program main

!*****************************************************************************80
!
!! MAIN is the main program for LATIN_RANDOM_DATASET.
!
!  Discussion:
!
!    LATIN_RANDOM_DATASET generates and saves a Latin Random Square dataset.
!
!    A "Latin Random Square" dataset is created by dividing each side
!    of the unit hypercube into N subintervals, and then choosing
!    a set of N subcubes.  The subcubes are selected in such a way
!    that if we project the subcubes onto any coordinate direction,
!    there is exactly one subcube in each subinterval.
!
!    That's the "Latin Square" part of the dataset.
!
!    Then we choose, uniformly at random, one point within each subcube
!    as a "representative".  This set of points constitutes the
!    "Latin Random Square" dataset, a terminology I made up to
!    distinguish it from the "Latin Random Square" and "Latin Edge Square"
!    datasets.
!
!  Usage:
!
!    latin_random_dataset m n seed
!
!    where
!
!    * M, the spatial dimension,
!    * N, the number of points to generate,
!    * SEED, the seed, a positive integer.
!
!    creates an M by N dataset and writes it to the
!    file "latin_random_M_N.txt".
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    12 November 2014
!
!  Author:
!
!    John Burkardt
!
  implicit none

  integer ( kind = 4 ) arg_num
  integer ( kind = 4 ) iarg
  integer ( kind = 4 ) iargc
  integer ( kind = 4 ) ierror
  integer ( kind = 4 ) ios
  integer ( kind = 4 ) last
  integer ( kind = 4 ) m
  integer ( kind = 4 ) n
  character ( len = 255 ) output_filename
  real ( kind = 8 ), allocatable, dimension ( :, : ) :: r
  integer ( kind = 4 ) seed
  character ( len = 255 ) string

  call timestamp ( )

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'LATIN_RANDOM_DATASET'
  write ( *, '(a)' ) '  FORTRAN90 version'
  write ( *, '(a)' ) '  Generate a Latin Random Square dataset.'
!
!  Get the number of command line arguments.
!
  arg_num = iargc ( )
!
!  Get the spatial dimension M.
!
  if ( 1 <= arg_num ) then
    iarg = 1
    call getarg ( iarg, string )
    call s_to_i4 ( string, m, ierror, last )
  else
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) '  Enter the spatial dimension M (1 or greater)'
    read ( *, * ) m
  end if

  write ( *, '(a)' ) ' '
  write ( *, '(a,i8)' ) '  Spatial dimension M = ', m
!
!  Get the number of points N.
!
  if ( 2 <= arg_num ) then
    iarg = 2
    call getarg ( iarg, string )
    call s_to_i4 ( string, n, ierror, last )
  else
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) '  Enter the number of points N (1 or greater)'
    read ( *, * ) n
  end if

  write ( *, '(a,i8)' ) '  Number of points N = ', n
!
!  Get the seed, SEED
!
  if ( 3 <= arg_num ) then
    iarg = 3
    call getarg ( iarg, string )
    call s_to_i4 ( string, seed, ierror, last )
  else
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) '  Enter the seed SEED (1 or greater)'
    read ( *, * ) seed
  end if

  write ( *, '(a,i12)' ) '  Seed SEED = ', seed

  if ( seed == 0 ) then
    call get_seed ( seed )
    write ( *, '(a,i12)' ) '  Randomized SEED = ', seed
  end if
!
!  Compute the data
!
  allocate ( r(1:m,1:n) )

  call latin_random ( m, n, seed, r )
!
!  Write it to a file.
!
  write ( output_filename, '(a,i2.2,a,i5.5,a)' ) &
    'latin_random_', m, '_', n, '.txt'

  call r8mat_write ( output_filename, m, n, r )

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) &
    '  The data was written to "' // trim ( output_filename ) // '".'
!
!  Free memory.
!
  deallocate ( r )
!
!  Terminate.
!
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'LATIN_RANDOM_DATASET'
  write ( *, '(a)' ) '  Normal end of execution.'
  write ( *, '(a)' ) ' '
  call timestamp ( )

  stop
end
subroutine get_seed ( seed )

