Oct 31 2013

## Windows Store App: Is my app on the left or right?

While writing code, I wondered if there was a simple way to detect where on the display my app would be rendered. If I could detect the location, I could write an app to automatically adjust the layout for easy access and usage. I’m going to describe one possible way to do it.

### Important Stuff

The class that will help us detect the location of the app is the ApplicationView class. The members of interest of this class are, AdjacentToLeftDisplayEdge, AdjacentToRightDisplayEdge, and IsFullScreen. We can acquire an instance of this class for the current application by calling, GetForCurrentView() static method.

### Code Stuff

In XAML based apps we must attach an event handler to Window.Current.SizeChanged event. This will trigger when the screen size changes or if the app is moved around. However, I have seen that this doesn’t trigger when the app is displayed in full screen mode. We may also need to attach an event to SizeChanged event for the XAML page. See the code snippet below.

For JavaScript based apps we only need to add the app.onresize event.

##### C# code snippet:

Be sure to include namespace Windows.UI.ViewManagement.

   1:  ApplicationView appView =
   2:      ApplicationView.GetForCurrentView();
   3:
   4:  if (appView.IsFullScreen)
   5:  {
   6:      // App is full screen
   7:  }
   8:  else
   9:  {
  10:      if (!appView.AdjacentToLeftDisplayEdge &&
  11:          !appView.AdjacentToRightDisplayEdge)
  12:      {
  13:          // App is in the center and not full-screen
  14:      }
  15:      else if (appView.AdjacentToLeftDisplayEdge)
  16:      {
  17:          // App is on the left edge
  18:      }
  19:      else if (appView.AdjacentToRightDisplayEdge)
  20:      {
  21:          // App is on the right edge
  22:      }
  23:  }
##### C++/CX code snippet:

Be sure to use namespace Windows::UI::ViewManagement.

   1:  ApplicationView^ appView =
   2:      ApplicationView::GetForCurrentView();
   3:
   4:  if (appView->IsFullScreen)
   5:  {
   6:      // App is full screen
   7:  }
   8:  else
   9:  {
  10:      if (!appView->AdjacentToLeftDisplayEdge &&
  11:          !appView->AdjacentToRightDisplayEdge)
  12:      {
  13:          // App is in the center and not full-screen
  14:      }
  15:      else if (appView->AdjacentToLeftDisplayEdge)
  16:      {
  17:          // App is on the left edge
  18:      }
  19:      else if (appView->AdjacentToRightDisplayEdge)
  20:      {
  21:          // App is on the right edge
  22:      }
  23:  }
##### JavaScript code snippet:

Most other parts of code are similar to C# snippet.

   1:  var appView =
   2:      Windows.UI.ViewManagement.ApplicationView.getForCurrentView();

May 26 2013

## RPC between C++ and Java

Chinese version (By Haosha Wang) : Link

A friend from my university posted a question about calling a method in Java from C++. Some of the recommendations were to use JNI. I, however, prefer RPC. This is how you do it.

### Preparation

I use XML-RPC as the wire protocol in my example. For Java I use apache XML-RPC implementation and for C++ I use XML-RPC for Windows. My example will work on Windows. However, this is not that hard to port to other OS.

### The Java Server

Let’s start with the server part. Here, the server is implemented using Java. Before we get to server code, we need to think through the method we want to execute. You can add more methods as necessary.

   1:  public class MathComputation {
   2:      public static double PI = 3.14159265358979323846;
   3:      public static final int DEFAULT  = 0;
   4:      public static final int INVERSE  = 1;
   5:
   6:      public double ComputePi(int valType)
   7:      {
   8:          double result = 0;
   9:
  10:          switch(valType)
  11:          {
  12:          case DEFAULT:
  13:              result = PI;
  14:              break;
  15:          case INVERSE:
  16:              result = 1.0/PI;
  17:              break;
  18:          }
  19:
  20:          return result;
  21:      }
  22:  }

Now, for the server part:

