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:
!
!    26 October 2008
!
!  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
subroutine kjacopols2 ( x, a, b, n, pols, ders )

!*****************************************************************************80
!
!! KJACOPOLS2 evaluates Jacobi polynomials and derivatives.
!
!  Discussion:
!
!    This routine evaluates Jacobi polynomials and  derivatives.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, real ( kind = 8 ) X, the evaluation point.
!
!    Input, real ( kind = 8 ) A, B, the parameter values.
!
!    Input, integer ( kind = 4 ) N, the highest degree to be evaluated.
!
!    Output, real ( kind = 8 ) POLS(N+1), the polynomial values.
!
!    Output, real ( kind = 8 ) DERS(N+1), the polynomial derivative values.
!
  implicit none

  integer ( kind = 4 ) n

  real ( kind = 8 ) a
  real ( kind = 8 ) alpha1
  real ( kind = 8 ) alpha2
  real ( kind = 8 ) b
  real ( kind = 8 ) beta
  real ( kind = 8 ) ders(n+1)
  real ( kind = 8 ) dk
  real ( kind = 8 ) dkm1
  real ( kind = 8 ) dkp1
  real ( kind = 8 ) gamma
  integer ( kind = 4 ) k
  real ( kind = 8 ) pk
  real ( kind = 8 ) pkm1
  real ( kind = 8 ) pkp1
  real ( kind = 8 ) pols(n+1)
  real ( kind = 8 ) x

  pkp1 = 1.0D+00
  pols(1) = pkp1

  dkp1 = 0.0D+00
  ders(1) = dkp1

  if ( n == 0 ) then
    return
  end if

  pk = pkp1
  pkp1 = ( a / 2.0D+00 - b / 2.0D+00 ) &
    + ( 1.0D+00 + a / 2.0D+00 + b / 2.0D+00 ) * x
  pols(2) = pkp1

  dk = dkp1
  dkp1 = ( 1.0D+00 + a / 2.0D+00 + b / 2.0D+00 )
  ders(2) = dkp1

  if ( n == 1 ) then
    return
  end if

  do k = 2, n

    pkm1 = pk
    pk = pkp1
    dkm1 = dk
    dk = dkp1

    alpha1 = ( 2.0D+00 * k + a + b - 1.0D+00 ) * ( a * a - b * b )
    alpha2 = ( 2.0D+00 * k + a + b - 1.0D+00 ) &
      * ( ( 2.0D+00 * k + a + b - 2.0D+00 ) &
      * ( 2.0D+00 * k + a + b ) )
    beta = 2.0D+00 * ( k + a - 1.0D+00 ) * ( k + b - 1.0D+00 ) &
      * ( 2.0D+00 * k + a + b )
    gamma = ( 2.0D+00 * k * ( k + a + b ) &
      * ( 2.0D+00 * k + a + b - 2.0D+00 ) )
    pkp1 = ( ( alpha1 + alpha2 * x ) * pk - beta * pkm1 ) / gamma
    dkp1 = ( ( alpha1 + alpha2 * x ) * dk &
      - beta * dkm1 + alpha2 * pk ) / gamma

    pols(k+1) = pkp1
    ders(k+1) = dkp1

  end do

  return
end
subroutine kjacopols ( x, a, b, n, pols )

!*****************************************************************************80
!
!! KJACOPOLS evaluates Jacobi polynomials.
!
!  Discussion:
!
!    This routine evaluates Jacobi polynomials.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, real ( kind = 8 ) X, the evaluation point.
!
!    Input, real ( kind = 8 ) A, B, the parameter values.
!
!    Input, integer ( kind = 4 ) N, the highest degree to be evaluated.
!
!    Output, real ( kind = 8 ) POLS(N+1), the polynomial values.
!
  implicit none

  integer ( kind = 4 ) n

  real ( kind = 8 ) a
  real ( kind = 8 ) alpha
  real ( kind = 8 ) b
  real ( kind = 8 ) beta
  integer ( kind = 4 ) k
  real ( kind = 8 ) pk
  real ( kind = 8 ) pkm1
  real ( kind = 8 ) pkp1
  real ( kind = 8 ) pols(n+1)
  real ( kind = 8 ) x

  pkp1 = 1.0D+00
  pols(1) = pkp1

  if ( n == 0 ) then
    return
  end if

  pk = pkp1
  pkp1 = ( a / 2.0D+00 - b / 2.0D+00 ) &
    + ( 1.0D+00 + a / 2.0D+00 + b / 2.0D+00 ) * x
  pols(2) = pkp1

  if ( n == 1 ) then
    return
  end if

  do k = 2, n

    pkm1 = pk
    pk = pkp1

    alpha = ( 2.0D+00 * k + a + b - 1.0D+00 ) &
      * ( a * a - b * b + ( 2.0D+00 * k + a + b - 2.0D+00 ) &
      * ( 2.0D+00 * k + a + b ) * x )

    beta = 2.0D+00 * ( k + a - 1.0D+00 ) * ( k + b - 1.0D+00 ) &
      * ( 2.0D+00 * k + a + b )

    pkp1 = ( alpha * pk - beta * pkm1 ) &
      / ( 2.0D+00 * k * ( k + a + b ) &
      * ( 2.0D+00 * k + a + b - 2.0D+00 ) )

    pols(k+1) = pkp1

  end do

  return
end
subroutine klegeypols3 ( x, y, n, pols, dersx, dersy )

!*****************************************************************************80
!
!! KLEGEYPOLS3 evaluate scaled Legendre polynomials and derivatives.
!
!  Discussion:
!
!    This routine evaluates a sequence of scaled Legendre polynomials
!    P_n(x/y) y^n, with the parameter y in [0,1], together with their
!    derivatives with respect to the parameters x and y.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, real ( kind = 8 ) X, the evaluation point.
!
!    Input, real ( kind = 8 ) Y, the parameter value.
!
!    Input, integer ( kind = 4 ) N, the highest degree to be evaluated.
!
!    Output, real ( kind = 8 ) POLS(N+1), the polynomial values.
!
!    Output, real ( kind = 8 ) DERSX(N+1), the derivatives with respect to X.
!
!    Output, real ( kind = 8 ) DERSY(N+1), the derivatives with respect to Y.
!
  implicit none

  integer ( kind = 4 ) n

  real ( kind = 8 ) dersx(n+1)
  real ( kind = 8 ) dersy(n+1)
  real ( kind = 8 ) dk
  real ( kind = 8 ) dkm1
  real ( kind = 8 ) dkp1
  integer ( kind = 4 ) k
  real ( kind = 8 ) pk
  real ( kind = 8 ) pkm1
  real ( kind = 8 ) pkp1
  real ( kind = 8 ) pols(n+1)
  real ( kind = 8 ) x
  real ( kind = 8 ) y
  real ( kind = 8 ) yk
  real ( kind = 8 ) ykm1
  real ( kind = 8 ) ykp1

  pkp1 = 1.0D+00
  pols(1) = pkp1
  dkp1 = 0.0D+00
  dersx(1) = dkp1
  ykp1 = 0.0D+00
  dersy(1) = ykp1

  if ( n == 0 ) then
    return
  end if

  pk = pkp1
  pkp1 = x
  pols(2) = pkp1
  dk = dkp1
  dkp1 = 1.0D+00
  dersx(2) = dkp1
  yk = ykp1
  ykp1 = 0.0D+00
  dersy(2) = ykp1

  if ( n == 1 ) then
    return
  end if

  do k = 1, n - 1
    pkm1 = pk
    pk = pkp1
    dkm1 = dk
    dk = dkp1
    ykm1 = yk
    yk = ykp1
    pkp1 = ( ( 2.0D+00 * k + 1.0D+00 ) * x * pk - k * pkm1 * y * y ) &
      / ( k + 1.0D+00 )
    dkp1 = ( ( 2.0D+00 * k + 1.0D+00 ) * ( x * dk + pk ) &
      - k * dkm1 * y * y ) / ( k + 1.0D+00 )
    ykp1 = ( ( 2.0D+00 * k + 1.0D+00 ) * ( x * yk ) &
      - k * ( pkm1 * 2.0D+00 * y + ykm1 * y * y ) ) &
      / ( k + 1.0D+00 )
    pols(k+2) = pkp1
    dersx(k+2) = dkp1
    dersy(k+2) = ykp1
  end do

  return
end
subroutine klegeypols ( x, y, n, pols )

!*****************************************************************************80
!
!! KLEGEYPOLS evaluates scaled Legendre polynomials.
!
!  Discussion:
!
!    This routine evaluate a sequence of scaled Legendre polynomials
!    P_n(x/y) y^n, with the parameter y in [0,1].
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, real ( kind = 8 ) X, the evaluation point.
!
!    Input, real ( kind = 8 ) Y, the parameter.
!
!    Input, integer ( kind = 4 ) N, the highest degree to be evaluated.
!
!    Output, real ( kind = 8 ) POLS(N+1), the polynomial values.
!
  implicit none

  integer ( kind = 4 ) n

  integer ( kind = 4 ) k
  real ( kind = 8 ) pk
  real ( kind = 8 ) pkm1
  real ( kind = 8 ) pkp1
  real ( kind = 8 ) pols(n+1)
  real ( kind = 8 ) x
  real ( kind = 8 ) y

  pkp1 = 1.0D+00
  pols(1) = pkp1
  if ( n == 0 ) then
    return
  end if

  pk = pkp1
  pkp1 = x
  pols(2) = pkp1
  if ( n == 1 ) then
    return
  end if

  do k = 1, n - 1
    pkm1 = pk
    pk = pkp1
    pkp1 = ( ( 2.0D+00 * k + 1.0D+00 ) * x * pk &
      - k * pkm1 * y * y ) / ( k + 1.0D+00 )
    pols(k+2) = pkp1
  end do

  return
end
subroutine ortho2eva0 ( mmax, z, pols )

!*****************************************************************************80
!
!! ORTHO2EVA0 evaluates the orthonormal polynomials on the triangle.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    28 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) MMAX, the maximum order to which the 
!    polynomials are to be evaluated.
!
!    Input, real ( kind = 8 ) Z(2), the coordinates of the evaluation point.
!
!    Output, real ( kind = 8 ) POLS((mmax+1)*(mmax+2)/2), the orthogonal
!    polynomials evaluated at the point Z.
!
  implicit none

  integer ( kind = 4 ) mmax

  real ( kind = 8 ) a
  real ( kind = 8 ) b
  real ( kind = 8 ) f1(mmax+1)
  real ( kind = 8 ) f2(mmax+1,mmax+1)
  integer ( kind = 4 ) kk
  integer ( kind = 4 ) m
  integer ( kind = 4 ) n
  real ( kind = 8 ) par1
  real ( kind = 8 ) par2
  real ( kind = 8 ) pols(*)
  real ( kind = 8 ) r11
  real ( kind = 8 ) r12
  real ( kind = 8 ) r21
  real ( kind = 8 ) r22
  real ( kind = 8 ) scale
  real ( kind = 8 ) sqrt2
  real ( kind = 8 ) sqrt3
  real ( kind = 8 ) x
  real ( kind = 8 ) y
  real ( kind = 8 ) z(2)
  real ( kind = 8 ) zero

  zero = 0.0D+00
  sqrt2 = sqrt ( 2.0D+00 )
  sqrt3 = sqrt ( 3.0D+00 )
  r11 = -1.0D+00 / 3.0D+00
  r12 = -1.0D+00 / sqrt3
  r21 = - 1.0D+00 / 3.0D+00
  r22 = 2.0D+00 / sqrt3

  a = z(1)
  b = z(2)
!
!  Map the reference triangle to the right
!  triangle with the vertices (-1,-1), (1,-1), (-1,1)
!
  x = r11 + r12 * b + a
  y = r21 + r22 * b
!
!  Evaluate the Koornwinder's polynomials via the three term recursion.
!
  par1 = ( 2.0D+00 * x + 1.0D+00 + y ) / 2.0D+00
  par2 = ( 1.0D+00 - y ) / 2.0D+00
  call klegeypols ( par1, par2, mmax, f1 )

  do m = 0, mmax
    par1 = 2 * m + 1
    call kjacopols ( y, par1, zero, mmax - m, f2(1:mmax+1,m+1) )
  end do

  kk = 0
  do m = 0, mmax
    do n = 0, m
      kk = kk + 1
!
!  Evaluate the polynomial (m-n, n)
!
      pols(kk) = f1(m-n+1) * f2(n+1,m-n+1)
!
!  Normalize.
!
      scale = sqrt &
      ( real &
        ( &
          ( 1 + ( m - n ) + n ) * &
          ( 1 + ( m - n ) + ( m - n ) ), kind = 8 &
        ) / sqrt3 &
      )

      pols(kk) = pols(kk) * scale

    end do

  end do

  return
end
subroutine ortho2eva30 ( mmax, z, pols, dersx, dersy, f1, f2, f3, f4, f5, f6 )

!*****************************************************************************80
!
!! ORTHO2EVA30: orthonormal polynomials and derivatives on triangle.
!
!  Discussion:
!
!    Evaluate the orthonormal polynomials on the triangle,
!    together with their derivatives with respect to X and Y.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) MMAX, the maximum order to which the 
!    polynomials are to be evaluated.
!
!    Input, real ( kind = 8 ) Z(2), the evaluation point.
!
!    Output, real ( kind = 8 ) POLS((mmax+1)*(mmax+2)/2), the orthogonal
!    polynomials evaluated at the point Z.
!
!    Output, real ( kind = 8 ) DERSX((mmax+1)*(mmax+2)/2), the derivatives
!    with respect to X of the polynomials returned in POLS.
!
!    Output, real ( kind = 8 ) DERSY((mmax+1)*(mmax+2)/2), the derivatives
!    with respect to Y of the polynomials returned in POLS.
!
!    Workspace, real ( kind = 8 ) F1(*), F2(*), F3(*), F4(*), F5(*), F6(*).
!
  implicit none

  real ( kind = 8 ) a
  real ( kind = 8 ) b
  real ( kind = 8 ) dersx(*)
  real ( kind = 8 ) dersy(*)
  real ( kind = 8 ) f1(*)
  real ( kind = 8 ) f2(*)
  real ( kind = 8 ) f3(*)
  real ( kind = 8 ) f4(*)
  real ( kind = 8 ) f5(*)
  real ( kind = 8 ) f6(*)
  integer ( kind = 4 ) kk
  integer ( kind = 4 ) m
  integer ( kind = 4 ) mmax
  integer ( kind = 4 ) n
  real ( kind = 8 ) par1
  real ( kind = 8 ) par2
  real ( kind = 8 ) pols(*)
  real ( kind = 8 ) r11
  real ( kind = 8 ) r12
  real ( kind = 8 ) r21
  real ( kind = 8 ) r22
  real ( kind = 8 ) scale
  real ( kind = 8 ) sqrt2
  real ( kind = 8 ) sqrt3
  real ( kind = 8 ) x
  real ( kind = 8 ) y
  real ( kind = 8 ) z(2)
  real ( kind = 8 ) zero

  zero = 0.0D+00
  sqrt2 = sqrt ( 2.0D+00 )
  sqrt3 = sqrt ( 3.0D+00 )
  r11 = -1.0D+00 / 3.0D+00
  r12 = -1.0D+00 / sqrt3
  r21 = - 1.0D+00 / 3.0D+00
  r22 = 2.0D+00 / sqrt3

  x = z(1)
  y = z(2)
!
!  Map the reference triangle to the right
!  triangle with the vertices (-1,-1), (1,-1), (-1,1)
!
  a = r11 + r12 * y + x
  b = r21 + r22 * y
!
!  Evaluate the Koornwinder's polynomials via the three term recursion.
!
  par1 = ( 2.0D+00 * a + 1.0D+00 + b ) / 2.0D+00
  par2 = ( 1.0D+00 - b ) / 2.0D+00
  call klegeypols3 ( par1, par2, mmax, f1, f3, f4 )

  do m = 0, mmax
    par1 = 2 * m + 1
    call kjacopols2 ( b, par1, zero, (mmax-m), f2(1+m*(mmax+1)), &
      f5(1+m*(mmax+1)) )
  end do

  kk = 0
  do m = 0, mmax
    do n = 0, m
      kk = kk + 1
!
!  Evaluate the polynomial (m-n, n), and their derivatives
!  with respect to x,y
!
      pols(kk) = f1(m-n+1) * f2(n+1+(m-n)*(mmax+1))

      dersx(kk) = &
        f3(m-n+1) * f2(n+1+(m-n)*(mmax+1))

      dersy(kk) = &
        f1(m-n+1) * f5(n+1+(m-n)*(mmax+1)) * r22 + &
        f3(m-n+1) * f2(n+1+(m-n)*(mmax+1)) &
        * ( r12 + r22 / 2.0D+00 ) + &
        f4(m-n+1) * f2(n+1+(m-n)*(mmax+1)) * (- r22 / 2.0D+00 )

!
!  Normalize.
!
      scale = sqrt &
      ( real &
        ( &
          ( 1 + ( m - n ) + n ) &
          * ( 1 + ( m - n ) + ( m - n ) ), kind = 8 &
        ) / sqrt3 &
      )
      pols(kk) = pols(kk) * scale
      dersx(kk) = dersx(kk) * scale
      dersy(kk) = dersy(kk) * scale

    end do
  end do

  return
end
subroutine ortho2eva3 ( mmax, z, pols, dersx, dersy, w )

!*****************************************************************************80
!
!! ORTHO2EVA3: orthogonal polynomial values and derivatives, reference triangle.
!
!  Discussion:
!
!     This routine evaluates at the user-supplied point Z
!     a collection of polynomials (of X,Y) orthogonal on the
!     reference triangle, together with their derivatives with
!     respect to X and Y.
!
!     The reference triangle has vertices
!       (0,2/sqrt(3)), (-1,-1/sqrt(3), (1,-1/sqrt(3)).
!
!     The polynomials evaluated by this routine are all
!     orthogonal polynomials up to order mmax, arranged in the
!     increasing order.
!
!     This routine is based on the Koornwinder's representation
!     of the orthogonal polynomials on the right triangle
!       (-1,-1), (-1,1), (1,-1)
!     given by
!       K_mn(x,y) = P_m ((2*x+1+y)/(1-y)) ((1-y)/2)^m P_n^{2m+1,0} (y)
!     where P_m are the Legendre polynomials or order m
!     and P_n^{2m+1,0} are the Jacobi polynomials of order n with
!     the parameters alpha=2*m+1 and beta=0.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) MMAX, the maximum order to which the 
!    polynomials are to be evaluated.
!
!    Input, real ( kind = 8 ) Z(2), the location where the polynomials are
!    to be evaluated; normally, expected to be inside (including boundary) the
!    reference triangle.
!
!    Output, real ( kind = 8 ) POLS((mmax+1)*(mmax+2)/2), the orthogonal
!    polynomials evaluated at the point Z.
!
!    Output, real ( kind = 8 ) DERSX((mmax+1)*(mmax+2)/2), the derivatives
!    with respect to X of the polynomials returned in array POLS.
!
!    Output, real ( kind = 8 ) DERSY((mmax+1)*(mmax+2)/2), the derivatives
!    with respect to Y of the polynomials returned in array POLS.
!
!    Workspace, real ( kind = 8 ) W(mmax+1+(mmax+1)**2).
!
  implicit none

  integer ( kind = 4 ) mmax

  real ( kind = 8 ) c0
  real ( kind = 8 ) c1
  real ( kind = 8 ) c2
  real ( kind = 8 ) dersx(*)
  real ( kind = 8 ) dersy(*)
  integer ( kind = 4 ) iw1
  integer ( kind = 4 ) iw2
  integer ( kind = 4 ) iw3
  integer ( kind = 4 ) iw4
  integer ( kind = 4 ) iw5
  integer ( kind = 4 ) iw6
  integer ( kind = 4 ) iw7
  real ( kind = 8 ) pols(*)
  real ( kind = 8 ) w(*)
  real ( kind = 8 ) z(2)

  c0 = 1.0D+00 / sqrt ( 3.0D+00 ) * sqrt ( sqrt ( 3.0D+00 ) )
  c1 = sqrt ( 2.0D+00 ) * sqrt ( sqrt ( 3.0D+00 ) )
  c2 = sqrt ( 2.0D+00 ) * sqrt ( sqrt ( 3.0D+00 ) )

  if ( mmax == 0 ) then

    pols(1) = c0
    dersx(1) = 0.0D+00
    dersy(1) = 0.0D+00

  else if ( mmax == 1 ) then

    pols(1) = c0
    pols(2) = z(1) * c1
    pols(3) = z(2) * c2
    dersx(1) = 0.0D+00
    dersx(2) = c1
    dersx(3) = 0.0D+00
    dersy(1) = 0.0D+00
    dersy(2) = 0.0D+00
    dersy(3) = c2

  else

    iw1 = 1
    iw2 = iw1 + mmax + 1
    iw3 = iw2 + ( mmax + 1 ) ** 2
    iw4 = iw3 + mmax + 1
    iw5 = iw4 + mmax + 1
    iw6 = iw5 + ( mmax + 1) ** 2
    iw7 = iw6 + ( mmax + 1 ) ** 2
    call ortho2eva30 ( mmax, z, pols, dersx, dersy, &
      w(iw1), w(iw2), w(iw3), w(iw4), w(iw5), w(iw6) )

  end if

  return
end
subroutine ortho2eva ( mmax, z, pols )

