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  • Different methods using Functors/Delegates in c#

    - by mo alaz
    I have a method that I call multiple times, but each time a different method with a different signature is called from inside. public void MethodOne() { //some stuff *MethodCall(); //some stuff } So MethodOne is called multiple times, each time with a different *MethodCall(). What I'm trying to do is something like this : public void MethodOne(Func<> MethodCall) { //some stuff *MethodCall; //some stuff } but the Methods that are called each have a different return type and different parameters. Is there a way to do this using Functors? If not, how would I go about doing this? Thank you!

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  • Facing difficulty in moving the two id's

    - by user1806560
    By means of <?php echo $productlist->productid;?> in href i am passing the productid,its fine based on that i can able to display the items. The url is looking like this when i am passing like this http://localhost/sample/index.php/userlogin/items/35 . <ul class="left_menu"> <li class="odd"><a href="<?php echo BASE_INDEX_URL;?>/userlogin/items/<?php echo $productlist->productid;?>"> <?php echo $productlist->productname; ?> </a></li> </ul> My model is taking the value like this public function items($productid=0) { } But i want to pass one more id as categoryid in the href, how can i do that My model is taking the value like this(for 2 parameters) public function items($productid=0,$categoryid=0) { }

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  • Call java program on server through web request

    - by Rossella
    I need to develop an application where a Java client calls a Java application located on the server with certain parameters, the Java application on the server computes data and sends the data back to the client. Everything needs to go through port 80 on which I have a IIS webserver listening. I cannot open any other port on the server. Is there any way I can do this? The server can write files in a directory that the client can read but I am not sure how to handle the synchronization and I don't know how to call a script on the server from the client through port 80. Every suggestion would be highly appreciated Thanks a lot in advance, this problem is making me crazy

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  • C# 4.0 how to pass variables to threads?

    - by Aviatrix
    How would i pass some parameters to a new thread that runs a function from another class ? What i'm trying to do is to pass an array or multiple variables to a function that sits in another class and its called by a new thread. i have tried to do it like this Functions functions = new Functions(); string[] data; Thread th = new Thread(new ParameterizedThreadStart(functions.Post())); th.Start(data); but it shows error "No overload for method 'Post' takes 0 arguments" Any ideas ?

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  • Submit POST form from url

    - by Martijn Van Mierloo
    Website: www.example.com <form method="POSt" action="" > <input type="hidden" name="test1" value="test11" /> <input type="hidden" name="test2" value="" /> <input type="hidden" name="test3" value="test33" /> <input type="submit" value="Submit"> </form> I want to sumbit this form with adding the correct parameters in the URL. With GET, I can simply use : http://ww.example.com/?test1=test11&test2=&test3=test33 and the form will be sumbitted. Can I do the same for a POST? If so, how? Thanks

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  • Passing enum or object through an intent (the best solution)

    - by jax
    I have an activity that when started needs access to two different ArrayLists. Both Lists are different Objects I have created myself. Basically I need a way to pass these objects to the activity from an Intent. I can use addExtras() but this requires a Parceable compatible class. I could make my classes to be passed serializable but as I understand this slows down the program. What are my options? Can I pass an Enum? As an an aside: is there a way to pass parameters to an Activity Constructor from an Intent?

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  • Multiple &(AND) fails in query

    - by N e w B e e
    here is my query $sql = 'SELECT * FROM Orders INNER JOIN [Order Details] ON Orders.OrderNumber = [Order Details].OrderNumber WHERE Orders.CartID =2 AND [Order Details].Option10 Is Null AND [Order Details].Status="Shipped"'; this queries when entered in MS_Access sql view, returns the correct results, but when I copy and paste the same query in my php script, it fails and gives the error Too few parameters, expected 1... although data is there, query is working in access... Please note if I omitted on AND condition, it works eg if I removed shipped conidtion or is null condition, it works then too.. any hint? whats wrong with it?? any help?thanks

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  • lua function as argument in C

    - by Nil
    I'm going to pass a function to another function which should operate with the passed function. For example: handler(fun1("foo",2)) handler(fun2(1e-10)) The handler is something like calling the passed function many times. I'm going to bind handler, fun1, fun2 to C-functions. fun1 and fun2 are going to return some user data with a pointer to some cpp-class so that I can further recover which function was it. The problem now is that fun1 and fun2 are going to be called before passed to handler. But I don't need this, what I need is the kind of function and its parameters. However, I should be able to call fun1 and fun2 alone without handler: fun1("bar",3) fun2(1e-5) Is it possible to get the context the function is called from? While typing the question, I realized I could do following handler(fun1, "foo",2); handler(fun2, 1e-10);

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  • c# asp.net problem with 'must declare the scalar variable'

    - by Verian
    I'm currently making a front end to display license information for my companies software audit but im no pro with sql or asp.net so iv ran into a bit of trouble. I'm trying to get a sum of how many licenses there are across several rows so i can put it in a text box, but im getting the error 'Must declare the scalar variable "@softwareID".' SqlConnection con1 = Connect.GetSQLConnection(); string dataEntry = softwareInputTxt.Text; string result; dataEntry = dataEntry + "%"; con1.Open(); SqlCommand Mycmd1; Mycmd1 = new SqlCommand("select sum(license_quantity_owned) from licenses where software_ID like @softwareID", con1); MyCmd.Parameters.AddWithValue("@softwareID", dataEntry); result = (string)Mycmd1.ExecuteScalar(); licenseOwnedTxt.Text = result; Could anyone point me in the right direction?