   1:  import org.apache.xmlrpc.server.*;
   2:  import org.apache.xmlrpc.webserver.*;
   3:
   4:  public class RPCServer {
   5:      public static void main(String[] args) {
   6:          try{
   7:              // TODO: put server code here
   8:          }
   9:          catch(Exception ex)
  10:          {
  11:              System.out.println(ex.getMessage());
  12:              ex.printStackTrace(System.out);
  13:          }
  14:      }
  15:  }

First, set up a webserver (a XML-RPC webserver) and the end-point for it (line 3). In this example, it will be localhost and port 8080. Second, get the instance of the XML-RPC server from the XML-RPC webserver (line 6). Use the PropertyHandlerMapping class to expose the classes and methods you would like to use (line 9-10). Then, we use our instance of the PropertyHandlerMapping class to set up the XML-RPC server (line 14). Third, you will need to set the server settings. In this case, I enabled extensions and usually the content length has to be there in the header for the RPC call (line 17-20). Last step, start the server (line 23).

   1:  // Create a web server end-point
   2:  // This is local host port:8080
   3:  WebServer webServer = new WebServer(8080);
   4:
   5:  // Get the instance of the RPC server
   6:  XmlRpcServer xmlRpcServer = webServer.getXmlRpcServer();
   7:
   8:  // All the classes you will be using over RPC here
   9:  PropertyHandlerMapping phm = new PropertyHandlerMapping();
  10:  phm.addHandler("MathComputation", MathComputation.class);
  11:
  12:  // This sets up XML-RPC server to have access to all
  13:  // the needed methods
  14:  xmlRpcServer.setHandlerMapping(phm);
  15:
  16:  // These are server properties, enable them as you need.
  17:  XmlRpcServerConfigImpl serverConfig =
  18:      (XmlRpcServerConfigImpl) xmlRpcServer.getConfig();
  19:  serverConfig.setEnabledForExtensions(true);
  20:  serverConfig.setContentLengthOptional(false);
  21:
  22:  // Start the server and you are ready
  23:  webServer.start();

That is all for the Java part. You can find the code files here, you also need apache XML-RPC for this to work.

### The CPP Client

The client part will be in CPP. Create a project in your favorite IDE and add the following lib: wininet.lib, for windows. The lib contains APIs to interact with FTP and HTTP protocols while using Internet resources. I used XML-RPC for Windows from sourceforge (download link here). Add the following files to your CPP Client project: timxmlrpc.h, timxmlrpc.cpp.

The following code is all you need to talk to the Java XML-RPC server. I repurposed this sample from the sample that is in the zip file for XML-RPC for Windows. First, create an array of arguments using the XmlRpcValue (line 10-13). In this case, we need only one argument. See the examples in the zip file (XML-RPC for Windows) for other types of arguments. Second, set up a connection to the Java server you created (line 16), remember to run it before you run the client. Make a call to Java server, if the call succeeds then the return values will be available in XML-RPC format. Last step, get it into a form that is useful to you.

   1:  #include "stdafx.h"
   2:  #include <iostream>
   3:  #include "TimXmlRpc.h"
   4:
   5:  #define MATH_DEFAULT             0
   6:  #define MATH_INVERSE             1
   7:
   8:  void main(int argc, char* argv[])
   9:  {
  10:      XmlRpcValue args, result;
  11:
  12:      // Pass arguments here
  13:      args[0] = MATH_DEFAULT;
  14:
  15:      // Setup a connection with the XML-RPC server endpoint
  16:      XmlRpcClient Connection("http://localhost:8080");
  17:      Connection.setIgnoreCertificateAuthority();
  18:
  19:      // Make the call to the XML-RPC Java webserver.
  20:      if (! Connection.execute(
  21:          "MathComputation.ComputePi",
  22:          args,
  23:          result))
  24:      {
  25:          // Something went wrong
  26:          std::cout << Connection.getError();
  27:          return;
  28:      }
  29:
  30:      // Retrieve the return value from the call
  31:      // Check if the return type is the same as expected
  32:      if (result.getType() != XmlRpcValue::TypeDouble)
  33:      {
  34:          std::cout << "Expecting Double.";
  35:          return;
  36:      }
  37:
  38:      // Get the result from the call in the form you want
  39:      double pi = (double)result;
  40:
  41:      std::cout.precision(15);
  42:      std::cout << pi;
  43:  }

C++ code files can be found here, don’t forget to download and include timxmlrpc.h, timxmlrpc.cpp. Also, remember to add wininet.lib to your CPP Client project. Let me know in the comments if you have any issue.

