def power_rank ( x, T ):

#*****************************************************************************80
#
## power_rank() takes one step of the power method.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    07 August 2022
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    real x(N): the current vector.
#
#    real T(N,N): the transition matrix.
#
#  Output:
#
#    real Tx(N): the product T*x
#
  import numpy as np

  n = T.shape[0]

  index = np.arange ( 0, n )

  Tx = np.matmul ( T, x )

  Output = np.column_stack ( [ index, x, Tx ] )
  print ( '' )
  print ( '  x -> T*x' )
  print ( Output )

  return Tx