!*****************************************************************************80
!
!! ORTHO2EVA evaluates orthogonal polynomials on the reference triangle.
!
!  Discussion:
!
!    This routine evaluates at the user-supplied point Z
!    a collection of polynomials (of X,Y) orthogonal on the
!    reference triangle.
!
!    The reference triangle has the vertices
!      (0,2/sqrt(3)), (-1,-1/sqrt(3)), (1,-1/sqrt(3))
!
!    The polynomials evaluated by this routine are all
!    orthogonal polynomials up to order mmax, arranged in the
!    increasing order.
!
!    This routine is based on the Koornwinder's representation
!    of the orthogonal polynomials on the right triangle
!      (-1,-1), (-1,1), (1,-1)
!    given by
!      K_mn(x,y) = P_m ((2*x+1+y)/(1-y)) ((1-y)/2)^m P_n^{2m+1,0} (y)
!    where P_m are the Legendre polynomials or order m
!    and P_n^{2m+1,0} are the Jacobi polynomials of order n with
!    the parameters alpha=2*m+1 and beta=0.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) MMAX, the maximum order to which the 
!    polynomials are to be evaluated;
!
!    Input, real ( kind = 8 ) Z(2), the location where the polynomials are
!    to be evaluated; normally, expected to be inside (including boundary)
!    the reference triangle.
!
!    Output, real ( kind = 8 ) POLS((mmax+1)*(mmax+2)/2), the orthogonal
!    polynomials evaluated at the point Z.
!
  implicit none

  integer ( kind = 4 ) mmax

  real ( kind = 8 ) pols(*)
  real ( kind = 8 ) z(2)

  if ( mmax == 0 ) then

    pols(1) = 1.0D+00 / sqrt ( 3.0D+00 ) * sqrt ( sqrt ( 3.0D+00 ) )

  else if ( mmax == 1 ) then

    pols(1) = 1.0D+00 / sqrt ( 3.0D+00 ) * sqrt ( sqrt ( 3.0D+00 ) )
    pols(2) = z(1) * sqrt ( 2.0D+00 ) * sqrt ( sqrt ( 3.0D+00 ) )
    pols(3) = z(2) * sqrt ( 2.0D+00 ) * sqrt ( sqrt ( 3.0D+00 ) )

  else

    call ortho2eva0 ( mmax, z, pols )

  end if

  return
end
subroutine quaecopy2 ( xs, ys, ws, xnew, ynew, w, kk )

!*****************************************************************************80
!
!! QUAECOPY2 copies a quadrature rule into a user arrays X, Y, and W.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, real ( kind = 8 ) XS(KK), YS(KK), the point coordinates to copy.
!
!    Input, real ( kind = 8 ) WS(KK), the weights to copy.
!
!    Output, real ( kind = 8 ) XNEW(KK), YNEW(KK), the copied point coordinates.
!
!    Output, real ( kind = 8 ) W(KK), the copied weights.
!
!    Input, integer ( kind = 4 ) KK, the number of values to copy.
!
  implicit none

  integer ( kind = 4 ) kk

  real ( kind = 8 ) w(kk)
  real ( kind = 8 ) ws(kk)
  real ( kind = 8 ) xnew(kk)
  real ( kind = 8 ) xs(kk)
  real ( kind = 8 ) ynew(kk)
  real ( kind = 8 ) ys(kk)

  xnew(1:kk) = xs(1:kk)
  ynew(1:kk) = ys(1:kk)
  w(1:kk) = ws(1:kk)

  return
end
subroutine quaecopy ( xs, ys, ws, z, w, kk )

!*****************************************************************************80
!
!! QUAECOPY copies a quadrature rule into user arrays Z and W.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, real ( kind = 8 ) XS(KK), YS(KK), the point coordinates to copy.
!
!    Input, real ( kind = 8 ) WS(KK), the weights to copy.
!
!    Output, real ( kind = 8 ) Z(2,KK), the copied point coordinates.
!
!    Output, real ( kind = 8 ) W(KK), the copied weights.
!
!    Input, integer ( kind = 4 ) KK, the number of values to copy.
!
  implicit none

  integer ( kind = 4 ) kk

  real ( kind = 8 ) w(kk)
  real ( kind = 8 ) ws(kk)
  real ( kind = 8 ) xs(kk)
  real ( kind = 8 ) ys(kk)
  real ( kind = 8 ) z(2,kk)

  z(1,1:kk) = xs(1:kk)
  z(2,1:kk) = ys(1:kk)
  w(1:kk) = ws(1:kk)

  return
end
subroutine quaeinside ( iitype, xsout, ysout, nbool )

!*****************************************************************************80
!
!! QUAEINSIDE checks whether a point is inside a triangle.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) IITYPE, indicates the check to perform.
!    * 0 check whether the point is inside the whole triangle
!    * 1 check whether the point is inside the bottom 1/3 of the triangle
!    * 2 check whether the point is inside the lower-left 1/6 of the triangle
!
!    Input, real ( kind = 8 ) XSOUT, YSOUT, the coordinates of the point.
!
!    Output, integer ( kind = 4 ) NBOOL.
!    * 1, the point is inside.
!    * 2, the point is outside.
!
  implicit none

  integer ( kind = 4 ) iitype
  integer ( kind = 4 ) nbool
  real ( kind = 8 ) s
  real ( kind = 8 ) xsout
  real ( kind = 8 ) ysout

  s = sqrt ( 3.0D+00 )
!
!  The 1/6 of triangle.
!
  if ( iitype == 2 ) then

    nbool = 1

    if ( xsout < -1.0D+00 .or. 0.0D+00 < xsout ) then
      nbool = 0
    end if
!
!  hx
!
    if ( ysout < -1.0D+00 / s - 1.0D-30 &
      .or. xsout / s < ysout ) then
      nbool = 0
    end if
!
!  The 1/3 of triangle.
!
  else if ( iitype == 1 ) then

    nbool = 0

    if ( xsout <= 0.0D+00 .and. &
         -1.0D+00 <= xsout .and. &
         -1.0D+00 / s <= ysout .and. &
         ysout <= xsout / s ) then
      nbool = 1
    end if

    if ( iitype == 1 ) then

      if  ( 0.0D+00 <= xsout .and. &
            xsout <= 1.0D+00 .and. &
            -1.0D+00 / s <= ysout.and. &
            ysout <= - xsout / s ) then
        nbool = 1
      end if

    end if
!
!  The entire triangle.
!
  else if ( iitype == 0 ) then

    nbool = 1

    if ( ysout < -1.0D+00 / s ) then
      nbool = 0
    end if

    if ( s * xsout + 2.0D+00 / s < ysout ) then
      nbool = 0
    end if

    if ( - s * xsout + 2.0D+00 / s < ysout ) then
      nbool = 0
    end if

  end if

  return
end
subroutine quaenodes2 ( nptsout, xsout, ysout, wsout, nptsoutout, &
    xs2, ys2, ws2 )

!*****************************************************************************80
!
!! QUAENODES2 expands nodes from 1/6 to 1/3 of the triangle.
!
!  Discussion:
!
!    This routine only expands to 1/3 of the triangle, assuming the points are
!    already in the lower-left 1/6 of the triangle.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) NPTSOUT, the number of points expanded.
!
!    Input, real ( kind = 8 ) XSOUT(NPTSOUT), YSOUT(NPTSOUT), WSOUT(NPTSOUT),
!    the coordinates and weights of the points to be expanded.
!
!    Output, integer ( kind = 4 ) NPTSOUTPUT, the number of points in the 
!    expanded set.
!
!    Output, real ( kind = 8 ) XS2(NPTSOUTOUT), YS2(NPTSOUTOUT), 
!    WS2(NPTSOUTOUT), the coordinates and weights of the expanded set of points.
!
  implicit none

  integer ( kind = 4 ) nptsout

  real ( kind = 8 ) eps
  parameter ( eps = 1.0D-12 )
  integer ( kind = 4 ) nptsoutout
  integer ( kind = 4 ) i
  integer ( kind = 4 ) ntot
  real ( kind = 8 ) ws2(*)
  real ( kind = 8 ) wsout(nptsout)
  real ( kind = 8 ) xs2(*)
  real ( kind = 8 ) xsout(nptsout)
  real ( kind = 8 ) ys2(*)
  real ( kind = 8 ) ysout(nptsout)

  ntot = 0

  do i = 1, nptsout

    if ( xsout(i)**2 + ysout(i)**2 < eps ) then

       ntot = ntot + 1
       xs2(ntot) = xsout(i)
       ys2(ntot) = ysout(i)
       ws2(ntot) = wsout(i)

    else if ( xsout(i)**2 < eps ) then

       ntot = ntot + 1
       xs2(ntot) = xsout(i)
       ys2(ntot) = ysout(i)
       ws2(ntot) = wsout(i)

    else

      ntot = ntot + 1
      xs2(ntot) = -xsout(i)
      ys2(ntot) = ysout(i)
      ws2(ntot) = wsout(i) / 2.0D+00

      ntot = ntot + 1
      xs2(ntot) = xsout(i)
      ys2(ntot) = ysout(i)
      ws2(ntot) = wsout(i) / 2.0D+00

    end if

  end do

  nptsoutout = ntot

  return
end
subroutine quaenodes ( nptsout, xsout, ysout, wsout, &
    nptsoutout, xs2, ys2, ws2 )

!*****************************************************************************80
!
!! QUAENODES expands nodes to the reference triangle.
!
!  Discussion:
!
!    This routine expands nodes to the reference triangle
!    assuming that the points are already in the lower-left 1/6 of the
!    triangle.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) NPTSOUT, the number of points expanded.
!
!    Input, real ( kind = 8 ) XSOUT(NPTSOUT), YSOUT(NPTSOUT), WSOUT(NPTSOUT),
!    the coordinates and weights of the points to be expanded.
!
!    Output, integer ( kind = 4 ) NPTSOUTPUT, the number of points in the 
!    expanded set.
!
!    Output, real ( kind = 8 ) XS2(NPTSOUTOUT), YS2(NPTSOUTOUT), 
!    WS2(NPTSOUTOUT), the coordinates and weights of the expanded set of points.
!
  implicit none

  integer ( kind = 4 ) nptsout

  real ( kind = 8 ) eps
  parameter ( eps = 1.0D-12 )
  integer ( kind = 4 ) i
  integer ( kind = 4 ) nptsoutout
  integer ( kind = 4 ) ntot
  real ( kind = 8 ) w0
  real ( kind = 8 ) ws2(*)
  real ( kind = 8 ) wsout(nptsout)
  real ( kind = 8 ) x0
  real ( kind = 8 ) x1
  real ( kind = 8 ) x2
  real ( kind = 8 ) xs2(*)
  real ( kind = 8 ) xsout(nptsout)
  real ( kind = 8 ) y0
  real ( kind = 8 ) y1
  real ( kind = 8 ) y2
  real ( kind = 8 ) ys2(*)
  real ( kind = 8 ) ysout(nptsout)

  ntot = 0

  do i = 1, nptsout

    if ( xsout(i)**2 + ysout(i)**2 < eps ) then

      ntot = ntot + 1
      xs2(ntot) = xsout(i)
      ys2(ntot) = ysout(i)
      ws2(ntot) = wsout(i)

    else if ( xsout(i)**2 < eps .or. &
      abs ( ysout(i) - xsout(i) / sqrt ( 3.0D+00 ) ) &
      < sqrt ( eps ) ) then

      x0 = xsout(i)
      y0 = ysout(i)
      w0 = wsout(i) / 3.0D+00

      ntot = ntot + 1
      xs2(ntot) = x0
      ys2(ntot) = y0
      ws2(ntot) = w0

      ntot = ntot + 1
      call quaerotate ( x0, y0, x1, y1 )
      xs2(ntot) = x1
      ys2(ntot) = y1
      ws2(ntot) = w0

      ntot = ntot + 1
      call quaerotate ( x1, y1, x2, y2 )
      xs2(ntot) = x2
      ys2(ntot) = y2
      ws2(ntot) = w0

    else

      x0 = xsout(i)
      y0 = ysout(i)
      w0 = wsout(i) / 6.0D+00

      ntot = ntot + 1
      xs2(ntot) = x0
      ys2(ntot) = y0
      ws2(ntot) = w0

      ntot = ntot + 1
      call quaerotate ( x0, y0, x1, y1 )
      xs2(ntot) = x1
      ys2(ntot) = y1
      ws2(ntot) = w0

      ntot = ntot + 1
      call quaerotate ( x1, y1, x2, y2 )
      xs2(ntot) = x2
      ys2(ntot) = y2
      ws2(ntot) = w0

      ntot = ntot + 1
      xs2(ntot) = -x0
      ys2(ntot) = y0
      ws2(ntot) = w0

      ntot = ntot + 1
      call quaerotate ( -x0, y0, x1, y1 )
      xs2(ntot) = x1
      ys2(ntot) = y1
      ws2(ntot) = w0

      ntot = ntot + 1
      call quaerotate ( x1, y1, x2, y2 )
      xs2(ntot) = x2
      ys2(ntot) = y2
      ws2(ntot) = w0

    end if

  end do

  nptsoutout = ntot

  return
end
subroutine quaequad0 ( mmax, kk, xnew, ynew, w )

!*****************************************************************************80
!
!! QUAEQUAD0 returns the requested quadrature rule.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    28 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) MMAX, the degree of the quadrature (the 
!    maximum degree of the polynomials of two variables that are integrated
!    exactly.  1 <= MMAX <= 50.
!
!    Input, integer ( kind = 4 ) KK, the number of points in the compressed 
!    rule.
!
!    Output, real ( kind = 8 ) XNEW(KK), YNEW(KK), the
!    coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(KK), the weights.
!
  implicit none

  integer ( kind = 4 ) kk

  integer ( kind = 4 ) i
  integer ( kind = 4 ) iitype
  integer ( kind = 4 ) mmax
  integer ( kind = 4 ) nbool0
  integer ( kind = 4 ) nbool1
  integer ( kind = 4 ) nbool2
  real ( kind = 8 ) w(kk)
  real ( kind = 8 ) x0
  real ( kind = 8 ) x1
  real ( kind = 8 ) xnew(kk)
  real ( kind = 8 ) y0
  real ( kind = 8 ) y1
  real ( kind = 8 ) ynew(kk)
!
!  Copy the arrays defining the compressed rule.
!
  if ( mmax == 1 ) then
    call rule01 ( xnew, ynew, w )
  else if ( mmax == 2 ) then
    call rule02 ( xnew, ynew, w )
  else if ( mmax == 3 ) then
    call rule03 ( xnew, ynew, w )
  else if ( mmax == 4 ) then
    call rule04 ( xnew, ynew, w )
  else if ( mmax == 5 ) then
    call rule05 ( xnew, ynew, w )
  else if ( mmax == 6 ) then
    call rule06 ( xnew, ynew, w )
  else if ( mmax == 7 ) then
    call rule07 ( xnew, ynew, w )
  else if ( mmax == 8 ) then
    call rule08 ( xnew, ynew, w )
  else if ( mmax == 9 ) then
    call rule09 ( xnew, ynew, w )
  else if ( mmax == 10 ) then
    call rule10 ( xnew, ynew, w )
  else if ( mmax == 11 ) then
    call rule11 ( xnew, ynew, w )
  else if ( mmax == 12 ) then
    call rule12 ( xnew, ynew, w )
  else if ( mmax == 13 ) then
    call rule13 ( xnew, ynew, w )
  else if ( mmax == 14 ) then
    call rule14 ( xnew, ynew, w )
  else if ( mmax == 15 ) then
    call rule15 ( xnew, ynew, w )
  else if ( mmax == 16 ) then
    call rule16 ( xnew, ynew, w )
  else if ( mmax == 17 ) then
    call rule17 ( xnew, ynew, w )
  else if ( mmax == 18 ) then
    call rule18 ( xnew, ynew, w )
  else if ( mmax == 19 ) then
    call rule19 ( xnew, ynew, w )
  else if ( mmax == 20 ) then
    call rule20 ( xnew, ynew, w )
  else if ( mmax == 21 ) then
    call rule21 ( xnew, ynew, w )
  else if ( mmax == 22 ) then
    call rule22 ( xnew, ynew, w )
  else if ( mmax == 23 ) then
    call rule23 ( xnew, ynew, w )
  else if ( mmax == 24 ) then
    call rule24 ( xnew, ynew, w )
  else if ( mmax == 25 ) then
    call rule25 ( xnew, ynew, w )
  else if ( mmax == 26 ) then
    call rule26 ( xnew, ynew, w )
  else if ( mmax == 27 ) then
    call rule27 ( xnew, ynew, w )
  else if ( mmax == 28 ) then
    call rule28 ( xnew, ynew, w )
  else if ( mmax == 29 ) then
    call rule29 ( xnew, ynew, w )
  else if ( mmax == 30 ) then
    call rule30 ( xnew, ynew, w )
  else if ( mmax == 31 ) then
    call rule31 ( xnew, ynew, w )
  else if ( mmax == 32 ) then
    call rule32 ( xnew, ynew, w )
  else if ( mmax == 33 ) then
    call rule33 ( xnew, ynew, w )
  else if ( mmax == 34 ) then
    call rule34 ( xnew, ynew, w )
  else if ( mmax == 35 ) then
    call rule35 ( xnew, ynew, w )
  else if ( mmax == 36 ) then
    call rule36 ( xnew, ynew, w )
  else if ( mmax == 37 ) then
    call rule37 ( xnew, ynew, w )
  else if ( mmax == 38 ) then
    call rule38 ( xnew, ynew, w )
  else if ( mmax == 39 ) then
    call rule39 ( xnew, ynew, w )
  else if ( mmax == 40 ) then
    call rule40 ( xnew, ynew, w )
  else if ( mmax == 41 ) then
    call rule41 ( xnew, ynew, w )
  else if ( mmax == 42 ) then
    call rule42 ( xnew, ynew, w )
  else if ( mmax == 43 ) then
    call rule43 ( xnew, ynew, w )
  else if ( mmax == 44 ) then
    call rule44 ( xnew, ynew, w )
  else if ( mmax == 45 ) then
    call rule45 ( xnew, ynew, w )
  else if ( mmax == 46 ) then
    call rule46 ( xnew, ynew, w )
  else if ( mmax == 47 ) then
    call rule47 ( xnew, ynew, w )
  else if ( mmax == 48 ) then
    call rule48 ( xnew, ynew, w )
  else if ( mmax == 49 ) then
    call rule49 ( xnew, ynew, w )
  else if ( mmax == 50 ) then
    call rule50 ( xnew, ynew, w )
  else
    write ( *, '(a)' ) ''
    write ( *, '(a)' ) 'QUAEQUAD0 - Fatal error!'
    write ( *, '(a)' ) '  Illegal input value of MMAX.'
    write ( *, '(a)' ) '  1 <= MMAX <= 50 required.'
    stop 1
  end if

  do i = 1, kk
!
!  The lower-left 1/6
!
    iitype = 2
    call quaeinside ( iitype, xnew(i), ynew(i), nbool2 )
!
!  The lower 1/3
!
    iitype = 1
    call quaeinside ( iitype, xnew(i), ynew(i), nbool1 )
!
!  The whole triangle
!
    iitype = 0
    call quaeinside ( iitype, xnew(i), ynew(i), nbool0 )

    if ( nbool2 == 1 ) then

    else if ( nbool1 == 1 ) then
      xnew(i) = -xnew(i)
      ynew(i) = ynew(i)
    else if ( nbool0 == 1 ) then
      x0 = xnew(i)
      y0 = ynew(i)
      call quaerotate ( x0, y0, x1, y1 )
      xnew(i) = x1
      ynew(i) = y1
    else
      write ( *, '(a)' ) ''
      write ( *, '(a)' ) 'QUAEQUAD0 - Fatal error!'
      write ( *, '(a)' ) '  Point does not lie inside triangle.'
      stop 1
    end if

  end do

  return
end
subroutine quaequad ( itype, mmax, zs, whts, numnodes )

