subroutine comp_next ( n, k, a, more, h, t )

!*****************************************************************************80
!
!! comp_next() computes the compositions of the integer N into K parts.
!
!  Discussion:
!
!    A composition of the integer N into K parts is an ordered sequence
!    of K nonnegative integers which sum to N.  The compositions (1,2,1)
!    and (1,1,2) are considered to be distinct.
!
!    The routine computes one composition on each call until there are no more.
!    For instance, one composition of 6 into 3 parts is
!    3+2+1, another would be 6+0+0.
!
!    On the first call to this routine, set MORE = FALSE.  The routine
!    will compute the first element in the sequence of compositions, and
!    return it, as well as setting MORE = TRUE.  If more compositions
!    are desired, call again, and again.  Each time, the routine will
!    return with a new composition.
!
!    However, when the LAST composition in the sequence is computed
!    and returned, the routine will reset MORE to FALSE, signaling that
!    the end of the sequence has been reached.
!
!    This routine originally used a SAVE statement to maintain the
!    variables H and T.  I have decided that it is safer
!    to pass these variables as arguments, even though the user should
!    never alter them.  This allows this routine to safely shuffle
!    between several ongoing calculations.
!
!
!    There are 28 compositions of 6 into three parts.  This routine will
!    produce those compositions in the following order:
!
!     I         A
!     -     ---------
!     1     6   0   0
!     2     5   1   0
!     3     4   2   0
!     4     3   3   0
!     5     2   4   0
!     6     1   5   0
!     7     0   6   0
!     8     5   0   1
!     9     4   1   1
!    10     3   2   1
!    11     2   3   1
!    12     1   4   1
!    13     0   5   1
!    14     4   0   2
!    15     3   1   2
!    16     2   2   2
!    17     1   3   2
!    18     0   4   2
!    19     3   0   3
!    20     2   1   3
!    21     1   2   3
!    22     0   3   3
!    23     2   0   4
!    24     1   1   4
!    25     0   2   4
!    26     1   0   5
!    27     0   1   5
!    28     0   0   6
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    02 July 2008
!
!  Author:
!
!    Original FORTRAN77 version by Albert Nijenhuis, Herbert Wilf.
!    FORTRAN90 version by John Burkardt
!
!  Reference:
!
!    Albert Nijenhuis, Herbert Wilf,
!    Combinatorial Algorithms for Computers and Calculators,
!    Second Edition,
!    Academic Press, 1978,
!    ISBN: 0-12-519260-6,
!    LC: QA164.N54.
!
!  Parameters:
!
!    Input, integer N, the integer whose compositions are desired.
!
!    Input, integer K, the number of parts in the composition.
!
!    Input/output, integer A(K), the parts of the composition.
!
!    Input/output, logical MORE, set by the user to start the
!    computation, and by the routine to terminate it.
!
!    Input/output, integer  H, T, two internal parameters needed
!    for the computation.  The user should allocate space for these in the
!    calling program, include them in the calling sequence, but never alter
!    them!
!
  implicit none

  integer k

  integer a(k)
  integer h
  logical more
  integer n
  integer t
!
!  The first computation.
!
  if ( .not. more ) then

    t = n
    h = 0
    a(1) = n
    a(2:k) = 0
!
!  The next computation.
!
  else

    if ( 1 < t ) then
      h = 0
    end if

    h = h + 1
    t = a(h)
    a(h) = 0
    a(1) = t - 1
    a(h+1) = a(h+1) + 1

  end if
!
!  This is the last element of the sequence if all the
!  items are in the last slot.
!
  more = ( a(k) /= n )

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

!*****************************************************************************80
!
!! MONOMIAL_VALUE evaluates a monomial.
!
!  Discussion:
!
!    This routine evaluates a monomial of the form
!
!      product ( 1 <= i <= m ) x(i)^e(i)
!
!    The combination 0.0^0 is encountered is treated as 1.0.
!
!  Licensing:
!
!    This code is distributed under the MIT license. 
!
!  Modified:
!
!    20 April 2014
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, integer M, the spatial dimension.
!
!    Input, integer N, the number of evaluation points.
!
!    Input, integer E(M), the exponents.
!
!    Input, real ( kind = rk ) X(M,N), the point coordinates.
!
!    Output, real ( kind = rk ) V(N), the monomial values.
!
  implicit none

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

  integer m
  integer n

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

  v(1:n) = 1.0D+00

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

  return
end
subroutine subcomp_next ( n, k, a, more, h, t )

