NAG Library Manual, Mark 30.3
Interfaces:  FL   CL   CPP   AD 

NAG CL Interface Introduction
Example description
nag_tsa_trans_hessenberg_controller (g13exc) Example Program Results

The transformed state transition matrix is

 60.3649  58.8853   5.0480  -5.4406   2.1382  -7.3870 
 54.5832  33.1865  36.5234   6.3272  -3.1377   8.8154 
 17.6406  21.4501 -13.5942   0.5417   1.6926   0.0786 
 -9.0567  10.7202   0.3531   1.5444  -1.2846  24.6407 
  0.0000   6.8796 -20.1372  -2.6440   2.4983 -21.8071 
  0.0000   0.0000   0.0000  -0.0000   0.0000  27.0000 

The transformed input matrix is

-16.8819  -8.8260  13.9202 
  0.0000  13.8240  39.9205 
  0.0000   0.0000   4.1928 
  0.0000   0.0000   0.0000 
  0.0000   0.0000   0.0000 
  0.0000   0.0000   0.0000 

The matrix that reduces (B,A) to controller Hessenberg form is

 -0.0592  -0.2962  -0.6516   0.0592  -0.2369  -0.6516 
 -0.3995  -0.1168   0.2350  -0.7579  -0.4406  -0.0543 
 -0.5311  -0.5286  -0.3131   0.1029   0.2119   0.5339 
 -0.2594   0.5309  -0.3641  -0.3950   0.5927  -0.1051 
  0.6357  -0.0637  -0.4542  -0.4149  -0.1423   0.4394 
 -0.2887   0.5774  -0.2887   0.2887  -0.5774   0.2887