!*****************************************************************************80
!
!! QUAEQUAD returns a symmetric quadrature formula for a reference triangle.
!
!  Discussion:
!
!    This routine constructs (or rather, retrieves)
!    D_3 symmetric quadrature formulae for smooth functions
!    on the triangle with vertices
!      (-1,-1/sqrt(3)), (1,-1/sqrt(3)), (0,2/sqrt(3)).
!
!    All quadratures are obtained to the extended precision.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) ITYPE, the configuration of the nodes.
!    * 0, all nodes on the reference triangle
!    * 1, quadrature nodes on the bottom 1/3 of the reference triangle
!    * 2, quadrature nodes on lower-left 1/6 of the reference triangle
!
!    Input, integer ( kind = 4 ) MMAX, the degree of the quadrature (the 
!    maximum degree of the polynomials of two variables that are integrated
!    exactly. 1 <= MMAX <= 50.
!
!    Output, real ( kind = 8 ) ZS(2,NUMNODES), the nodes.
!
!    Output, real ( kind = 8 ) WHTS(NUMNODES), the weights.
!
!    Input, integer ( kind = 4 ) NUMNODES, the number of nodes.
!
  implicit none

  integer ( kind = 4 ) numnodes

  integer ( kind = 4 ) itype
  integer ( kind = 4 ) kk
  integer ( kind = 4 ) mmax
  integer ( kind = 4 ) nptsout
  real ( kind = 8 ) whts(numnodes)
  real ( kind = 8 ) wsout(3000)
  real ( kind = 8 ) xnew(300)
  real ( kind = 8 ) xsout(3000)
  real ( kind = 8 ) ynew(300)
  real ( kind = 8 ) ysout(3000)
  real ( kind = 8 ) zs(2,numnodes)

  if ( mmax < 1 .or. 50 < mmax ) then
    write ( *, '(a)' ) ''
    write ( *, '(a)' ) 'QUAEQUAD - Fatal error!'
    write ( *, '(a)' ) '  1 <= MMAX <= 50 is required.'
    stop 1
  end if

  if ( itype < 0 .or. 2 < itype ) then
    write ( *, '(a)' ) ''
    write ( *, '(a)' ) 'QUAEQUAD - Fatal error!'
    write ( *, '(a)' ) '  0 <= ITYPE <= 2 is required.'
    stop 1
  end if
!
!  Retrieve the compressed rule.
!
  call rule_compressed_size ( mmax, kk )

  call quaequad0 ( mmax, kk, xnew, ynew, whts )

  nptsout = kk
!
!  Expand the nodes to the entire triangle.
!
  if ( itype == 0 ) then

    call quaenodes ( kk, xnew, ynew, whts, nptsout, xsout, &
      ysout, wsout )

    call quaecopy ( xsout, ysout, wsout, zs, whts, nptsout )
!
!  Expand the nodes to the lower 1/3 of the triangle.
!
  else if ( itype == 1 ) then

    call quaenodes2 ( kk, xnew, ynew, whts, nptsout, xsout, &
      ysout, wsout )

    call quaecopy ( xsout, ysout, wsout, zs, whts, nptsout )
!
!  Simply copy the nodes; they are already in the lower-left
!  1/6 of the triangle.
!
  else if ( itype == 2 ) then
    call quaecopy ( xnew, ynew, whts, zs, whts, nptsout )
  end if

  return
end
subroutine quaerotate ( xin, yin, xout, yout )

!*****************************************************************************80
!
!! QUAEROTATE applies a rotation.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, real ( kind = 8 ) XIN, YIN, the coordinates of the point.
!
!    Output, real ( kind = 8 ) XOUT, YOUT, the coordinates of the point
!    after rotation.
!
  implicit none

  real ( kind = 8 ) a11
  real ( kind = 8 ) a12
  real ( kind = 8 ) a21
  real ( kind = 8 ) a22
  real ( kind = 8 ) r8_pi
  parameter ( r8_pi = 3.141592653589793D+00 )
  real ( kind = 8 ) theta
  real ( kind = 8 ) xin
  real ( kind = 8 ) xout
  real ( kind = 8 ) yin
  real ( kind = 8 ) yout
!
!  Initialize the matrix of rotation.
!
  theta = 2.0D+00 * r8_pi / 3.0D+00
  a11 = cos ( theta )
  a22 = cos ( theta )
  a12 = - sin ( theta )
  a21 = -a12
!
!  Apply the rotation matrix to the input vector.
!
  xout = a11 * xin + a12 * yin
  yout = a21 * xin + a22 * yin

  return
end
subroutine r8vec_uniform_01 ( n, seed, r )

!*****************************************************************************80
!
!! R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
!
!  Discussion:
!
!    An R8VEC is a vector of R8's.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    05 July 2006
!
!  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 ) N, the number of entries in the vector.
!
!    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(N), the vector of pseudorandom values.
!
  implicit none

  integer ( kind = 4 ) n

  integer ( kind = 4 ) i
  integer ( kind = 4 ) k
  integer ( kind = 4 ) seed
  real ( kind = 8 ) r(n)

  if ( seed == 0 ) then
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) 'R8VEC_UNIFORM_01 - Fatal error!'
    write ( *, '(a)' ) '  Input value of SEED = 0.'
    stop 1
  end if

  do i = 1, n

    k = seed / 127773

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

    if ( seed < 0 ) then
      seed = seed + 2147483647
    end if

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

  end do

  return
end
subroutine ref_to_koorn ( r, u )

!*****************************************************************************80
!
!! REF_TO_KOORN maps points from the reference to Koornwinder's triangle.
!
!  Discussion:
!
!    The reference triangle has vertices:
!
!      ( -1, -1/sqrt(3) )
!      ( +1, -1/sqrt(3) )
!      (  0, +2/sqrt(3) )
!
!    Koornwinder's triangle has vertices:
!
!      ( -1, -1 )
!      ( +1, -1 )
!      ( -1, +1 )
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, real ( kind = 8 ) R(2), the coordinates of a point in the
!    reference triangle.
!
!    Output, real ( kind = 8 ) U(2), the coordinates of the point in
!    the Koornwinder triangle.
!
  implicit none

  real ( kind = 8 ) a10
  real ( kind = 8 ) a11
  real ( kind = 8 ) a12
  real ( kind = 8 ) a20
  real ( kind = 8 ) a21
  real ( kind = 8 ) a22
  real ( kind = 8 ) r(2)
  real ( kind = 8 ) u(2)

  a10 = -1.0D+00 / 3.0D+00
  a11 =  1.0D+00
  a12 = -1.0D+00 / sqrt ( 3.0D+00 )

  a20 = - 1.0D+00 / 3.0D+00
  a21 =   0.0D+00
  a22 =   2.0D+00 * sqrt ( 3.0D+00 ) / 3.0D+00

  u(1) = a10 + r(1) + a12 * r(2)
  u(2) = a20 +        a22 * r(2)

  return
end
subroutine ref_to_triangle ( tvert1, tvert2, tvert3, r, t )

!*****************************************************************************80
!
!! REF_TO_TRIANGLE maps points from the reference triangle to a triangle.
!
!  Discussion:
!
!    The reference triangle has vertices:
!
!      ( -1, -1/sqrt(3) )
!      ( +1, -1/sqrt(3) )
!      (  0, +2/sqrt(3) )
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, real ( kind = 8 ) TVERT1(2), TVERT2(2), TVERT3(2), the coordinates
!    of the vertices of the triangle.  These vertices will be taken
!    to be the images of (0,0), (1,0) and (0,1) respectively.
!
!    Input, real ( kind = 8 ) R(2), the coordinates of a point in the
!    reference triangle.
!
!    Output, real ( kind = 8 ) T(2), the coordinates of the point in
!    the triangle.
!
  implicit none

  integer ( kind = 4 ) n

  integer ( kind = 4 ) i
  real ( kind = 8 ) r(2)
  real ( kind = 8 ) s(2)
  real ( kind = 8 ) t(2)
  real ( kind = 8 ) rvert1(2)
  real ( kind = 8 ) rvert2(2)
  real ( kind = 8 ) rvert3(2)
  real ( kind = 8 ) tvert1(2)
  real ( kind = 8 ) tvert2(2)
  real ( kind = 8 ) tvert3(2)

  rvert1(1) = - 1.0D+00
  rvert1(2) = - 1.0D+00 / sqrt ( 3.0D+00 )
  rvert2(1) = + 1.0D+00
  rvert2(2) = - 1.0D+00 / sqrt ( 3.0D+00 )
  rvert3(1) =   0.0D+00
  rvert3(2) =   2.0D+00 / sqrt ( 3.0D+00 )

  call triangle_to_simplex ( rvert1, rvert2, rvert3, r, s )

  do i = 1, 2
    t(i) = tvert1(i) * ( 1.0D+00 - s(1) - s(2) ) &
         + tvert2(i) * s(1) &
         + tvert3(i) * s(2)
  end do

  return
end
subroutine rule_compressed_size ( mmax, npts )

!*****************************************************************************80
!
!! RULE_COMPRESSED_SIZE returns the compressed size of a quadrature rule.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) MMAX, the degree of the quadrature (the 
!    maximum degree of the polynomials of two variables that are integrated
!    exactly.  1 <= MMAX <= 50.
!
!    Output, integer ( kind = 4 ) NPTS, the number of nodes in the rule.
!
  implicit none

  integer ( kind = 4 ) mmax
  integer ( kind = 4 ) nnodes(50)
  integer ( kind = 4 ) npts

  save nnodes

  data nnodes / &
     1,  1,  2,  2,  3, &
     3,  4,  5,  6,  7, &
     8,  8, 10, 10, 12, &
    13, 13, 15, 17, 18, &
    19, 20, 23, 24, 25, &
    27, 29, 30, 32, 34, &
    37, 39, 41, 44, 46, &
    46, 49, 51, 54, 58, &
    58, 62, 65, 67, 70, &
    73, 75, 78, 82, 84 /

  if ( 1 <= mmax .and. mmax <= 50 ) then
    npts = nnodes(mmax)
  else
    write ( *, '(a)' ) ''
    write ( *, '(a)' ) 'RULE_COMPRESSED_SIZE - Fatal error!'
    write ( *, '(a)' ) '  Degree MMAX must be between 1 and 50.'
    stop 1
  end if

  return
end
subroutine rule_full_size ( mmax, npts )

!*****************************************************************************80
!
!! RULE_FULL_SIZE returns the full size of the requested quadrature rule.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) MMAX, the degree of the quadrature (the 
!    maximum degree of the polynomials of two variables that are integrated
!    exactly.  1 <= MMAX <= 50.
!
!    Output, integer ( kind = 4 ) NPTS, the number of nodes in the full rule.
!
  implicit none

  integer ( kind = 4 ) mmax
  integer ( kind = 4 ) nnodes(50)
  integer ( kind = 4 ) npts

  save nnodes

  data nnodes / &
      1,   3,   6,   6,   7,  12,  15,  16,  19,  25, &
     28,  33,  37,  42,  49,  55,  60,  67,  73,  79, &
     87,  96, 103, 112, 120, 130, 141, 150, 159, 171, &
    181, 193, 204, 214, 228, 243, 252, 267, 282, 295, &
    309, 324, 339, 354, 370, 385, 399, 423, 435, 453 /

  if ( 1 <= mmax .and. mmax <= 50 ) then
    npts = nnodes(mmax)
  else
    write ( *, '(a)' ) ''
    write ( *, '(a)' ) 'RULE_FULL_SIZE - Fatal error!'
    write ( *, '(a)' ) '  Degree MMAX must be between 1 and 50.'
    stop 1
  end if

  return
end
subroutine rule01 ( x, y, w )

!*****************************************************************************80
!
!! RULE01 returns the rule of degree 1.
!
!  Discussion:
!
!    Order 1 (1 pts)
!    1/6 data for 2-th order quadrature with 1 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 1 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00/
  data ys / &
       0.00000000000000000000000000000000D+00/
  data ws / &
       0.21934566882541541013653648363283D+00/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule02 ( x, y, w )

!*****************************************************************************80
!
!! RULE02 returns the rule of degree 2.
!
!  Discussion:
!
!    Order 2 (3 pts)
!    1/6 data for 2-th order quadrature with 1 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 1 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00/
  data ys / &
       0.57735026918962576450914878050196D+00/
  data ws / &
       0.21934566882541541013653648363283D+00/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule03 ( x, y, w )

!*****************************************************************************80
!
!! RULE03 returns the rule of degree 3.
!
!  Discussion:
!
!    Order 3 (6 pts)
!    1/6 data for 4-th order quadrature with 2 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 2 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00/
  data ys / &
      -0.39011034927098671317419951524681D+00, &
       0.83747122925185483484415621413487D+00/
  data ws / &
       0.14699335257362380894667320570121D+00, &
       0.72352316251791601189863277931619D-01/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule04 ( x, y, w )

!*****************************************************************************80
!
!! RULE04 returns the rule of degree 4.
!
!  Discussion:
!
!    Order 4 (6 pts)
!    1/6 data for 4-th order quadrature with 2 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 2 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs/ &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00/
  data ys/ &
      -0.39011034927098671317419951524681D+00, &
       0.83747122925185483484415621413487D+00/
  data ws/ &
       0.14699335257362380894667320570121D+00, &
       0.72352316251791601189863277931619D-01/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule05 ( x, y, w )

!*****************************************************************************80
!
!! RULE05 returns the rule of degree 5.
!
!  Discussion:
!
!    Order 5 (7 pts)
!    1/6 data for 5-th order quadrature with 3 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 3 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs/ &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00/
  data ys/ &
       0.80383378476840441740523498549521D+00, &
      -0.47391934523147540911429282520838D+00, &
       0.00000000000000000000000000000000D+00/
  data ws/ &
       0.82872641363789568276918148034109D-01, &
       0.87120251975907374578897626781336D-01, &
       0.49352775485718467280720708817387D-01/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule06 ( x, y, w )

!*****************************************************************************80
!
!! RULE06 returns the rule of degree 6.
!
!  Discussion:
!
!    Order 6 (12 pts)
!    1/6 data for 6-th order quadrature with 3 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 3 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs/ &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.69739024379082289479659372931424D+00/
  data ys/ &
       0.39457278141889907274877084543840D+00, &
      -0.50854615859082585320530997387282D+00, &
      -0.54379745836573696334891625304668D+00/
  data ws/ &
       0.11274353612785067755726196993061D+00, &
       0.53124044525363740527637434536885D-01, &
       0.53478088172200992051637079165337D-01/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule07 ( x, y, w )

!*****************************************************************************80
!
!! RULE07 returns the rule of degree 7.
!
!  Discussion:
!
!    Order 7 (15 pts)
!    1/6 data for 7-th order quadrature with 4 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 4 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.43435077013834314810201324540358D+00, &
       0.00000000000000000000000000000000D+00/
  data ys / &
      -0.48449728984184861759282345604996D+00, &
       0.95448364011528521109785290893117D+00, &
      -0.49599375367952699580224212194439D+00, &
       0.31755324913853224106767424614158D+00/
  data ws / &
       0.34994956344512530405766865129365D-01, &
       0.26925670356590145219766443119660D-01, &
       0.73377101909709748747894757835629D-01, &
       0.84047940214602985763108417548179D-01/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule08 ( x, y, w )

!*****************************************************************************80
!
!! RULE08 returns the rule of degree 8.
!
!  Discussion:
!
!    Order 8 (16 pts)
!    1/6 data for 8-th order quadrature with 5 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 5 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.46537956332076616781921459289142D+00/
  data ys / &
       0.56383112390345027361169431475509D+00, &
      -0.43633565854637050936665616521528D+00, &
       0.00000000000000000000000000000000D+00, &
       0.97959980312548768236416519395659D+00, &
      -0.56281008819734772609629802285497D+00/
  data ws / &
       0.67920849523015500098940229347144D-01, &
       0.62573814354178010612492306599248D-01, &
       0.31655003488030481682328160339460D-01, &
       0.21358892610685618050556600653540D-01, &
       0.35837108849505799692219186693442D-01/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule09 ( x, y, w )

!*****************************************************************************80
!
!! RULE09 returns the rule of degree 9.
!
!  Discussion:
!
!    Order 9 (19 pts)
!    1/6 data for 9-th order quadrature with 6 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 6 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.51923560962373232501497734583023D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00/
  data ys / &
      -0.54160946728182000656873212814730D+00, &
       0.00000000000000000000000000000000D+00, &
       0.50274436666672432312125361006830D+00, &
      -0.51354426784066472011973483470318D+00, &
      -0.35942222147133163342323862565198D+00, &
       0.99975295878520206908663626641606D+00/
  data ws / &
       0.20619392336297146785884881219859D-01, &
       0.21306316202539810241408079330466D-01, &
       0.52411159696263022262999116690283D-01, &
       0.56964341363056457388652374913231D-01, &
       0.51213402104188971492967950562937D-01, &
       0.16831057123070001964624080916057D-01/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule10 ( x, y, w )

!*****************************************************************************80
!
!! RULE10 returns the rule of degree 10.
!
!  Discussion:
!
!    Order 10 (25 pts)
!    1/6 data for   10-th order quadrature with   7 nodes
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 7 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.69780686931593427582366555189730D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.30903100009613455447142535490429D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00/
  data ys / &
      -0.56063064349133316993278274030104D+00, &
       0.10883996591237330573849553975247D+01, &
      -0.51720719429149531106975531479846D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.51225507594767383123122215407598D+00, &
       0.51562570796758001502147445483555D+00, &
      -0.32874839651011214404597359718045D+00/
  data ws / &
       0.64438869372269120316756176676570D-02, &
       0.42018026730627469477523487256964D-02, &
       0.38116505989607355372802824839739D-01, &
       0.18340560543312397707554978722912D-01, &
       0.50983455788600478135692116331631D-01, &
       0.51743930451848519084272818465418D-01, &
       0.49515526441757000856785778879781D-01/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule11 ( x, y, w )

