#! /usr/bin/env python
#
def index_rank2 ( n, lo, hi, a ):

#*****************************************************************************80
#
## INDEX_RANK2 ranks an index vector within given lower and upper limits.
#
#  Example:
#
#    N = 3,
#    LO(1) = 1, LO(2) = 10, LO(3) = 4
#    HI(1) = 2, HI(2) = 11, HI(3) = 6
#    A = ( 1, 11, 5 )
#
#    RANK = 7
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    06 June 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer N, the number of entries in A.
#
#    Input, integer LO(N), HI(N), the lower and upper limits for the array
#    indices.  LO(I) should be less than or equal to HI(I), for each I.
#
#    Input, integer A(N), the index vector to be ranked.
#
#    Output, integer RANK, the rank of the index vector, or -1 if A
#    is not a legal index vector.
#
  for i in range ( 0, n ):
    if ( a[i] < lo[i] or hi[i] < a[i] ):
      rank = -1
      return rank

  rank = 1
  rang = 1
  for i in range ( 0, n ):
    rank = rank + ( a[i] - lo[i] ) * rang
    rang = rang * ( hi[i] + 1 - lo[i] )

  return rank

def index_rank2_test ( ):

#*****************************************************************************80
#
## INDEX_RANK2_TEST tests INDEX_RANK2.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    06 June 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from i4vec_print import i4vec_print

  n = 3

  a = np.array ( [ 1, 11, 5 ] )
  hi = np.array ( [ 2, 11, 6 ] )
  lo = np.array ( [ 1, 10, 4 ] )

  print ( '' )
  print ( 'INDEX_RANK2_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  INDEX_RANK2 ranks an index with given' )
  print ( '  lower and upper limits.' )
  print ( '' )
  print ( '  Number of index entries = %d' % ( n ) )
  print ( '' )
  print ( '  Coordinate, Minimum index, Maximum Index' )
  print ( '' )

  for i in range ( 0, n ):
    print ( '  %8d  %8d  %8d' % ( i, lo[i], hi[i] ) )
 
  i4vec_print ( n, a, '  The index array:' )

  rank = index_rank2 ( n, lo, hi, a )

  print ( '' )
  print ( '  The rank of this object is %d' % ( rank ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'INDEX_RANK2_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  index_rank2_test ( )
  timestamp ( )