README.md

QR_matrix_decomposition

Using Householder method

Main source file: qr.c

Purpose

Demonstrate the QR decomposition. The method of Householder reflections should be used.

Input

rectangular MxN matrix A from the file A.txt which is the matrix of linear algebraic equasions system. The input file contains the M and N numbers at the first line. Below them there are the coefficients of the matrix.

Output

the Q matrix, the R matrix and the QR multiplication (A matrix)

Compilation

Using gcc:

gcc -g -Wall -O3 -o qr qr.c

or via makefile:

make

Usage

./qr

The file A.txt containing the input matrix should be in the same folder with the executable file

Example

Input file A.txt contains:

  5 3
  12.000  -51.000    4.000
   6.000  167.000  -68.000
  -4.000   24.000  -41.000
  -1.000    1.000   -0.000
   2.000   -0.000    3.000

after running ./qr we will get output

    Q:
    0.846   -0.391    0.343    0.082    0.078
    0.423    0.904   -0.029    0.026    0.045
   -0.282    0.170    0.933   -0.047   -0.137
   -0.071    0.014   -0.001    0.980   -0.184
    0.141   -0.017   -0.106   -0.171   -0.969

    R:
   14.177   20.667  -13.402
   -0.000  175.043  -70.080
    0.000    0.000  -35.202
   -0.000   -0.000   -0.000
    0.000    0.000   -0.000

    Q * R:
   12.000  -51.000    4.000
    6.000  167.000  -68.000
   -4.000   24.000  -41.000
   -1.000    1.000   -0.000
    2.000   -0.000    3.000

License

This code is free for any use and anyone can modify it as he wants.