!*****************************************************************************80
!
!! RULE11 returns the rule of degree 11.
!
!  Discussion:
!
!    Order 11 (28 pts)
!    1/6 data for   11-th order quadrature with   8 nodes
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 8 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.66702609775505741425256941082402D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.33107350040092300374508907880435D+00/
  data ys / &
       0.10478437573860252650592594105291D+01, &
      -0.57312463741413046743394091946546D+00, &
      -0.55246647968395743746723714345900D+00, &
       0.00000000000000000000000000000000D+00, &
       0.76253712102917906246868919741961D+00, &
      -0.35791680916635253698118135523597D+00, &
       0.41170804295590891080211946164601D+00, &
      -0.49479368349849501640395735410577D+00/
  data ws / &
       0.80604906968824787275184319645950D-02, &
       0.82027549569428763887170584691844D-02, &
       0.19158909765241473284488780746507D-01, &
       0.17864637545398712988860649788563D-01, &
       0.26406526528755833416145171420307D-01, &
       0.41518760800101172427427091335633D-01, &
       0.44644591603719541882313987831736D-01, &
       0.53488996928373321021065312076308D-01/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule12 ( x, y, w )

!*****************************************************************************80
!
!! RULE12 returns the rule of degree 12.
!
!  Discussion:
!
!    Order 12 (33 pts)
!    1/6 data for   12-th order quadrature with   8 nodes
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 8 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.37279552304503872030654041088416D+00, &
      -0.72405807527665067283016173568468D+00, &
      -0.39365448416805093945053087420319D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00/
  data ys / &
       0.21432682937950204373207766849052D+00, &
       0.77622032111803989421823022245158D+00, &
      -0.36989093457992084889029420576697D+00, &
      -0.37591965438942697512621254516818D+00, &
      -0.54031470967359184488712033281188D+00, &
      -0.53745394007281752834331765730183D+00, &
      -0.53648686378750904365565925207548D+00, &
       0.10693230309921692958873012567969D+01/
  data ws / &
       0.41154432712824560996161389102816D-01, &
       0.18744876429730660409284009808805D-01, &
       0.32848111684339866575373457398258D-01, &
       0.56890409960601999633893263927781D-01, &
       0.19851236078200935116627045158968D-01, &
       0.28668810178252124180808712582749D-01, &
       0.15968477487762470187363091359494D-01, &
       0.52193142937027930370255142939621D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule13 ( x, y, w )

!*****************************************************************************80
!
!! RULE13 returns the rule of degree 13.
!
!  Discussion:
!
!    Order 13 (37 pts)
!    1/6 data for 13-th order quadrature with 10 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 10 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.39685461846296817096661395897363D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.36877346231328110106712038942974D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.72443410422579609569939260421083D+00, &
      0.00000000000000000000000000000000D+00/
  data ys / &
     -0.56396461592102123502624022053391D+00, &
     -0.47207168193213434618577598142010D+00, &
      0.35411102701218903723318259570554D+00, &
     -0.54446208086261457427222068671521D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.40806649765315498179968814806897D+00, &
     -0.28109188226279360944191830212271D+00, &
      0.76131746182322280252086625652347D+00, &
     -0.53930344496737094791136532996013D+00, &
      0.10684585018901699613124809207464D+01/
  data ws / &
      0.65418593445945714253573279005246D-02, &
      0.21571270093488444532084979604155D-01, &
      0.30310770119514528295026716361971D-01, &
      0.23854497740070562467907639645715D-01, &
      0.11323203959116968208057898102191D-01, &
      0.48973694128817658616454407740346D-01, &
      0.30892926213314122881388117756484D-01, &
      0.20335382082811117457514058128897D-01, &
      0.20258422938614600267531787728451D-01, &
      0.52836422050728359852135506640993D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule14 ( x, y, w )

!*****************************************************************************80
!
!! RULE14 returns the rule of degree 14.
!
!  Discussion:
!
!    Order 14 (42 pts)
!    1/6 data for 14-th order quadrature with 10 nodes
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 10 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00, &
      -0.38860728567183008438779563596070D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.23336083105033817175364101627343D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.59834186695364090421374367255377D+00, &
      -0.76078267367321428411638967504470D+00/
  data ys / &
      -0.29206320844176911462814202555440D+00, &
      -0.55198100751730853202008670921318D+00, &
       0.94061946354883534183314930438733D+00, &
      -0.41641460445461153990144627293196D+00, &
       0.20734659086072252500578277182211D+00, &
       0.54084256733761408785791946134147D+00, &
       0.10875282781985526175124163597842D+01, &
      -0.53912013325044374969918965513440D+00, &
      -0.47840728699646114957331822352154D+00, &
      -0.57515345557308018596067002721924D+00/
  data ws / &
       0.21575950013461064401435712745522D-01, &
       0.18999249951197107599659818693116D-01, &
       0.94979085230770220958819598950727D-02, &
       0.50762962987167304291061144573638D-01, &
       0.34069276742966482732002423831004D-01, &
       0.27744543677779980654066228474803D-01, &
       0.32397817681977165704923716215682D-02, &
       0.14400206375318340262255497721148D-01, &
       0.32461956812954507173175490962641D-01, &
       0.65938319732958843565058351143197D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule15 ( x, y, w )

!*****************************************************************************80
!
!! RULE15 returns the rule of degree 15.
!
!  Discussion:
!
!    Order 15 (49 pts)
!    1/6 data for 15-th order quadrature with 12 nodes
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 12 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.55076221170342555936584321474523D+00, &
      -0.68357214208317707300355657115991D+00, &
      -0.25612692724233233019551175197799D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.36565038512802113430475383248411D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.92281600612376773678051247314954D+00/
  data ys / &
       0.70444274213533005064746095394944D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.43905276476834389171283475266302D+00, &
      -0.43082877955573503227054242095029D+00, &
      -0.54959053538220730475284121644503D+00, &
      -0.40821474151886640425221018734748D+00, &
      -0.54854909315008697510886410926313D+00, &
       0.38728999882555268441925180574268D+00, &
      -0.22031826248214061224887524925114D+00, &
      -0.54538656727512647368330462485919D+00, &
       0.95952641028823274876646693877390D+00, &
      -0.57542156951901391210911429306642D+00/
  data ws / &
       0.48678314316748716941104750027452D-02, &
       0.65212388041010424283650376293385D-02, &
       0.14209708983278779348806400026132D-01, &
       0.31888484893082254935417221561584D-01, &
       0.14777542712078757890433156238493D-01, &
       0.40897290108008783478410013863721D-01, &
       0.10418223735073013293430828867470D-01, &
       0.30458747186574088002369116260931D-01, &
       0.30490829969029447439964565952835D-01, &
       0.21631995447453411916722584709018D-01, &
       0.99261422781568007641581796089061D-02, &
       0.32576332769041589443489039116581D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule16 ( x, y, w )

!*****************************************************************************80
!
!! RULE16 returns the rule of degree 16.
!
!  Discussion:
!
!    Order 16 (55 pts)
!    1/6 data for 16-th order quadrature with 13 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 13 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       -0.16279607394216944053888791563128D+00, &
       -0.36133516018585422888297687826246D+00, &
        0.00000000000000000000000000000000D+00, &
       -0.80996884917848457646874211083899D+00, &
       -0.30011609466308557056235128866156D+00, &
        0.00000000000000000000000000000000D+00, &
        0.00000000000000000000000000000000D+00, &
       -0.60911897435540735910318766737015D+00, &
        0.00000000000000000000000000000000D+00, &
       -0.56820549744094988938273289446974D+00, &
        0.00000000000000000000000000000000D+00, &
        0.00000000000000000000000000000000D+00, &
        0.00000000000000000000000000000000D+00/
  data ys / &
       -0.56061007710964974635124810013984D+00, &
       -0.52485883552713864174217026883955D+00, &
        0.92373339140338472305543117791951D+00, &
       -0.55862165096055508852660603004778D+00, &
       -0.39262157635321675549452096003032D+00, &
        0.31873771449384928263441293513356D+00, &
       -0.27527401254502863816148429232788D+00, &
       -0.48840198582588110096280723102788D+00, &
        0.63486450609449659829895244998069D+00, &
       -0.57094697658781472615514574003317D+00, &
       -0.47186155418111734634796824747685D+00, &
        0.00000000000000000000000000000000D+00, &
        0.10956666024303233991933608013003D+01/
  data ws / &
        0.10768394677601291424698896830942D-01, &
        0.18403461944093881198776232104775D-01, &
        0.81763898630962949174826141110659D-02, &
        0.75698865940531301551762664596891D-02, &
        0.41648559391949793671705497882676D-01, &
        0.27100623100161070449309097892289D-01, &
        0.26969791338286996589221138520990D-01, &
        0.23232761214636807134379750252095D-01, &
        0.18940606006195797095777111782639D-01, &
        0.60732744287626264990846070830020D-02, &
        0.17828637150989055090637459591942D-01, &
        0.10139891906267619230864844708608D-01, &
        0.24933912093210466794229664121214D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule17 ( x, y, w )

!*****************************************************************************80
!
!! RULE17 returns the rule of degree 17.
!
!  Discussion:
!
!    Order 17 (60 pts)
!    1/6 data for 17-th order quadrature with 13 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 13 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00, &
      -0.84341388249881453210290659667990D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.15581940864945499700831493674102D+00, &
      -0.44328038905528761799845288018270D+00, &
      -0.24405663711918945323690771490419D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.32008743864026572053341280894294D+00, &
      -0.58451263244119866196418566874803D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.66559778269229534571098852849491D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00/
  data ys / &
      -0.29018817691328482198192482970493D+00, &
      -0.55730147641876997108891034072276D+00, &
       0.52992169651771413561569476668012D+00, &
      -0.55443580380164528313259557057725D+00, &
      -0.55459827350347093500389453629695D+00, &
      -0.30454277894986876852327724535219D+00, &
       0.16498418183331297460767706117349D+00, &
      -0.46069772486520133352908482893009D+00, &
      -0.44217697018376683763624710581761D+00, &
       0.92380408942408538210867783233523D+00, &
      -0.54960689880096757714733164550461D+00, &
       0.11035860158850820902562773489079D+01, &
      -0.45817780070044727282559523202757D+00/
  data ws / &
       0.17971600336645011505239938032544D-01, &
       0.60333417978448673307205126288851D-02, &
       0.17314684664654665424326078868145D-01, &
       0.13685116601127277244126428127471D-01, &
       0.11439597619776484984723997813429D-01, &
       0.34443796770210477782263821006565D-01, &
       0.24818679791573586362196055551041D-01, &
       0.29595573057886602948646133219328D-01, &
       0.27055715740469881665013596685831D-01, &
       0.81984835916342231806329716122509D-02, &
       0.10500033568557456872117406813490D-01, &
       0.18253206778903200987505636654074D-02, &
       0.16463724607144554737778979608446D-01/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule18 ( x, y, w )

!*****************************************************************************80
!
!! RULE18 returns the rule of degree 18.
!
!  Discussion:
!
!    Order 18 (67 pts)
!    1/6 data for 18-th order quadrature with 15 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 15 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      -0.13948489081933204088461180178994D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.89294878385120099482738372845036D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.34186434923523414986986916455812D+00, &
      -0.47648266163227498302335864700291D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.57691929083982134519411643537248D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.31378647708219846613556828441497D+00, &
      -0.16617683797609618890338301653712D+00, &
      -0.72011081467827938658866318769494D+00, &
       0.00000000000000000000000000000000D+00/
  data ys / &
      -0.42072604091782665082295117027375D+00, &
      -0.49046440452670875509062398243114D+00, &
       0.62940934145837335576901873813141D+00, &
      -0.55570148308783861437134955410860D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.48379919937747237041994289927636D+00, &
      -0.55915504286023151615285736575981D+00, &
      -0.26927767315911711440578206048817D+00, &
      -0.46282281236309048295631522905634D+00, &
       0.23458453920186008350135824349789D+00, &
       0.11416791732161437494841337947029D+01, &
      -0.31915880712448193443612017530713D+00, &
      -0.55709943481991491343285204410962D+00, &
      -0.55252734012256597819639469738327D+00, &
       0.90376550142496547719360163488612D+00/
  data ws / &
       0.20173122273677479015897043873638D-01, &
       0.86249091344656329557281505991774D-02, &
       0.13370218870435472743618008520977D-01, &
       0.55505642264323721863858554667335D-02, &
       0.67445549565863583016393815247161D-02, &
       0.21538746762008261153428035301757D-01, &
       0.10173035336419548391103790096248D-01, &
       0.22025810771933006688763669533528D-01, &
       0.22256988236841747085623568927686D-01, &
       0.20475740472311754752083054066923D-01, &
       0.35007938360486604839471917528428D-03, &
       0.36314280849967402171385914715287D-01, &
       0.12616049305635046682659603780667D-01, &
       0.10057049329246148211330983846490D-01, &
       0.90745189158503137484947042037209D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule19 ( x, y, w )

!*****************************************************************************80
!
!! RULE19 returns the rule of degree 19.
!
!  Discussion:
!
!    Order 19 (73 pts)
!    1/6 data for 19-th order quadrature with 17 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 17 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      -0.71015029250539571205725188857831D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.87005513863591847539846627491196D+00, &
      -0.69945621064432203805136450119586D+00, &
      -0.24805042378404735475371987811852D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.48257092691741797006456094245205D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.25105983153559812324481383767489D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.50128815307877630097134071409913D+00, &
      -0.26869006747347756381758551053812D+00/
  data ys / &
      -0.56868110833624004481988611063840D+00, &
       0.97274416749947380836266322101212D+00, &
      -0.56041590202911501559258672039248D+00, &
      -0.50955355803618757246691504082806D+00, &
      -0.35337391260199717622188423519488D+00, &
       0.76863314856603408380627827197299D+00, &
       0.11143817650139625458794243310849D+01, &
       0.27079298080151709690311725774220D+00, &
      -0.44820650104172157467171108779575D+00, &
      -0.24469161409484972069659993886505D+00, &
      -0.50652963110043023623110954119541D+00, &
       0.53749806844809532876819461539117D+00, &
      -0.43599548606828934030698875208946D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.55141263467657578807862062425378D+00, &
      -0.55150176836813067274425858670454D+00, &
      -0.57376647619684422448809207050633D+00/
  data ws / &
       0.38504278531892868609886548778606D-02, &
       0.46782440974053020444480928944566D-02, &
       0.43790899840937610846456372822265D-02, &
       0.12760020705410626922975774421129D-01, &
       0.34673634319836242706583072061103D-01, &
       0.10025165180245639919338696393626D-01, &
       0.11615619347983174558257617949020D-02, &
       0.20894553379853770048532357879375D-01, &
       0.23831566393070936109285638209472D-01, &
       0.20752749075081240697538867154710D-01, &
       0.21191699422660145703833059227548D-01, &
       0.16221915816210101079240533113508D-01, &
       0.15124040243920516850764130389157D-01, &
       0.75606611406926425730513610639911D-02, &
       0.67921804525194115915872354653919D-02, &
       0.11128622936210414622021183322419D-01, &
       0.43195358902170538658764280819587D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule20 ( x, y, w )

!*****************************************************************************80
!
!! RULE20 returns the rule of degree 20.
!
!  Discussion:
!
!    Order 20 (79 pts)
!    1/6 data for 20-th order quadrature with 18 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 18 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.86696389117550812661190351318543D+00, &
     -0.46255868049954115157854976204512D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.67416180418116902260753583861473D+00, &
     -0.22447168033665606945391317277106D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.55640337063475932672618703937903D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.76173172264834809386157300085862D+00, &
     -0.15012093407474928012860293037678D+00, &
     -0.27874288623783821051052255615910D+00, &
     -0.42809996429665844299450237790398D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00/
  data ys / &
      0.50935573580030290124442500215952D+00, &
      0.10254518566344431484070667698816D+01, &
     -0.49506265376045875810405496904400D+00, &
     -0.56894127058564452950719739998646D+00, &
     -0.39335935346809758365690922062188D+00, &
     -0.38873359764810130895317005413822D+00, &
     -0.56423729270253943031731484496373D+00, &
     -0.33519558519158101515864503661923D+00, &
      0.27281208605145075547218518170954D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.49670535155060417023204843137510D+00, &
     -0.20816484443009696237324462486882D+00, &
     -0.51090241799312035370196362374051D+00, &
     -0.56032152802942467258347810157577D+00, &
     -0.48210916153383866244702005141785D+00, &
     -0.55875287099133282930781054909746D+00, &
      0.11166780705147990599713407600049D+01, &
      0.77578464434062421187747427697944D+00/
  data ws / &
      0.12072956229196140184720818378917D-01, &
      0.28443984028101927395806965629882D-02, &
      0.93465277263442986124162626755397D-02, &
      0.29739840427656477081802036308844D-02, &
      0.20327046933776882823607497409423D-01, &
      0.12440057912161099228836551604472D-01, &
      0.57983520915299366578479709959397D-02, &
      0.30774405447413411002155380888934D-01, &
      0.18534535260005961010495899016617D-01, &
      0.61022450704916040183649592581025D-02, &
      0.15757087201875994349887096272192D-01, &
      0.18146095122192897098014042659411D-01, &
      0.10912126413380354963231665469691D-01, &
      0.97275807652705556020653743902143D-02, &
      0.22813420666829580712213934309259D-01, &
      0.94183526939491428417826897656981D-02, &
      0.10513336056091899919123590224643D-02, &
      0.10305163239812520591223081322085D-01/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule21 ( x, y, w )

!*****************************************************************************80
!
!! RULE21 returns the rule of degree 21.
!
!  Discussion:
!
!    Order 21 (87 pts)
!    1/6 data for 21-th order quadrature with 19 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 19 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00, &
      -0.21632544850764896966019269484948D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.51732142577254394519688365999304D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.23848997800485075950680771153334D+00, &
      -0.49726138663597772473398444337837D+00, &
      -0.72412950658754887280604342699955D+00, &
      -0.25333184867896101624130032052433D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.46634273354592047897176529761299D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.69288931850735639864308358232905D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.26783854808923110943600296777461D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.87825896621183219776432484250545D+00/
  data ys / &
       0.11915504280142053470339944811982D+00, &
      -0.22176792985285491406799950307586D+00, &
      -0.56698524576800618707986473265874D+00, &
      -0.56534402375875828330832096864561D+00, &
      -0.24347179507408359903990857698094D+00, &
      -0.36295805875690062325727639767329D+00, &
      -0.50981524806986605698152573307478D+00, &
      -0.56083300395461387753780504376756D+00, &
      -0.48546117771023431955108992405636D+00, &
       0.74251201445344514748786620220395D+00, &
       0.49552108269676082383881281439860D+00, &
      -0.40335187439348537560379590829971D+00, &
      -0.51360341626925635313747432894532D+00, &
      -0.40349668011940382629268981404988D+00, &
      -0.49169851113649364618692601028995D+00, &
       0.96892916731392889311013905422251D+00, &
      -0.55958871884460214682886011537049D+00, &
       0.11174875776997437235819388085953D+01, &
      -0.55950684866453675407246048332841D+00/
  data ws / &
       0.14115632059803205472519666814894D-01, &
       0.23025262548389042223555118865658D-01, &
       0.29202561691086176915750601020522D-02, &
       0.55355656065861078854118874771594D-02, &
       0.15135314836891179901866111095885D-01, &
       0.24278255412699264374036359934954D-01, &
       0.13779168816408564476674209048439D-01, &
       0.58970817066310603066620906137064D-02, &
       0.19083475799818969202994305068534D-01, &
       0.89861747152080313144225770269461D-02, &
       0.12802269114319752046734087041489D-01, &
       0.20930889409056329487663117084041D-01, &
       0.80375338997864963118800061347869D-02, &
       0.12907050562519806085002873135871D-01, &
       0.12913281131480700366519063232496D-01, &
       0.47063366701120542614104893201110D-02, &
       0.90017947131145907457116462987061D-02, &
       0.99277995286896342401230585292059D-03, &
       0.42975457006126745578855094841825D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule22 ( x, y, w )