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  • Query "where clause" fails when calling a function

    - by guest1
    Hi All, I have a function in Access VBA that takes four parameters.The fourth parameter is a "where clause" that I use in an SQL statement inside the function. The function fails when I include the fourth parameter (where clause). When I remove this fourth parameter, the function just works fine. I am not sure if there is anything wrong with the syntax of the fourth parameter ? Please help. here is the function as called in the Query FunctionA('Table1','Field1',0.3,'Field2=#' & [Field2] & '# and Value3="' & [Value3] & '"') AS Duration_Field

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  • Client-server application between two computers in the same network (using boost::asio)

    - by Edwin
    I'm trying to set up a basic communication between my desktop PC and my laptop (latter one using wireless connection) both being in the same network, using the boost::asio tutorials: synchronous client and synchronous server (in c++). When I run both the server and client on the same machine (using the localhost and the datetime port as parameters), it works splendidly. But if I try to set up the laptop as server (tested it with netstat -anb from the command prompt, it is indeed running and listening to port 13 as it's supposed to, and I even deactivated the firewall to make sure it doesn't cause any problems), I cannot connect to it with the client (set up on the PC), no matter what IP I tried (localhost, and basically any IPs that ipconfig -all gave me). So no matter what I tried, I cannot find the correct address that which the client can use to connect to the server. Could anyone help me please?

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  • DatePicker with ShowUpDown set to true

    - by mhar
    I set the datepicker ShowUpDown to true. I notice that every time it reaches JANUARY of the following year it is throwing an error. Year, Month, and Day parameters describe an un-representable DateTime. reading on MSDN, it says that month should be between 1 and 12. So my guess is after the month of December, which is 12, when a user increase it again it will become 13, hence, throwing an error. Is is possible to loop this? From December(12) to January(1) instead of increasing it to 13.

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  • Get size of jar file loaded by urlclassloader

    - by Aliya
    Does anybody know a good way to find the file size that is dynamically loaded by urlclassloader? I am using the urlclassloader in the following manner, but need to keep track of how much bandwidth is being used. URLClassLoader sysloader = (URLClassLoader) ClassLoader .getSystemClassLoader(); Class<URLClassLoader> sysclass = URLClassLoader.class; Method method = sysclass.getDeclaredMethod("addURL", parameters); method.setAccessible(true); method.invoke(sysloader, (Object[]) urls); Thanks in advance!

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  • function declaration

    - by robUK
    Hello, gcc 4.1.2 c89 I am reviewing some code and I have come across the following function. I have never seen a function declared like this before. There are no data types for the paraemeters. My best guess is that the function is using a list of data types separated by semi-colons. The return type seems to be returning a function with those parameters. However, the read function is not defined anywhere. What is the advantage and purpose of declaring a function like this? Many thanks for any advice, int my_read(fd, ptr, cnt) int fd; char *ptr; unsigned cnt; { printf("Read\n"); return(read(fd, ptr, cnt)); }

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  • Problem with SDL 1.2 when setting videomode with SDL_SetVideoMode

    - by user574911
    I have a very simple program, in which I am initialising with SDL_Init(flags) and using SDL_SetVideoMode but It fails by returning null. I think I am missing some config parameters/options, if any one knows about this erro please let me know. My code is as below : if(SDL_Init(SDL_INIT_VIDEO | SDL_INIT_AUDIO | SDL_INIT_TIMER)) { fprintf(stderr, "Could not initialize SDL\n"); exit(1); } screen = SDL_SetVideoMode(640, 480, 0, 0); if(!screen) { fprintf(stderr, "SDL: could not set video mode - exiting\n"); exit(1); }

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  • Problem with a large CSV file

    - by moustafa
    I have a very large CSV file. 51427 lines to be exact. I need to import the entire file into a MySQL database, however, the script times out due to server settings and slow connection (and maybe other reasons that I am not aware of). So - I am now passing parameters START and LIMIT via address bar to import, like this: http://my.server.address/import.php?...000&limit=1000 This reads the entire CSV file into an array, and starts at line 10000 of the array and inserts into the database until it reaches line 11000, and then terminates the script. This works very nicely, however, I am not happy having to reach the entire 51427 lines of the CSV file into an array before processing. Is there not a way where I can only read the required lines into an array? That would speed things up significantly.

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  • Pass database data to multiples views-Laravel

    - by user3696018
    I have a database with details of daily sales. To query a database, I have a form in a view with parameters that will query as date of admission, client and others. The result is shown in another view with the daily details of income, and below is a summary of the article do all entered. The summary I wish to transfer to another view, try to view :: composer but only transfer the empty query (I saw it with debug bar). Just appeared an empty view. How I can transfer data from the database without the latter view is empty? The second html view is totaly diferent , only the data is the same.

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  • PHP $_REQUEST doesn't contain all $_GET varaibles

    - by pinky0x51
    Until today I thought that $_REQUEST always contains all variables form $_POST and $_GET. But today I had the strange experience that one variable is part of $_GET but not part of $_REQUEST. I played a little bit around with the URL which hands over the parameters and it seems like always the fist parameter is missing in the $_REQUEST array. Do you have any idea why this could happen? Thanks! URL: localhost/?app=files&getfile=ajax/newfile.php?dir=%2Ftest4&source=http%3A%2F%2Fl??ocalhost%2Fimg%2Flogo.svg&filename=logo.svg&requesttoken=e250827c341650990cd4

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  • In a JDBC ResultSet, what should happen when getLong() or getShort() is called on an int result colu

    - by Uri
    Say that I have a JDBC ResultSet, and I call the getLong() or getshort() method. For which of the following SQL types {SMALLINT, INT, BIGINT} should I get long, and for which types should I get an error? In other words, if I have an INT and I want a SMALLINT (A short), would I get it, or would I get an error? Similarly, if I have an INT and want a BIGINT (a long), would I get it, or would I get an error? The Javadocs (listed below) say nothing. public long getLong(int columnIndex) throws SQLException Retrieves the value of the designated column in the current row of this ResultSet object as a long in the Java programming language. Parameters: columnIndex - the first column is 1, the second is 2, ... Returns: the column value; if the value is SQL NULL, the value returned is 0 Throws: SQLException - if a database access error occurs

