def qr_demo ( ):

## qr_demo() suggests how the QR algorithm 
  from scipy.linalg import qr
  import numpy as np
#
#  Set up an array of 5 vectors.
#
  A = np.array ( [ \
    [ 3, 2,  6, 16, 7 ], \
    [ 4, 1,  8, 18, 2 ], \
    [ 5,-2, 10, 16, 9 ] ] )
#
#  Add one vector at a time to A.
#
  for i in range ( 1, 6 ):
    Q, R = qr ( A[:,0:i] )
    QR = np.matmul ( Q, R )
    print ( '' )
    print ( '  Compute QR factorization A = Q * R.' )
    print ( '' )
    print ( '  A:' )
    print ( A[:,0:i] )
    print ( '' )
    print ( '  Q:' )
    print ( Q )
    print ( '  R:' )
    print ( R )
    print ( '  Q * R = A?:' )
    print ( QR )

    wait = input ( 'Pause' )

  return

if ( __name__ == "__main__" ):
  qr_demo ( )