hsberg_test
  Test hsberg()

  Original matrix:

   0.110000E+02  0.120000E+02  0.130000E+02  0.140000E+02  0.150000E+02
   0.210000E+02  0.220000E+02  0.230000E+02  0.240000E+02  0.250000E+02
   0.310000E+02  0.320000E+02  0.330000E+02  0.340000E+02  0.350000E+02
   0.410000E+02  0.420000E+02  0.430000E+02  0.440000E+02  0.450000E+02
   0.510000E+02  0.520000E+02  0.530000E+02  0.540000E+02  0.550000E+02

  Hessenberg form:

   0.110000E+02 -0.264483E+02 -0.587250E+01 -0.282293E-04  0.622578E-05
  -0.753923E+02  0.154387E+03  0.434751E+02  0.211460E-03 -0.396770E-04
   0.000000E+00  0.322584E+01 -0.387057E+00 -0.142384E-05 -0.142163E-05
   0.000000E+00  0.000000E+00 -0.109598E-04 -0.153608E-05 -0.465441E-05
   0.000000E+00  0.000000E+00  0.000000E+00 -0.189518E-05  0.275638E-05

  Hessenberg info:

   0.000000E+00  0.000000E+00  0.000000E+00  0.000000E+00  0.000000E+00  0.000000E+00 -0.669383E+17
   0.000000E+00  0.000000E+00  0.000000E+00  0.000000E+00  0.000000E+00  0.963923E+02  0.726724E+04
   0.310000E+02  0.000000E+00  0.000000E+00  0.000000E+00  0.000000E+00 -0.357462E+01  0.115312E+02
   0.410000E+02  0.129299E+01  0.000000E+00  0.000000E+00  0.000000E+00  0.183359E-04  0.200958E-09
   0.510000E+02  0.293472E+01 -0.810623E-05  0.000000E+00  0.000000E+00  0.000000E+00  0.000000E+00