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  • Simple parameter checking function, here just want the % to be allowed

    - by abas_rafiq
    I'm using PDO's bindParam. This is the function which checks every GET variable on the website. After changing it will echo it out: function Check_Get_Param($val){ $value1=addslashes($val); $string1=htmlspecialchars($value1); $string2=strip_tags($string1); $string3=intval($string2); return $string3; } Hhere this will output the result: Check_Get_Param($_GET['id']); Now the idea is any id or id= any or id = % $_GET['id'] = % will result 0 as % is not integer. How to allow % also? How do I modify this function or any other function that I could filter the GET parameters so I could keep out the web from injections?

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  • trying to validate user input in php

    - by user225269
    I'm trying to validate user input in php. This code will check if the values are null or not. If it is null, this will require the user to input the values that are null. When all the text boxes in the html form that came before this. This code will show the submit button, and that submit button will save the inputted data into the mysql database. But the problem is that the value that is saved is zero zero and zero, what might be the cause of this? <html> <head> <title>Admission Information Sheet</title> <meta http-equiv="Content-Type" content="text/html; Western (ISO-8859-1)"> <meta name="author" content=" "> <title> <style> input { font-size: 16px;} </style> <?php include('header.php'); ?> <div id="main_content"> </div> <?php include('footer.php'); ?> <table border="1" width="900" border="0" align="left" cellpadding="0" cellspacing="1" bgcolor="#CCCCCC"> <tr> <form name="form1.1" method="POST" action="aisaction.php"> <?php $NURSE = $_POST[nurse]; $TELNUM = $_POST[telnum]; $HOSPNUM = $_POST[hnum]; $ROOMNUM = $_POST[rnum]; $LASTNAME = $_POST[lname]; $FIRSTNAME = $_POST[fname]; $MIDNAME = $_POST[mname]; $AD = $_POST[ad]; $ADATE = $_POST[adate]; $ADTIME = $_POST[adtime]; $CSTAT = $_POST[cs]; $AGE = $_POST[age]; $BDAY = $_POST[bday]; $SEX = $_POST[sex]; ?> <td> <table width="100%" border="0" cellpadding="2" cellspacing="1" bgcolor="#FFFFFF"> <tr> <td colspan="12" style="background:#9ACD32; color:white; border:white 1px solid; text-align: center"><strong><font size="3">ADMISSION INFORMATION SHEET</strong></td> </tr> <tr> </td><br> <td width="54"><font size="3">Hospital #</td> <td width="3">:</td> <td width="168"><input type="display" name="hnum" disabled="true" value= "<?php print "$HOSPNUM";?>"><br> <font color="red"> <?php if(empty($HOSPNUM)) print "* Hospital Number required!<br>"; ?> </td> <td width="41"><font size="3">Room #</td> <td width="3">:</td> <td width="168"><input type="display" name="rnum" disabled="true" value= "<?php print "$ROOMNUM";?>"><br> <font color="red"> <?php if(empty($ROOMNUM)) print "* Room Number required!<br>"; ?> </td> <td width="67"><font size="3">Admission Date</td> <td width="3">:</td> <td width="168"><input type="display" name="adate" disabled="true" value= "<?php print "$ADATE";?>"><br> <font color="red"> <?php if(empty($ADATE)) print "* Admission Date required!<br>"; ?> </td> </tr> <tr> <td><font size="3">Last Name</td> <td>:</td> <td><input type="display" name="lname" disabled="true" value= "<?php print "$LASTNAME";?>"><br> <font color="red"> <?php if(empty($LASTNAME)) print "* Last Name required!<br>"; ?> </td> <td><font size="3">First Name</td> <td>:</td> <td><input type="display" name="fname" disabled="true" value= "<?php print "$FIRSTNAME";?>"><br> <font color="red"> <?php if(empty($FIRSTNAME)) print "* First Name required!<br>"; ?> </td> <td><font size="3">Middle Name</td> <td>:</td> <td><input type="display" name="mname" disabled="true" value= "<?php print "$MIDNAME";?>"><br> <font color="red"> <?php if(empty($MIDNAME)) print "* Middle Name required!<br>"; ?> </td> <td><font size="3">Admit time</td> <td>:</td> <td><input type="display" name="mname" disabled="true" value= "<?php print "$ADTIME";?>"><br> <font color="red"> <?php if(empty($ADTIME)) print "* Adtime required!<br>"; ?> </td> </tr> <tr> <td><font size="3">Civil Status</td> <td>:</td> <td><input type="display" name="cs" disabled="true" value= "<?php print "$CSTAT";?>"><br> <font color="red"> <?php if(empty($CSTAT)) print "* Civil Status required!<br>"; ?> </td> <td><font size="3">Age</td> <td>:</td> <td><input type="display" name="age" disabled="true" value= "<?php print "$AGE";?>"><br> <font color="red"> <?php if(empty($AGE)) print "* Age required!<br>"; ?> </td> <td><font size="3">Birthday</td> <td>:</td> <td><input type="display" name="bday" disabled="true" value= "<?php print "$BDAY";?>"><br> <font color="red"> <?php if(empty($BDAY)) print "* Birthday required!<br>"; ?> </td> </tr> <tr> <td><font size="3">Address</td> <td>:</td> <td><input type="display" name="address" disabled="true" value= "<?php print "$AD";?>"><br> <font color="red"> <?php if(empty($AD)) print "* Address required!<br>"; ?> </td> <td><font size="3">Telephone #</td> <td>:</td> <td><input type="display" name="telnum" disabled="true" value= "<?php print "$TELNUM";?>"></td> <td width="23"><font size="3">Sex</td> <td width="3">:</td> <td width="174"><input type="display" name="sex" disabled="true" value= "<?php print "$SEX";?>"><br> <font color="red"> <?php if(empty($SEX)) print "* Gender required!<br>"; ?> </td> </tr> <tr> <td><font size="3">Pls. Check</td> <td>:</td> <td><input name="stats1" type="checkbox" id="SSS" value="SSS">SSS</td> <td><font size="3"></td> <td>:</td> <td><input name="stats1" type="checkbox" id="nonmed" value="NonMedicare">Non Medicare</td> <td><font size="3"></td> <td>:</td> <td><input name="stats1" type="checkbox" id="sh" value="stockholder">Stockholder</td> </tr> <tr> <td><font size="3"></td> <td></td> <td><input name="stats1" type="checkbox" id="gsis" value="GSIS">GSIS</td> <td><font size="3"></td> <td></td> <td><input name="stats1" type="checkbox" id="senior" value="seniorcitizen">Senior-Citizen</td> <tr> <td><font size="3"></td> <td></td> <td><input name="stats1" type="checkbox" id="dep" value="dependent">Dependent</td> <td><font size="3"></td> <td></td> <td><input name="stats1" type="checkbox" id="emp" value="employee">Employee</td> </tr> <tr> <td><font size="3">Attending Nurse</td> <td>:</td> <td><input type="display" name="nurse" disabled="true" value= "<?php print "$NURSE";?>"><br> <font color="red"> <?php if(empty($NURSE)) print "* Admitting/Attending Nurse required!<br>"; ?> </td> </tr> <tr> <td>&nbsp;</td> <td>&nbsp;</td> <td><input type="button" value="Back" onClick="history.go(-1);return true;"> <?php $val1 = $_POST['NURSE']; if($_POST['NURSE'] !="") { ?> <form action="aisaction.php" method="POST" target="_window"> <input type="hidden" name="submit" value="yes"> <input type="submit" value="submit"> </form> <?php } ?> </td> </td> </tr> </table> </td> </form> </tr> </table> </head> </html>