!*****************************************************************************80
!
!! SUBCOMP_NEXT computes the next subcomposition of N into K parts.
!
!  Discussion:
!
!    A composition of the integer N into K parts is an ordered sequence
!    of K nonnegative integers which sum to a value of N.
!
!    A subcomposition of the integer N into K parts is a composition
!    of M into K parts, where 0 <= M <= N.
!
!    A subcomposition of the integer N into K parts is also a lattice
!    point in the simplex whose vertices are the origin, and the K direction
!    vectors N*E(I) for I = 1 to K.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    09 July 2007
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, integer N, the integer whose subcompositions
!    are desired.
!
!    Input, integer K, the number of parts in the subcomposition.
!
!    Input/output, integer A(K), the parts of the subcomposition.
!
!    Input/output, logical MORE, set by the user to start the computation,
!    and by the routine to terminate it.
!
!    Input/output, integer H, T, two internal parameters needed for the
!    computation.  The user should allocate space for these in the calling
!    program, include them in the calling sequence, but never alter them!
!
  implicit none

  integer k

  integer a(k)
  integer h
  logical more
  logical, save :: more2 = .false.
  integer n
  integer, save :: n2 = 0
  integer t
!
!  The first computation.
!
  if ( .not. more ) then

    n2 = 0
    a(1:k) = 0
    more2 = .false.
    h = 0
    t = 0

    more = .true.
!
!  Do the next element at the current value of N.
!
  else if ( more2 ) then

    call comp_next ( n2, k, a, more2, h, t )

  else

    more2 = .false.
    n2 = n2 + 1

    call comp_next ( n2, k, a, more2, h, t )

  end if
!
!  Termination occurs if MORE2 = FALSE and N2 = N.
!
  if ( .not. more2 .and. n2 == n ) then
    more = .false.
  end if

  return
end
subroutine tetrahedron_unit_monomial ( expon, value )

!*****************************************************************************80
!
!! TETRAHEDRON_UNIT_MONOMIAL integrates a monomial over the unit tetrahedron.
!
!  Discussion:
!
!    This routine integrates a monomial of the form
!
!      product ( 1 <= dim <= 3 ) x(dim)^expon(dim)
!
!    where the exponents are nonnegative integers.  Note that
!    if the combination 0^0 is encountered, it should be treated
!    as 1.
!
!    Integral ( over unit tetrahedron ) x^l y^m z^n dx dy =
!    l! * m! * n! / ( m + n + 3 )!
!
!    The integration region is:
!
!      0 <= X
!      0 <= Y
!      0 <= Z
!      0 <= X + Y + Z <= 1.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    07 April 2009
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, integer EXPON(3), the exponents.
!
!    Output, real ( kind = rk ) VALUE, the integral of the monomial.
!
  implicit none

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

  integer expon(3)
  integer i
  integer k
  real ( kind = rk ) value
!
!  The first computation ends with VALUE = 1.0;
!
  value = 1.0D+00
!
!  The first loop simply calculates 1, so we short circuit it.
!
! k = 0
!
! do i = 1, expon(1)
!   k = k + 1
!   value = value * real ( i, kind = rk ) / real ( k, kind = rk )
! end do

  k = expon(1)
  do i = 1, expon(2)
    k = k + 1
    value = value * real ( i, kind = rk ) / real ( k, kind = rk )
  end do

  do i = 1, expon(3)
    k = k + 1
    value = value * real ( i, kind = rk ) / real ( k, kind = rk )
  end do

  k = k + 1
  value = value / real ( k, kind = rk )

  k = k + 1
  value = value / real ( k, kind = rk )

  k = k + 1
  value = value / real ( k, kind = rk )

  return
end
subroutine tetrahedron_unit_o01 ( w, xyz )

!*****************************************************************************80
!
!! TETRAHEDRON_UNIT_O01: 1 point quadrature rule for the unit tetrahedron.
!
!  Discussion:
!
!    The integration region is:
!
!      0 <= X
!      0 <= Y
!      0 <= Z
!      X + Y + Z <= 1.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    07 April 2009
!
!  Author:
!
!    John Burkardt
!
!  Reference:
!
!    Carlos Felippa,
!    A compendium of FEM integration formulas for symbolic work,
!    Engineering Computation,
!    Volume 21, Number 8, 2004, pages 867-890.
!
!  Parameters:
!
!    Output, real ( kind = rk ) W(1), the weights.
!
!    Output, real ( kind = rk ) XYZ(3,1), the abscissas.
!
  implicit none