!*****************************************************************************80
!
!! RULE22 returns the rule of degree 22.
!
!  Discussion:
!
!    Order 22 (96 pts)
!    1/6 data for 22-th order quadrature with 20 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 20 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.85243937884353040180383114561341D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.77445005331884859316935899829027D+00, &
      -0.13904123725801872358993428337677D+00, &
      -0.23304071399817585574874678659693D+00, &
      -0.26744719790035475459155300021176D+00, &
      -0.22878505379994225637259252841697D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.38014474895820048454509648055133D+00, &
      -0.45773619140744569728808634071512D+00, &
      -0.69910784887798561027380170772980D+00, &
      -0.59915020623635852909092766037930D+00, &
      -0.50285479867282866077430913574272D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.96233289290517364585870888247669D+00/
  data ys / &
      -0.17961779550825402665053150536356D+00, &
      -0.43105921890016050589097298460315D+00, &
      -0.56370814820709365122621895231987D+00, &
       0.13432079752143621239079354899726D+00, &
       0.50168092900112124608440590878512D+00, &
      -0.30708760414931325796548069627474D+00, &
      -0.49983703894353862614316233613125D+00, &
      -0.51105561801610634168636959252531D+00, &
      -0.39938711325112050072985537594951D+00, &
      -0.56453267538284060850226818603628D+00, &
      -0.24638775273505893357364918660516D+00, &
      -0.56405220111847180239219000037482D+00, &
      -0.50115450425960692839217225970244D+00, &
      -0.38909376761177045913072941229458D+00, &
      -0.56151116446763500432595204778315D+00, &
      -0.49377028890768631789742714088225D+00, &
      -0.56147791277581875684420297893483D+00, &
       0.10538658381143172910281642949327D+01, &
       0.75483396039626819990343725694118D+00, &
      -0.57423523645313343793449840203234D+00/
  data ws / &
       0.88789485269040415184442000093073D-02, &
       0.91213138484983310796492167899650D-02, &
       0.34157891281528518722433813845768D-02, &
       0.13868632623761798604503963871564D-01, &
       0.10542607716173479246541995276511D-01, &
       0.12406032586949329015430983875961D-01, &
       0.98936888063393894436023103307196D-02, &
       0.14736493275333048326268550862834D-01, &
       0.23319638474620094676086399806944D-01, &
       0.64543696619767795008356091295137D-02, &
       0.28567254691249129006535922249255D-01, &
       0.34805812400404550009501818114158D-02, &
       0.15348348448970428911081050216648D-01, &
       0.20675736766822369708334848331883D-01, &
       0.54047041342285612785845222377716D-02, &
       0.13902459659667285747407760303210D-01, &
       0.66515392643746496117585264091036D-02, &
       0.23486059112870622145372854661800D-02, &
       0.94860727130382766679283796797328D-02, &
       0.84285134702804870581139558973652D-03/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule23 ( x, y, w )

!*****************************************************************************80
!
!! RULE23 returns the rule of degree 23.
!
!  Discussion:
!
!    Order 23 (103 pts)
!    1/6 data for 23-th order quadrature with 23 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 23 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      -0.65712214849613188354910369404174D+00, &
      -0.76660745759442637356707284950207D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.77617921446782377203133884585557D+00, &
      -0.37522786404062973902300110350405D+00, &
      -0.58004024629858734710994966045544D+00, &
      -0.89831420119030494322671376626199D+00, &
      -0.21445385867353683733519417564443D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.41730612660269037167833945853218D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.59578381850403663485092059957580D+00, &
      -0.21256122928680759054743806564239D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.18972387666403954451075595735093D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.40941795217926264839064707861320D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00/
  data ys / &
      -0.53600577707072872244385605785502D+00, &
      -0.56836123421761655516206642728715D+00, &
       0.10195753956759042232454257963319D+01, &
      -0.52064114314269073816779046417287D+00, &
      -0.57311090188249385547279923552875D+00, &
      -0.56223762431711984631227409503690D+00, &
      -0.56494438615384257743957669387858D+00, &
      -0.45865810284942809229483887487305D+00, &
      -0.50920750140222330666237718651679D+00, &
      -0.40115163422567045202527649710931D+00, &
       0.85387432302293394609857524739803D+00, &
      -0.21127615568211163281540431623842D+00, &
       0.23237891808812345451062467122205D+00, &
      -0.47628237617657111987911856906806D+00, &
      -0.30917657348348663047591112852387D+00, &
       0.67967040631012229365709649358046D+00, &
      -0.57374563316209184490726633368261D+00, &
      -0.55178698374998971587781023092642D+00, &
      -0.38575926863496184163982523488357D+00, &
       0.46621101303269434423430967614670D+00, &
      -0.52020349027005747473328130414494D+00, &
       0.11234666733002454051771461134785D+01, &
       0.00000000000000000000000000000000D+00/
  data ws / &
       0.33272536459172081243423482336248D-02, &
       0.29282906445970122313947765632691D-02, &
       0.25767019981925537648569711133608D-02, &
       0.70120823907155191278558743427503D-02, &
       0.30021012691706992785886911937141D-02, &
       0.54153159980733361962405203321805D-02, &
       0.25697547045533841474189815315258D-02, &
       0.19716254021883959296530794843124D-01, &
       0.75002329339313453980338046569360D-02, &
       0.21216747175005973181144357747315D-01, &
       0.58959569777444837996575869478525D-02, &
       0.15578768482573967095704720947014D-01, &
       0.15666454825087261920671374524318D-01, &
       0.13779632479555575444967581228253D-01, &
       0.27432767705683395855549801326363D-01, &
       0.95806564943421797133558151503143D-02, &
       0.15842534442935738142299813918141D-02, &
       0.93412022737984016156870664924120D-02, &
       0.12471084885337250207089191625388D-01, &
       0.13118150579496436724006564496384D-01, &
       0.13391809372550109677210592618043D-01, &
       0.70104711646684561385279668637298D-03, &
       0.55391494064449379081462896405052D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule24 ( x, y, w )

!*****************************************************************************80
!
!! RULE24 returns the rule of degree 24.
!
!  Discussion:
!
!    Order 24 (112 pts)
!    1/6 data for 24-th order quadrature with 24 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 24 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.34667319739036827052339346563820D+00, &
     -0.17228858629081128185759902607603D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.77534695461921828552255298716799D+00, &
     -0.11830295887885374209920762360797D+00, &
     -0.63345645296256978775220168640372D+00, &
     -0.45325106659208302305278781769339D+00, &
     -0.23690281718952127487435067945971D+00, &
     -0.34221988285107932085443071544544D+00, &
     -0.22606667538238729829778396624439D+00, &
     -0.44495329180516622777269400394083D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.80452275594748579655555201318815D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.54364142669910333813418299173702D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.64253738555354065050641405694698D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.91734214502720875776048093000479D+00, &
      0.00000000000000000000000000000000D+00/
  data ys / &
      0.00000000000000000000000000000000D+00, &
     -0.29638036437519615283072347461721D+00, &
      0.59226680488565760168026231308527D+00, &
     -0.28226548001723516079013789395034D+00, &
     -0.28331767767631024291018810948384D+00, &
      0.10127221547590450105942364741960D+01, &
      0.11313827320245876948911869224423D+01, &
     -0.51098115521172256268950056659125D+00, &
     -0.41686453554510700393115126619431D+00, &
     -0.50600932341283035759161511854566D+00, &
     -0.50881145127983229474141858425667D+00, &
     -0.51050575168543342224214849423552D+00, &
     -0.41361091237025662602034980078080D+00, &
     -0.56455388712044611888415763422386D+00, &
     -0.56428020831842462418864564259509D+00, &
     -0.56437817053789745666612468626219D+00, &
     -0.56481964637042001394869703493070D+00, &
      0.23937641179955802312096963113378D+00, &
     -0.41182463487840787556899445189961D+00, &
     -0.51019021318165292778033437868107D+00, &
     -0.56351478264510604651378681421503D+00, &
      0.82100884119022006576877128851229D+00, &
     -0.56336411329583398015443759191052D+00, &
     -0.14556014125612880230802044190807D+00/
  data ws / &
      0.27518427300594242408167672948018D-02, &
      0.86272156924574954117622248939788D-02, &
      0.68297766559224770708029514748518D-02, &
      0.18615927197937334900149347500352D-01, &
      0.20102296969937806928616412243917D-01, &
      0.25227162946694301850912768013948D-02, &
      0.40617630703098676858295809545372D-03, &
      0.70624104072789811560052517607139D-02, &
      0.19783032876181461967862187704075D-01, &
      0.94811737732738431203731642290050D-02, &
      0.11719477113696286147199954244934D-01, &
      0.13091319693878567354029144297298D-01, &
      0.18888756936770716280013255717068D-01, &
      0.55829824091059095164775149600824D-02, &
      0.53712600687036400647412622640952D-02, &
      0.28580170714449744209873764706737D-02, &
      0.34075951304887990048003455619043D-02, &
      0.13502925079066951153738813940684D-01, &
      0.15587004356588926954110113389875D-01, &
      0.68123246685728385281460756274493D-02, &
      0.48789848045465228958508578200054D-02, &
      0.65983957168252596123510923456370D-02, &
      0.23649160198439673642978641242145D-02, &
      0.12499140851132809089730270870368D-01/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule25 ( x, y, w )

!*****************************************************************************80
!
!! RULE25 returns the rule of degree 25.
!
!  Discussion:
!
!    Order 25 (120 pts)
!    1/6 data for 25-th order quadrature with 25 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 25 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      0.0000000000000000000000000000000000D+00, &
      0.0000000000000000000000000000000000D+00, &
     -0.1173472784070389885314628951496541D+00, &
      0.0000000000000000000000000000000000D+00, &
     -0.6450240460256727525710559747446056D+00, &
      0.0000000000000000000000000000000000D+00, &
     -0.5664343384798589665228955002024030D+00, &
      0.0000000000000000000000000000000000D+00, &
     -0.3910189989265832790334726502623686D+00, &
     -0.2012181263167401097079073382399585D+00, &
     -0.2038066062734541936977294977052958D+00, &
     -0.7946055588153782250820470421122720D+00, &
     -0.1972942521563999602645401846428416D+00, &
      0.0000000000000000000000000000000000D+00, &
     -0.6355041410448193873418685582169463D+00, &
     -0.2629485129580234408600628587611446D+00, &
     -0.7847262192370077797696941981117842D+00, &
     -0.3957476856294985173592517287113179D+00, &
      0.0000000000000000000000000000000000D+00, &
     -0.4622691203344359376572172601919067D+00, &
      0.0000000000000000000000000000000000D+00, &
     -0.9106735335147376498998363730530587D+00, &
      0.0000000000000000000000000000000000D+00, &
      0.0000000000000000000000000000000000D+00, &
     -0.4402761583839805030337834115210799D+00/
    data ys / &
     -0.1881308452404751474791770362222539D+00, &
      0.4237594812020736794258174198266686D+00, &
     -0.5741998997668708578748305284336055D+00, &
      0.1172287234795072247760841771164101D+00, &
     -0.5133334261186957616800512329664083D+00, &
      0.1025756540328684422937411013290944D+01, &
     -0.4407640888171437954387566505919770D+00, &
      0.6520273733414071456865438634979216D+00, &
     -0.4581028502386777788723229469606161D+00, &
     -0.3764327086872663044277454612227560D+00, &
     -0.4936620181125184332135804336351929D+00, &
     -0.5650036663011180322305141381076653D+00, &
     -0.2245437989161187688779317294631657D+00, &
     -0.3167088545245427646354993582346312D+00, &
     -0.5648168693903931904010878260331929D+00, &
     -0.5549827672775567477688079143971306D+00, &
     -0.5120728253301845715218718158194338D+00, &
     -0.3400477140537724278182036849058156D+00, &
     -0.4464373961278773726299668315862868D+00, &
     -0.5348456380201123672101389788730482D+00, &
      0.8327133265910420576580234570528976D+00, &
     -0.5648988533934863981864107760207050D+00, &
      0.1127558109594723670980720926142653D+01, &
     -0.5393815319272739058039649892539370D+00, &
     -0.5758062076985843575874824269557718D+00/
    data ws / &
      0.9008428931929272978284555982082135D-02, &
      0.7624848013076671474981932002250592D-02, &
      0.2204184225038700283242061056342968D-02, &
      0.1185627435111220996327302583177423D-01, &
      0.8306372211706409316335445471098323D-02, &
      0.2235547623030763175546447504392690D-02, &
      0.1252247261761103193500179756735477D-01, &
      0.7561849278446502447261825323255299D-02, &
      0.1432466758007433215998170125431021D-01, &
      0.2084707600211569027917629357552928D-01, &
      0.1400325214573775947713571136961477D-01, &
      0.3349765842027190344172740201222808D-02, &
      0.2357591414900995147064953536612743D-01, &
      0.1047023089196828804219791222697079D-01, &
      0.4295322980586838056654945868959874D-02, &
      0.7178707806144740205045671854952271D-02, &
      0.6939081726476119924677787292839119D-02, &
      0.1808296563518180275001928371748139D-01, &
      0.8985018370003820265092102638348177D-02, &
      0.9626213990805757770654565513598145D-02, &
      0.6042636212818408481919357354311341D-02, &
      0.2228091765228852260396032167229650D-02, &
      0.5307136158214250141007056133594507D-03, &
      0.5556521038676869804672708399129014D-02, &
      0.1989511820786002256062338480298376D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule26 ( x, y, w )

!*****************************************************************************80
!
!! RULE26 returns the rule of degree 26.
!
!  Discussion:
!
!    Order 26 (130 pts)
!    1/6 data for 26-th order quadrature with 27 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 27 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
     -0.83506202914393021027297979613591D+00, &
     -0.90755758065010263994368282125220D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.82303054094670403650886493052722D+00, &
     -0.92810181341106024720340709798891D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.69330289802874450653761692118936D+00, &
     -0.68258007506466821571212258497636D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.37884097121369810169657547549398D+00, &
     -0.19241793339756862919367432495484D+00, &
     -0.19560294198083243085696241887367D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.54994973953459751935852183658111D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.16853064985401657599005512286299D+00, &
     -0.19069066073587361426189189987171D+00, &
     -0.70452513950898761906235841668280D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.38125784859592138782794589237690D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.54412206780215007658051815811596D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.36472969593802653513797826614735D+00, &
     -0.54666639745238929451134867455648D+00/
  data ys / &
     -0.56904567277510180660027224756771D+00, &
     -0.52685198805474673472457890788666D+00, &
      0.92351636427246864597020638848735D+00, &
     -0.53195431906859035819325095761412D+00, &
     -0.56748083945007940043218005705387D+00, &
      0.11327377305988868881940987951170D+01, &
     -0.50508092946854773292053923643775D+00, &
     -0.40406610454040422598363913049004D+00, &
     -0.55571014035627985057841942377748D+00, &
     -0.36843999644558691382643352539671D+00, &
     -0.52618905199929260038296168881663D+00, &
     -0.42600632803845996222493394451907D+00, &
     -0.19209885829653007293204006471099D+00, &
     -0.44517417854698789674258323696018D+00, &
      0.20849122488063464188861120733336D+00, &
     -0.57378652101945731348551401873832D+00, &
     -0.28207244982265046632145543744881D+00, &
     -0.56349454153453596561203489840544D+00, &
     -0.47976154988972600729665936044323D+00, &
      0.62053111439688169923700812019236D+00, &
     -0.48872837635331578543021077756047D+00, &
      0.42016147390516239342109813663991D+00, &
     -0.35559725708670166364713905486076D+00, &
     -0.53788618565697879751607695617128D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.56094203589043577139583078831749D+00, &
     -0.57654658422239277276250600074448D+00/
  data ws / &
      0.18405643148504851636845096658812D-02, &
      0.15866124696197450917004000667221D-02, &
      0.32334788927109915113560216754175D-02, &
      0.43503414953892562281646670251570D-02, &
      0.14288712197897272562630508508321D-02, &
      0.34675465145466701985841712380871D-03, &
      0.84276087852092015548095244572855D-02, &
      0.60726432878990522834955233622811D-02, &
      0.34890169558965309347553212683802D-02, &
      0.18924451034788801438603304001786D-01, &
      0.10870464987444917886855259943024D-01, &
      0.18067009059088050381787430564450D-01, &
      0.12810709081456309849270481375969D-01, &
      0.13684071075521919559699025257164D-01, &
      0.12855178620950701539792686120650D-01, &
      0.24441435248010210095439152942177D-02, &
      0.23161806576119345400252126809257D-01, &
      0.39044779268459560333810079419447D-02, &
      0.75861820209001453910764490554566D-02, &
      0.87224512475867079263341905985161D-02, &
      0.13301723810749135614147082883679D-01, &
      0.11150006112175140167331504007601D-01, &
      0.10799966961615883203916038065002D-01, &
      0.82509126176461880950437831298571D-02, &
      0.44936607076337887632843933697535D-02, &
      0.60428306726093991162278907047231D-02, &
      0.14997307146623417159024790140175D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule27 ( x, y, w )

!*****************************************************************************80
!
!! RULE27 returns the rule of degree 29.
!
!  Discussion:
!
!    Order 27 (141 pts)
!    1/6 data for 27-th order quadrature with 29 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 29 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.39518500208573395738563214277924D+00, &
      -0.18067167650541349528945895328146D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.22010619980742642366080422865661D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.15697790099606730648797798168280D+00, &
      -0.11950430106482160834133342082078D+00, &
      -0.53186222626517032602651279993926D+00, &
      -0.33699460349041562232377307811535D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.65833539230075168484436817404932D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.34054463966780382785672888075568D+00, &
      -0.48855088636612117128392523236728D+00, &
      -0.11439817909230903220469204061727D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.32048121511116152782316941977578D+00, &
      -0.82912386550847366110475798016042D+00, &
      -0.92517649077195119501691703892095D+00, &
      -0.80474142977810041392358745728250D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.68622113488411601370378338983970D+00, &
      -0.53322822093527312322581065671644D+00, &
      -0.70419862931679748024077449725206D+00/
  data ys / &
      -0.16413151730008831921378959939565D+00, &
      -0.39260212186133936931290882404374D+00, &
      -0.28685548406622891421303264493955D+00, &
       0.87651707827225350568041079993505D+00, &
      -0.52412330045467293432896313035733D+00, &
      -0.35365133466807523825318937197025D+00, &
       0.34617781266034228041185039673984D+00, &
      -0.52879484695937722926887109757979D+00, &
       0.11143276407223406542419307680993D+00, &
       0.54924497463551990458204709806308D+00, &
      -0.21512488834550352002334718330313D+00, &
      -0.46296751685726527586026447389785D+00, &
      -0.50628322547494511263210318063682D+00, &
      -0.56817102280382668923519285087070D+00, &
      -0.52734615007802219988019679750528D+00, &
      -0.46810290449456450390041493630006D+00, &
       0.10418694827155926471229736250245D+01, &
      -0.31933904292428472681005197948760D+00, &
      -0.41333011108690526666610282415552D+00, &
      -0.56768418377653115453110237898598D+00, &
       0.71278197104667799412847982912227D+00, &
      -0.44731325970043847901381172777520D+00, &
      -0.56525617363432326597137998165819D+00, &
      -0.56679589738285794930315523889142D+00, &
      -0.51666886935781835232132779079591D+00, &
       0.11317016084912388514794935172145D+01, &
      -0.54383161967864243507848420517516D+00, &
      -0.56465005418958368460329453488175D+00, &
      -0.57650099541315185890062370844174D+00/
  data ws / &
       0.62908896936458875949825510480729D-02, &
       0.61922333914763423137964574348267D-02, &
       0.79294953183311154387033613859802D-02, &
       0.34300980930711509534751164464939D-02, &
       0.72802514257052478410465398503156D-02, &
       0.16526515457441278585611916710974D-01, &
       0.88646240578297716926902784284285D-02, &
       0.84164942766149210573921235710888D-02, &
       0.10362744260858240831238545743647D-01, &
       0.74242647178535630111397120532648D-02, &
       0.18050472608152491107489365033227D-01, &
       0.12979477412320056876744738018169D-01, &
       0.84957485240956053915702977121675D-02, &
       0.38532361892010405972617343674236D-02, &
       0.46834056015487726028700708666340D-02, &
       0.93844438279733984004320414434716D-02, &
       0.18275921896011569137278968805752D-02, &
       0.16250438567218251268133507322890D-01, &
       0.14073701448288708561589196775091D-01, &
       0.42673273430936345003913524443316D-02, &
       0.64114157223758639239090891131632D-02, &
       0.14385493205073417350192096372167D-01, &
       0.26520511807255348074799784674523D-02, &
       0.15750426454989104155554651654759D-02, &
       0.56948602402767961466213505376975D-02, &
       0.37866239802690712287683217368769D-03, &
       0.60834035556216461895312643871598D-02, &
       0.44670891390107651705739274528023D-02, &
       0.11141963344849334695096764261554D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule28 ( x, y, w )