!*****************************************************************************80
!
!! GET_SEED returns a seed for the random number generator.
!
!  Discussion:
!
!    The seed depends on the current time, and ought to be (slightly)
!    different every millisecond.  Once the seed is obtained, a random
!    number generator should be called a few times to further process
!    the seed.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    02 August 2004
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Output, integer ( kind = 4 ) SEED, a pseudorandom seed value.
!
  implicit none

  integer ( kind = 4 ) seed
  real ( kind = 8 ) temp
  character ( len = 10 ) time
  character ( len = 8 ) today
  integer ( kind = 4 ) values(8)
  character ( len = 5 ) zone

  call date_and_time ( today, time, zone, values )

  temp = 0.0D+00

  temp = temp + real ( values(2) - 1, kind = 8 ) /  11.0D+00
  temp = temp + real ( values(3) - 1, kind = 8 ) /  30.0D+00
  temp = temp + real ( values(5),     kind = 8 ) /  23.0D+00
  temp = temp + real ( values(6),     kind = 8 ) /  59.0D+00
  temp = temp + real ( values(7),     kind = 8 ) /  59.0D+00
  temp = temp + real ( values(8),     kind = 8 ) / 999.0D+00
  temp = temp                                    /   6.0D+00

  do while ( temp <= 0.0D+00 )
    temp = temp + 1.0D+00
  end do

  do while ( 1.0D+00 < temp )
    temp = temp - 1.0D+00
  end do

  seed = int ( real ( huge ( 1 ), kind = 8 ) * temp )
!
!  Never use a seed of 0 or maximum integer ( kind = 4 ).
!
  if ( seed == 0 ) then
    seed = 1
  end if

  if ( seed == huge ( 1 ) ) then
    seed = seed - 1
  end if

  return
end
subroutine get_unit ( iunit )

!*****************************************************************************80
!
!! GET_UNIT returns a free FORTRAN unit number.
!
!  Discussion:
!
!    A "free" FORTRAN unit number is a value between 1 and 99 which
!    is not currently associated with an I/O device.  A free FORTRAN unit
!    number is needed in order to open a file with the OPEN command.
!
!    If IUNIT = 0, then no free FORTRAN unit could be found, although
!    all 99 units were checked (except for units 5, 6 and 9, which
!    are commonly reserved for console I/O).
!
!    Otherwise, IUNIT is a value between 1 and 99, representing a
!    free FORTRAN unit.  Note that GET_UNIT assumes that units 5 and 6
!    are special, and will never return those values.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    18 September 2005
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Output, integer ( kind = 4 ) IUNIT, the free unit number.
!
  implicit none

  integer ( kind = 4 ) i
  integer ( kind = 4 ) ios
  integer ( kind = 4 ) iunit
  logical lopen

  iunit = 0

  do i = 1, 99

    if ( i /= 5 .and. i /= 6 .and. i /= 9 ) then

      inquire ( unit = i, opened = lopen, iostat = ios )

      if ( ios == 0 ) then
        if ( .not. lopen ) then
          iunit = i
          return
        end if
      end if

    end if

  end do

  return
end
function i4_uniform_ab ( a, b, seed )

!*****************************************************************************80
!
!! I4_UNIFORM_AB returns a scaled pseudorandom I4 between A and B.
!
!  Discussion:
!
!    An I4 is an integer ( kind = 4 ) value.
!
!    The pseudorandom number will be scaled to be uniformly distributed
!    between A and B.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    02 October 2012
!
!  Author:
!
!    John Burkardt
!
!  Reference:
!
!    Paul Bratley, Bennett Fox, Linus Schrage,
!    A Guide to Simulation,
!    Second Edition,
!    Springer, 1987,
!    ISBN: 0387964673,
!    LC: QA76.9.C65.B73.
!
!    Bennett Fox,
!    Algorithm 647:
!    Implementation and Relative Efficiency of Quasirandom
!    Sequence Generators,
!    ACM Transactions on Mathematical Software,
!    Volume 12, Number 4, December 1986, pages 362-376.
!
!    Pierre L'Ecuyer,
!    Random Number Generation,
!    in Handbook of Simulation,
!    edited by Jerry Banks,
!    Wiley, 1998,
!    ISBN: 0471134031,
!    LC: T57.62.H37.
!
!    Peter Lewis, Allen Goodman, James Miller,
!    A Pseudo-Random Number Generator for the System/360,
!    IBM Systems Journal,
!    Volume 8, Number 2, 1969, pages 136-143.
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) A, B, the limits of the interval.
!
!    Input/output, integer ( kind = 4 ) SEED, the "seed" value, which
!    should NOT be 0.  On output, SEED has been updated.
!
!    Output, integer ( kind = 4 ) I4_UNIFORM_AB, a number between A and B.
!
  implicit none

