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  • Integration features enabled but drives not available

    - by dsjbirch
    Frustratingly, after a recent update to Windows XP mode integration features, the availability of shared disks from the hosts has been impaired. Does anyone know any kind of workaround or fix (excluding dropbox et al)? I have tried completely uninstalling and reinstalling as per http://www.sevenforums.com/virtualization/63710-refreshing-xp-mode.html#post568715 At one point restarting the machine appeared to have worked, but today again I am without access to my host. Interestingly audio and copy and paste to and from the machine are working.

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  • Virtual Machine Manager Error - Error determing default hypervisor

    - by dallasclark
    I have Fedora 11 and trying to get Xen working (which I think it is already) but the Virtual Machine Manager cannot find the hypervisor. When starting Virtual Machine Manager, I receive the following error Error determining default hypervisor. Could not populate a default connection. Make sure the appropriate virtualization packages are installed (kvm, qemu, etc.) and that libvirtd has been restarted to notice the change. A hypervisor connection can be manually added via File - Add Connection I've restarted libvirtd a few times and tried connecting manually but can't work it out. Some useful information: # lsof | grep xen libvirtd 2962 root mem REG 253,0 19776 13379 /usr/lib/libxenstore.so.3.0.0 # service libvirtd status libvirtd (pid 2962) is running...

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  • Virtual functions and polymorphism

    - by ritmbo
    Suppose I have this: class A { public: virtual int hello(A a); }; class B : public A { public: int hello(B b){ bla bla }; }; So, A it's an abstract class. 1)In the class B, I'm defining a method that its suppose overrides the A class. But the parameter it's slightly different. I'm not sure about this, is this correct? Maybe because of polymorphism, this is ok but its rather confusing. 2) If I do: A a = new B;, and then a.hello(lol); if "lol" it's not of type B, then it would give compile error?, and if it's of type A from another class C (class C : public A), what would happend? I'm confused about the overriding and virtual thing.. all examples I found work with methods without parameters. Any answer, link, or whatever it's appreciated. thanks pd: sorry for my english

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  • Accessing Bluetooth virtual COM port on Windows without manual pairing

    - by oo_olo_oo
    I need to connect to a Bluetooth device through virtual COM port created in Windows. It's easy when the port has been already created during manual pairing procedure. But I would like my application to relieve an user from the manual pairing of a device. I would like to present all devices in the range, allow user to chose one, and then create virtual COM port connected with the selected device. I'm not trying to avoid the pairing procedure itself, but rather I would like to invoke it by my application. I started getting familiar with Microsoft Bluetooth API. And then some doubts arose. I've been wondering what happen if some user would use different (than Microsoft's) Bluetooth stack? Is the Microsoft's API the real Bluetooth API, which have to be implemented by any other Bluetooth stack provider? Or rather each provider has its own API, and the Microsoft's is only one of many other?

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  • Java input method for Virtual Keyboad

    - by shekhar
    Hi, I am facing problem in implementing Input method for Virtual Keyboard, currently I am using robot class for sending input to any application from virtual keyboard. but for that I need to create mapping of key-code and unicode, which is not consistent on different keyboard layout, can I directly pass the UNICODE to any application using Input method without worry about mapping between keycode and unicode. any useful link or sample code will be useful. It is simple Java program which is always on top of any application and work as onscreen keyboard. using a mouse while you press any button (key) of the keyboard, the corresponding character will be typed in the application running below. This is working perfectly for English Alphabets. I am facing problem while I am doing for unicode.

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  • How to free virtual memory ?

    - by Mehdi Amrollahi
    I have a crawler application (with C#) that downloads pages from web . The application take more virtual memory , even i dispose every object and even use GC.Collect() . This , have 10 thread and each thread has a socket that downloads pages . I use dispose method and even use GC.Collect() in my application , but in 3 hour my application take 500 MB on virtual memory (500 MB on private bytes in Process explorer) . Then my system will be hang and i should restart my pc . Is there any way that i use to free vitual memory ? Thanks .