!*****************************************************************************80
!
!! RULE28 returns the rule of degree 28.
!
!  Discussion:
!
!    Order 28 (150 pts)
!    1/6 data for 28-th order quadrature with 30 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 30 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      0.00000000000000000000000000000000D+00, &
     -0.88746481351385107345127069412778D+00, &
     -0.52414142110826588794486451384092D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.33813652586499035853666003249694D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.15580617966892316052928987225377D+00, &
     -0.71154528411036221771832562317249D+00, &
     -0.56152923713272450305409461113685D+00, &
     -0.15254044569676028218764760621125D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.32755930579423371309923889584162D+00, &
     -0.62891280297171951404385772231420D+00, &
     -0.42562113948455467103037050486861D+00, &
     -0.94140501712803148246323405238881D+00, &
     -0.40187196592587673308438468971732D+00, &
     -0.53523254211119856990013167468684D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.34633469607556379390839833888773D+00, &
     -0.70700191257838956126529249352041D+00, &
     -0.22662440063670192933975301253849D+00, &
     -0.10878662096604677283105449627330D+00, &
     -0.20631360388374033702271668616836D+00, &
     -0.79729933059714082413378391932539D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.85821826344224735007618585707670D+00/
  data ys / &
      0.10167280551560398976220492653467D+00, &
     -0.54006894012803566318386100608171D+00, &
     -0.49235910875172712775847678059386D+00, &
      0.11380585570620829080112594647327D+01, &
     -0.43282761808513505745779087778619D+00, &
     -0.26963680688236239861351493942337D+00, &
     -0.18337097274071869661622880573497D+00, &
     -0.24858562418623951123781187881298D+00, &
     -0.56962812500573696889109864019987D+00, &
     -0.42548755921389883340768034668690D+00, &
     -0.46791873168797857582730644925957D+00, &
      0.26004754891078197570252274618257D+00, &
     -0.57016318648548524036109080252581D+00, &
     -0.53786850890931757394897545264776D+00, &
     -0.53803125336295947108113127503277D+00, &
     -0.56669876546503991682732553682320D+00, &
     -0.38330233101247314078613426299384D+00, &
     -0.56906848596694110780690954139249D+00, &
      0.78786657352369156249728778058495D+00, &
     -0.33331193876680684460752457704886D+00, &
     -0.46918587486573210609633873244633D+00, &
     -0.49038194407928164918552182401052D+00, &
     -0.53278806818989164900646131251018D+00, &
     -0.56757013000065183447611373867027D+00, &
     -0.37281400062453798641014279266735D+00, &
     -0.54575369430987430575525395306512D+00, &
     -0.52483841201603278034315141768996D+00, &
      0.60516346416700599387343286263650D+00, &
      0.94394739374781944379137982654772D+00, &
     -0.57527136550578091340619030932143D+00/
  data ws / &
      0.94510343300931478888807464349302D-02, &
      0.27868387832627458914989081520856D-02, &
      0.77591410167297521729327740749191D-02, &
      0.20473848133013403509762806085984D-03, &
      0.58247494675789234908196566576895D-02, &
      0.16526278580754572911455183578579D-01, &
      0.93510917286426097352060797088729D-02, &
      0.17248616209516818765814273146624D-01, &
      0.23411580330424100035578129796391D-02, &
      0.10544291927832240582270995892779D-01, &
      0.11140166083431255028726297685594D-01, &
      0.86155130881102002892400222873137D-02, &
      0.31279976876179532211383324626933D-02, &
      0.56287726620134695271354834891188D-02, &
      0.67531408157501848324491455305183D-02, &
      0.12483494047479294769456871723105D-02, &
      0.13484476650919357880017855769673D-01, &
      0.30592737461003165508862947478784D-02, &
      0.51392317566586590413074635030704D-02, &
      0.89148192557630731697759322343474D-02, &
      0.11746113414800820107755108695172D-01, &
      0.77883730444682187225229982545828D-02, &
      0.82393269507997219649806927417388D-02, &
      0.41327061926490009393858952877356D-02, &
      0.16828820578478445853343577421317D-01, &
      0.42179069123934048296232732334268D-02, &
      0.50551130485581726523795360821379D-02, &
      0.78587185794036915888389747222587D-02, &
      0.33745795976141645086914914308322D-02, &
      0.95433079635401447385836219413628D-03/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule29 ( x, y, w )

!*****************************************************************************80
!
!! RULE29 returns the rule of degree 29.
!
!  Discussion:
!
!    Order 29 (159 pts)
!    1/6 data for 29-th order quadrature with 32 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 32 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      -0.87938703907162049393738648870781D+00, &
      -0.14324628011414286412542273880746D+00, &
      -0.35189538626807214171525397778246D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.61554248268722133288024470174652D+00, &
      -0.93007010487368394982733169286299D+00, &
      -0.19742931116675328671024827830067D+00, &
      -0.82766874673327517194764945031097D+00, &
      -0.72491944440609982649676161027856D+00, &
      -0.97606406728761785676875297522146D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.48236271621499169294961905466403D+00, &
      -0.17405270877030766542159522724513D+00, &
      -0.18672840783491580658483096931098D+00, &
      -0.49956457122986497525117031568907D+00, &
      -0.64840539960610806885812016702526D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.76445927822389460704185764718864D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.34535027682270612143829088272072D+00, &
      -0.51325936500558699339036907718902D+00, &
      -0.35532987585108812184220678363790D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.32573169227336622410380909993533D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.18040262369805029614059002911543D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.62723509783699348733500748068739D+00/
  data ys / &
      -0.57262394724341608181908512435579D+00, &
      -0.30511050720283478498316524226896D+00, &
      -0.57371128821577701886180134696590D+00, &
      -0.57359111146432687487737878042109D+00, &
      -0.45928362498519066569504746311567D+00, &
      -0.55859049859349923530121259720141D+00, &
      -0.19814832945992239613993592077499D+00, &
      -0.54048028336522896166963698554618D+00, &
      -0.50660081473204674367166958460713D+00, &
      -0.57457293178871935440458908351462D+00, &
      -0.35003739955028665529791783308077D+00, &
       0.10123351916554935691973791840677D+01, &
      -0.40146746347211072112690881875070D+00, &
      -0.50542328918299929386212475640451D+00, &
      -0.41479896168463444735644949768926D+00, &
      -0.56230562425237497147426436905503D+00, &
      -0.54688501268470743019578735701145D+00, &
       0.43276338426682519796086695407376D+00, &
      -0.56778324409762155852431972748668D+00, &
       0.59786046049173946734694450915043D+00, &
      -0.53602539551087235345778481154042D+00, &
      -0.50755670245009570927755668717151D+00, &
      -0.45978142418549716875276682521809D+00, &
      -0.53717224317544601306267373599653D+00, &
      -0.33566750808701799356359087057475D+00, &
       0.10720328289321576370831152259048D+00, &
      -0.56337853290640048165947671108094D+00, &
       0.75831443067019621851290191888360D+00, &
      -0.45528374978288560170739457877104D+00, &
       0.89932044998481280953329700019771D+00, &
      -0.19844398974763577810899514361613D+00, &
      -0.57713645303871158784974277557031D+00/
  data ws / &
       0.10123938451463759970089359052465D-02, &
       0.13755888140419727618158412742168D-01, &
       0.17804164437108562499941904599297D-02, &
       0.99788818279604048507240176161182D-03, &
       0.84743804866337155687860067687316D-02, &
       0.16743020381843061998817864135626D-02, &
       0.17826547012452998087762815394247D-01, &
       0.36343788555051997590886515586824D-02, &
       0.59390298859384334961673129484654D-02, &
       0.35467172304180440218981679487014D-03, &
       0.73509973972781686569789083069102D-02, &
       0.18823092677622066092420624317723D-02, &
       0.12353105880035723559433384108907D-01, &
       0.10295539688423531976513712860782D-01, &
       0.13990388400987746999801020264183D-01, &
       0.40156561227163462310099803253767D-02, &
       0.50344656666784366169434955781421D-02, &
       0.82512598969804302641269300260534D-02, &
       0.22921998323995127511965450098240D-02, &
       0.69563841616376041067990591845970D-02, &
       0.74610255726590545841053915581726D-02, &
       0.86623962103173048554261254624063D-02, &
       0.12080143560322868032076843683152D-01, &
       0.40366629789560296898640227002180D-02, &
       0.16475096833731066604740732689647D-01, &
       0.10732740719960036973478529643535D-01, &
       0.47922734876003179932483846983130D-02, &
       0.53780564637593511319450846071907D-02, &
       0.67864123981058792365600157845442D-02, &
       0.36908289770711881028317444421851D-02, &
       0.10471484548953909836949668724134D-01, &
       0.90634414524923745915451079527243D-03/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule30 ( x, y, w )

!*****************************************************************************80
!
!! RULE30 returns the rule of degree 30.
!
!  Discussion:
!
!    Order 30 (171 pts)
!    1/6 data for 30-th order quadrature with 34 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 34 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      -0.43405710781709278714048879994740D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.13719609648588667050981701694674D+00, &
      -0.23002603213365866154430597150794D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.35671356772393844272156480720059D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.49401409080195115810253005052280D+00, &
      -0.37062552685345952318116499093046D+00, &
      -0.51430581999606514802110718905564D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.54607380091083807654188300887860D+00, &
      -0.84275872174416357830668461312136D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.57724024570193215242188127722161D+00, &
      -0.39821033011703771207712265483060D+00, &
      -0.30605985322806922570625655304903D+00, &
      -0.68776182141386689567302952570524D+00, &
      -0.19684758015531914348305332007873D+00, &
      -0.96321844715106605579144337343699D-01, &
      -0.28286197991210025994286433769979D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.10333424594611078538852107076057D+00, &
      -0.64379410387887037331359309442254D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.89873358431890446012484882993312D+00, &
      -0.78478618004244445633333163168023D+00, &
      -0.72349108151471496801951044440950D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.20239462350406048608674549751121D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.94049820614395764193267866092540D+00/
  data ys / &
      -0.49449740552349402097090260436227D+00, &
       0.11432041379660233658011039218632D+01, &
      -0.43937592123719222447451521408216D+00, &
      -0.47742236692181668651784560731673D+00, &
       0.90399516562083738727059247641795D+00, &
      -0.44352953384065130754596083984676D+00, &
       0.99134074534282262769308436316314D+00, &
      -0.53793159129250810586076585776398D+00, &
      -0.36290163137317815520540870562751D+00, &
      -0.37663681425566764191708385069014D+00, &
      -0.46660354209881582130470470379699D+00, &
       0.11107528506358136609304671750972D+01, &
      -0.46213867523774957532303180078394D+00, &
      -0.56966207432086504530851133019367D+00, &
       0.73349519835786388112994533410054D+00, &
      -0.56927271273635792416671462689250D+00, &
      -0.56920325339091635438895039029322D+00, &
      -0.53373365021893670540255969319794D+00, &
      -0.46342190137736602703775671709799D+00, &
      -0.35889692861698105392115484048066D+00, &
      -0.23982388127083061470496201687854D+00, &
      -0.24652609751239687685958293412409D+00, &
       0.52281528171007302347717037989158D+00, &
      -0.52966101087647732119998666908062D+00, &
      -0.52874213045823877050213253058208D+00, &
      -0.10029941117116486849674700598946D+00, &
      -0.54980647624872101250977315077756D+00, &
      -0.53007527494669219480580008827439D+00, &
      -0.56749280180954759083517414571717D+00, &
      -0.35822245431797926788870429663662D+00, &
       0.21098212229083163080456906246771D+00, &
      -0.56840882187053609024013730511891D+00, &
      -0.56806418709095800771552792081267D+00, &
      -0.57642585867286344650886243834268D+00/
  data ws / &
       0.55469340852267197383357734501536D-02, &
       0.11300463022066637667549395901160D-03, &
       0.77976368535667454572847114089957D-02, &
       0.78230337119887396150629609702565D-02, &
       0.25018123919483940113671864156512D-02, &
       0.90508836547186347263240388076065D-02, &
       0.18717426158053290329737464178677D-02, &
       0.53860315402766333154068593578253D-02, &
       0.11677070021275261169640320523198D-01, &
       0.99157266127682177040571302280702D-02, &
       0.51222447690487278622934837026924D-02, &
       0.55706132346425325140873159634701D-03, &
       0.89545764756588636881737594179016D-02, &
       0.15881019953772277632781829119128D-02, &
       0.48608613509509536172532545379762D-02, &
       0.25781213160755392530469248853581D-02, &
       0.29933391441706776190700124360794D-02, &
       0.70603223137458408522017573340119D-02, &
       0.77254463220316942248431581666276D-02, &
       0.14875615552650235020592865135842D-01, &
       0.18841554220226669798776264579558D-01, &
       0.17011603553515205522964322169417D-01, &
       0.70757738603786203845878772981467D-02, &
       0.82670460199627466892622746876773D-02, &
       0.61880970884828196145627428599983D-02, &
       0.10262805248776557218482365083790D-01, &
       0.24090825302303188401346360674076D-02, &
       0.50298776686404106640379168657878D-02, &
       0.25267049096575867286260646250422D-02, &
       0.81629221043416840383932440429541D-02, &
       0.98143263368157515388390143296277D-02, &
       0.34778149711369936288944433476055D-02, &
       0.18367906196371196197648328999357D-02, &
       0.44170301264357154992013311250048D-03/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule31 ( x, y, w )

!*****************************************************************************80
!
!! RULE31 returns the rule of degree 31.
!
!  Discussion:
!
!    Order 31 (181 pts)
!    1/6 data for 31-th order quadrature with 37 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 37 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.61514906219173326038112958639798D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.60227258275696561313011448174463D+00, &
     -0.50981188019097632901132686993753D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.93815432009933315159290706133886D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.20647073303633426254589462709978D+00, &
     -0.14400331667261834628330435968823D+00, &
     -0.48161033312898040755998550507708D+00, &
     -0.10037070511088677024119003378018D+00, &
     -0.69003405314433981556933467756463D+00, &
     -0.45131857503676764396920554079559D+00, &
     -0.84660740995916577326254742794424D+00, &
     -0.14911203462776176458914390755779D+00, &
     -0.55167853197329218224541056875306D+00, &
     -0.88689641508961216382151190186048D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.27328678036217323411592305906149D+00, &
     -0.33518301010596487973294137974615D+00, &
     -0.41995122085501584151906684983796D+00, &
     -0.18328764721779652677839208920087D+00, &
     -0.36991861294507902457366355095885D+00, &
     -0.19826213773515198256349732520883D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.32037552704774453797884509286080D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.78037306571931027109013054924730D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.63930924222334969496336881416464D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.73284741377468351220017427799278D+00/
  data ys / &
      0.00000000000000000000000000000000D+00, &
     -0.52938101092158436217989944700065D+00, &
     -0.39259296230588589577692024633618D+00, &
     -0.29879521023518401246203229051833D+00, &
     -0.57170178188865743017272606769990D+00, &
     -0.55459143708784673167882967475209D+00, &
      0.88032014667050929273459147232799D+00, &
     -0.57328995909056364047175904022464D+00, &
      0.10932773428047454311567544236664D+01, &
     -0.57395302409498325748592469605497D+00, &
     -0.31297598217411644944584755018888D+00, &
     -0.38089192422910876315233159687303D+00, &
     -0.48291646123243918459436362644262D+00, &
     -0.47237945269405575937245782085877D+00, &
     -0.51224429424952928367019627443114D+00, &
     -0.56975292247630686483425195330683D+00, &
     -0.54743183795864664399668537119941D+00, &
     -0.46896195562367563745199360999814D+00, &
     -0.54546676966840707030987521015721D+00, &
      0.39801431704076458186329655275394D+00, &
      0.55731348796377460751706837305857D+00, &
      0.97770163996668454891174645987393D+00, &
     -0.50303973149300230512177279576695D+00, &
     -0.55450610597908806787792991531332D+00, &
     -0.57527720939459095316883310890960D+00, &
     -0.19780119278968994222147469745240D+00, &
     -0.43682917497899069302689014620258D+00, &
     -0.41232373405740865931876786653227D+00, &
     -0.56955126226549368079464495424716D+00, &
     -0.32293156387181891591095890622273D+00, &
     -0.17956217803484541051959756627326D+00, &
      0.12415978610574965002707225626963D+00, &
     -0.52966581912912838443677982459313D+00, &
      0.11370931699099784490463357476566D+01, &
     -0.53253326710134984412140457620381D+00, &
     -0.40532624526153890211957544149763D+00, &
     -0.56730901867998811775513569725020D+00/
  data ws / &
      0.18300274150131503530218918260118D-02, &
      0.26610940186702783315047214273191D-02, &
      0.76415116557529348094479438274031D-02, &
      0.58190756304798839792080800346536D-02, &
      0.16896438572357084969785073782623D-02, &
      0.37199019857877275953974147517983D-02, &
      0.27793705473843310754776111206512D-02, &
      0.66528731990096257950775283571449D-03, &
      0.64939444386637490706930367932606D-03, &
      0.17144436271854393525611545784889D-02, &
      0.13414188931651306592837821888099D-01, &
      0.10353383822703655875877567178813D-01, &
      0.93715119938232228413834490764269D-02, &
      0.65331420598530105269402018636481D-02, &
      0.71547540812742549665898738315076D-02, &
      0.15168844552172759195105122436401D-02, &
      0.54989950731761515927595152639621D-02, &
      0.83734196392879596672486354136481D-02, &
      0.23857385517888400677977593831317D-02, &
      0.73943641501760668515497495971065D-02, &
      0.62903046982657749327353939866577D-02, &
      0.21445996231349418275012329739199D-02, &
      0.88044815101158239329257671015790D-02, &
      0.47901323321320787218271749114584D-02, &
      0.12231201498467946837374439661990D-02, &
      0.16971546653439500088953398556642D-01, &
      0.11154908721966859054415465858694D-01, &
      0.12663626772734683766437904485010D-01, &
      0.15316868409913918465476865568287D-02, &
      0.15266022971056427587974399198100D-01, &
      0.90410304859438967096315948145332D-02, &
      0.81327060196892968093589471350676D-02, &
      0.48254994785913298058391441904342D-02, &
      0.22662885264281957658336382036483D-03, &
      0.58503938090777195674071616162139D-02, &
      0.68659431853565733752147231623839D-02, &
      0.23969034602009614667762140991332D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule32 ( x, y, w )