  integer ( kind = 4 ) a
  integer ( kind = 4 ) b
  integer ( kind = 4 ), parameter :: i4_huge = 2147483647
  integer ( kind = 4 ) i4_uniform_ab
  integer ( kind = 4 ) k
  real ( kind = 4 ) r
  integer ( kind = 4 ) seed
  integer ( kind = 4 ) value

  if ( seed == 0 ) then
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) 'I4_UNIFORM_AB - Fatal error!'
    write ( *, '(a)' ) '  Input value of SEED = 0.'
    stop 1
  end if

  k = seed / 127773

  seed = 16807 * ( seed - k * 127773 ) - k * 2836

  if ( seed < 0 ) then
    seed = seed + i4_huge
  end if

  r = real ( seed, kind = 4 ) * 4.656612875E-10
!
!  Scale R to lie between A-0.5 and B+0.5.
!
  r = ( 1.0E+00 - r ) * ( real ( min ( a, b ), kind = 4 ) - 0.5E+00 ) & 
    +             r   * ( real ( max ( a, b ), kind = 4 ) + 0.5E+00 )
!
!  Use rounding to convert R to an integer between A and B.
!
  value = nint ( r, kind = 4 )

  value = max ( value, min ( a, b ) )
  value = min ( value, max ( a, b ) )

  i4_uniform_ab = value

  return
end
subroutine latin_random ( dim_num, point_num, seed, x )

!*****************************************************************************80
!
!! LATIN_RANDOM returns points in a Latin Random square.
!
!  Discussion:
!
!    In each spatial dimension, there will be exactly one
!    point whose coordinate value lies between consecutive
!    values in the list:
!
!      ( 0, 1, 2, ..., point_num ) / point_num
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    08 April 2003
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) DIM_NUM, the spatial dimension.
!
!    Input, integer ( kind = 4 ) POINT_NUM, the number of points.
!
!    Input/output, integer ( kind = 4 ) SEED, a seed for the random
!    number generator.
!
!    Output, real ( kind = 8 ) X(DIM_NUM,POINT_NUM), the points.
!
  implicit none

  integer ( kind = 4 ) dim_num
  integer ( kind = 4 ) point_num

  integer ( kind = 4 ) i
  integer ( kind = 4 ) j
  integer ( kind = 4 ) perm(point_num)
  real ( kind = 8 ) r8_uniform_01
  integer ( kind = 4 ) seed
  real ( kind = 8 ) x(dim_num,point_num)
!
!  Pick DIM_NUM * POINT_NUM random numbers between 0 and 1.
!
  call r8mat_uniform_01 ( dim_num, point_num, seed, x )
!
!  For spatial dimension I,
!    pick a random permutation of 1 to POINT_NUM,
!    force the corresponding I-th components of X to lie in the
!    interval ( PERM(J)-1, PERM(J) ) / POINT_NUM.
!
  do i = 1, dim_num

    call perm_uniform ( point_num, seed, perm )

    do j = 1, point_num
      x(i,j) = ( real ( perm(j) - 1, kind = 8 ) + x(i,j) ) &
               / real ( point_num, kind = 8 )
    end do

  end do

  return
end
subroutine perm_uniform ( n, seed, p )

!*****************************************************************************80
!
!! PERM_UNIFORM selects a random permutation of N objects.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    18 November 2008
!
!  Author:
!
!    John Burkardt
!
!  Reference:
!
!    Albert Nijenhuis, Herbert Wilf,
!    Combinatorial Algorithms for Computers and Calculators,
!    Academic Press, 1978,
!    ISBN: 0-12-519260-6,
!    LC: QA164.N54.
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) N, the number of objects to be permuted.
!
!    Input/output, integer ( kind = 4 ) SEED, a seed for the random
!    number generator.
!
!    Output, integer ( kind = 4 ) P(N), the permutation.  P(I) is the "new"
!    location of the object originally at I.
!
  implicit none

  integer ( kind = 4 ) n

  integer ( kind = 4 ) i
  integer ( kind = 4 ) i4_uniform_ab
  integer ( kind = 4 ) j
  integer ( kind = 4 ) k
  integer ( kind = 4 ) p(n)
  integer ( kind = 4 ) seed

  do i = 1, n
    p(i) = i
  end do

  do i = 1, n - 1
    j = i4_uniform_ab ( i, n, seed )
    k    = p(i)
    p(i) = p(j)
    p(j) = k
  end do

  return
end
subroutine r8mat_uniform_01 ( m, n, seed, r )