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  • Using Unity – Part 3

    - by nmarun
    The previous blog was about registering and invoking different types dynamically. In this one I’d like to show how Unity manages/disposes the instances – say hello to Lifetime Managers. When a type gets registered, either through the config file or when RegisterType method is explicitly called, the default behavior is that the container uses a transient lifetime manager. In other words, the unity container creates a new instance of the type when Resolve or ResolveAll method is called. Whereas, when you register an existing object using the RegisterInstance method, the container uses a container controlled lifetime manager - a singleton pattern. It does this by storing the reference of the object and that means so as long as the container is ‘alive’, your registered instance does not go out of scope and will be disposed only after the container either goes out of scope or when the code explicitly disposes the container. Let’s see how we can use these and test if something is a singleton or a transient instance. Continuing on the same solution used in the previous blogs, I have made the following changes: First is to add typeAlias elements for TransientLifetimeManager type: 1: <typeAlias alias="transient" type="Microsoft.Practices.Unity.TransientLifetimeManager, Microsoft.Practices.Unity"/> You then need to tell what type(s) you want to be transient by nature: 1: <type type="IProduct" mapTo="Product2"> 2: <lifetime type="transient" /> 3: </type> 4: <!--<type type="IProduct" mapTo="Product2" />--> The lifetime element’s type attribute matches with the alias attribute of the typeAlias element. Now since ‘transient’ is the default behavior, you can have a concise version of the same as line 4 shows. Also note that I’ve changed the mapTo attribute from ‘Product’ to ‘Product2’. I’ve done this to help understand the transient nature of the instance of the type Product2. By making this change, you are basically saying when a type of IProduct needs to be resolved, Unity should create an instance of Product2 by default. 1: public string WriteProductDetails() 2: { 3: return string.Format("Name: {0}<br/>Category: {1}<br/>Mfg Date: {2}<br/>Hash Code: {3}", 4: Name, Category, MfgDate.ToString("MM/dd/yyyy hh:mm:ss tt"), GetHashCode()); 5: } Again, the above change is purely for the purpose of making the example more clear to understand. The display will show the full date and also displays the hash code of the current instance. The GetHashCode() method returns an integer when an instance gets created – a new integer for every instance. When you run the application, you’ll see something like the below: Now when you click on the ‘Get Product2 Instance’ button, you’ll see that the Mfg Date (which is set in the constructor) and the Hash Code are different from the one created on page load. This proves to us that a new instance is created every single time. To make this a singleton, we need to add a type alias for the ContainerControlledLifetimeManager class and then change the type attribute of the lifetime element to singleton. 1: <typeAlias alias="singleton" type="Microsoft.Practices.Unity.ContainerControlledLifetimeManager, Microsoft.Practices.Unity"/> 2: ... 3: <type type="IProduct" mapTo="Product2"> 4: <lifetime type="singleton" /> 5: </type> Running the application now gets me the following output: Click on the button below and you’ll see that the Mfg Date and the Hash code remain unchanged => the unity container is storing the reference the first time it is created and then returns the same instance every time the type needs to be resolved. Digging more deeper into this, Unity provides more than the two lifetime managers. ExternallyControlledLifetimeManager – maintains a weak reference to type mappings and instances. Unity returns the same instance as long as the some code is holding a strong reference to this instance. For this, you need: 1: <typeAlias alias="external" type="Microsoft.Practices.Unity.ExternallyControlledLifetimeManager, Microsoft.Practices.Unity"/> 2: ... 3: <type type="IProduct" mapTo="Product2"> 4: <lifetime type="external" /> 5: </type> PerThreadLifetimeManager – Unity returns a unique instance of an object for each thread – so this effectively is a singleton behavior on a  per-thread basis. 1: <typeAlias alias="perThread" type="Microsoft.Practices.Unity.PerThreadLifetimeManager, Microsoft.Practices.Unity"/> 2: ... 3: <type type="IProduct" mapTo="Product2"> 4: <lifetime type="perThread" /> 5: </type> One thing to note about this is that if you use RegisterInstance method to register an existing object, this instance will be returned for every thread, making this a purely singleton behavior. Needless to say, this type of lifetime management is useful in multi-threaded applications (duh!!). I hope this blog provided some basics on lifetime management of objects resolved in Unity and in the next blog, I’ll talk about Injection. Please see the code used here.

