QR decomposition with Givens rotations:
random matrix A:
     0.700      0.339      1.807 
     0.442      1.564      1.184 
     2.175      1.083      4.169 
     1.960      2.792      0.974 
     4.983      5.516      1.480 
R=
     5.838      6.208      3.449 
     0.000      1.850     -1.918 
     0.000      0.000      3.099 
Q=
     0.120     -0.219      0.314 
     0.076      0.592      0.664 
     0.372     -0.664      0.519 
     0.336      0.383      0.178 
     0.853      0.118     -0.400 

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=
     0.700      0.339      1.807 
     0.442      1.564      1.184 
     2.175      1.083      4.169 
     1.960      2.792      0.974 
     4.983      5.516      1.480 
test passed

testing inverse
random square matrix A:
     0.395      0.558      1.062 
     1.164      1.132      1.804 
     2.081      0.886      3.394 
inverse=
    -3.562      1.515      0.309 
     0.315      1.380     -0.832 
     2.101     -1.289      0.322 
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