!*****************************************************************************80
!
!! R8MAT_UNIFORM_01 fills an R8MAT with unit pseudorandom numbers.
!
!  Discussion:
!
!    An R8MAT is an MxN array of R8's, stored by (I,J) -> [I+J*M].
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    11 August 2004
!
!  Author:
!
!    John Burkardt
!
!  Reference:
!
!    Paul Bratley, Bennett Fox, Linus Schrage,
!    A Guide to Simulation,
!    Springer Verlag, pages 201-202, 1983.
!
!    Bennett Fox,
!    Algorithm 647:
!    Implementation and Relative Efficiency of Quasirandom
!    Sequence Generators,
!    ACM Transactions on Mathematical Software,
!    Volume 12, Number 4, pages 362-376, 1986.
!
!    Peter Lewis, Allen Goodman, James Miller,
!    A Pseudo-Random Number Generator for the System/360,
!    IBM Systems Journal,
!    Volume 8, pages 136-143, 1969.
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) M, N, the number of rows and columns in
!    the array.
!
!    Input/output, integer ( kind = 4 ) SEED, the "seed" value, which
!    should NOT be 0.  On output, SEED has been updated.
!
!    Output, real ( kind = 8 ) R(M,N), the array of pseudorandom values.
!
  implicit none

  integer ( kind = 4 ) m
  integer ( kind = 4 ) n

  integer ( kind = 4 ) i
  integer ( kind = 4 ), parameter :: i4_huge = 2147483647
  integer ( kind = 4 ) j
  integer ( kind = 4 ) k
  integer ( kind = 4 ) seed
  real ( kind = 8 ) r(m,n)

  do j = 1, n

    do i = 1, m

      k = seed / 127773

      seed = 16807 * ( seed - k * 127773 ) - k * 2836

      if ( seed < 0 ) then
        seed = seed + i4_huge
      end if

      r(i,j) = real ( seed, kind = 8 ) * 4.656612875D-10

    end do
  end do

  return
end
subroutine r8mat_write ( output_filename, m, n, table )

!*****************************************************************************80
!
!! R8MAT_WRITE writes an R8MAT file.
!
!  Discussion:
!
!    An R8MAT is an array of R8 values.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    31 May 2009
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, character ( len = * ) OUTPUT_FILENAME, the output file name.
!
!    Input, integer ( kind = 4 ) M, the spatial dimension.
!
!    Input, integer ( kind = 4 ) N, the number of points.
!
!    Input, real ( kind = 8 ) TABLE(M,N), the table data.
!
  implicit none

  integer ( kind = 4 ) m
  integer ( kind = 4 ) n

  integer ( kind = 4 ) j
  character ( len = * ) output_filename
  integer ( kind = 4 ) output_status
  integer ( kind = 4 ) output_unit
  character ( len = 30 ) string
  real ( kind = 8 ) table(m,n)
!
!  Open the file.
!
  call get_unit ( output_unit )

  open ( unit = output_unit, file = output_filename, &
    status = 'replace', iostat = output_status )

  if ( output_status /= 0 ) then
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) 'R8MAT_WRITE - Fatal error!'
    write ( *, '(a,i8)' ) '  Could not open the output file "' // &
      trim ( output_filename ) // '" on unit ', output_unit
    output_unit = -1
    stop
  end if
!
!  Create a format string.
!
!  For less precision in the output file, try:
!
!                                            '(', m, 'g', 14, '.', 6, ')'
!
  if ( 0 < m .and. 0 < n ) then

    write ( string, '(a1,i8,a1,i8,a1,i8,a1)' ) '(', m, 'g', 24, '.', 16, ')'
!
!  Write the data.
!
    do j = 1, n
      write ( output_unit, string ) table(1:m,j)
    end do

  end if
!
!  Close the file.
!
  close ( unit = output_unit )

  return
end
subroutine s_to_i4 ( s, value, ierror, length )

