program main

!*****************************************************************************80
!
!! simplex_coordinates_test() tests simplex_coordinates().
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    19 September 2010
!
!  Author:
!
!    John Burkardt
!
  implicit none

  integer, parameter :: rk = kind ( 1.0D+00 )

  integer n

  call timestamp ( )
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'simplex_coordinates_test():'
  write ( *, '(a)' ) '  FORTRAN90 version'
  write ( *, '(a)' ) '  Test simplex_coordinates().'

  n = 3
  call simplex_coordinates1_test ( n )
  call simplex_coordinates2_test ( n )

  n = 4
  call simplex_coordinates1_test ( n )
  call simplex_coordinates2_test ( n )
!
!  Terminate.
!
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'simplex_coordinates_test():'
  write ( *, '(a)' ) '  Normal end of execution.'
  write ( *, '(a)' ) ' '
  call timestamp ( )

  stop 0
end
subroutine simplex_coordinates1_test ( n )

!*****************************************************************************80
!
!! simplex_coordinates1_test() tests simplex_coordinates1().
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    19 September 2010
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, integer N, the spatial dimension.
!
  implicit none

  integer, parameter :: rk = kind ( 1.0D+00 )

  integer n

  real ( kind = rk ) r8_factorial
  real ( kind = rk ) side
  real ( kind = rk ) volume
  real ( kind = rk ) volume2
  real ( kind = rk ) x(n,n+1)
  real ( kind = rk ) xtx(n+1,n+1)

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'simplex_coordinates1_test()'
  write ( *, '(a)' ) '  Test simplex_coordinates1()'

  call simplex_coordinates1 ( n, x )

  call r8mat_transpose_print ( n, n + 1, x, '  Simplex vertex coordinates:' )

  side = sqrt ( sum ( ( x(1:n,1) - x(1:n,2) )**2 ) )

  call simplex_volume ( n, x, volume )

  volume2 = sqrt ( real ( n + 1, kind = rk ) ) / r8_factorial ( n ) &
    / sqrt ( 2.0D+00**n ) * side**n

  write ( *, '(a)' ) ' '
  write ( *, '(a,g14.6)' ) '  Side length =     ', side
  write ( *, '(a,g14.6)' ) '  Volume =          ', volume
  write ( *, '(a,g14.6)' ) '  Expected volume = ', volume2

  xtx = matmul ( transpose ( x ), x )

  call r8mat_transpose_print ( n + 1, n + 1, xtx, '  Dot product matrix:' )

  return
end
subroutine simplex_coordinates2_test ( n )

!*****************************************************************************80
!
!! simplex_coordinates2_test() tests simplex_coordinates2().
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    19 September 2010
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, integer N, the spatial dimension.
!
  implicit none

  integer, parameter :: rk = kind ( 1.0D+00 )

  integer n

  real ( kind = rk ) r8_factorial
  real ( kind = rk ) side
  real ( kind = rk ) volume
  real ( kind = rk ) volume2
  real ( kind = rk ) x(n,n+1)
  real ( kind = rk ) xtx(n+1,n+1)

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'simplex_coordinates2_test():'
  write ( *, '(a)' ) '  Test simplex_coordinates2()'

  call simplex_coordinates2 ( n, x )

  call r8mat_transpose_print ( n, n + 1, x, '  Simplex vertex coordinates:' )

  side = sqrt ( sum ( ( x(1:n,1) - x(1:n,2) )**2 ) )

  call simplex_volume ( n, x, volume )

  volume2 = sqrt ( real ( n + 1, kind = rk ) ) / r8_factorial ( n ) &
    / sqrt ( 2.0D+00**n ) * side**n

  write ( *, '(a)' ) ' '
  write ( *, '(a,g14.6)' ) '  Side length =     ', side
  write ( *, '(a,g14.6)' ) '  Volume =          ', volume
  write ( *, '(a,g14.6)' ) '  Expected volume = ', volume2

  xtx = matmul ( transpose ( x ), x )

  call r8mat_transpose_print ( n + 1, n + 1, xtx, '  Dot product matrix:' )

  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 MIT license.
!
!  Modified:
!
!    18 May 2013
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    None
!
  implicit none

  integer, parameter :: rk = kind ( 1.0D+00 )

  character ( len = 8 ) ampm
  integer d
  integer h
  integer m
  integer mm
  character ( len = 9 ), parameter, dimension(12) :: month = (/ &
    'January  ', 'February ', 'March    ', 'April    ', &
    'May      ', 'June     ', 'July     ', 'August   ', &
    'September', 'October  ', 'November ', 'December ' /)
  integer n
  integer s
  integer values(8)
  integer 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 ( *, '(i2,1x,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