#! /usr/bin/env python
#
def r8vec_mirror_next ( n, a ):

#*****************************************************************************80
#
## R8VEC_MIRROR_NEXT steps through all sign variations of an R8VEC.
#
#  Discussion:
#
#    In normal use, the user would set every element of A to be positive.
#    The routine will take the input value of A, and output a copy in
#    which the signs of one or more entries have been changed.  Repeatedly
#    calling the routine with the output from the previous call will generate
#    every distinct "variation" of A; that is, all possible sign variations.
#
#    When the output variable DONE is TRUE (or equal to 1), then the
#    output value of A is the last in the series.
#
#    Note that A may have some zero values.  The routine will essentially
#    ignore such entries; more exactly, it will not stupidly assume that -0
#    is a proper "variation" of 0!
#
#    Also, it is possible to call this routine with the signs of A set
#    in any way you like.  The routine will operate properly, but it
#    will nonethess terminate when it reaches the value of A in which
#    every nonzero entry has negative sign.
#
#    More efficient algorithms using the Gray code seem to require internal
#    memory in the routine,
#    or the passing back and forth of a "memory array", or the use of
#    global variables, or unnatural demands on the user.  This form of
#    the routine is about as clean as I can make it.
#
#  Example:
#
#      Input         Output
#    ---------    --------------
#    A            A         DONE
#    ---------    --------  ----
#     1  2  3     -1  2  3  false
#    -1  2  3      1 -2  3  false
#     1 -2  3     -1 -2  3  false
#    -1 -2  3      1  2 -3  false
#     1  2 -3     -1  2 -3  false
#    -1  2 -3      1 -2 -3  false
#     1 -2 -3     -1 -2 -3  false
#    -1 -2 -3      1  2  3  true
#
#     1  0  3     -1  0  3  false
#    -1  0  3      1  0 -3  false
#     1  0 -3     -1  0 -3  false
#    -1  0 -3      1  0  3  true
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    08 May 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Albert Nijenhuis, Herbert Wilf,
#    Combinatorial Algorithms,
#    Academic Press, 1978, second edition,
#    ISBN 0-12-519260-6.
#
#  Parameters:
#
#    Input, integer N, the number of entries in the vector.
#
#    Input, real A(N), a vector of real numbers.
#
#    Output, real A(N), some signs have been changed.
#
#    Output, logical DONE, is TRUE if the input vector A was the last element
#    in the series (every entry was nonpositive); the output vector is reset 
#    so that all entries are nonnegative, but presumably the ride is over!
#

#
#  Seek the first strictly positive entry of A.
#
  positive = 0
  for i in range ( 0, n ):
    if ( 0.0 < a[i] ):
      positive = i + 1
      break
#
#  If there is no strictly positive entry of A, there is no successor.
#
  if ( positive == 0 ):
    for i in range ( 0, n ):
      a[i] = - a[i]
    done = True
  else:
    for i in range ( 0, positive ):
      a[i] = - a[i]
    done = False

  return a, done

def r8vec_mirror_next_test ( ):

#*****************************************************************************80
#
## R8VEC_MIRROR_NEXT_TEST tests R8VEC_MIRROR_NEXT.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    08 May 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from r8vec_print import r8vec_print

  n = 3

  print ( '' )
  print ( 'R8VEC_MIRROR_NEXT_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  R8VEC_MIRROR_NEXT generates all sign variations' )
  print ( '  of a real vector.' )
  print ( '' )

  a = np.array ( [ 1.0, 2.0, 3.0 ] )

  k = 0

  while ( True ):

    print ( '  %2d' % ( k ), end = '' )
    for i in range ( 0, n ):
      print ( '  %6g' % ( a[i] ), end = '' )
    print ( '' )

    a, done = r8vec_mirror_next ( n, a )

    if ( done ):
      print ( '' )
      print ( '  Done.' )
      break

  a = np.array ( [ 1.0, 0.0, 3.0 ] )

  print ( '' )
  
  while ( True ):

    print ( '  %2d' % ( k ), end = '' )
    for i in range ( 0, n ):
      print ( '  %6g' % ( a[i] ), end = '' )
    print ( '' )

    a, done = r8vec_mirror_next ( n, a )

    if ( done ):
      print ( '' )
      print ( '  Done.' )
      break
#
#  Terminate.
#
  print ( '' )
  print ( 'R8VEC_MIRROR_NEXT_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  r8vec_mirror_next_test ( )
  timestamp ( )