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  • Virtual Machine Performance - More RAM or More Processor?

    - by webworm
    When looking to improve Virtual Machine performance what would be better ... Increasing the available RAM or increasing the processor power? Here is my choice ... Core 2 Duo @ 2.4 GHz with 8 GB RAM and integrated graphics (Mac Book Pro 13") Core i7 @ 2.6 GHz with 4 GB RAM and 512 MB dedicated graphics (Mac Book Pro 15") I plan to run Windows x64 in the VM with SQL Server 2008, Visual Studio 2010, and SharePoint 2010. I am planning to run VMWare Fusion v3. I also didn't know if a dedicated graphics card makes a difference when using a Virtual Machine. Thank you.

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  • Assembly - Read next sector of a virtual disk

    - by ali
    As any programmer in the world at least once in his/her life, I am trying to create my "revolutionary", the new and only one operating system. :D Well, I am using a virtual emulator (Oracle VM Virtual Box), for which I create a new unknwon operating system, with a vmdk disk. I like vmdk because they are just plain files, so I can paste my boot-loader over the first 512 bytes of the virtual hard disk. Now, I am trying to read the next sector of this virtual disk, on which I would paste a simple kernel that would display a message. I have two questions: Am I reading the second segment (the first -512 bytes- is occupied by the bootloader) correctly? CODE: CitesteDisc: mov bx, 0x8000 ; segment mov es, bx mov bx, 0x0000 ; offset mov ah, 0x02 ; read function mov al, 0x01 ; sectors - this might be wrong, trying to read from hd mov ch, 0x00 ; cylinder mov cl, 0x02 ; sector mov dh, 0x00 ; head mov dl, 0x80 ; drive - trying to read from hd int 0x13 ; disk int mov si, ErrorMessage ; - This will display an error message jc ShowMessage jmp [es:bx] ; buffer Here, I get the error message, after checking CF. However, if I use INT 13, 1 to get last status message, AL is 0 - so no error is saved. Am I pasting my simple kernel in the correct place inside the vmdk? What I do is pasting it after the 512th byte of the file, the first 512 bytes, as I said, are the boot-loader. The file would look like this: BE 45 7C E8 16 00 EB FE B4 0E B7 00 B3 07 CD 10 <- First sector C3 AC 08 C0 74 05 E8 EF FF EB F6 C3 B4 00 B2 80 CD 13 BE 5D 7C 72 F5 BB 00 80 8E C3 BB 00 00 B4 02 B0 06 B5 00 B1 01 B6 00 B2 07 CD 13 BE 4E 7C 72 CF 26 FF 27 57 65 6C 63 6F 6D 65 21 00 52 65 61 64 69 6E 67 20 65 72 72 6F 72 21 00 52 65 73 65 74 74 69 6E 67 20 65 72 72 6F 72 21 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 55 AA <- Boot-loader signature B4 0E B0 2E CD 10 EB FE 00 00 00 00 00 00 00 00 <- Start of the second sector 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 So, this is the way I am trying to add the kernel to the second sector. What do you think is wrong with this? Thanks!

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  • Caching for a Custom Repositiory Adapter for WebSphere Portal Virtual Member Manager

    - by Spike Williams
    I'm looking at writing a custom repository adapter to interact with Virtual Member Manager on WebSphere Portal 6.1. Basically, its a layer that takes a request in the form of a commonj.sco.DataObject and passes that on to an external web service, to get various information on our logged in users that is not otherwise available in LDAP. I'm concerned about the performance hit of going to a service every time we want to pull some permission from the back end. My question is, can the Virtual Member Manager handle caching of data going in and out of the custom repository adapters, or is that something I'm going to have to build into the adapter myself?

