index	ija		sa
1	7	    3.000000
2	8	    4.000000
3	8	    5.000000
4	10	    0.000000
5	11	    5.000000
6	12	    0.000000
7	3	    1.000000
8	2	    7.000000
9	4	    9.000000
10	5	    2.000000
11	4	    6.000000
Original Matrix
 3.00	 0.00	 1.00	 0.00	 0.00	
 0.00	 4.00	 0.00	 0.00	 0.00	
 0.00	 7.00	 5.00	 9.00	 0.00	
 0.00	 0.00	 0.00	 0.00	 2.00	
 0.00	 0.00	 0.00	 6.00	 5.00	
Reconstructed Matrix
 3.00	 0.00	 1.00	 0.00	 0.00	
 0.00	 4.00	 0.00	 0.00	 0.00	
 0.00	 7.00	 5.00	 9.00	 0.00	
 0.00	 0.00	 0.00	 0.00	 2.00	
 0.00	 0.00	 0.00	 6.00	 5.00