QR decomposition with Givens rotations:
random matrix A:
     0.822      0.063      2.861 
     1.963      0.773      0.195 
     0.634      1.760      1.610 
     3.050      0.839      0.590 
     0.304      2.236      4.096 
R=
     3.785      1.565      1.797 
     0.000      2.637      3.795 
     0.000      0.000      3.211 
Q=
     0.217     -0.105      0.894 
     0.519     -0.015     -0.212 
     0.167      0.568     -0.263 
     0.806     -0.160     -0.078 
     0.080      0.800      0.285 

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=
     0.822      0.063      2.861 
     1.963      0.773      0.195 
     0.634      1.760      1.610 
     3.050      0.839      0.590 
     0.304      2.236      4.096 
test passed

testing inverse
random square matrix A:
     0.786      0.289      1.073 
     0.304      1.809      1.131 
     0.537      2.424      4.452 
inverse=
     1.433      0.355     -0.436 
    -0.201      0.788     -0.152 
    -0.063     -0.472      0.360 
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