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  • Display virtual keyword asp.net for password

    - by Nicole
    Hi! I have a login page with an input of type "password" I would like to have a virtual keyboard to enter the password. I've searched and I found the jquery script for virtual keyboard. The code said to add this to my page $('input[type=password]').keyboard({ layout: "qwerty", customLayout: [["q w e r t y {bksp}", "Q W E R T Y {bksp}"], ["s a m p l e {shift}", "S A M P L E {shift}"], ["{accept} {space} {cancel}", "{accept} {space} {cancel}"]] }); but I cant make it work!!!! nothing happens when y set focus on my password control. Any suggestions?? thank you!! Nicole.

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  • Junctions or Virtual Directories for Web Applications?

    - by Kevin
    I see that junctions are a common way of referencing shared code in many projects. However, I have not seen them used in web applications before. Our team is exploring the possibility of abandoning virtual directories in favor of junctions to simplify our build process. My goal is to compile a list of pros and cons in order to make an informed decision regarding this change. Is it more appropriate to use junctions or virtual directories on web application projects? Environment is ASP.NET, IIS6/IIS7, VS.NET.

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  • apache on windows virtual directory config help

    - by sprugman
    I'm running Apache on Windows XP via Xampplite, and could use help configuring my virtual directory. Here's what I'm hoping to do on my dev box: I want my source files to live outside of the xampp htdocs dir on my local machine I can access the project at http://myproject others on my local network can access the project at my.ip.address/myproject keep localhost pointing to the xampp's htdocs folder so I can easily add other projects. I've got 1 & 2 working by editing the windows hosts file, and adding a virtual directory in xampp's apache\conf\extra\httpd-vhosts.conf file. I don't immediately see how to do 3 without messing up 4.

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  • C++ virtual + protected?

    - by user346113
    Hi, In C++, I have a base class A, a sub class B. Both have the virtual method Visit. I would like to redefine 'Visit' in B, but B need to access the 'Visit' function of each A (and all subclass to). I have something like that, but it tell me that B cannot access the protected member of A! But B is a A too :-P So, what can I do? class A { protected: virtual Visit(...); } class B : public class A { protected: vector<A*> childs; Visit(...); } B::Visit(...) { foreach(A* a in childs) { a->Visit(...); } } Thx

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  • Overriding vs Virtual

    - by anonymous
    What is the purpose of using the reserved word virtual in front of functions? If I want a child class to override a parent function, I just declare the same function such as "void draw(){}". class Parent{ public: void say(){ std::cout << "1"; }}; class Child : public Parent{public:void say(){ std::cout << "2"; } }; int main() { Child* a = new Child(); a->say(); return 0; } The output is 2. So again, why would the reserved word "virtual" be necessary in the header of say() ? Thanks a bunch.

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  • Why I have to redeclare a virtual function while overriding [C++]

    - by Neeraj
    #include <iostream> using namespace std; class Duck { public: virtual void quack() = 0; }; class BigDuck : public Duck { public: // void quack(); (uncommenting will make it compile) }; void BigDuck::quack(){ cout << "BigDuckDuck::Quack\n"; } int main() { BigDuck b; Duck *d = &b; d->quack(); } Consider this code, the code doesn't compiles. However when I declare the virtual function in the subclass, then it compiles fine. The compiler already has the signature of the function which the subclass will override, then why a redeclaration is required? Any insights.

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

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

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  • Apache virtual host does not work properly