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

  integer, parameter :: order = 1

  real ( kind = rk ) w(order)
  real ( kind = rk ) :: w_save(1) = (/ &
    1.0000000000000000000D+00 /)
  real ( kind = rk ) xyz(3,order)
  real ( kind = rk ) :: xyz_save(3,1) = reshape ( (/ &
    0.25000000000000000000D+00,  0.25000000000000000000D+00,  &
    0.25000000000000000000D+00 /), &
  (/ 3, 1 /) )

  w(1:order) = w_save(1:order)
  xyz(1:3,1:order) = xyz_save(1:3,1:order)

  return
end
subroutine tetrahedron_unit_o04 ( w, xyz )

!*****************************************************************************80
!
!! TETRAHEDRON_UNIT_O04: 4 point quadrature rule for the unit tetrahedron.
!
!  Discussion:
!
!    The integration region is:
!
!      0 <= X
!      0 <= Y
!      0 <= Z
!      X + Y + Z <= 1.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    07 April 2009
!
!  Author:
!
!    John Burkardt
!
!  Reference:
!
!    Carlos Felippa,
!    A compendium of FEM integration formulas for symbolic work,
!    Engineering Computation,
!    Volume 21, Number 8, 2004, pages 867-890.
!
!  Parameters:
!
!    Output, real ( kind = rk ) W(4), the weights.
!
!    Output, real ( kind = rk ) XYZ(3,4), the abscissas.
!
  implicit none

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

  integer, parameter :: order = 4

  real ( kind = rk ) w(order)
  real ( kind = rk ) :: w_save(4) = (/ &
    0.25000000000000000000D+00, &
    0.25000000000000000000D+00, &
    0.25000000000000000000D+00, &
    0.25000000000000000000D+00 /)
  real ( kind = rk ) xyz(3,order)
  real ( kind = rk ) :: xyz_save(3,4) = reshape ( (/ &
    0.58541019662496845446D+00, &
    0.13819660112501051518D+00, &
    0.13819660112501051518D+00, &
    0.13819660112501051518D+00, &
    0.58541019662496845446D+00, &
    0.13819660112501051518D+00, &
    0.13819660112501051518D+00, &
    0.13819660112501051518D+00, &
    0.58541019662496845446D+00, &
    0.13819660112501051518D+00, &
    0.13819660112501051518D+00, &
    0.13819660112501051518D+00 /), (/ 3, 4 /) )

  w(1:order) = w_save(1:order)
  xyz(1:3,1:order) = xyz_save(1:3,1:order)

  return
end
subroutine tetrahedron_unit_o08 ( w, xyz )

!*****************************************************************************80
!
!! TETRAHEDRON_UNIT_O08: 8 point quadrature rule for the unit tetrahedron.
!
!  Discussion:
!
!    The integration region is:
!
!      0 <= X
!      0 <= Y
!      0 <= Z
!      X + Y + Z <= 1.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    07 April 2009
!
!  Author:
!
!    John Burkardt
!
!  Reference:
!
!    Carlos Felippa,
!    A compendium of FEM integration formulas for symbolic work,
!    Engineering Computation,
!    Volume 21, Number 8, 2004, pages 867-890.
!
!  Parameters:
!
!    Output, real ( kind = rk ) W(8), the weights.
!
!    Output, real ( kind = rk ) XYZ(3,8), the abscissas.
!
  implicit none

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

  integer, parameter :: order = 8

  real ( kind = rk ) w(order)
  real ( kind = rk ) :: w_save(8) = (/ &
    0.13852796651186214232D+00, &
    0.13852796651186214232D+00, &
    0.13852796651186214232D+00, &
    0.13852796651186214232D+00, &
    0.11147203348813785768D+00, &
    0.11147203348813785768D+00, &
    0.11147203348813785768D+00, &
    0.11147203348813785768D+00 /)
  real ( kind = rk ) xyz(3,order)
  real ( kind = rk ) :: xyz_save(3,8) = reshape ( (/ &
    0.015835909865720057993D+00, &
    0.32805469671142664734D+00,  &
    0.32805469671142664734D+00,  &
    0.32805469671142664734D+00,  &
    0.015835909865720057993D+00, &
    0.32805469671142664734D+00,  &
    0.32805469671142664734D+00,  &
    0.32805469671142664734D+00,  &
    0.015835909865720057993D+00, &
    0.32805469671142664734D+00,  &
    0.32805469671142664734D+00,  &
    0.32805469671142664734D+00,  &
    0.67914317820120795168D+00,  &
    0.10695227393293068277D+00,  &
    0.10695227393293068277D+00,  &
    0.10695227393293068277D+00,  &
    0.67914317820120795168D+00,  &
    0.10695227393293068277D+00,  &
    0.10695227393293068277D+00,  &
    0.10695227393293068277D+00,  &
    0.67914317820120795168D+00,  &
    0.10695227393293068277D+00,  &
    0.10695227393293068277D+00,  &
    0.10695227393293068277D+00 /), &
  (/ 3, 8 /) )

  w(1:order) = w_save(1:order)
  xyz(1:3,1:order) = xyz_save(1:3,1:order)

  return
end
subroutine tetrahedron_unit_o08b ( w, xyz )

