random matrix A:
    -0.994     -0.307      -1.15    -0.0497 
      -1.3     -0.906      -1.29     -0.845 
     -1.35      -1.14     -0.159     -0.503 
     -1.43      -1.12      -1.03     -0.195 
random vector b:
    0.0865      0.523      0.675      0.241 
givnesQR: solution x to system A*x=b:
    -0.528      0.252      0.339     -0.596 
GSQR    : solution x to system A*x=b:
    -0.528      0.252      0.339     -0.596 
check: A*x (should be equal b):
    0.0865      0.523      0.675      0.241 
test passed
givens:
A^-1*A=
         1  -4.44e-16  -1.33e-15  -3.33e-16 
  4.44e-16          1   4.44e-16   1.67e-16 
         0          0          1   2.78e-17 
         0          0          0          1 
givens:
A*A^-1=
         1  -6.94e-17  -3.02e-16  -1.53e-16 
  8.33e-17          1   2.78e-16  -4.44e-16 
  2.08e-16  -2.22e-16          1  -1.11e-15 
 -2.08e-17  -8.33e-17   1.11e-16          1 
GramSchmidt:
A^-1*A=
         1  -5.77e-15  -5.33e-15  -2.39e-15 
  8.44e-15          1   6.22e-15   2.44e-15 
     4e-15   3.11e-15          1   1.22e-15 
 -8.88e-16  -6.66e-16  -8.88e-16          1 
GramSchmidt:
A*A^-1=
         1   4.16e-17  -3.19e-16   1.53e-16 
 -1.11e-16          1          0   8.88e-16 
 -7.63e-16   2.22e-16          1   2.22e-16 
 -1.39e-16   3.61e-16   -1.8e-16          1 

tall matrix:
random matrix A:
     -1.88      -1.74      -1.12 
    -0.173     -0.972     -0.586 
     -0.55      -1.64      -1.82 
     -1.59     -0.162       -1.5 

pinvA (pseudo inverse of A):
    -0.476      0.155      0.437     -0.233 
    -0.379      -0.25      -0.11      0.516 
      0.52    -0.0016     -0.507     -0.441 

pinvA*A:
         1  -2.98e-16  -3.33e-16 
  2.22e-16          1   2.22e-16 
  2.22e-16   4.58e-16          1