    - by Jori
    I have read a lot of information all over the Internet regarding this subject, and can not figure out what I'am doing wrong. I'm trying to host two websites under different names locally under Windows 7 with Apaches Virtual Hosting functionality. This is what I have done already: In the httpd.conf file I uncommented the following line, so that the virtual host configuration file will be included in the main configuration sequence. # Virtual hosts Include conf/extra/httpd-vhosts.conf This is how I edited my httpd-vhosts.conf: # # Virtual Hosts # # If you want to maintain multiple domains/hostnames on your # machine you can setup VirtualHost containers for them. Most configurations # use only name-based virtual hosts so the server doesn't need to worry about # IP addresses. This is indicated by the asterisks in the directives below. # # Please see the documentation at # <URL:http://httpd.apache.org/docs/2.2/vhosts/> # for further details before you try to setup virtual hosts. # # You may use the command line option '-S' to verify your virtual host # configuration. # # Use name-based virtual hosting. # NameVirtualHost *:80 # # VirtualHost example: # Almost any Apache directive may go into a VirtualHost container. # The first VirtualHost section is used for all requests that do not # match a ServerName or ServerAlias in any <VirtualHost> block. # #<VirtualHost *:80> # ServerAdmin [email protected] # DocumentRoot "C:/apache/docs/dummy-host.localhost" # ServerName dummy-host.localhost # ServerAlias www.dummy-host.localhost # ErrorLog "logs/dummy-host.localhost-error.log" # CustomLog "logs/dummy-host.localhost-access.log" common #</VirtualHost> # #<VirtualHost *:80> # ServerAdmin [email protected] # DocumentRoot "C:/apache/docs/dummy-host2.localhost" # ServerName dummy-host2.localhost # ErrorLog "logs/dummy-host2.localhost-error.log" # CustomLog "logs/dummy-host2.localhost-access.log" common #</VirtualHost> <VirtualHost *:80> ServerName arterieur DocumentRoot "J:/webcontent/www20" <Directory "J:/webcontent/www20"> Order allow,deny Allow from all </Directory> </VirtualHost> As you can see I commented the Virtual Host examples out and added my own one (I did one for this example). Also am I sure that J:\webcontent\www20 exists. At last I edited the Windows host file located in: C:\Windows\System32\drivers\etc\hosts, now it looks this: # Copyright (c) 1993-2009 Microsoft Corp. # # This is a sample HOSTS file used by Microsoft TCP/IP for Windows. # # This file contains the mappings of IP addresses to host names. Each # entry should be kept on an individual line. The IP address should # be placed in the first column followed by the corresponding host name. # The IP address and the host name should be separated by at least one # space. # # Additionally, comments (such as these) may be inserted on individual # lines or following the machine name denoted by a '#' symbol. # # For example: # # 102.54.94.97 rhino.acme.com # source server # 38.25.63.10 x.acme.com # x client host # localhost name resolution is handled within DNS itself. # 127.0.0.1 localhost # ::1 localhost 127.0.0.1 arterieur Then I restarted Apache with the Apache Service Monitor, and it gave me the following fatal error: The requested operation has failed!, I tried to look at the apache/logs/error.log file but I did not log anything, I guess it only logs the errors after startup. Does anyone knows what I'am doing wrong?

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  • Problems Allocating Objects of Derived Class Where Base Class has Abstract Virtual Functions