!*****************************************************************************80
!
!! RULE32 returns the rule of degree 32.
!
!  Discussion:
!
!    Order 32 (193 pts)
!    1/6 data for 32-th order quadrature with 39 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 39 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      0.00000000000000000000000000000000D+00, &
     -0.42746868613914916208067002398662D+00, &
     -0.91710704502811275874385926715291D-01, &
      0.00000000000000000000000000000000D+00, &
     -0.48363645746700960769905958976308D+00, &
     -0.74677040622149170601230763257760D+00, &
     -0.33090034155997483681589019846520D+00, &
     -0.46023597931812041521733845612288D+00, &
     -0.55152849427095291026768125922720D+00, &
     -0.20577133469764029385252414280604D+00, &
     -0.20092303305428395370178245682808D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.25879477956175550900580265426342D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.72262398109805332027279578058226D+00, &
     -0.32997225542915476024532745217312D+00, &
     -0.40104907184189418029309583833701D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.69151287469732085458587108553859D+00, &
     -0.81882407794345790149465089749751D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.15979469018140228096803155997403D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.59877821961446415276093759190966D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.42015173485047987871656798146767D+00, &
     -0.28990563943088228305314863137265D+00, &
     -0.84085334890089953008631910023907D+00, &
     -0.12723619924623591749401870286216D+00, &
     -0.12551628141173309089569225449278D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.55077303550427213809118028350091D+00, &
     -0.61718975394462310684988723266656D+00, &
     -0.90920085094674871327008780126851D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.97068830122109422411832138489096D+00/
  data ys / &
      0.11496517991990804340276319918613D+01, &
     -0.30218292328705052033455030789710D+00, &
     -0.55177404065234470341871573116633D+00, &
     -0.57267682745711810079098827470171D+00, &
     -0.48826894371900250566656288607256D+00, &
     -0.54347180509529604896284843807779D+00, &
     -0.55549427045965430240427224834972D+00, &
     -0.54086954371044273649778573751227D+00, &
     -0.37375893906115265347255148781801D+00, &
     -0.52660317145013860310284351646008D+00, &
     -0.57138712716648846304698735307588D+00, &
     -0.51211470939471719438254705852599D+00, &
     -0.42082435075243723269873387979224D+00, &
     -0.41206328125638506041335006800986D+00, &
     -0.48953938794088206965231133840212D+00, &
     -0.49430799576545804368134930045435D+00, &
     -0.57513903374312331695098163467832D+00, &
     -0.14894052019732994524801638469381D+00, &
     -0.56996729278416821373273663004497D+00, &
     -0.57067752268839624045481729672027D+00, &
      0.17429645803883591285042159190117D+00, &
     -0.22764895370246828181434158209954D+00, &
     -0.27832827065225098989964142553377D+00, &
     -0.46007242792992039354306838595294D+00, &
      0.10498449848071351612896202347394D+01, &
      0.11103247160622636896577670049089D+01, &
     -0.41181398695180711307526515295114D+00, &
     -0.31690029177033716996969306425727D+00, &
     -0.53517509064720514075419136628404D+00, &
     -0.35324390902713134915617189643158D+00, &
     -0.46783716452744596679002275357204D+00, &
      0.00000000000000000000000000000000D+00, &
      0.93988934616034742698090141489668D+00, &
     -0.56822819321283957200082177635155D+00, &
     -0.53204175653167234191507273763322D+00, &
     -0.56772912901378600226993106149821D+00, &
      0.36045825890517508775557027645869D+00, &
      0.80150480143647657259482305879194D+00, &
     -0.57627103176029262025065680355071D+00/
  data ws / &
      0.35089101065112855884820534496463D-04, &
      0.10988190324830709992823329341192D-01, &
      0.40017234188803658556418944416512D-02, &
      0.93087707933178618554865620359439D-03, &
      0.69568246166267704238682724201103D-02, &
      0.32813277551329795738555421297416D-02, &
      0.39753082327573825644781696272502D-02, &
      0.47960047753629003693425154224810D-02, &
      0.98456677416312611477210982996463D-02, &
      0.60120289449877842202024432440538D-02, &
      0.22178527178401095681968551311850D-02, &
      0.36718564604057522445250408427746D-02, &
      0.10803923534388294394797611307667D-01, &
      0.55134227454329365414727793248372D-02, &
      0.58771612493962009794350932546429D-02, &
      0.81633895836356217774190986558429D-02, &
      0.11698483763495028290383571359353D-02, &
      0.83316003706962053904317473673468D-02, &
      0.19546717234154615848859112275635D-02, &
      0.14644039054791717956440739265680D-02, &
      0.84773151751406951264947448004187D-02, &
      0.15757826762525756648322149683424D-01, &
      0.71597492934303095837773594696045D-02, &
      0.77415633062502329911450279233184D-02, &
      0.12234738959380913656810149160128D-02, &
      0.52757528161206686084277006574669D-03, &
      0.11119171725536887499648558701843D-01, &
      0.13439031765939374980048747865869D-01, &
      0.32769705348614632852685205970683D-02, &
      0.13014005319508587872203236381061D-01, &
      0.97509412664434843717560320628702D-02, &
      0.28580896374081882633069151128591D-02, &
      0.26165845261107117861016768586572D-02, &
      0.25605447042338306730739080320977D-02, &
      0.56075763180908099390771878498063D-02, &
      0.13889507817898641123545037024783D-02, &
      0.82488872017764297885488574625852D-02, &
      0.43623899484098009158061336724647D-02, &
      0.22384872276251377786582863606787D-03/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule33 ( x, y, w )

!*****************************************************************************80
!
!! RULE33 returns the rule of degree 33.
!
!  Discussion:
!
!    Order 33 (204 pts)
!    1/6 data for 33-th order quadrature with 41 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 41 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.39676550645769949223549079823286D+00, &
     -0.31598316073300286874362023003082D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.64019940087608054570302313946691D+00, &
     -0.13023310833724125410060567348685D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.77591825174786530058425772428980D+00, &
     -0.19029241130244378942621074383698D+00, &
     -0.66275085646437554778774954725515D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.13890838462723977815572667811625D+00, &
     -0.52593106350448959206487843135769D+00, &
     -0.74112180754338096384725945089585D+00, &
     -0.49295570914510750117532576951889D+00, &
     -0.51670323488631757686566331872787D+00, &
     -0.64505375945992157587556971416084D+00, &
     -0.61872928859268166187915712963621D+00, &
     -0.87492200353713827567393201652485D+00, &
     -0.33145619841996054218301251037654D+00, &
     -0.97409390068179509856666677924027D-01, &
      0.00000000000000000000000000000000D+00, &
     -0.86499638747373789749985796834781D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.24972283611883747878887622813179D+00, &
     -0.47779523112848852807050836313123D+00, &
     -0.16616445416618183551509983345254D+00, &
     -0.36279240961074976308711123134325D+00, &
     -0.77375327602359261325494586474574D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.30711355053101709037576993455102D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.18486459332759578217311403693356D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.42184939757610775040328718080002D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.94593887427662142045742644100072D+00/
  data ys / &
      0.85441752281491986952742561507422D+00, &
     -0.26359952191974260301537245052622D+00, &
     -0.42678545506855360887308799127774D+00, &
     -0.37973706727153893912099920904950D+00, &
     -0.15588528269354452279063922983879D+00, &
     -0.57381590818073294683247861206343D+00, &
     -0.41858125784281633932442886389431D+00, &
     -0.20333227220053604130569869278831D+00, &
      0.25520959894249213064365318384422D+00, &
     -0.53856910378372629185609575858799D+00, &
     -0.40545819052596609782356418100840D+00, &
     -0.54194078514648208041737749935800D+00, &
     -0.50291356104093599630234744015635D+00, &
     -0.47583110208346099057285412944826D+00, &
     -0.54370533785038485941253752308528D+00, &
     -0.48924051171923119683779249416411D+00, &
     -0.57075764711609390637957695741143D+00, &
     -0.41461766926988511673184437368405D+00, &
     -0.57099887763461860406270665329696D+00, &
     -0.49001038870971575141844877415585D+00, &
     -0.57022781943877866932429672746875D+00, &
     -0.56983893491575439638788166530905D+00, &
     -0.32834341163271889420656088222861D+00, &
      0.10732337258984243455437606728791D+01, &
     -0.53947756141543200561909733382606D+00, &
      0.94602784584493370468772946259542D-01, &
      0.64724758119173276973587947838225D+00, &
      0.96632545246884377179105403347845D+00, &
     -0.28583342001808206268947748302965D+00, &
     -0.49332159111642935520258261160453D+00, &
     -0.56914512902820977690651047487837D+00, &
     -0.53901095406565886298444238871685D+00, &
     -0.56974068564230494042674463877735D+00, &
      0.39886122381719090545979996295666D+00, &
     -0.48180999095667246889253860020090D+00, &
     -0.54960747258649002726722665090028D+00, &
     -0.53508842266119758145398714640325D+00, &
     -0.41592300096438369677257895846249D+00, &
     -0.31644289654629315370197407113192D+00, &
      0.11383269060703847163981510995473D+01, &
     -0.56955190911504415394155156282000D+00/
  data ws / &
      0.21072740283763039964528368286828D-02, &
      0.44974723243006456842650776075088D-02, &
      0.65946145346910002385096276412626D-02, &
      0.82474035280720032563304370435810D-02, &
      0.58790090916007076226614232725982D-02, &
      0.68507656125260760567769180226135D-03, &
      0.67199953862190751868955790397041D-02, &
      0.12685962295354290443758741902940D-01, &
      0.64085284625279664423720130246453D-02, &
      0.31865284621268815383673784463267D-02, &
      0.10130277996161918616988936043147D-01, &
      0.39327511834173456227281919359377D-02, &
      0.35957285155409189611031640004502D-02, &
      0.81581506936299909146481456622838D-02, &
      0.43654139395527354256349689343937D-02, &
      0.48812258789986847763530046372840D-02, &
      0.20302369941307448210755634209178D-02, &
      0.87021082793685719718873832596530D-02, &
      0.17835148063472755026619148855589D-02, &
      0.64535378321272648894894135877724D-02, &
      0.12052160414072912400513700553737D-02, &
      0.23976450419859318170667605866734D-02, &
      0.12163656006474426058122295662701D-01, &
      0.90899196307377903030326256967572D-03, &
      0.25803358156466235366918919356997D-02, &
      0.79548382691120458192515870842605D-02, &
      0.48546328081496349968870545571536D-02, &
      0.21118713588645547377857629192177D-02, &
      0.13437007473057861497945927056313D-01, &
      0.71907262853635647670060927729590D-02, &
      0.26467590924742060643044789761419D-02, &
      0.56174443807205437983099746393445D-02, &
      0.16949406736417696510033206105949D-02, &
      0.65319228663443823255328913298067D-02, &
      0.86859349355210683062499905616676D-02, &
      0.25415771481263707182156665796150D-02, &
      0.65111877505010114950629655024188D-02, &
      0.61419843433928965634632131426334D-02, &
      0.12083509278790420262130603712492D-01, &
      0.19312249945614427939614114959174D-03, &
      0.84755399951394965389373925159078D-03/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule34 ( x, y, w )

!*****************************************************************************80
!
!! RULE34 returns the rule of degree 34.
!
!  Discussion:
!
!    Order 34 (214 pts)
!    1/6 data for 34-th order quadrature with 44 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 44 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
     -0.20865073605333605259133081748132D+00, &
     -0.89097175315861241014243393897698D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.87999414063426440899680777462237D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.68124048521147079022287669759749D+00, &
     -0.78844430308137329865810016089767D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.28883149528014893210917834177554D+00, &
     -0.80036260521166327118670792806244D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.14656285308642525770840545989704D+00, &
     -0.14791223778178358225012515887081D+00, &
     -0.14888251010183166048943112172279D+00, &
     -0.14412341550112265052276598150328D+00, &
     -0.56021943491268762662833110324255D+00, &
     -0.56775489079636195195819292013723D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.43438042322624036290148813406327D+00, &
     -0.42883411933471152581183344420389D+00, &
     -0.69612085434081448660482017170361D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.29429125011188233571351981822902D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.69057074957270704503616084061837D+00, &
     -0.14635945730951804290474707357531D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.43610043846910337710191570745380D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.29361459879318225343484932066898D+00, &
     -0.29217524245073863070988162069564D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.29404250943783623341704803057639D+00, &
     -0.95251437348711362491282542183012D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.57112662404759029584585818705102D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.57210738184377731997454761477038D+00, &
     -0.43576534554125907389165005866616D+00, &
     -0.80626144515788714899642746572657D+00/
  data ys / &
     -0.54080960852670874887477002688154D+00, &
     -0.57148188680340885268957968075793D+00, &
      0.99541215623761383488320268143123D+00, &
     -0.54581251858802002963651717370634D+00, &
      0.10825129994552011239408759106716D+01, &
     -0.47254254003026177485543685475103D+00, &
     -0.51513519234555459140932034419392D+00, &
      0.89225266841244135802626470038980D+00, &
     -0.14988699059565575877251167626283D+00, &
     -0.29318823199080331034093749074232D+00, &
     -0.55884631397612334218448641893041D+00, &
      0.15927070953202400003601747376533D+00, &
     -0.52342688512318759090959018821675D+00, &
     -0.34665387857625309237224070668568D+00, &
     -0.44866353740446774321091903079561D+00, &
     -0.22199147096348917763877176210378D+00, &
     -0.42108532754196956310264613688775D+00, &
     -0.50128574606027466276226199416617D+00, &
     -0.48871256531163417297535112276726D+00, &
     -0.45790141180639478630175258882333D+00, &
     -0.36052903462331485421264904911911D+00, &
     -0.56926107479496737145288159890053D+00, &
      0.76958700429572619540848652285881D+00, &
     -0.54916967076805156376085658979603D+00, &
     -0.49260808560575517970684223356176D+00, &
      0.63201013425192545991254006499216D+00, &
     -0.53464092774804677680478041519000D+00, &
     -0.56702734467084155713753902149103D+00, &
      0.11402969514608451589323215865362D+01, &
      0.32180957687924744604856694624021D+00, &
     -0.52795439225981246678322066497151D+00, &
     -0.28467385501300634121071117733737D+00, &
     -0.57576434340793074190688904900431D+00, &
     -0.55039498029219558132681857598373D+00, &
     -0.57574687817495954263227255109469D+00, &
     -0.39917165954426298474560583795016D+00, &
     -0.40538150617520055089614596703473D+00, &
     -0.57046622308344295569063522362823D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.55348323362954892556316690015126D+00, &
      0.48132579880630916313439867481111D+00, &
     -0.57601288500270791096736728894872D+00, &
     -0.56789016986039254576904292632732D+00, &
     -0.57734211176549375189279322347485D+00/
  data ws / &
      0.13382626571418695846413420959349D-03, &
      0.86077553205023877867589308006139D-03, &
      0.15128050789281141606424158029908D-02, &
      0.20001846280203786077172851326386D-02, &
      0.72363050803554618757272999467355D-03, &
      0.61455888057448998470789535942896D-02, &
      0.38852026646137484310391372656345D-02, &
      0.26304196612070312222228001589138D-02, &
      0.77253587933225472077027128073975D-02, &
      0.12977714128349407406048789350468D-01, &
      0.22719033752163729514493246145023D-02, &
      0.77393098675853113647899856957649D-02, &
      0.66279889144916813462020297846060D-02, &
      0.12710485190182604950478151438930D-01, &
      0.10017843547790636952167111558575D-01, &
      0.14563495893338662830933135825511D-01, &
      0.85595344302267414192383009908361D-02, &
      0.63601741070384869392179065287274D-02, &
      0.42668601490321023633055488964966D-02, &
      0.86775530450313316070466948384888D-02, &
      0.10904023948277298869126932531947D-01, &
      0.18417526470910829459939716211994D-02, &
      0.38386152359715808879730672139045D-02, &
      0.24540640916463922042739572558992D-02, &
      0.80218185952419318245374428395049D-02, &
      0.50585349116444063800445633458038D-02, &
      0.41366919289449465339947189819144D-02, &
      0.29365977875069631100768219443565D-02, &
      0.14934897179533907877154395103507D-03, &
      0.71158143270123038007615755398533D-02, &
      0.58377502625954269481520792337924D-02, &
      0.70064127307723735616871240238792D-02, &
      0.50071757656760638993478483434402D-03, &
      0.45908969684050017035075831240866D-02, &
      0.96316333582374746961054859980204D-03, &
      0.58308259716404371642003962574066D-02, &
      0.10858660084749162408673215897113D-01, &
      0.65536218237774572732745631345446D-03, &
      0.26542942460412844806471662947295D-02, &
      0.36926643355893676151865055391569D-02, &
      0.61856406685725288566265475154246D-02, &
      0.76023090931745106769467860453136D-03, &
      0.25829647679686151643244490553125D-02, &
      0.37816775394238441141631154528165D-03/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule35 ( x, y, w )

