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:
    3.0    0.0    1.0    0.0    0.0
    0.0    4.0    0.0    0.0    0.0
    0.0    7.0    5.0    9.0    0.0
    0.0    0.0    0.0    0.0    2.0
    0.0    0.0    0.0    6.0    5.0
 Reconstructed matrix:
    3.0    0.0    1.0    0.0    0.0
    0.0    4.0    0.0    0.0    0.0
    0.0    7.0    5.0    9.0    0.0
    0.0    0.0    0.0    0.0    2.0
    0.0    0.0    0.0    6.0    5.0