    - by user1743901
    I am trying to get this Zombie/Human agent based simulation running, but I am having problems with these derived classes (Human and Zombie) who have parent class "Creature". I have 3 virtual functions declared in "Creature" and all three of these are re-declared AND DEFINED in both "Human" and "Zombie". But for some reason when I have my program call "new" to allocate memory for objects of type Human or Zombie, it complains about the virtual functions being abstract. Here's the code: definitions.h #ifndef definitions_h #define definitions_h class Creature; class Item; class Coords; class Grid { public: Creature*** cboard; Item*** iboard; int WIDTH; int HEIGHT; Grid(int WIDTHVALUE, int HEIGHTVALUE); void FillGrid(); //initializes grid object with humans and zombies void Refresh(); //calls Creature::Die(),Move(),Attack(),Breed() on every square void UpdateBuffer(char** buffer); bool isEmpty(int startx, int starty, int dir); char CreatureType(int xcoord, int ycoord); char CreatureType(int startx, int starty, int dir); }; class Random { public: int* rptr; void Print(); Random(int MIN, int MAX, int LEN); ~Random(); private: bool alreadyused(int checkthis, int len, int* rptr); bool isClean(); int len; }; class Coords { public: int x; int y; int MaxX; int MaxY; Coords() {x=0; y=0; MaxX=0; MaxY=0;} Coords(int X, int Y, int WIDTH, int HEIGHT) {x=X; y=Y; MaxX=WIDTH; MaxY=HEIGHT; } void MoveRight(); void MoveLeft(); void MoveUp(); void MoveDown(); void MoveUpRight(); void MoveUpLeft(); void MoveDownRight(); void MoveDownLeft(); void MoveDir(int dir); void setx(int X) {x=X;} void sety(int Y) {y=Y;} }; class Creature { public: bool alive; Coords Location; char displayletter; Creature() {Location.x=0; Location.y=0;} Creature(int i, int j) {Location.setx(i); Location.sety(j);} virtual void Attack() =0; virtual void AttackCreature(Grid G, int attackdirection) =0; virtual void Breed() =0; void Die(); void Move(Grid G); int DecideSquare(Grid G); void MoveTo(Grid G, int dir); }; class Human : public Creature { public: bool armed; //if armed, chances of winning fight increased for next fight bool vaccinated; //if vaccinated, no chance of getting infected int bitecount; //if a human is bitten, bite count is set to a random number int breedcount; //if a human goes x steps without combat, will breed if next to a human int starvecount; //if a human does not eat in x steps, will die Human() {displayletter='H';} Human(int i, int j) {displayletter='H';} void Attack(Grid G); void AttackCreature(Grid G, int attackdirection); void Breed(Grid G); //will breed after x steps and next to human int DecideAttack(Grid G); }; class Zombie : public Creature { public: Zombie() {displayletter='Z';} Zombie(int i, int j) {displayletter='Z';} void Attack(Grid G); void AttackCreature(Grid G, int attackdirection); void Breed() {} //does nothing int DecideAttack(Grid G); void AttackCreature(Grid G, int attackdirection); }; class Item { }; #endif definitions.cpp #include <cstdlib> #include "definitions.h" Random::Random(int MIN, int MAX, int LEN) //constructor { len=LEN; rptr=new int[LEN]; //allocate array of given length for (int i=0; i<LEN; i++) { int random; do { random = rand() % (MAX-MIN+1) + MIN; } while (alreadyused(random,LEN,rptr)); rptr[i]=random; } } bool Random::alreadyused(int checkthis, int len, int* rptr) { for (int i=0; i<len; i++) { if (rptr[i]==checkthis) return 1; } return 0; } Random::~Random() { delete rptr; } Grid::Grid(int WIDTHVALUE, int HEIGHTVALUE) { WIDTH = WIDTHVALUE; HEIGHT = HEIGHTVALUE; //builds 2d array of creature pointers cboard = new Creature**[WIDTH]; for(int i=0; i<WIDTH; i++) { cboard[i] = new Creature*[HEIGHT]; } //builds 2d array of item pointers iboard = new Item**[WIDTH]; for (int i=0; i<WIDTH; i++) { iboard[i] = new Item*[HEIGHT]; } } void Grid::FillGrid() { /* For each creature pointer in grid, randomly selects