!*****************************************************************************80
!
!! S_TO_I4 reads an integer value from a string.
!
!  Discussion:
!
!    Instead of ICHAR, we now use the IACHAR function, which
!    guarantees the ASCII collating sequence.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    12 January 2009
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, character ( len = * ) S, a string to be examined.
!
!    Output, integer ( kind = 4 ) VALUE, the integer value read from the string.
!    If the string is blank, then VALUE will be returned 0.
!
!    Output, integer ( kind = 4 ) IERROR, an error flag.
!    0, no error.
!    1, an error occurred.
!
!    Output, integer ( kind = 4 ) LENGTH, the number of characters 
!    of S used to make the integer.
!
  implicit none

  character c
  integer ( kind = 4 ) i
  integer ( kind = 4 ) ierror
  integer ( kind = 4 ) isgn
  integer ( kind = 4 ) length
  character ( len = * ) s
  integer ( kind = 4 ) state
  character :: TAB = achar ( 9 )
  integer ( kind = 4 ) value

  value = 0
  ierror = 0
  length = 0

  state = 0
  isgn = 1

  do i = 1, len_trim ( s )

    c = s(i:i)
!
!  STATE = 0, haven't read anything.
!
    if ( state == 0 ) then

      if ( c == ' ' .or. c == TAB ) then

      else if ( c == '-' ) then
        state = 1
        isgn = -1
      else if ( c == '+' ) then
        state = 1
        isgn = +1
      else if ( lle ( '0', c ) .and. lle ( c, '9' ) ) then
        state = 2
        value = iachar ( c ) - iachar ( '0' )
      else
        ierror = 1
        return
      end if
!
!  STATE = 1, have read the sign, expecting digits or spaces.
!
    else if ( state == 1 ) then

      if ( c == ' ' .or. c == TAB ) then

      else if ( lle ( '0', c ) .and. lle ( c, '9' ) ) then
        state = 2
        value = iachar ( c ) - iachar ( '0' )
      else
        ierror = 1
        return
      end if
!
!  STATE = 2, have read at least one digit, expecting more.
!
    else if ( state == 2 ) then

      if ( lle ( '0', c ) .and. lle ( c, '9' ) ) then

        value = 10 * value + iachar ( c ) - iachar ( '0' )

      else

        value = isgn * value
        ierror = 0
        length = i - 1
        return

      end if

    end if

  end do
!
!  If we read all the characters in the string, see if we're OK.
!
  if ( state == 2 ) then

    value = isgn * value
    ierror = 0
    length = len_trim ( s )

  else

    value = 0
    ierror = 1
    length = 0

  end if

  return
end
subroutine timestamp ( )

!*****************************************************************************80
!
!! TIMESTAMP prints the current YMDHMS date as a time stamp.
!
!  Example:
!
!    31 May 2001   9:45:54.872 AM
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    18 May 2013
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    None
!
  implicit none

  character ( len = 8 ) ampm
  integer ( kind = 4 ) d
  integer ( kind = 4 ) h
  integer ( kind = 4 ) m
  integer ( kind = 4 ) mm
  character ( len = 9 ), parameter, dimension(12) :: month = (/ &
    'January  ', 'February ', 'March    ', 'April    ', &
    'May      ', 'June     ', 'July     ', 'August   ', &
    'September', 'October  ', 'November ', 'December ' /)
  integer ( kind = 4 ) n
  integer ( kind = 4 ) s
  integer ( kind = 4 ) values(8)
  integer ( kind = 4 ) y

  call date_and_time ( values = values )

  y = values(1)
  m = values(2)
  d = values(3)
  h = values(5)
  n = values(6)
  s = values(7)
  mm = values(8)

  if ( h < 12 ) then
    ampm = 'AM'
  else if ( h == 12 ) then
    if ( n == 0 .and. s == 0 ) then
      ampm = 'Noon'
    else
      ampm = 'PM'
    end if
  else
    h = h - 12
    if ( h < 12 ) then
      ampm = 'PM'
    else if ( h == 12 ) then
      if ( n == 0 .and. s == 0 ) then
        ampm = 'Midnight'
      else
        ampm = 'AM'
      end if
    end if
  end if

  write ( *, '(i2.2,1x,a,1x,i4,2x,i2,a1,i2.2,a1,i2.2,a1,i3.3,1x,a)' ) &
    d, trim ( month(m) ), y, h, ':', n, ':', s, '.', mm, trim ( ampm )

  return
end