!*****************************************************************************80
!
!! TETRAHEDRON_UNIT_O08B: 8 point quadrature rule for the unit tetrahedron.
!
!  Discussion:
!
!    The integration region is:
!
!      0 <= X
!      0 <= Y
!      0 <= Z
!      X + Y + Z <= 1.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    07 April 2009
!
!  Author:
!
!    John Burkardt
!
!  Reference:
!
!    Carlos Felippa,
!    A compendium of FEM integration formulas for symbolic work,
!    Engineering Computation,
!    Volume 21, Number 8, 2004, pages 867-890.
!
!  Parameters:
!
!    Output, real ( kind = rk ) W(8), the weights.
!
!    Output, real ( kind = rk ) XYZ(3,8), the abscissas.
!
  implicit none

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

  integer, parameter :: order = 8

  real ( kind = rk ) w(order)
  real ( kind = rk ) :: w_save(8) = (/ &
    0.025000000000000000000D+00, &
    0.025000000000000000000D+00, &
    0.025000000000000000000D+00, &
    0.025000000000000000000D+00, &
    0.22500000000000000000D+00, &
    0.22500000000000000000D+00, &
    0.22500000000000000000D+00, &
    0.22500000000000000000D+00 /)
  real ( kind = rk ) xyz(3,order)
  real ( kind = rk ) :: xyz_save(3,8) = reshape ( (/ &
    1.00000000000000000000D+00, &
    0.00000000000000000000D+00, &
    0.00000000000000000000D+00, &
    0.00000000000000000000D+00, &
    1.00000000000000000000D+00, &
    0.00000000000000000000D+00, &
    0.00000000000000000000D+00, &
    0.00000000000000000000D+00, &
    1.00000000000000000000D+00, &
    0.00000000000000000000D+00, &
    0.00000000000000000000D+00, &
    0.00000000000000000000D+00, &
    0.00000000000000000000D+00, &
    0.33333333333333333333D+00, &
    0.33333333333333333333D+00, &
    0.33333333333333333333D+00, &
    0.00000000000000000000D+00, &
    0.33333333333333333333D+00, &
    0.33333333333333333333D+00, &
    0.33333333333333333333D+00, &
    0.00000000000000000000D+00, &
    0.33333333333333333333D+00, &
    0.33333333333333333333D+00, &
    0.33333333333333333333D+00 /), &
  (/ 3, 8 /) )

  w(1:order) = w_save(1:order)
  xyz(1:3,1:order) = xyz_save(1:3,1:order)

  return
end
subroutine tetrahedron_unit_o14 ( w, xyz )

!*****************************************************************************80
!
!! TETRAHEDRON_UNIT_O14: 14 point quadrature rule for the unit tetrahedron.
!
!  Discussion:
!
!    The integration region is:
!
!      0 <= X
!      0 <= Y
!      0 <= Z
!      X + Y + Z <= 1.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    07 April 2009
!
!  Author:
!
!    John Burkardt
!
!  Reference:
!
!    Carlos Felippa,
!    A compendium of FEM integration formulas for symbolic work,
!    Engineering Computation,
!    Volume 21, Number 8, 2004, pages 867-890.
!
!  Parameters:
!
!    Output, real ( kind = rk ) W(ORDER), the weights.
!
!    Output, real ( kind = rk ) XYZ(3,ORDER), the abscissas.
!
  implicit none

