxValue, // Next, we supply the body, which takes the original item, loop state, // and local state, and returns a new local state (item, loopState, localState) => { double value = item.PerformComputation(); return System.Math.Min(localState, value); }, // Finally, we provide an Action<TLocal>, to "merge" results together localState => { // This requires locking, but it's only once per used thread lock(syncObj) min = System.Math.Min(min, localState); } ); Here, we’re doing the same computation as above, but fully parallelized.  Describing this in English becomes quite a feat: Create a very large number, and save it in min Create a temporary object we can use for locking Call Parallel.ForEach, specifying three delegates For the first delegate: Initialize a local variable to hold the local state to a very large number For the second delegate: For each item in the collection, perform some computation, save the result If the result is less than our local state, save the result in local state For the final delegate: Take a lock on our temporary object to protect our min variable Save the min of our min and local state variables Although this solves our problem, and does it in a very efficient way, we’ve created a set of code that is quite a bit more difficult to understand and maintain. PLINQ provides us with a very nice alternative.  In order to use PLINQ, we need to learn one new extension method that works on IEnumerable<T> – ParallelEnumerable.AsParallel(). That’s all we need to learn in order to use PLINQ: one single method.  We can write our minimum aggregation in PLINQ very simply: double min = collection.AsParallel().Min(item => item.PerformComputation()); By simply adding “.AsParallel()” to our LINQ to Objects query, we converted this to using PLINQ and running this computation in parallel!  This can be loosely translated into English easily, as well: Process the collection in parallel Get the Minimum value, determined by calling PerformComputation on each item Here, our intention is very clear and easy to understand.  We just want to perform the same operation we did in serial, but run it “as parallel”.  PLINQ completely extends LINQ to Objects: the entire functionality of LINQ to Objects is available.  By simply adding a call to AsParallel(), we can specify that a collection should be processed in parallel.  This is simple, safe, and incredibly useful.

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  • Serious about Embedded: Java Embedded @ JavaOne 2012

    - by terrencebarr
    It bears repeating: More than ever, the Java platform is the best technology for many embedded use cases. Java’s platform independence, high level of functionality, security, and developer productivity address the key pain points in building embedded solutions. Transitioning from 16 to 32 bit or even 64 bit? Need to support multiple architectures and operating systems with a single code base? Want to scale on multi-core systems? Require a proven security model? Dynamically deploy and manage software on your devices? Cut time to market by leveraging code, expertise, and tools from a large developer ecosystem? Looking for back-end services, integration, and management? The Java platform has got you covered. Java already powers around 10 billion devices worldwide, with traditional desktops and servers being only a small portion of that. And the ‘Internet of Things‘ is just really starting to explode … it is estimated that within five years, intelligent and connected embedded devices will outnumber desktops and mobile phones combined, and will generate the majority of the traffic on the Internet. Is your platform and services strategy ready for the coming disruptions and opportunities? It should come as no surprise that Oracle is keenly focused on Java for Embedded. At JavaOne 2012 San Francisco the dedicated track for Java ME, Java Card, and Embedded keeps growing, with 52 sessions, tutorials, Hands-on-Labs, and BOFs scheduled for this track alone, plus keynotes, demos, booths, and a variety of other embedded content. To further prove Oracle’s commitment, in 2012 for the first time there will be a dedicated sub-conference focused on the business aspects of embedded Java: Java Embedded @ JavaOne. This conference will run for two days in parallel to JavaOne in San Francisco, will have its own business-oriented track and content, and targets C-level executives, architects, business leaders, and decision makers. Registration and Call For Papers for Java Embedded @ JavaOne are now live. We expect a lot of interest in this new event and space is limited, so be sure to submit your paper and register soon. Hope to see you there! Cheers, – Terrence Filed under: Mobile & Embedded Tagged: ARM, Call for Papers, Embedded Java, Java Embedded, Java Embedded @ JavaOne, Java ME, Java SE Embedded, Java SE for Embedded, JavaOne San Francisco, PowerPC

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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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