================= QR Eigenvalues  ===================================
--------------------- DESCRIPTION ----------------------
This program computes eigenvalues of a matrix A
 by using the QR algorithm. The program returns
 the eigenvalues ordered in a vector and
 compares values of eigenvalues computed using 
 the built-in gsl eigenvalue function.

--------------------------------------------------------
---------------- RUNNING THE PROGRAM -------------------
---------------------   INPUT   ------------------------
TERMINAL$ Haytham_hw_14 < MATRIX_FILE_NAME
--------------------   OUTPUT   ------------------------
my QR		built-in gsl-QR		error
#.#		#.#			#.#
--------------------------------------------------------
++++++++++++++++++++++++++++++++++++++++++
++++++++++++++ EXAMPLE RUN 1 +++++++++++++
TERMINAL$ Haytham_hw_14 < A.mat
++++++++++++++    A.mat   ++++++++++++++++
4	4
1.2532				
0.723
0.32
0.45
0.723
0.1463
0.3426
0.1234
0.32
0.3426
1.3
0.25
0.45
0.1234
0.25
2.745
++++++++++++++ EXAMPLE RUN 1 OUTPUT ++++++
my QR            gsl-QR           error         
2.99709          2.99709          3.48323e-08   
1.68031          1.68031          2.46749e-08   
1.00089          1.00089          1.08202e-08   
-0.233784        -0.233784        6.07649e-09   
++++++++++++++++++++++++++++++++++++++++++
++++++++++++++++++++++++++++++++++++++++++
++++++++++++++ EXAMPLE RUN 2 +++++++++++++
TERMINAL$ Haytham_hw_14 < nonSymA.mat
++++++++++++++  nonSymA.mat  +++++++++++++
4	4
1.2532				
0.723
0.32
0.45
0.723
0.1463
0.3426
0.1234
0.32
0.3426
1.3
0.28
0.45
0.1234
0.25
2.745
++++++++++++++ EXAMPLE RUN 2 OUTPUT ++++++
Matrix is not symmetric.
Program aborted.
 
++++++++++++++++++++++++++++++++++++++++++
++++++++++++++++++++++++++++++++++++++++++
=====================================================================