May 12 2012

## Self-replicating program

Self-replicating or self-copying programs are kind of interesting to play with. They are also called Quine. Here is one written in C, by Vlad Taeerov and Rashit Fakhreyev.

main(a)
{
    printf(a,34,a="main(a){printf(a,34,a=%c%s%c,34);}",34);
}

I adjusted it to work on Code::Blocks:

#include <stdio.h>
main(char*a)
{
  printf(
    a,
    34,
    a="#include <stdio.h>\nmain(char*a){printf(a,34,a=%c%s%c,34);}",
    34);
}

This a prolog version I created:

q :-
        listing(q),
        write(':-q.').

:-q.

It could have been shorter, but you would have to query ‘q’. This is it:

q:-listing(q).

May 9 2012

## Sorting with Function Pointers

This is a simple application of function pointers. Here I am trying to sort an array points based on X values, Y values or the distance from the origin. I have a simple sorting algorithm and the sorting criteria can be changed by using function pointers.

Lets start with the types we need. First, I need a structure to hold the X and Y values of the point. Point2D structure takes care of that. Second, a type that will define the sorting criteria, see in line 9. It define a pointer to a function that accepts two arguments both of which are Point2D structures and returns a bool. Typically comparison operations have this format.

   1:  #include <iostream>
   2:  #include <math.h>
   3:  using namespace std;
   4:
   5:  // 2D co-ordinate system
   6:  typedef struct _Point2D
   7:  {    double X, Y;}Point2D;
   8:  // function pointer type definiton
   9:  typedef bool (*Compare)(Point2D&,Point2D&);

Lets define a function to create and initialize a Point2D structure. This will make it easier to control or set default values to the Point2D structure.

  10:  // function that returns a 2D point
  11:  Point2D fnCreatePoint(const double x=0.0,const double y=0.0)
  12:  {
  13:      Point2D point;
  14:      point.X = x;
  15:      point.Y = y;
  16:      return point;
  17:  }

Lets further define swap function usually used in sorting algorithms and a simple sorting function. There are fairly direct, if you need more help with this see: Swap, Bubble Sort. Note that the sorting algorithm takes a additional argument of type Compare. That is the type of the function pointer that will define the comparison criteria while sorting.

  18:  // swaps the two values
  19:  void swap(Point2D& a,Point2D& b)
  20:  {
  21:      Point2D t;
  22:      t.X = a.X;t.Y = a.Y;
  23:      a.X = b.X;a.Y = b.Y;
  24:      b.X = t.X;b.Y = t.Y;
  25:  }
  26:  // sorts an array of values
  27:  Point2D* sort(Point2D* points,const int len,Compare fnCompare)
  28:  {
  29:      for(int i = 0;i<len;i++)
  30:          for(int j = i+1;j<len;j++)
  31:              if(!fnCompare(points[i],points[j]))
  32:                  swap(points[i],points[j]);
  33:      return points;
  34:  }

Now, that we have the framework we need, let us define a few comparing functions. These are simple functions that perform a particular type com comparison. The compare_x function compares only the X value of the Point2D structure. Similarly, compare_y function compares the Y value. The compare_distance function calculates the distance from the origin for the two points and then compares the distance. Note that each of these functions follow the argument types and return value type defined previously in line 9.

