subroutine cube01_monomial_integral ( e, integral )

!*****************************************************************************80
!
!! cube01_monomial_integral(): integral over interior of unit cube in 3D.
!
!  Discussion:
!
!    The integration region is 
!
!      0 <= X <= 1, 
!      0 <= Y <= 1,
!      0 <= Z <= 1.
!
!    The monomial is F(X,Y,Z) = X^E(1) * Y^E(2) * Z^E(3).
!
!  Licensing:
!
!    This code is distributed under the MIT license. 
!
!  Modified:
!
!    16 January 2014
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, integer E(3), the exponents.  
!    Each exponent must be nonnegative.
!
!    Output, real ( kind = rk ) INTEGRAL, the integral.
!
  implicit none

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

  integer, parameter :: m = 3

  integer e(m)
  integer i
  real ( kind = rk ) integral

  if ( any ( e(1:m) < 0 ) ) then
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) 'CUBE01_MONOMIAL_INTEGRAL - Fatal error!'
    write ( *, '(a)' ) '  All exponents must be nonnegative.'
    stop 1
  end if

  integral = 1.0D+00
  do i = 1, m
    integral = integral / real ( e(i) + 1, kind = rk )
  end do

  return
end
subroutine cube01_sample ( n, x )

!*****************************************************************************80
!
!! cube01_sample() samples the interior of the unit cube in 3D.
!
!  Licensing:
!
!    This code is distributed under the MIT license. 
!
!  Modified:
!
!    16 January 2014
!
!  Author:
!
!    John Burkardt
!
!  Reference:
!
!    Russell Cheng,
!    Random Variate Generation,
!    in Handbook of Simulation,
!    edited by Jerry Banks,
!    Wiley, 1998, pages 168.
!
!    Reuven Rubinstein,
!    Monte Carlo Optimization, Simulation, and Sensitivity 
!    of Queueing Networks,
!    Krieger, 1992,
!    ISBN: 0894647644,
!    LC: QA298.R79.
!
!  Parameters:
!
!    Input, integer N, the number of points.
!
!    Output, real ( kind = rk ) X(3,N), the points.
!
  implicit none

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

  integer, parameter :: m = 3
  integer n

  real ( kind = rk ) x(m,n)

  call random_number ( harvest = x(1:m,1:n) )

  return
end
function cube01_volume ( )

!*****************************************************************************80
!
!! cube01_volume(): volume of the unit cube in 3D.
!
!  Licensing:
!
!    This code is distributed under the MIT license. 
!
!  Modified:
!
!    16 January 2014
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Output, real ( kind = rk ) CUBE01_VOLUME, the volume.
!
  implicit none

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

  real ( kind = rk ) cube01_volume

  cube01_volume = 1.0D+00

  return
end
subroutine i4vec_uniform_ab ( n, a, b, x )

!*****************************************************************************80
!
!! i4vec_uniform_ab() returns a scaled pseudorandom I4VEC.
!
!  Discussion:
!
!    An I4VEC is a vector of I4's.
!
!    The pseudorandom numbers should be scaled to be uniformly distributed
!    between A and B.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    27 November 2006
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, integer N, the dimension of the vector.
!
!    Input, integer A, B, the limits of the interval.
!
!    Output, integer X(N), a vector of numbers between A and B.
!
  implicit none

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

  integer n

  integer a
  integer b
  integer i
  real r
  integer value
  integer x(n)

  do i = 1, n

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

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

    x(i) = value

  end do

  return
end
subroutine monomial_value ( m, n, e, x, value )

!*****************************************************************************80
!
!! monomial_value() evaluates a monomial.
!
!  Discussion:
!
!    This routine evaluates a monomial of the form
!
!      product ( 1 <= i <= m ) x(i)^e(i)
!
!    where the exponents are nonnegative integers.  Note that
!    if the combination 0^0 is encountered, it should be treated
!    as 1.
!
!  Licensing:
!
!    This code is distributed under the MIT license. 
!
!  Modified:
!
!    07 May 2014
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, integer M, the spatial dimension.
!
!    Input, integer N, the number of points at which the
!    monomial is to be evaluated.
!
!    Input, integer E(M), the exponents.
!
!    Input, real ( kind = rk ) X(M,N), the point coordinates.
!
!    Output, real ( kind = rk ) VALUE(N), the value of the monomial.
!
  implicit none

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

  integer m
  integer n

  integer e(m)
  integer i
  real ( kind = rk ) value(n)
  real ( kind = rk ) x(m,n)

  value(1:n) = 1.0D+00

  do i = 1, m
    if ( 0 /= e(i) ) then
      value(1:n) = value(1:n) * x(i,1:n) ** e(i)
    end if
  end do

  return
end