main: QR decomposition:
main: some random matrix A:
  0.840  0.394  0.783
  0.798  0.912  0.198
  0.335  0.768  0.278
  0.554  0.477  0.629
main: matrix Q:
  0.633 -0.578  0.156
  0.601  0.314 -0.712
  0.252  0.752  0.439
  0.417 -0.031  0.525
main: matrix R:
  1.328  1.191  0.947
  0.000  0.621 -0.201
  0.000  0.000  0.433
main: matrix Q^TQ (should be 1):
  1.000  0.000  0.000
  0.000  1.000  0.000
  0.000  0.000  1.000
main: matrix QR (should be equal A):
  0.840  0.394  0.783
  0.798  0.912  0.198
  0.335  0.768  0.278
  0.554  0.477  0.629

main: Linear System: 
main: a square random matrix A:
  0.365  0.513  0.952
  0.916  0.636  0.717
  0.142  0.607  0.016
main: a random right-hand side b:
  0.243
  0.137
  0.804
main: solution x:
 -0.647
  1.484
 -0.297
main: Ax, should be equal b:
  0.243
  0.137
  0.804
main: inverse matrix A^{-1}:
 -1.275  1.709 -0.711
  0.260 -0.387  1.833
  1.399 -0.446 -0.716
main: matrix AA^-1, should be 1:
  1.000 -0.000 -0.000
  0.000  1.000  0.000
 -0.000 -0.000  1.000
main: matrix A^-1A, should be 1:
  1.000  0.000  0.000
 -0.000  1.000 -0.000
 -0.000 -0.000  1.000