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

  integer, parameter :: order = 14

  real ( kind = rk ) w(order)
  real ( kind = rk ) :: w_save(14) = (/ &
    0.073493043116361949544D+00, &
    0.073493043116361949544D+00, &
    0.073493043116361949544D+00, &
    0.073493043116361949544D+00, &
    0.11268792571801585080D+00, &
    0.11268792571801585080D+00, &
    0.11268792571801585080D+00, &
    0.11268792571801585080D+00, &
    0.042546020777081466438D+00, &
    0.042546020777081466438D+00, &
    0.042546020777081466438D+00, &
    0.042546020777081466438D+00, &
    0.042546020777081466438D+00, &
    0.042546020777081466438D+00 /)
  real ( kind = rk ) xyz(3,order)
  real ( kind = rk ) :: xyz_save(3,14) = reshape ( (/ &
    0.72179424906732632079D+00, &
    0.092735250310891226402D+00, &
    0.092735250310891226402D+00, &
    0.092735250310891226402D+00, &
    0.72179424906732632079D+00, &
    0.092735250310891226402D+00, &
    0.092735250310891226402D+00, &
    0.092735250310891226402D+00, &
    0.72179424906732632079D+00, &
    0.092735250310891226402D+00, &
    0.092735250310891226402D+00, &
    0.092735250310891226402D+00, &
    0.067342242210098170608D+00, &
    0.31088591926330060980D+00, &
    0.31088591926330060980D+00, &
    0.31088591926330060980D+00, &
    0.067342242210098170608D+00, &
    0.31088591926330060980D+00, &
    0.31088591926330060980D+00, &
    0.31088591926330060980D+00, &
    0.067342242210098170608D+00, &
    0.31088591926330060980D+00, &
    0.31088591926330060980D+00, &
    0.31088591926330060980D+00, &
    0.045503704125649649492D+00, &
    0.045503704125649649492D+00, &
    0.45449629587435035051D+00, &
    0.045503704125649649492D+00, &
    0.45449629587435035051D+00, &
    0.045503704125649649492D+00, &
    0.045503704125649649492D+00, &
    0.45449629587435035051D+00, &
    0.45449629587435035051D+00, &
    0.45449629587435035051D+00, &
    0.045503704125649649492D+00, &
    0.045503704125649649492D+00, &
    0.45449629587435035051D+00, &
    0.045503704125649649492D+00, &
    0.45449629587435035051D+00, &
    0.45449629587435035051D+00, &
    0.45449629587435035051D+00, &
    0.045503704125649649492D+00 /), &
  (/ 3, 14 /) )

  w(1:order) = w_save(1:order)
  xyz(1:3,1:order) = xyz_save(1:3,1:order)

  return
end
subroutine tetrahedron_unit_o14b ( w, xyz )

!*****************************************************************************80
!
!! TETRAHEDRON_UNIT_O14B: 14 point quadrature rule for the unit tetrahedron.
!
!  Discussion:
!
!    The integration region is:
!
!      0 <= X
!      0 <= Y
!      0 <= Z
!      X + Y + Z <= 1.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    08 April 2009
!
!  Author:
!
!    John Burkardt
!
!  Reference:
!
!    Carlos Felippa,
!    A compendium of FEM integration formulas for symbolic work,
!    Engineering Computation,
!    Volume 21, Number 8, 2004, pages 867-890.
!
!  Parameters:
!
!    Output, real ( kind = rk ) W(14), the weights.
!
!    Output, real ( kind = rk ) XYZ(3,14), the abscissas.
!
  implicit none

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

  integer, parameter :: order = 14

  real ( kind = rk ) w(order)
  real ( kind = rk ) :: w_save(14) = (/ &
    0.13283874668559071814D+00, &
    0.13283874668559071814D+00, &
    0.13283874668559071814D+00, &
    0.13283874668559071814D+00, &
    0.088589824742980710434D+00, &
    0.088589824742980710434D+00, &
    0.088589824742980710434D+00, &
    0.088589824742980710434D+00, &
    0.019047619047619047619D+00, &
    0.019047619047619047619D+00, &
    0.019047619047619047619D+00, &
    0.019047619047619047619D+00, &
    0.019047619047619047619D+00, &
    0.019047619047619047619D+00  /)
  real ( kind = rk ) xyz(3,order) 
  real ( kind = rk ) :: xyz_save(3,14) = reshape ( (/ &
    0.056881379520423421748D+00, &
    0.31437287349319219275D+00, &
    0.31437287349319219275D+00, &
    0.31437287349319219275D+00, &
    0.056881379520423421748D+00, &
    0.31437287349319219275D+00, &
    0.31437287349319219275D+00, &
    0.31437287349319219275D+00, &
    0.056881379520423421748D+00, &
    0.31437287349319219275D+00, &
    0.31437287349319219275D+00, &
    0.31437287349319219275D+00, &
    0.69841970432438656092D+00, &
    0.10052676522520447969D+00, &
    0.10052676522520447969D+00, &
    0.10052676522520447969D+00, &
    0.69841970432438656092D+00, &
    0.10052676522520447969D+00, &
    0.10052676522520447969D+00, &
    0.10052676522520447969D+00, &
    0.69841970432438656092D+00, &
    0.10052676522520447969D+00, &
    0.10052676522520447969D+00, &
    0.10052676522520447969D+00, &
    0.50000000000000000000D+00, &
    0.50000000000000000000D+00, &
    0.00000000000000000000D+00, &
    0.50000000000000000000D+00, &
    0.00000000000000000000D+00, &
    0.50000000000000000000D+00, &
    0.50000000000000000000D+00, &
    0.00000000000000000000D+00, &
    0.00000000000000000000D+00, &
    0.00000000000000000000D+00, &
    0.50000000000000000000D+00, &
    0.50000000000000000000D+00, &
    0.00000000000000000000D+00, &
    0.50000000000000000000D+00, &
    0.00000000000000000000D+00, &
    0.00000000000000000000D+00, &
    0.00000000000000000000D+00, &
    0.50000000000000000000D+00 /), &
  (/ 3, 14 /) )