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  • Creating STA COM compatible ASP.NET Applications

    - by Rick Strahl
    When building ASP.NET applications that interface with old school COM objects like those created with VB6 or Visual FoxPro (MTDLL), it's extremely important that the threads that are serving requests use Single Threaded Apartment Threading. STA is a COM built-in technology that allows essentially single threaded components to operate reliably in a multi-threaded environment. STA's guarantee that COM objects instantiated on a specific thread stay on that specific thread and any access to a COM object from another thread automatically marshals that thread to the STA thread. The end effect is that you can have multiple threads, but a COM object instance lives on a fixed never changing thread. ASP.NET by default uses MTA (multi-threaded apartment) threads which are truly free spinning threads that pay no heed to COM object marshaling. This is vastly more efficient than STA threading which has a bit of overhead in determining whether it's OK to run code on a given thread or whether some sort of thread/COM marshaling needs to occur. MTA COM components can be very efficient, but STA COM components in a multi-threaded environment always tend to have a fair amount of overhead. It's amazing how much COM Interop I still see today so while it seems really old school to be talking about this topic, it's actually quite apropos for me as I have many customers using legacy COM systems that need to interface with other .NET applications. In this post I'm consolidating some of the hacks I've used to integrate with various ASP.NET technologies when using STA COM Components. STA in ASP.NET Support for STA threading in the ASP.NET framework is fairly limited. Specifically only the original ASP.NET WebForms technology supports STA threading directly via its STA Page Handler implementation or what you might know as ASPCOMPAT mode. For WebForms running STA components is as easy as specifying the ASPCOMPAT attribute in the @Page tag:<%@ Page Language="C#" AspCompat="true" %> which runs the page in STA mode. Removing it runs in MTA mode. Simple. Unfortunately all other ASP.NET technologies built on top of the core ASP.NET engine do not support STA natively. So if you want to use STA COM components in MVC or with class ASMX Web Services, there's no automatic way like the ASPCOMPAT keyword available. So what happens when you run an STA COM component in an MTA application? In low volume environments - nothing much will happen. The COM objects will appear to work just fine as there are no simultaneous thread interactions and the COM component will happily run on a single thread or multiple single threads one at a time. So for testing running components in MTA environments may appear to work just fine. However as load increases and threads get re-used by ASP.NET COM objects will end up getting created on multiple different threads. This can result in crashes or hangs, or data corruption in the STA components which store their state in thread local storage on the STA thread. If threads overlap this global store can easily get corrupted which in turn causes problems. STA ensures that any COM object instance loaded always stays on the same thread it was instantiated on. What about COM+? COM+ is supposed to address the problem of STA in MTA applications by providing an abstraction with it's own thread pool manager for COM objects. It steps in to the COM instantiation pipeline and hands out COM instances from its own internally maintained STA Thread pool. This guarantees that the COM instantiation threads are STA threads if using STA components. COM+ works, but in my experience the technology is very, very slow for STA components. It adds a ton of overhead and reduces COM performance noticably in load tests in IIS. COM+ can make sense in some situations but for Web apps with STA components it falls short. In addition there's also the need to ensure that COM+ is set up and configured on the target machine and the fact that components have to be registered in COM+. COM+ also keeps components up at all times, so if a component needs to be replaced the COM+ package needs to be unloaded (same is true for IIS hosted components but it's more common to manage that). COM+ is an option for well established components, but native STA support tends to provide better performance and more consistent usability, IMHO. STA for non supporting ASP.NET Technologies As mentioned above only WebForms supports STA natively. However, by utilizing the WebForms ASP.NET Page handler internally it's actually possible to trick various other ASP.NET technologies and let them work with STA components. This is ugly but I've used each of these in various applications and I've had minimal problems making them work with FoxPro STA COM components which is about as dififcult as it gets for COM Interop in .NET. In this post I summarize several STA workarounds that enable you to use STA threading with these ASP.NET Technologies: ASMX Web Services ASP.NET MVC WCF Web Services ASP.NET Web API ASMX Web Services I start with classic ASP.NET ASMX Web Services because it's the easiest mechanism that allows for STA modification. It also clearly demonstrates how the WebForms STA Page Handler is the key technology to enable the various other solutions to create STA components. Essentially the way this works is to override the WebForms Page class and hijack it's init functionality for processing requests. Here's what this looks like for Web Services:namespace FoxProAspNet { public class WebServiceStaHandler : System.Web.UI.Page, IHttpAsyncHandler { protected override void OnInit(EventArgs e) { IHttpHandler handler = new WebServiceHandlerFactory().GetHandler( this.Context, this.Context.Request.HttpMethod, this.Context.Request.FilePath, this.Context.Request.PhysicalPath); handler.ProcessRequest(this.Context); this.Context.ApplicationInstance.CompleteRequest(); } public IAsyncResult BeginProcessRequest( HttpContext context, AsyncCallback cb, object extraData) { return this.AspCompatBeginProcessRequest(context, cb, extraData); } public void EndProcessRequest(IAsyncResult result) { this.AspCompatEndProcessRequest(result); } } public class AspCompatWebServiceStaHandlerWithSessionState : WebServiceStaHandler, IRequiresSessionState { } } This class overrides the ASP.NET WebForms Page class which has a little known AspCompatBeginProcessRequest() and AspCompatEndProcessRequest() method that is responsible for providing the WebForms ASPCOMPAT functionality. These methods handle routing requests to STA threads. Note there are two classes - one that includes session state and one that does not. If you plan on using ASP.NET Session state use the latter class, otherwise stick to the former. This maps to the EnableSessionState page setting in WebForms. This class simply hooks into this functionality by overriding the BeginProcessRequest and EndProcessRequest methods and always forcing it into