  35:  // comparing functions
  36:  bool compare_x(Point2D& a,Point2D& b)
  37:  {     return a.X < b.X;}
  38:  bool compare_y(Point2D& a,Point2D& b)
  39:  {     return a.Y < b.Y;}
  40:  bool compare_distance(Point2D& a,Point2D& b)
  41:  {     return
  42:          sqrt(pow(a.X,2.0) + pow(a.Y,2.0)) <
  43:          sqrt(pow(b.X,2.0) + pow(b.Y,2.0));
  44:  }

We have all the components that are needed to make this work. Here, I create an array with five points in it and call the sorting algorithm with the appropriate comparison criteria. Finally, display the sorted array of points.

int main()
{
    Point2D points[]={
        fnCreatePoint(-1,1),
        fnCreatePoint(-2,2),
        fnCreatePoint(1,-1),
        fnCreatePoint(2,-2),
        fnCreatePoint(0,0)};
    int length = 5;

    cout << "Sorted by X value:" << endl;
    // Sorts the points based on X
    sort(points,length,compare_x);
    Display(points,length);

    cout << endl << "Sorted by Y value:" << endl;
    // Sorts the points based on Y
    sort(points,length,compare_y);
    Display(points,length);

    cout << endl << "Sorted by distance from the origin:" << endl;
    // Sorts the points based on distance from the origin
    sort(points,length,compare_distance);
    Display(points,length);

    return 0;
}

I hope this helps you understand function pointers. Source code: fptr_example.cpp

Mar 14 2012

## What is ‘void’?

I have often seen that there is a confusion around the ‘void’ concept in C++ among the new comers to C++. Especially when it is used as a pointer. A commonly seen definition is that void means lack of something. Hence you cannot have a variable of type void. But you can have a pointer which is of void type. This is a bit confusing, so I am going to try and give examples and explain about each one.

Before I start, a pointer stores the address to some content. So, the size of all pointers are the same regardless of the content they point to. However, the pointer arithmetic depends on the type of content it is pointing to. Here I am going to talk about a type that means nothing and can be used to point to any type.

#### 1. void vX;

This is NOT allowed in C++. You cannot have a variable of type void. This makes some sense, void means nothing, hence you cannot declare a variable of type nothing. A variable is a name for a location in memory, and since void does not define the amount of memory needed you cannot allocate it.

#### 2. void fnDoSomething(void);

This is allowed in C++. This says that the function fnDoSomething accepts nothing and returns nothing. There is no memory  needed to store the variables here. However, void fnDoSomething(int iX, void); is invalid. This is trying to say fnDoSomething accepts an integer and the next argument is nothing. The compiler will show an error indicating that the type of the second argument is not known or invalid use of void. Since we are passing values the compiler has to put code in there to copy the value that will go into ‘iX’, so before copying memory has to be allocated for that argument. The first argument is fine because the compiler knows the cost of int and it can allocate the amount of memory needed for it. When the compiler looks at the second argument, it cannot allocate memory because of the problem we saw in section 1. Finally, void fnDoSomething(); has the same meaning as void fnDoSomething(void); . Here is a simple example:

   1:  void fnSomething(void)
   2:  {
   3:      cout << "Something was done.";
   4:  }

#### 3. void *vpX;

This is allowed in C++. First, a pointer is being declared. This is allowed but NOTvoid vX;’ because here a pointer was created and we are telling the compiler not to care about the type of the item it is pointing to. Usually, the amount of memory for any type of pointer is 4 bytes (8 bytes for x64). Second, since it is a pointer the compiler knows the amount of memory it needs to allocate, and ‘vpX’ is the name for that allocated memory.  A void pointer can point to any variable (except for those which are const or volatile) or can point to a function (except for member functions of a class).  Here is an example, the program  prints the byte sequence from memory for int and double data types using the same function.

   1:  void fnPrintHex(void *vpData,int iSize)
   2:  {
   3:      unsigned char* cpData = (unsigned char*)vpData;
   4:      for(int i=iSize-1;i>=0;i--)
   5:          cout << hex << (int)*(cpData+i);
   6:  }
   7:
   8:  int main()
   9:  {
  10:      int iX =1234;
  11:      fnPrintHex(&iX,sizeof(iX));
  12:      cout << endl;
  13:
  14:      double dX = 1234.5678;
  15:      fnPrintHex(&dX,sizeof(dX));
  16:      cout << endl;
  17:
  18:      return 0;
  19:  }