  w(1:order) = w_save(1:order)
  xyz(1:3,1:order) = xyz_save(1:3,1:order)

  return
end
subroutine tetrahedron_unit_o15 ( w, xyz )

!*****************************************************************************80
!
!! TETRAHEDRON_UNIT_O15: 15 point quadrature rule for the unit tetrahedron.
!
!  Discussion:
!
!    The integration region is:
!
!      0 <= X
!      0 <= Y
!      0 <= Z
!      X + Y + Z <= 1.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    08 April 2009
!
!  Author:
!
!    John Burkardt
!
!  Reference:
!
!    Carlos Felippa,
!    A compendium of FEM integration formulas for symbolic work,
!    Engineering Computation,
!    Volume 21, Number 8, 2004, pages 867-890.
!
!  Parameters:
!
!    Output, real ( kind = rk ) W(15), the weights.
!
!    Output, real ( kind = rk ) XYZ(3,15), the abscissas.
!
  implicit none

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

  integer, parameter :: order = 15

  real ( kind = rk ) w(order)
  real ( kind = rk ) :: w_save(15) = (/ &
    0.071937083779018620010D+00, &
    0.071937083779018620010D+00, &
    0.071937083779018620010D+00, &
    0.071937083779018620010D+00, &
    0.069068207226272385281D+00, &
    0.069068207226272385281D+00, &
    0.069068207226272385281D+00, &
    0.069068207226272385281D+00, &
    0.052910052910052910053D+00, &
    0.052910052910052910053D+00, &
    0.052910052910052910053D+00, &
    0.052910052910052910053D+00, &
    0.052910052910052910053D+00, &
    0.052910052910052910053D+00, &
    0.11851851851851851852D+00 /)
  real ( kind = rk ) xyz(3,order)
  real ( kind = rk ) :: xyz_save(3,15) = reshape ( (/ &
    0.72408676584183090163D+00, &
  0.091971078052723032789D+00, &
  0.091971078052723032789D+00, &
    0.091971078052723032789D+00, &
  0.72408676584183090163D+00, &
  0.091971078052723032789D+00, &
    0.091971078052723032789D+00, &
  0.091971078052723032789D+00, &
  0.72408676584183090163D+00, &
    0.091971078052723032789D+00, &
  0.091971078052723032789D+00, &
  0.091971078052723032789D+00, &
    0.040619116511110274837D+00, &
  0.31979362782962990839D+00, &
  0.31979362782962990839D+00, &
    0.31979362782962990839D+00, &
  0.040619116511110274837D+00, &
  0.31979362782962990839D+00, &
    0.31979362782962990839D+00, &
  0.31979362782962990839D+00, &
  0.040619116511110274837D+00, &
    0.31979362782962990839D+00, &
  0.31979362782962990839D+00, &
  0.31979362782962990839D+00, &
    0.44364916731037084426D+00, &
  0.44364916731037084426D+00, &
  0.056350832689629155741D+00, &
    0.44364916731037084426D+00, &
  0.056350832689629155741D+00, &
  0.44364916731037084426D+00, &
    0.44364916731037084426D+00, &
  0.056350832689629155741D+00, &
  0.056350832689629155741D+00, &
    0.056350832689629155741D+00, &
  0.44364916731037084426D+00, &
  0.44364916731037084426D+00, &
    0.056350832689629155741D+00, &
  0.44364916731037084426D+00, &
  0.056350832689629155741D+00, &
    0.056350832689629155741D+00, &
  0.056350832689629155741D+00, &
  0.44364916731037084426D+00, &
    0.25000000000000000000D+00, &
  0.25000000000000000000D+00, &
  0.25000000000000000000D+00 /), &
  (/ 3, 15 /) )

  w(1:order) = w_save(1:order)
  xyz(1:3,1:order) = xyz_save(1:3,1:order)

  return
end
subroutine tetrahedron_unit_o15b ( w, xyz )

