Testing QR decomposition with Gram-Schmidt orthogonalization:
random tall matrix A=
     0.343      0.265      0.961 
     0.527      0.612      0.368 
     0.647      0.565      0.122 
     0.218      0.417      0.873 
     0.024      0.433      0.882 
calling gramschmidt...
R=
     0.928      0.948      0.876 
     0.000      0.476      0.974 
     0.000      0.000      0.946 
Q=
     0.370     -0.179      0.857 
     0.568      0.155     -0.297 
     0.696     -0.201     -0.309 
     0.234      0.408      0.285 
     0.025      0.858      0.024 

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 QR == A
QR=
     0.343      0.265      0.961 
     0.527      0.612      0.368 
     0.647      0.565      0.122 
     0.218      0.417      0.873 
     0.024      0.433      0.882 
test passed