#### 4. const void *vpX;

This is allowed in C++. This means that the void pointer points to a constant value. The following will cause a type-cast error during compilation:

   1:  const int iX = 10;
   2:  void *vpX = &iX; // Type cast error

Only a const void type pointer is allowed to point to a constant. This means that the pointer itself is NOT constant and its value can be changed. But, the value it is pointing to is supposed to be constant. Note, const T *pX = &X is valid, T here is the same type as X. In the following code, in line 3 the ‘vpZ’ pointer is assigned the address of ‘iX’ and in line 4 it is reassigned with address of ‘iY’. The following code should print 1234 and 10, on separate lines.

   1:  const int iX = 1234;
   2:  const int iY = 10;
   3:  const void *vpZ = &iX;
   4:  vpZ = &iY;
   5:  cout << iX << endl << *(const int*)vpZ;

There is a minor issue here. Note that in the above code both ‘iX’ and ‘iY’ are constants and their value cannot be changed. But, you’ll see that you can do something as shown in the code below. If you read the code it may seem like it’ll print 1000 and 1000 on separate lines. Well it actually prints 1234 and 1000 on separate lines. Constants are optimized, hence the value of ‘iX’ gets placed wherever it is used. But, the original memory location is still alterable since it was type-cast to a editable type. Note, some debuggers will show the value of ‘iX’ on line 4 as 1000, you may have to test this on your compiler and debugger.

   1:  const int iX = 1234;
   2:  const void * vpZ = &iX;
   3:  *(int*)vpZ = 1000;
   4:  cout << iX << endl << *(int*)vpZ;

In the figure above, the number is highlighted in red because the compiler would have already picked up the value and applied everywhere ‘iX’ is used. So even if the value is changed it no longer matters wherever ‘iX’ used.

#### 5. void *const vpX;

This is allowed in C++. This means that the void pointer itself is a constant but it points to a variable. So, once an address is assigned to the pointer, you cannot reassign another address to it. In line 3 an address is assigned to ‘vpZ’ and after that line ‘vpZ’ cannot be assigned another address.

   1:  int iX = 1234;
   2:  int iY = 10;
   3:  void *const vpZ = &iX;
   4:  vpZ = &iY; // This is NOT allowed

But, the content at the address where the void pointer points to can be changed. You need to type-cast before you can make any changes. See the following code, it prints out 1000 and 1000, on separate lines.

   1:  int iX = 1234;
   2:  void *const vpZ = &iX;
   3:  *(int*)vpZ = 1000;
   4:  cout << iX << endl << *(int*)vpZ;

#### 6. const void* const vpX;

This is allowed in C++. This is a void pointer which is a constant pointing to an address whose contents are also constant. This is a combination of section 4 and 5 and the same rules apply. The following code will fail to compile, see section 5 for the reason:

   1:  const int iX = 1234;
   2:  const int iY = 5432;
   3:  const void *const vpZ = &iX;
   4:  vpZ = &iY; // This is NOT allowed

But the following code is allowed, see section 4 for the reason:

   1:  const int iX = 1234;
   2:  const void *const vpZ = &iX;
   3:  *(int*)vpZ = 1000;
   4:  cout << iX << endl << *(int*)vpZ;

I tested all of my code in visual C++ and GNU GCC. Please let me know if there are any mistakes. This is an introduction, I’ll try and write more advanced usage of void pointers in the future. Thanks for your patience.

Mar 1 2012

## Sudoku in Prolog

This is a simple Sudoku solver in Prolog. I was experimenting with Prolog and its backtracking mechanism. In the code, there is a ‘start’ predicate which can be called to run the code and test it out. It is fairly easy to modify and adapt to other problems of this kind. This was written and tested on SWI-Prolog (download here). Source for the Sudoku Solver: sudoku

Dec 27 2010

## Hint of personality

In “Errors as we speak”, we saw how error prone communicating with words can be. Let’s explore a deeper level of translation between idiolects, and how our mind achieves this translation.