whether to initalize as zombie, human, or empty square. This methodology can be changed to initialize different creature types with different probabilities */ int random; for (int i=0; i<WIDTH; i++) { for (int j=0; j<HEIGHT; j++) { Random X(1,100,1); //create a single random integer from [1,100] at X.rptr random=*(X.rptr); if (random < 20) cboard[i][j] = new Human(i,j); else if (random < 40) cboard[i][j] = new Zombie(i,j); else cboard[i][j] = NULL; } } //at this point every creature pointer should be pointing to either //a zombie, human, or NULL with varying probabilities } void Grid::UpdateBuffer(char** buffer) { for (int i=0; i<WIDTH; i++) { for (int j=0; j<HEIGHT; j++) { if (cboard[i][j]) buffer[i][j]=cboard[i][j]->displayletter; else buffer[i][j]=' '; } } } bool Grid::isEmpty(int startx, int starty, int dir) { Coords StartLocation(startx,starty,WIDTH,HEIGHT); switch(dir) { case 1: StartLocation.MoveUp(); if (cboard[StartLocation.x][StartLocation.y]) return 0; case 2: StartLocation.MoveUpRight(); if (cboard[StartLocation.x][StartLocation.y]) return 0; case 3: StartLocation.MoveRight(); if (cboard[StartLocation.x][StartLocation.y]) return 0; case 4: StartLocation.MoveDownRight(); if (cboard[StartLocation.x][StartLocation.y]) return 0; case 5: StartLocation.MoveDown(); if (cboard[StartLocation.x][StartLocation.y]) return 0; case 6: StartLocation.MoveDownLeft(); if (cboard[StartLocation.x][StartLocation.y]) return 0; case 7: StartLocation.MoveLeft(); if (cboard[StartLocation.x][StartLocation.y]) return 0; case 8: StartLocation.MoveUpLeft(); if (cboard[StartLocation.x][StartLocation.y]) return 0; } return 1; } char Grid::CreatureType(int xcoord, int ycoord) { if (cboard[xcoord][ycoord]) //if there is a creature at location xcoord,ycoord return (cboard[xcoord][ycoord]->displayletter); else //if pointer at location xcoord,ycoord is null, return null char return '\0'; } char Grid::CreatureType(int startx, int starty, int dir) { Coords StartLocation(startx,starty,WIDTH,HEIGHT); switch(dir) { case 1: StartLocation.MoveUp(); if (cboard[StartLocation.x][StartLocation.y]) return (cboard[StartLocation.x][StartLocation.y]->displayletter); case 2: StartLocation.MoveUpRight(); if (cboard[StartLocation.x][StartLocation.y]) return (cboard[StartLocation.x][StartLocation.y]->displayletter); case 3: StartLocation.MoveRight(); if (cboard[StartLocation.x][StartLocation.y]) return (cboard[StartLocation.x][StartLocation.y]->displayletter); case 4: StartLocation.MoveDownRight(); if (cboard[StartLocation.x][StartLocation.y]) return (cboard[StartLocation.x][StartLocation.y]->displayletter); case 5: StartLocation.MoveDown(); if (cboard[StartLocation.x][StartLocation.y]) return (cboard[StartLocation.x][StartLocation.y]->displayletter); case 6: StartLocation.MoveDownLeft(); if (cboard[StartLocation.x][StartLocation.y]) return (cboard[StartLocation.x][StartLocation.y]->displayletter); case 7: StartLocation.MoveLeft(); if (cboard[StartLocation.x][StartLocation.y]) return (cboard[StartLocation.x][StartLocation.y]->displayletter); case 8: StartLocation.MoveUpLeft(); if (cboard[StartLocation.x][StartLocation.y]) return (cboard[StartLocation.x][StartLocation.y]->displayletter); } //if function hasn't returned by now, square being looked at is pointer to null return '\0'; //return null char } void Coords::MoveRight() {(x==MaxX)? (x=0):(x++);} void Coords::MoveLeft() {(x==0)? (x=MaxX):(x--);} void Coords::MoveUp() {(y==0)? (y=MaxY):(y--);} void Coords::MoveDown() {(y==MaxY)? (y=0):(y++);} void Coords::MoveUpRight() {MoveUp(); MoveRight();} void Coords::MoveUpLeft() {MoveUp(); MoveLeft();} void Coords::MoveDownRight() {MoveDown(); MoveRight();} void Coords::MoveDownLeft() {MoveDown(); MoveLeft();} void Coords::MoveDir(int dir) { switch(dir) { case 1: MoveUp(); break; case 2: MoveUpRight(); break; case 3: MoveRight(); break; case 4: MoveDownRight(); break; case 5: MoveDown(); break; case 6: MoveDownLeft(); break; case 7: MoveLeft(); break; case 8: MoveUpLeft(); break; case 0: break; } } void Creature::Move(Grid G) { int movedir=DecideSquare(G); MoveTo(G,movedir); } int Creature::DecideSquare(Grid G) { Random X(1,8,8); //X.rptr now points to 8 unique random integers from [1,8] for (int i=0; i<8; i++) { int dir=X.rptr[i]; if (G.isEmpty(Location.x,Location.y,dir)) return dir; } return 0; } void Creature::MoveTo(Grid G, int dir) { Coords OldLocation=Location; Location.MoveDir(dir); G.cboard[Location.x][Location.y]=this; //point new location to this creature G.cboard[OldLocation.x][OldLocation.y]=NULL; //point old location to NULL } void Creature::Die() { if (!alive) { delete this; this=NULL; } } void Human::Breed(Grid G) { if (!breedcount) { Coords BreedLocation=Location; Random X(1,8,8); for (int i=0; i<8; i++) { BreedLocation.MoveDir(X.rptr[i]); if (!G.cboard[BreedLocation.x][BreedLocation.y]) { G.cboard[BreedLocation.x][BreedLocation.y])=new Human(BreedLocation.x,BreedLocation.y); return; } } } } int Human::DecideAttack(Grid G) { Coords AttackLocation=Location; Random X(1,8,8); int attackdir; for (int i=0; i<8; i++) { attackdir=X.rptr[i]; switch(G.CreatureType(Location.x,Location.y,attackdir)) { case 'H': break; case 'Z': return attackdir; case '\0': break; default: break; } } return 0; //no zombies! } int AttackRoll(int para1, int para2) { //outcome 1: Zombie wins, human dies //outcome 2: Human wins, zombie dies //outcome 3: Human wins, zombie dies, but human is bitten Random X(1,100,1); int roll= *(X.rptr); if (roll < para1) return 1; else if (roll < para2) return 2; else return 3; } void Human::AttackCreature(Grid G, int attackdirection) { Coords AttackLocation=Location; AttackLocation.MoveDir(attackdirection); int para1=33; int para2=33; if (vaccinated) para2=101; //makes attackroll > para 2 impossible, never gets infected if (armed) para1-=16; //reduces chance of zombie winning fight int roll=AttackRoll(para1,para2); //outcome 1: Zombie wins, human dies //outcome 2: Human wins, zombie dies //outcome 3: Human wins, zombie dies, but human is bitten switch(roll) { case 1: alive=0; //human (this) dies return; case 2: G.cboard[AttackLocation.x][AttackLocation.y]->alive=0; return; //zombie dies case 3: G.cboard[AttackLocation.x][AttackLocation.y]->alive=0; //zombie dies Random X(3,7,1); //human is bitten bitecount=*(X.rptr); return; } } int Zombie::DecideAttack(Grid G) { Coords AttackLocation=Location; Random X(1,8,8); int attackdir; for (int i=0; i<8; i++) { attackdir=X.rptr[i]; switch(G.CreatureType(Location.x,Location.y,attackdir)) { case 'H': return attackdir; case 'Z': break; case '\0': break; default: break; } } return 0; //no zombies! } void Zombie::AttackCreature(Grid G, int attackdirection) { int reversedirection; if (attackdirection < 9 && attackdirection>0) { (attackdirection<5)? (reversedirection=attackdirection+4):(reversedirection=attackdirection-4); } else reversedirection=0; //this should never happen //when a zombie attacks a human, the Human::AttackZombie() function is called //in the "reverse" direction, utilizing that function that has already been written Coords ZombieLocation=Location; Coords HumanLocation=Location; HumanLocation.MoveDir(attackdirection); if (G.cboard[HumanLocation.x][HumanLocation.y]) //if there is a human there, which there should be G.cboard[HumanLocation.x][HumanLocation.y]->AttackCreature(G,reversedirection); } void Zombie::Attack(Grid G) { int attackdirection=DecideAttack(G); AttackCreature(G,attackdirection); } main.cpp #include <cstdlib> #include <iostream> #include "definitions.h" using namespace std; int main(int argc, char *argv[]) { Grid G(500,500); system("PAUSE"); return EXIT_SUCCESS; }

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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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