!*****************************************************************************80
!
!! TETRAHEDRON_UNIT_O15B: 15 point quadrature rule for the unit tetrahedron.
!
!  Discussion:
!
!    The integration region is:
!
!      0 <= X
!      0 <= Y
!      0 <= Z
!      X + Y + Z <= 1.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    19 April 2009
!
!  Author:
!
!    John Burkardt
!
!  Reference:
!
!    Carlos Felippa,
!    A compendium of FEM integration formulas for symbolic work,
!    Engineering Computation,
!    Volume 21, Number 8, 2004, pages 867-890.
!
!  Parameters:
!
!    Output, real ( kind = rk ) W(15), the weights.
!
!    Output, real ( kind = rk ) XYZ(3,15), the abscissas.
!
  implicit none

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

  integer, parameter :: order = 15

  real ( kind = rk ) w(order)
  real ( kind = rk ) :: w_save(15) = (/ &
    0.036160714285714285714D+00, &
    0.036160714285714285714D+00, &
    0.036160714285714285714D+00, &
    0.036160714285714285714D+00, &
    0.069871494516173816465D+00, &
    0.069871494516173816465D+00, &
    0.069871494516173816465D+00, &
    0.069871494516173816465D+00, &
    0.065694849368318756074D+00, &
    0.065694849368318756074D+00, &
    0.065694849368318756074D+00, &
    0.065694849368318756074D+00, &
    0.065694849368318756074D+00, &
    0.065694849368318756074D+00, &
    0.18170206858253505484D+00 /)
  real ( kind = rk ) xyz(3,order)
  real ( kind = rk ) :: xyz_save(3,15) = reshape ( (/ &
    0.00000000000000000000D+00, &
  0.33333333333333333333D+00, &
  0.33333333333333333333D+00, &
    0.33333333333333333333D+00, &
  0.00000000000000000000D+00, &
  0.33333333333333333333D+00, &
    0.33333333333333333333D+00, &
  0.33333333333333333333D+00, &
  0.00000000000000000000D+00, &
    0.33333333333333333333D+00, &
  0.33333333333333333333D+00, &
  0.33333333333333333333D+00, &
    0.72727272727272727273D+00, &
  0.090909090909090909091D+00, &
  0.090909090909090909091D+00, &
    0.090909090909090909091D+00, &
  0.72727272727272727273D+00, &
  0.090909090909090909091D+00, &
    0.090909090909090909091D+00, &
  0.090909090909090909091D+00, &
  0.72727272727272727273D+00, &
    0.090909090909090909091D+00, &
  0.090909090909090909091D+00, &
  0.090909090909090909091D+00, &
    0.43344984642633570176D+00, &
  0.43344984642633570176D+00, &
  0.066550153573664298240D+00, &
    0.43344984642633570176D+00, &
  0.066550153573664298240D+00, &
  0.43344984642633570176D+00, &
    0.43344984642633570176D+00, &
  0.066550153573664298240D+00, &
  0.066550153573664298240D+00, &
    0.066550153573664298240D+00, &
  0.43344984642633570176D+00, &
  0.43344984642633570176D+00, &
    0.066550153573664298240D+00, &
  0.43344984642633570176D+00, &
  0.066550153573664298240D+00, &
    0.066550153573664298240D+00, &
  0.066550153573664298240D+00, &
  0.43344984642633570176D+00, &
    0.25000000000000000000D+00, &
  0.25000000000000000000D+00, &
  0.250000000000000000D+00 /), &
  (/ 3, 15 /) )

  w(1:order) = w_save(1:order)
  xyz(1:3,1:order) = xyz_save(1:3,1:order)

  return
end
subroutine tetrahedron_unit_o24 ( w, xyz )

!*****************************************************************************80
!
!! TETRAHEDRON_UNIT_O24: 24 point quadrature rule for the unit tetrahedron.
!
!  Discussion:
!
!    The integration region is:
!
!      0 <= X
!      0 <= Y
!      0 <= Z
!      X + Y + Z <= 1.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    08 April 2009
!
!  Author:
!
!    John Burkardt
!
!  Reference:
!
!    Carlos Felippa,
!    A compendium of FEM integration formulas for symbolic work,
!    Engineering Computation,
!    Volume 21, Number 8, 2004, pages 867-890.
!
!  Parameters:
!
!    Output, real ( kind = rk ) W(24), the weights.
!
!    Output, real ( kind = rk ) XYZ(3,24), the abscissas.
!
  implicit none