Psychology has taught us that we communicate people with a mental “looking glass”, which filters content based on the idiosyncrasies of the individuals it has picked up. We have a general looking glass that we use to communicate with strangers. This general looking glass is conditioned by every experience accumulated till date. It allows us to make choices such as mode of speech, body language, subtleties in the intonation of words, etc. This general looking glass works until the conversation remains general (definition of ‘general’ is relative to each individual).

As we learn more about a person, we seize to use the general looking glass and we switch to a specialized one, dedicated to the person. This can be observed in our daily life and we understand some people who are close to us, even if they were not able create a complete sentence about whatever they were trying to say. This is because, the looking glass, with time, has now tuned to pickup and translate, a person’s idiolect to one’s own idiolect. In essence, our mind captures the personality of the individuals. One might ask, why do we need this mechanism? What purpose does capturing one’s personality have?

Our mind is a sucker for running simulations. Call it imagination, prediction or contemplating outcome, it is an important feature which allows us to form social groups. Capturing personalities allows our mind to estimate the consequences of our actions by predicting reactions of people. By using the feedback from the predicted reactions our mind to improve its strategy, prepare itself for consequences.

This ability of our mind is so good that it can associate personality to everything, be it an animate (pet animals) or inanimate (bike, tools), existing (anything tangible) or imagined (characters in a book) objects. It so well evolved that sometimes we can communicate using the looking glass, within our mind, and yet come up with a response which exactly reflects the response of the person we just simulated, this almost sounds like telepathy. Although our mind has evolved this feature, we don’t have complete control over it.

Dec 19 2010

## Errors as we speak

It is all about exchange of ideas. In this world of information exchange, we designed transmission mechanisms that are, in effect, error free. But, we have forgotten the most fundamental of transmission mechanisms that isn’t yet perfect. It took nature millions of years of evolution to perfect some of its technologies, and communication mechanism of humans, i.e., speech, isn’t one of them.

The Source: Information exchange, in any form, has two terminal components a Source and a Destination. Let’s, begin with the source. We are yet to figure out how information content is stored and operated on in the brain. But we sure don’t think with words, although, words do contribute, in part, in guiding the thought process. The problem appears when it is time to transfer the idea from our mind to any form of media tangible or intangible. One form of presenting our idea is with words and this is where conversion from abstract idea to words has to happen.

The Encoder: We convert an idea to words by selecting those which, to us, at that moment, are our best approximation to the abstractness of the idea. My friend, Tom Horton, calls it “bag of words”. We pick words, depending on the vocabulary and our meaning for that (based on visceral feeling we have for the word). Since our choice is an approximation, finally, our presented idea, after conversion, is an accumulation of approximation.

The Medium: Words can be transferred using a myriad of media, but I want to look at the medium we were born with. I believe that it is easily subjected to errors compared to other forms. Firstly, words have to be converted to sound, this happens by picking up a sequence of pulses which control the vocal chords. These sequences of pulses were learnt, which means another layer of approximation is introduced.  Then we expect the vocal chords to reproduce the sound and we have introduced another layer of errors. Secondly, the generated sound travels through the air (assumed to be speaking with someone in person), superimposed by noise, introducing a major layer of error. Lastly, the transfer is incomplete without reception. Ears pick up this sound, slightly obfuscated, and compares and picks up the words that have the highest probability of correctness, based on physical comparison of sounds, context and several hundreds of other fact0rs, etc.

The Decoder: Let’s face it; this is a real tough one. It is difficult to find someone who has at least one neuron that can fire, let alone find someone and get them to completely understand something by explaining it to them. As with the encoder, the words after being captured have to be transformed into the idea, or the abstract form. Since each person has a different visceral feel for words the transformation is never prefect.

The Destination: I believe that the destination for a transferred idea is reached when the intended person begins to understand the concept. However, each person thinks with physics of his own. The rules that govern the through process in each individual person is different, which brings us to a conclusion that each person understands the world differently. I conclude my rant here, that have patience when explaining things to others.

Disclaimer: I have not added any references to the claims I have made here because it is a rant. If you did learn anything from it, I beg your pardon, it was purely accidental.