the AspCompat methods. The way this works is that BeginProcessRequest() fires first to set up the threads and starts intializing the handler. As part of that process the OnInit() method is fired which is now already running on an STA thread. The code then creates an instance of the actual WebService handler factory and calls its ProcessRequest method to start executing which generates the Web Service result. Immediately after ProcessRequest the request is stopped with Application.CompletRequest() which ensures that the rest of the Page handler logic doesn't fire. This means that even though the fairly heavy Page class is overridden here, it doesn't end up executing any of its internal processing which makes this code fairly efficient. In a nutshell, we're highjacking the Page HttpHandler and forcing it to process the WebService process handler in the context of the AspCompat handler behavior. Hooking up the Handler Because the above is an HttpHandler implementation you need to hook up the custom handler and replace the standard ASMX handler. To do this you need to modify the web.config file (here for IIS 7 and IIS Express): <configuration> <system.webServer> <handlers> <remove name="WebServiceHandlerFactory-Integrated-4.0" /> <add name="Asmx STA Web Service Handler" path="*.asmx" verb="*" type="FoxProAspNet.WebServiceStaHandler" precondition="integrated"/> </handlers> </system.webServer> </configuration> (Note: The name for the WebServiceHandlerFactory-Integrated-4.0 might be slightly different depending on your server version. Check the IIS Handler configuration in the IIS Management Console for the exact name or simply remove the handler from the list there which will propagate to your web.config). For IIS 5 & 6 (Windows XP/2003) or the Visual Studio Web Server use:<configuration> <system.web> <httpHandlers> <remove path="*.asmx" verb="*" /> <add path="*.asmx" verb="*" type="FoxProAspNet.WebServiceStaHandler" /> </httpHandlers> </system.web></configuration> To test, create a new ASMX Web Service and create a method like this: [WebService(Namespace = "http://foxaspnet.org/")] [WebServiceBinding(ConformsTo = WsiProfiles.BasicProfile1_1)] public class FoxWebService : System.Web.Services.WebService { [WebMethod] public string HelloWorld() { return "Hello World. Threading mode is: " + System.Threading.Thread.CurrentThread.GetApartmentState(); } } Run this before you put in the web.config configuration changes and you should get: Hello World. Threading mode is: MTA Then put the handler mapping into Web.config and you should see: Hello World. Threading mode is: STA And you're on your way to using STA COM components. It's a hack but it works well! I've used this with several high volume Web Service installations with various customers and it's been fast and reliable. ASP.NET MVC ASP.NET MVC has quickly become the most popular ASP.NET technology, replacing WebForms for creating HTML output. MVC is more complex to get started with, but once you understand the basic structure of how requests flow through the MVC pipeline it's easy to use and amazingly flexible in manipulating HTML requests. In addition, MVC has great support for non-HTML output sources like JSON and XML, making it an excellent choice for AJAX requests without any additional tools. Unlike WebForms ASP.NET MVC doesn't support STA threads natively and so some trickery is needed to make it work with STA threads as well. MVC gets its handler implementation through custom route handlers using ASP.NET's built in routing semantics. To work in an STA handler requires working in the Page Handler as part of the Route Handler implementation. As with the Web Service handler the first step is to create a custom HttpHandler that can instantiate an MVC request pipeline properly:public class MvcStaThreadHttpAsyncHandler : Page, IHttpAsyncHandler, IRequiresSessionState { private RequestContext _requestContext; public MvcStaThreadHttpAsyncHandler(RequestContext requestContext) { if (requestContext == null) throw new ArgumentNullException("requestContext"); _requestContext = requestContext; } public IAsyncResult BeginProcessRequest(HttpContext context, AsyncCallback cb, object extraData) { return this.AspCompatBeginProcessRequest(context, cb, extraData); } protected override void OnInit(EventArgs e) { var controllerName = _requestContext.RouteData.GetRequiredString("controller"); var controllerFactory = ControllerBuilder.Current.GetControllerFactory(); var controller = controllerFactory.CreateController(_requestContext, controllerName); if (controller == null) throw new InvalidOperationException("Could not find controller: " + controllerName); try { controller.Execute(_requestContext); } finally { controllerFactory.ReleaseController(controller); } this.Context.ApplicationInstance.CompleteRequest(); } public void EndProcessRequest(IAsyncResult result) { this.AspCompatEndProcessRequest(result); } public override void ProcessRequest(HttpContext httpContext) { throw new NotSupportedException("STAThreadRouteHandler does not support ProcessRequest called (only BeginProcessRequest)"); } } This handler code figures out which controller to load and then executes the controller. MVC internally provides the information needed to route to the appropriate method and pass the right parameters. Like the Web Service handler the logic occurs in the OnInit() and performs all the processing in that part of the request. Next, we need a RouteHandler that can actually pick up this handler. Unlike the Web Service handler where we simply registered the handler, MVC requires a RouteHandler to pick up the handler. RouteHandlers look at the URL's path and based on that decide on what handler to invoke. The route handler is pretty simple - all it does is load our custom handler: public class MvcStaThreadRouteHandler : IRouteHandler { public IHttpHandler GetHttpHandler(RequestContext requestContext) { if (requestContext == null) throw new ArgumentNullException("requestContext"); return new MvcStaThreadHttpAsyncHandler(requestContext); } } At this point you can instantiate this route handler and force STA requests to MVC by specifying a route. The following sets up the ASP.NET Default Route:Route mvcRoute = new Route("{controller}/{action}/{id}", new RouteValueDictionary( new { controller = "Home", action = "Index", id = UrlParameter.Optional }), new MvcStaThreadRouteHandler()); RouteTable.Routes.Add(mvcRoute);   To make this code a little easier to work with and mimic the behavior of the routes.MapRoute() functionality extension method that MVC provides, here is an extension method for MapMvcStaRoute(): public static class RouteCollectionExtensions { public static void MapMvcStaRoute(this RouteCollection routeTable, string name, string url, object defaults = null) { Route mvcRoute = new Route(url, new RouteValueDictionary(defaults), new MvcStaThreadRouteHandler()); RouteTable.Routes.Add(mvcRoute); } } With this the syntax to add  route becomes a little easier and matches the MapRoute() method:RouteTable.Routes.MapMvcStaRoute( name: "Default", url: "{controller}/{action}/{id}", defaults: new { controller = "Home", action = "Index", id = UrlParameter.Optional } ); The nice thing about this route handler, STA Handler and extension method is that it's fully self contained. You can put all three into a single class file and stick it into your Web app, and then simply call MapMvcStaRoute() and it just works. Easy! To see whether this works create an MVC controller like this: public class ThreadTestController : Controller { public string ThreadingMode() { return Thread.CurrentThread.GetApartmentState().ToString(); } } Try this test both with only the MapRoute() hookup in the RouteConfiguration in which case you should get MTA as the value. Then change the MapRoute() call to MapMvcStaRoute() leaving all the parameters the same and re-run the request. You now should see STA as the result. You're on your way using STA COM components reliably in ASP.NET MVC. WCF Web Services running through IIS WCF Web Services provide a more robust and wider range of services for Web Services. You can use WCF over HTTP, TCP, and Pipes, and WCF services support WS* secure services. There are many features in WCF that go way beyond what ASMX can do. But it's also a bit more complex than ASMX. As a basic rule if you need to serve straight SOAP Services over HTTP I 'd recommend sticking with the simpler ASMX services especially if COM is involved. If you need WS* support or want to serve data over non-HTTP protocols then WCF makes more sense. WCF is not my forte but I found a solution from Scott Seely on his blog that describes the progress and that seems to work well. I'm copying his code below so this STA information is all in one place and quickly explain. Scott's code basically works by creating a custom OperationBehavior which can be specified via an [STAOperation] attribute on every method. Using his attribute you end up with a class (or Interface if you separate the contract and class) that looks like this: [ServiceContract] public class WcfService { [OperationContract] public string HelloWorldMta() { return Thread.CurrentThread.GetApartmentState().ToString(); } // Make sure you use this custom STAOperationBehavior // attribute to force STA operation of service methods [STAOperationBehavior] [OperationContract] public string HelloWorldSta() { return Thread.CurrentThread.GetApartmentState().ToString(); } } Pretty straight forward. The latter method returns STA while the former returns MTA. To make STA work every method needs to be marked up. The implementation consists of the attribute and OperationInvoker implementation. Here are the two classes required to make this work from Scott's post:public class STAOperationBehaviorAttribute : Attribute, IOperationBehavior { public void AddBindingParameters(OperationDescription operationDescription, System.ServiceModel.Channels.BindingParameterCollection bindingParameters) { } public void ApplyClientBehavior(OperationDescription operationDescription, System.ServiceModel.Dispatcher.ClientOperation clientOperation) { // If this is applied on the client, well, it just doesn’t make sense. // Don’t throw in case this attribute was applied on the contract // instead of the implementation. } public void ApplyDispatchBehavior(OperationDescription operationDescription, System.ServiceModel.Dispatcher.DispatchOperation dispatchOperation) { // Change the IOperationInvoker for this operation. dispatchOperation.Invoker = new STAOperationInvoker(dispatchOperation.Invoker); } public void Validate(OperationDescription operationDescription) { if (operationDescription.SyncMethod == null) { throw new InvalidOperationException("The STAOperationBehaviorAttribute " + "only works for synchronous method invocations."); } } } public class STAOperationInvoker : IOperationInvoker { IOperationInvoker _innerInvoker; public STAOperationInvoker(IOperationInvoker invoker) { _innerInvoker = invoker; } public object[] AllocateInputs() { return _innerInvoker.AllocateInputs(); } public object Invoke(object instance, object[] inputs, out object[] outputs) { // Create a new, STA thread object[] staOutputs = null; object retval = null; Thread thread = new Thread( delegate() { retval = _innerInvoker.Invoke(instance, inputs, out staOutputs); }); thread.SetApartmentState(ApartmentState.STA); thread.Start(); thread.Join(); outputs = staOutputs; return retval; } public IAsyncResult InvokeBegin(object instance, object[] inputs, AsyncCallback callback, object state) { // We don’t handle async… throw new NotImplementedException(); } public object InvokeEnd(object instance, out object[] outputs, IAsyncResult result) { // We don’t handle async… throw new NotImplementedException(); } public bool IsSynchronous { get { return true; } } } The key in this setup is the Invoker and the Invoke method which creates a new thread and then fires the request on this new thread. Because this approach creates a new thread for every request it's not super efficient. There's a bunch of overhead involved in creating the thread and throwing it away after each thread, but it'll work for low volume requests and insure each thread runs in STA mode. If better performance is required it would be useful to create a custom thread manager that can pool a number of STA threads and hand off threads as needed rather than creating new threads on every request. If your Web Service needs are simple and you need only to serve standard SOAP 1.x requests, I would recommend sticking with ASMX services. It's easier to set up and work with and for STA component use it'll be significantly better performing since ASP.NET manages the STA thread pool for you rather than firing new threads for each request. One nice thing about Scotts code is though that it works in any WCF environment including self hosting. It has no dependency on ASP.NET or WebForms for that matter. STA - If you must STA components are a  pain in the ass and thankfully there isn't too much stuff out there anymore that requires it. But when you need it and you need to access STA functionality from .NET at least there are a few options available to make it happen. Each of these solutions is a bit hacky, but they work - I've used all of them in production with good results with FoxPro components. I hope compiling all of these in one place here makes it STA consumption a little bit easier. I feel your pain :-) Resources Download STA Handler Code Examples Scott Seely's original STA WCF OperationBehavior Article© Rick Strahl, West Wind Technologies, 2005-2012Posted in FoxPro   ASP.NET  .NET  COM   Tweet !function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0];if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src="//platform.twitter.com/widgets.js";fjs.parentNode.insertBefore(js,fjs);}}(document,"script","twitter-wjs"); (function() { var po = document.createElement('script'); po.type = 'text/javascript'; po.async = true; po.src = 'https://apis.google.com/js/plusone.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(po, s); })();

