QR decomposition with Givens rotations:
random matrix A:
     0.562      1.093      1.945 
     0.786      1.218      0.075 
     0.231      2.368      4.054 
     0.967      0.584      5.904 
     3.546      2.475      3.916 
R=
     3.808      3.010      5.694 
     0.000      2.386      3.277 
     0.000      0.000      5.220 
Q=
     0.148      0.272      0.041 
     0.207      0.250     -0.368 
     0.061      0.916      0.135 
     0.254     -0.075      0.901 
     0.931     -0.138     -0.179 

testing Q^T*Q == 1 ?
Q.t*Q=
     1.000      0.000      0.000 
     0.000      1.000     -0.000 
     0.000     -0.000      1.000 
test passed

testing Q*R == A ?
QR=
     0.562      1.093      1.945 
     0.786      1.218      0.075 
     0.231      2.368      4.054 
     0.967      0.584      5.904 
     3.546      2.475      3.916 
test passed

testing inverse
random square matrix A:
     0.686      0.216      0.636 
     0.390      1.157      3.614 
     2.495      3.301      4.448 
inverse=
     1.654     -0.278     -0.011 
    -1.775     -0.357      0.544 
     0.390      0.421     -0.173 
testing A*inverse == 1 ?
A*inverse=
     1.000      0.000     -0.000 
    -0.000      1.000      0.000 
     0.000      0.000      1.000 
test passed
testing inverse*A == 1 ?
inverse*A=
     1.000     -0.000     -0.000 
     0.000      1.000      0.000 
    -0.000      0.000      1.000 
test passed