Wednesday, June 19, 2013

Random Numbers Generation & Chi-Squared Test for their Uniformity in C++

Continuous uniformly distributed random numbers means the set of random numbers where probability of any number in any integral within a certain range of values is proportional to the ratio of the interval size to the range. The generated random numbers require to be independent & uniform in distribution. There are many different methods to generate the random numbers. 
They are: 
  • Random numbers from table. 
  • From hardwired device. 
  • Using pseudo Number generation. 

In linear congruential method, we use one initial number (rcalled seed) and few constants. Using the seed and the formula, 
                       ri+1 = (ri ×a + b) (modulo m) 

Wednesday, June 12, 2013

Determinant Calculation of Nth Order Square Matrix| Cramer's Rule Implementation in C

Determinant calculation of a square matrix is widely used in solving many applied Mathematics problems. Some of them are while solving a set of linear equations using Cramer's rule (iff they have unique solutions), calculation of inverse matrix, Eigen values/ Eigen vectors problem and so on.

The determinant of a square matrix A∈Rn×n is the real number det(A) defined as follows:

det(A) = SUMperm [sign(ν1,ν2,...,νn)a1ν1a2ν2...anνn]

Saturday, June 8, 2013

Autodesk AutoCAD 2010 is Already Installed| Problem Re-installing AutoCAD 2010| Solution

After facing some of the troubles and uninstalling the AutoDesk AutoCAD 2010, when you try to re-install the AutoCAD, you may often have to go through this problem. This is actually the problem which remained after  uninstalling the AutoCAD. Before trying to provide the solution, I would like to suggest to clean up your computer system using some clean up tools such as Windows Installer Clean UP Utility, CCleaner etc. after you uninstall a software.

CD/DVD Drive not Found Problem| CD/DVD Drive is not Detected Problem| Windows 7 Problem Solution

In windows 7, if you are facing the optical drives not detected/ not found problem even if it is visible in BIOS and using the standard driver, then you can try out the following options. The standard solution that worked in my desktop is as follows:

  • Press Win key and type regedit.exe, a new window- Registry Editor will open
  • After that, navigate to the following path from the left pane:

Friday, June 7, 2013

Huffman Algorithm Implementation in C| Huffman Encoding| Huffman Algorithm Example

Huffman Algorithm is an encoding technique for symbols where most frequently occuring symbols are represented with short length bit strings and least frequently occuring symbols are represented with long bit strings.

This algorithm is widely used as the fundamental encoding algorithm in compressing audio and image files.