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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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  • SQLAuthority News – Meeting with Allen Bailochan Tuladhar – An Unlimited Experience

    - by pinaldave
    Allen  Tuladhar I recently came back from my 9-day trip in Nepal and I must say that this is one of the best trips I had in my lifetime. Allen Bailochan Tuladhar is a wonderful person and an extreme enthusiast for Microsoft Technology. Allen is the Chief Executive Officer of Unlimited Technologies Pvt Ltd., Country Manager of Microsoft MDP Nepal, the Member Secretary of Nepali Language in Information Technology, and member of the Steering Committee of the Government of Nepal. He is the person who keeps the Nepal’s Tech Community constantly motivating and taking it to the next level. I have met Allen for many times before, but this was the first time I was with him in Kathmandu, Nepal. I was very impressed with the amount of the work he does in the community. During my 9 days of stay, every single day was a new lesson for me. I was amazed and overwhelmed with the many things he does every single day. Not only he does he work closely with Government of Nepal ministry, but he is also the most known person in the Student Community. His expertise in the technical subject matter is not limited to one technology; rather, I have seen him actively engaging himself in  discussions of various tech topics. Allen presending at TechMela Kathmandu, Nepal Allen is currently active in working out to localize Windows and Office and incorporate it using the Nepali language. I was able to witness and experience how the localization works, as well as the procedure on how to do such. If you know the whole localization process, you must have realized how big and daunting of a process it is. I was glad that I became a part of it. Prominent Personality of Nepal on Panel Discussion Another great opportunity I had when I was at Allen’s office is that I have learned how the radio technology talk show works. Nepali Radio station has the weekly program in their local language, in which MS technology is discussed and industry leaders are invited to talk about their experience with the technology. I found the program so interesting because it has so much variety in terms of technology subjects. Well, my understanding of Nepali language is limited but I did understand quite a bit. Ravi, Nutan, Pinal, Gandip I got the chance to meet lots of Database Professionals as well. People in Nepal are very polite even though they are very strong in their technology fundamentals. I had in-depth discussion regarding High Availability scenarios, as well Query Tuning. Database professionals from the leading financial sectors of Nepal wanted me to visit their Data Center and help them out with a few advances. In no time, Allen organized a visit for me. He sent me a Nepali-speaking expert from his own organization to accompany me in overcoming any difficulties while I was on my way helping this financial district. Pinal (SQLAuthority) and Deependra (Unlimited) When I was going to Nepal, I was really not sure if I would be able to stay busy for 9 days straight in Community-related activity. However, on the 9th day I realize that I can still stay here for more than 9 days because in every single day, I feel enthusiastic enough to do something new. Allen Bailochan Tuladhar Even though I was working  very hard every day, I hardly had the chance to work with and talk to him one-on-one for the first few days. One of the evenings, Allen invited me to his home and we discussed about his future ideas. I was really surprised to see how much a man can do for his technical community and for his country. When I asked Allen’s wife and daughter if they ever think it’s getting too much with regards to Allen putting tough efforts to the community, their answer was something I did not expect. I found out that Allen’s wife manages all the back office and logistics of the community events and his daughter manages the websites. I felt that they do not have any complain,  and instead, their whole family is in this activity as deeply as it can get, which I thought is a very good thing. Pinal and Allen I want to end this post with an interesting story that happened during our lunch hour at one of the Nepali restaurants. While we were having our lunch and having some chitchat, Allen suddenly stood up and called several people walking along the pavement. He introduced them all to me as Microsoft Student Partners. He asked all of them to order their favorite dish and called the waiter to inform that he will pick up their tab. Figuring out the question written on my face, he just said one sentence: “They are all future technology professionals who are going to make all of us proud.” I guess I have a lot of things to learn. Hats off to Allen! Pinal and Allen at Microsoft MDP Unlimited Reference: Pinal Dave (http://blog.SQLAuthority.com) Filed under: MVP, SQL, SQL Authority, SQL Query, SQL Server, SQL Tips and Tricks, SQLAuthority Author Visit, T SQL, Technology

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