Feb 16 2010

## Simple Algorithm to Play a Simple Game

Anyone who has worked with Machine Learning would have used the Logistic Regression algorithm, or at least heard about it. Well, here is a simple application that observes you play, and learns, how to play the game of Tic-Tac-Toe.

### How does it work?

As you play the game the algorithm observes the game. It isolates the choices that you made which led you to win the game. The draw and losing cases are not used. It then uses Logistic Regression to train the underlying intelligence, let us represent it by “$\theta$”. As it gains more experience, it’ll be able to make more accurate predictions about the game and hence it learns to play the game.

### The math behind it

It uses Gradient Descent along with Logistic Sigmoid function to train and predict. Prediction in this application is done by nine individual Logistic Regression units, and the outcome of each of them corresponds to one of the nine possible spaces  in the Tic-Tac-Toe game.

 $inputs$ Layout of Inputs Layout of Outputs Figure 1

Let $k = 0, 1, \ldots, 8$ be the indexes of nine spaces in the game. Also let, $y_0, y_1, \ldots, y_8$ represent the space chosen by you (to mark either X or O). Let, $X = \lbrace x_0, x_1, \ldots, x_8 \rbrace$ represent the input to the algorithm (see Figure 1). The intelligence that maps the input to a predicted output be represented by $\theta = \lbrace \theta_0, \theta_1, \ldots, \theta_8 \rbrace$. The prediction $h_{k}(X)$ for the $k^{th}$ space is made as per the equations shown below:

$\nu_{k}(X) = b_{k} + \sum_{i=0}^{8}(\theta_{ki}.x_i)$

$h_{k}(X) = \frac{1}{1 + e^{-\nu_k(X)}}$

Note: $b_{k}$ is the bias parameter. It has the same effect as applying Affine Transform to the $\nu_{k}(X)$ polynomial.

Here, $h_{k}(X)$ represents the predicted output and $y_{k}$ represents the move made by you. So, the purpose of training process is to adjust the values of $\theta$ until $h_{k} \approx y_{k}$. This is done using the Gradient Descent algorithm.

$\theta_{kj} := \theta_{kj} - \alpha.\sum_{i=0}^{m}( h_k(X^{(i)}) - y_k^{(i)}).x_j^{(i)}$
 $\alpha$ Learning Rate, a real valued number that indicates how fast the training algorithm converges. $m$ Number of training samples. $\theta_{kj}$ Intelligence parameter indicating how the $j^{th}$ input affects the $k^{th}$ output. $y_k^{(i)}$ Actual output for the $k^{th}$ space given $i^{th}$ sample as input. $h_k(X^{(i)})$ Predicted output for the $k^{th}$ space given $i^{th}$ sample as input. $X^{(i)}$ Represents the $i^{th}$ input sample. $X^{(i)} = \lbrace x_0^{(i)}, x_1^{(i)}, \ldots, x_8^{(i)} \rbrace$ $x_j^{(i)}$ Represents the value of the $j^{th}$ space in the $i^{th}$ input sample.

### How does all that work?

Below is a Silverlight version of the application, try it out. After you play the first game, you should see some prediction. The darkest circle is where the prediction algorithm thinks that you will make the next move. Here is the link to the source code: TicTacToe.zip. Note, you have to move for both the players. The predictor only predicts the moves. Until you play the first game with a winning outcome the predictor will not be trained.

Feb 11 2010

## Morphology in Frequency Domain

To put it simply,

$GrayScale(Image) \rightarrow DFT(Image) \rightarrow f(Image) \rightarrow IDFT(Image)$

Replace $f(Image) = f(x)$ by any of the functions from the following table, it also shows the effect of the function on the “Lenna” image. The images show effect of morphology or filter applied in the frequency domain.

Source Code: C++

 f(x) Processed Image Dilate(x) : Morphological Dilate Erode(x) : Morphological Erode Open(x) : Morphological Open Close(x) : Morphological Close Gradient(x) : Morphological Gradient Gaussian(x) : Simple Gaussian Blur

Images processed with FFTW and OpenCV libraries.