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

  integer, parameter :: order = 24

  real ( kind = rk ) w(order)
  real ( kind = rk ) :: w_save(24) = (/ &
    0.039922750257869636194D+00, &
    0.039922750257869636194D+00, &
    0.039922750257869636194D+00, &
    0.039922750257869636194D+00, &
    0.010077211055345822612D+00, &
    0.010077211055345822612D+00, &
    0.010077211055345822612D+00, &
    0.010077211055345822612D+00, &
    0.055357181543927398338D+00, &
    0.055357181543927398338D+00, &
    0.055357181543927398338D+00, &
    0.055357181543927398338D+00, &
    0.048214285714285714286D+00, &
    0.048214285714285714286D+00, &
    0.048214285714285714286D+00, &
    0.048214285714285714286D+00, &
    0.048214285714285714286D+00, &
    0.048214285714285714286D+00, &
    0.048214285714285714286D+00, &
    0.048214285714285714286D+00, &
    0.048214285714285714286D+00, &
    0.048214285714285714286D+00, &
    0.048214285714285714286D+00, &
    0.048214285714285714286D+00 /)
  real ( kind = rk ) xyz(3,order)
  real ( kind = rk ) :: xyz_save(3,24) = reshape ( (/ &
    0.35619138622025439121D+00, &
    0.21460287125991520293D+00, &
    0.21460287125991520293D+00, &
    0.21460287125991520293D+00, &
    0.35619138622025439121D+00, &
    0.21460287125991520293D+00, &
    0.21460287125991520293D+00, &
    0.21460287125991520293D+00, &
    0.35619138622025439121D+00, &
    0.21460287125991520293D+00, &
    0.21460287125991520293D+00, &
    0.21460287125991520293D+00, &
    0.87797812439616594065D+00, &
    0.040673958534611353116D+00, &
    0.040673958534611353116D+00, &
    0.040673958534611353116D+00, &
    0.87797812439616594065D+00, &
    0.040673958534611353116D+00, &
    0.040673958534611353116D+00, &
    0.040673958534611353116D+00, &
    0.87797812439616594065D+00, &
    0.040673958534611353116D+00, &
    0.040673958534611353116D+00, &
    0.040673958534611353116D+00, &
    0.032986329573173468968D+00, &
    0.32233789014227551034D+00, &
    0.32233789014227551034D+00, &
    0.32233789014227551034D+00, &
    0.032986329573173468968D+00, &
    0.32233789014227551034D+00, &
    0.32233789014227551034D+00, &
    0.32233789014227551034D+00, &
    0.032986329573173468968D+00, &
    0.32233789014227551034D+00, &
    0.32233789014227551034D+00, &
    0.32233789014227551034D+00, &
    0.60300566479164914137D+00, &
    0.26967233145831580803D+00, &
    0.063661001875017525299D+00, &
    0.60300566479164914137D+00, &
    0.063661001875017525299D+00, &
    0.26967233145831580803D+00, &
    0.60300566479164914137D+00, &
    0.063661001875017525299D+00, &
    0.063661001875017525299D+00, &
    0.063661001875017525299D+00, &
    0.60300566479164914137D+00, &
    0.26967233145831580803D+00, &
    0.063661001875017525299D+00, &
    0.60300566479164914137D+00, &
    0.063661001875017525299D+00, &
    0.063661001875017525299D+00, &
    0.063661001875017525299D+00, &
    0.60300566479164914137D+00, &
    0.26967233145831580803D+00, &
    0.60300566479164914137D+00, &
    0.063661001875017525299D+00, &
    0.26967233145831580803D+00, &
    0.063661001875017525299D+00, &
    0.60300566479164914137D+00, &
    0.26967233145831580803D+00, &
    0.063661001875017525299D+00, &
    0.063661001875017525299D+00, &
    0.063661001875017525299D+00, &
    0.26967233145831580803D+00, &
    0.60300566479164914137D+00, &
    0.063661001875017525299D+00, &
    0.26967233145831580803D+00, &
    0.063661001875017525299D+00, &
    0.063661001875017525299D+00, &
    0.063661001875017525299D+00, &
    0.26967233145831580803D+00 /), &
  (/ 3, 24 /) )

  w(1:order) = w_save(1:order)
  xyz(1:3,1:order) = xyz_save(1:3,1:order)

  return
end
function tetrahedron_unit_volume ( )

!*****************************************************************************80
!
!! TETRAHEDRON_UNIT_VOLUME returns the volume of the unit tetrahedron.
!
!  Discussion:
!
!    The integration region is:
!
!      0 <= X,
!      0 <= Y,
!      0 <= Z,
!      X + Y + Z <= 1.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    27 October 2000
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Output, real ( kind = rk ) TETRAHEDRON_UNIT_VOLUME, the volume.
!
  implicit none

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

  real ( kind = rk ) tetrahedron_unit_volume

  tetrahedron_unit_volume = 1.0D+00 / 6.0D+00

  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
!
  implicit none

  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