!*****************************************************************************80
!
!! RULE35 returns the rule of degree 35.
!
!  Discussion:
!
!    Order 35 (228 pts)
!    1/6 data for 35-th order quadrature with 46 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 46 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.88784082040153075383913617100652D+00, &
      -0.10034207598327724033582632199321D+00, &
      -0.69311601738832964374229025488167D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.20170550651440610611345276285483D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.64267456637991915772112509507131D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.59680262574112570330708343507959D+00, &
      -0.88583797294857920950727599039044D+00, &
      -0.21481054147146732337946003185254D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.97750969393388806071547935914909D-01, &
      -0.55225246543256484131744271704192D+00, &
      -0.73330302740947963883782960844096D+00, &
      -0.35377855031176987704663393999516D+00, &
      -0.51564990450718314801776121220598D+00, &
      -0.21973987181432191570664654404377D+00, &
      -0.60482829086183809094609158655982D+00, &
      -0.10540651029785986602106161987810D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.44461399827537925801209489543884D+00, &
      -0.23876011572551469292227793760715D+00, &
      -0.10680624500393084714250643212956D+00, &
      -0.49845820778025588899721360580822D+00, &
      -0.47118728299279689577235187734666D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.33861070795850472330848428220997D+00, &
      -0.70498953851611867618296732663118D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.11540856290209161674967217397369D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.35516859452256584748215994566211D+00, &
      -0.95143357699664369331063333170408D+00, &
      -0.80625540528872521995344375173798D+00, &
      -0.39094238101462525709590836324919D+00, &
      -0.26704107522244421375617609033818D+00, &
      -0.80012284035409657436386927229493D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00/
  data ys / &
       0.11049848391267878160942425437432D+00, &
      -0.54839524322647351656910274265446D+00, &
      -0.84731241225870783138119631392495D-01, &
      -0.57376800669530175521786194508562D+00, &
      -0.56192636681814703241337147158792D+00, &
      -0.57368528854276496320410931239880D+00, &
       0.24567191532977353520899699695488D+00, &
      -0.57170157791299617481071719582110D+00, &
      -0.24069657869901295964844222588206D+00, &
      -0.49911718050236027863216490838426D+00, &
      -0.48412771111544869326449479743582D+00, &
      -0.56244420234421444672958208328214D+00, &
      -0.55314597935499411028041061203470D+00, &
      -0.25264039633717009571608632345015D+00, &
       0.93691922814514350972936873734162D+00, &
      -0.37503784513189034216209663360014D+00, &
       0.10867100617799430553354204728332D+01, &
      -0.17426334519355714993668083479551D+00, &
      -0.52711753152174214154822817555781D+00, &
      -0.48456866722910133562449136216106D+00, &
      -0.57129468294377403989555329497135D+00, &
      -0.57531330331362051925464151910002D+00, &
      -0.37997627488267737489770886024621D+00, &
      -0.43023229931186750876181610790903D+00, &
      -0.31309961497003354510619289311518D+00, &
       0.10151427309957352682750877998298D+01, &
      -0.55376202677277905332098019475239D+00, &
      -0.47996330941134033797610668708564D+00, &
      -0.43574907178404019355497831707649D+00, &
      -0.46711834658382799515239504110706D+00, &
      -0.37748161580172233726943066542578D+00, &
       0.81339592685777538075733642892247D+00, &
      -0.32068265475981446715948171913088D+00, &
      -0.54513781159869833529380365664930D+00, &
       0.67133897977061262700017196648536D+00, &
       0.38727728656145265547624996623580D+00, &
      -0.52024278749878884072085026914167D+00, &
       0.52856305553369069237166742739323D+00, &
      -0.42946854793782251649705803709131D+00, &
      -0.57105763188292920761880945578841D+00, &
      -0.53228217266152343324657869863566D+00, &
      -0.50900886837618163733840811909782D+00, &
      -0.54310638162348937349259853010943D+00, &
      -0.56864030976986894926046466151582D+00, &
       0.11398838577722204060015136163662D+01, &
      -0.57704966306400061720563422243113D+00/
  data ws / &
       0.37823533023071117552498633546329D-02, &
       0.15110951850926768597510849257431D-02, &
       0.52612367337077241481150311006990D-02, &
       0.59776000384333233272193666149629D-03, &
       0.25949680545647278336391650188551D-02, &
       0.10300467854022705106865695429020D-02, &
       0.57842676116151487639100767425388D-02, &
       0.16644297264251806023973860743196D-02, &
       0.54751091383596566484521677047910D-02, &
       0.46816125223955569111350042656706D-02, &
       0.34712691077662295851692973049338D-02, &
       0.24253041782253153086402273893358D-02, &
       0.17490359570497127164220966999176D-02, &
       0.11875479166746748231460750630995D-01, &
       0.19531898113644349044152767302173D-02, &
       0.50044915460995835332657889685798D-02, &
       0.66667113158108803350566280388053D-03, &
       0.11325480833009634041680955354389D-01, &
       0.47516431054402191637098512902079D-02, &
       0.46372667587850735462627390787042D-02, &
       0.18136506984725309737491530658395D-02, &
       0.91471037630436898650123223221922D-03, &
       0.10699314011695035989362484260043D-01, &
       0.72247940752599472272602792262149D-02, &
       0.10839168886619908505604562425067D-01, &
       0.13587382545922657958478769707436D-02, &
       0.36583876907265655319114947846825D-02, &
       0.83330935899037325736589164743249D-02, &
       0.91410693800006639894202414819246D-02, &
       0.73251904599782639661305917852163D-02, &
       0.96568380444916204234246412306618D-02, &
       0.32925800341072999195193696158169D-02, &
       0.11464882195010925904138963396459D-01, &
       0.36017648083679220604863221387225D-02, &
       0.44214031660381166110271695499832D-02, &
       0.60288751331023346137831096345316D-02, &
       0.61877293600659226814496412622813D-02, &
       0.55090243819186250387827772801666D-02, &
       0.94428428348687329331168226963113D-02, &
       0.62282804392723232782667478677435D-03, &
       0.33358029363864306610289766382805D-02, &
       0.66727022641263705281781993426708D-02, &
       0.53354589201841413526093533076666D-02, &
       0.16509864052584545067812812415452D-02, &
       0.15814849311712982200162693233010D-03, &
       0.41297372110944178234379022954739D-03/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule36 ( x, y, w )

!*****************************************************************************80
!
!! RULE36 returns the rule of degree 36.
!
!  Discussion:
!
!    Order 36 (243 pts)
!    1/6 data for 36-th order quadrature with 46 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 46 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      -0.45770306387539169487915756826196D+00, &
      -0.36361676298891185295386221029935D+00, &
      -0.74962911892600870983032844542448D+00, &
      -0.26737758237748029380439006185063D+00, &
      -0.37317732959222391549799088251508D+00, &
      -0.14975882871475764975924141602265D+00, &
      -0.98352138144106149192683092192778D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.53788829941643881420320023927424D+00, &
      -0.25563046668462188936725827478982D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.83136119811518354383269937195326D+00, &
      -0.13003286298009251819823947174789D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.60110699315720762998855042089700D+00, &
      -0.63205241025983805117322394914783D+00, &
      -0.52716585532238106513416234938719D+00, &
      -0.28230973261381914542579826867683D+00, &
      -0.71047632569890861227787925936018D+00, &
      -0.95056420733325419196436293042879D+00, &
      -0.28616499791046129448997529539718D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.13633349630546001365985579457732D+00, &
      -0.80918371229769335783766611724880D-01, &
      -0.44770259704283524854791791199685D+00, &
      -0.48011047223406774553422252507270D+00, &
      -0.41323708163607651211902687274295D+00, &
      -0.65560184610300882914185718548851D+00, &
      -0.57620923725166014923400127915066D+00, &
      -0.24925193834014909515080159065743D+00, &
      -0.78377703132887513374849375170181D+00, &
      -0.98306369371972070224522934512975D-01, &
       0.00000000000000000000000000000000D+00, &
      -0.15401622396033279817412492899376D+00, &
      -0.35730985892987794548052370157585D+00, &
      -0.72653937769578913812744606839955D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.83027114581134724322172615184608D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.88144405800714427701736717808599D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.91784551568339890614029102074855D+00, &
      -0.17476902776510310686941360192574D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00/
  data ys / &
      -0.52141842729563126012047058298966D+00, &
      -0.41429464277319715623346981701418D+00, &
      -0.46477792693460978350876606581729D+00, &
      -0.44967445714422062537104312954445D+00, &
      -0.49063516603887538827137270218634D+00, &
      -0.46321446291835242797318542339315D+00, &
      -0.57521271319697780857478481745947D+00, &
      -0.27374719021510399523990036642840D+00, &
      -0.39427972611017856706920948711432D+00, &
      -0.36279824244610613498688160674974D+00, &
      -0.36620767514629492498613572227248D+00, &
      -0.57248771387722136932451719517558D+00, &
      -0.38562994925042077844843752485788D+00, &
       0.34045539811756807080574481636674D+00, &
      -0.57257600517555581330832753808181D+00, &
      -0.45255306558366174094217160197888D+00, &
      -0.55235918086652448153563150959453D+00, &
      -0.57260000432656212732742831820917D+00, &
      -0.50975814717158154135559916631247D+00, &
      -0.56440377229715042680745590073970D+00, &
      -0.27325102827656031685861861579114D+00, &
       0.63223872333035094330098051711355D+00, &
      -0.28077682324477788489838234773238D+00, &
      -0.51793028571538908930758218474956D+00, &
      -0.57210278655469173709707059163532D+00, &
      -0.45179917425831580211503767552840D+00, &
      -0.34557238584596557842323790994865D+00, &
      -0.54673762175281423328617405554397D+00, &
      -0.50424349278017526914470934564358D+00, &
      -0.51773945365247080611701750038930D+00, &
      -0.54712080331353357214461326692730D+00, &
      -0.57522359685526201507706056294147D+00, &
      -0.45359100459111562262893708000554D+00, &
      -0.16813042003647684568253959866018D+00, &
      -0.55046376829560201599703664333391D+00, &
      -0.57068525840467165716710741013583D+00, &
       0.49249815594813255797249024870368D+00, &
      -0.51140681795255970991370425926398D+00, &
       0.10530289859103386181163034523952D+01, &
       0.87254187575228190842967598185962D-01, &
      -0.55627077065397527838016283877844D+00, &
       0.76956773175760798113534871535368D+00, &
      -0.57586320130293542669591032679490D+00, &
      -0.55598397134820992601771756543425D+00, &
      -0.16513031625331098943557133545280D+00, &
      -0.55823188110938432057255915241886D+00/
  data ws / &
       0.40294016520725152813048610101848D-02, &
       0.64793903053765145181715901682133D-02, &
       0.43742626283010051684766029946910D-02, &
       0.62417922487631623395376249125259D-02, &
       0.54140669757067043817444691914728D-02, &
       0.68900982432856468561811786486874D-02, &
       0.17153699268662009594629984868070D-03, &
       0.50474692507570505960794202203366D-02, &
       0.68800457554916895631729667842012D-02, &
       0.87270677947457016043671196486654D-02, &
       0.45248570442564970883554024651669D-02, &
       0.91498024223602954229350467916617D-03, &
       0.91050902425828265328119448284342D-02, &
       0.53090410657138158843888963628538D-02, &
       0.13393775372397616562830163994317D-02, &
       0.59631198989805405320442107067512D-02, &
       0.31313092298346458015049957705066D-02, &
       0.16015029731880952140633711164508D-02, &
       0.40969742526751036868296166462955D-02, &
       0.85305987209231664440378714676407D-03, &
       0.10982854456089695449388211470504D-01, &
       0.40607862976056182266227222376222D-02, &
       0.11718063546352663453334801471048D-01, &
       0.62695317676519732186303155045592D-02, &
       0.16229081033223297129772742579429D-02, &
       0.69502345508257539200837869664982D-02, &
       0.94809421287883652563970965623795D-02, &
       0.33560498861862835325040698854943D-02, &
       0.53868503871236664135869203894291D-02, &
       0.58820503274730197860770659304124D-02, &
       0.27653642263897575237831549083688D-02, &
       0.10819301104675578264822260694178D-02, &
       0.43833382315646555911862314735351D-02, &
       0.13441518749900172007698067515263D-01, &
       0.40011563187151066613912579689780D-02, &
       0.14603290876836360969200891041503D-02, &
       0.53256416015449335120955671226641D-02, &
       0.35098393196898440174721922929817D-02, &
       0.10314228067656089530374958038011D-02, &
       0.72438530919178505538177420621044D-02, &
       0.17577599858575697519932889346354D-02, &
       0.35688958985136608389688752740980D-02, &
       0.35030971685040415436169439133341D-03, &
       0.38004098068192230521610341307517D-02, &
       0.69135644753295898893485091923938D-02, &
       0.19056197400002277482559131629861D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule37 ( x, y, w )

!*****************************************************************************80
!
!! RULE37 returns the rule of degree 37.
!
!  Discussion:
!
!    Order 37 (252 pts)
!    1/6 data for 37-th order quadrature with 49 nodes
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 49 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00, &
      -0.33412271632399888890129019512936D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.75613518652324771803726882164662D+00, &
      -0.84800448035565502181663502981330D+00, &
      -0.70551641007683071137220723820188D+00, &
      -0.12346882279099691408072860937378D+00, &
      -0.14115293561514993591833853717433D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.31129235394249030634514266109515D+00, &
      -0.25517618371949366971568295794296D+00, &
      -0.22738491727535507077740696347565D+00, &
      -0.82431411808054765778463063897013D+00, &
      -0.96025084028127376878602592691577D+00, &
      -0.88743516782176053029087010855756D+00, &
      -0.14743801672844793582653341492985D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.63852651231947468903625801359977D+00, &
      -0.91244418004082918428945065210440D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.53650720489459350535466965366810D+00, &
      -0.85277881576583532724521330388158D-01, &
      -0.16435656319638607339573924940553D+00, &
      -0.81381272571201343203517786852045D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.41910547578514426267307171420310D+00, &
      -0.48677494045468852012238429335006D+00, &
      -0.35909034523353810535799934366341D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.25248858363296016573959873583852D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.39948855862139271795827453837350D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.74822550833094322230914938071543D+00, &
      -0.61214302766947216204021932607674D+00, &
      -0.82456232718866158786784556422156D-01, &
       0.00000000000000000000000000000000D+00, &
      -0.28849633742385887838307907599387D+00, &
      -0.69338845905777882473767890474803D+00, &
      -0.17221861996121408821061372532618D+00, &
      -0.49166762890981157665024971850791D+00, &
      -0.33772735494586915349190113708600D+00, &
      -0.56199209754321689406198698034801D+00, &
      -0.62908155899883917171575081362878D+00, &
      -0.47085424810000757697255495637523D+00, &
       0.00000000000000000000000000000000D+00/
  data ys / &
       0.80030932175661049330529129464111D+00, &
      -0.51875656535329760898448830295380D+00, &
       0.10333868827205359544088392857986D+01, &
      -0.51993973121116010442502084667746D+00, &
      -0.57382818530981477957536290227481D+00, &
      -0.48120343056361501578369820373486D+00, &
      -0.16501678669005198586553208123293D+00, &
      -0.44697785411625922396526760726341D+00, &
       0.25665474437476898507539344982761D+00, &
      -0.48447626446390567150790800247712D+00, &
      -0.41922309411584432631191867018353D+00, &
      -0.34332292689716552850094371729457D+00, &
      -0.50673434341218750366276527969451D+00, &
      -0.57217095597866797982914123136412D+00, &
      -0.54747072920426972017807350995914D+00, &
      -0.26364744637852948251388994918932D+00, &
       0.67166192797723746626700329929959D+00, &
      -0.44283386491499269166138431840481D+00, &
      -0.42124005904839257204244609933248D+00, &
      -0.57039245293560439673032555344414D+00, &
      -0.15872646837427968615407557344963D+00, &
      -0.43711422090147355697061182546047D+00, &
      -0.54811072534421336521000509462082D+00, &
      -0.50551055464016532277335287814759D+00, &
      -0.55356126813574196138633993389223D+00, &
       0.10946289447927698298356343395322D+01, &
      -0.54631433608883669102312593267134D+00, &
      -0.35483129429226142896168273650094D+00, &
      -0.33950304358022085403206973553427D+00, &
       0.88453895937762153767287377553499D+00, &
      -0.54714013952455212484601864326434D+00, &
      -0.50545261693006535308892323009918D+00, &
      -0.27272204187887408822459840414627D+00, &
      -0.42805065874848260516272058041530D+00, &
      -0.57184433744987283372049694766113D+00, &
       0.83856840257338103751495755746255D-01, &
      -0.57144178004035639723831793597820D+00, &
      -0.50017785048732220313797140417802D+00, &
      -0.36587111104193859470979519681048D+00, &
       0.11419818578211332577350031418259D+01, &
      -0.23836996263996572403671622331600D+00, &
      -0.54563400792324411093065715450446D+00, &
      -0.57169987252525305855247428576888D+00, &
      -0.57133062792022124429581677109025D+00, &
      -0.57122090496927329315283644781684D+00, &
      -0.54470987727952378493452147796822D+00, &
      -0.57104889149424033456087085228856D+00, &
      -0.49810325155934541668515841885833D+00, &
       0.49872349530628412097743604970645D+00/

  data ws / &
       0.99626129730910408577949008400168D-03, &
       0.27626921675168826283774018443100D-02, &
       0.72692273468131503092373352604759D-03, &
       0.25303170257571451860803668676728D-02, &
       0.63229856016814473011800273541530D-03, &
       0.39910569052688676630224931092243D-02, &
       0.96322224231485228364344323861314D-02, &
       0.70914264027495165913238721401754D-02, &
       0.49912714680319196696789614840510D-02, &
       0.60134263305403734057625688074224D-02, &
       0.75284170176253568400370133216087D-02, &
       0.88334951566927715848362109377594D-02, &
       0.30494454960037220959042145422116D-02, &
       0.40623159427664301328639018693128D-03, &
       0.15854780081932780104600463914237D-02, &
       0.10744094290784490004353067282619D-01, &
       0.34547338677747299508167133011287D-02, &
       0.38698068479336796185125547322801D-02, &
       0.57440366524074741575884680707207D-02, &
       0.72357295271785506116849988932337D-03, &
       0.56884381303256696164588543099345D-02, &
       0.69047009212170979910711955177161D-02, &
       0.42884132950362761878776351004925D-02, &
       0.62924591180266519167258563983064D-02, &
       0.21172628941575284289686456117100D-02, &
       0.57748488832703718923029245549870D-03, &
       0.39252782695269835705405080071355D-02, &
       0.80200877092618206400095291824248D-02, &
       0.93274649768244852461773810704269D-02, &
       0.23598744244779275367141637367377D-02, &
       0.41453075810464728064443485645257D-02, &
       0.32896867854980720978623838536080D-02, &
       0.59742143446146166209795010947358D-02, &
       0.82279235776610154350252369267537D-02, &
       0.93156858510830936728471952983330D-03, &
       0.67163446268129400718735416067323D-02, &
       0.12493560653618925032728437197660D-02, &
       0.53054261077983319226673244613556D-02, &
       0.10755243143420365190907771759900D-01, &
       0.11403474399353258205391049010235D-03, &
       0.11790258338603034214469882053681D-01, &
       0.32403041710010828670599208753256D-02, &
       0.18705266785451222748868057200548D-02, &
       0.17176825471147128641632325800221D-02, &
       0.19029239546031546635251984688755D-02, &
       0.38621442944772685484213090942755D-02, &
       0.15746286043986147827363630712349D-02, &
       0.64138925190696845281721401600690D-02, &
       0.54555303295239163064914865711407D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule38 ( x, y, w )

!*****************************************************************************80
!
!! RULE38 returns the rule of degree 38.
!
!  Discussion:
!
!    Order 38 (267 pts)
!    1/6 data for 38-th order quadrature with 51 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 51 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00, &
      -0.38017185669450718257184066048831D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.64388710735877083783416282124044D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.91532058656497198671471150555246D+00, &
      -0.78472586424382273509683032899814D+00, &
      -0.99643590876239824517695137609747D-01, &
      -0.41959606976158875740459488513640D+00, &
      -0.90709796569683108888235443082745D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.31006871991021548748342323634250D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.55804669150858522261961383013874D+00, &
      -0.23391252232540839712384994231650D+00, &
      -0.84191118240738060068532375730213D+00, &
      -0.53335107942756502512226568928935D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.47291121570664026204475560732776D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.72785722160360793350295551572105D+00, &
      -0.49855221184504938895139013840901D+00, &
      -0.54925671022190333222562093502386D+00, &
      -0.44686452030684963518394665288121D+00, &
      -0.61953974615995630087673220975416D+00, &
      -0.62648548681833042070303279649082D+00, &
      -0.67197877643540341416126929672985D+00, &
      -0.41335885239677796031890142990207D+00, &
      -0.25346463551838318570541525347334D+00, &
      -0.69573906885921915728856348088559D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.38636910084523127223009550231297D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.33658056387534557504382625690100D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.87843541547485157244218200006356D-01, &
      -0.85039120745944430746903967678568D-01, &
      -0.84482245043808986751701243019350D+00, &
      -0.23361755931365234413765013776635D+00, &
      -0.84712737676102112301556527859528D-01, &
      -0.30228200141771618391567732367974D+00, &
      -0.17281546621195622411401122869585D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.16293712483088177437982114203995D+00, &
      -0.96366288222453288706533712520860D+00, &
      -0.25373681319593324282811397911950D+00, &
      -0.15001122172665224948595080689653D+00, &
      -0.75738968673027804907685927008861D+00, &
      -0.76664557469367476317397564232357D+00/
  data ys / &
      -0.43557198951312314492372904354947D+00, &
      -0.48676901082212536688741381364887D+00, &
      -0.20761979727194592905202199533091D+00, &
      -0.40573908618816893429385257585425D+00, &
      -0.46713152507187031292455455867277D+00, &
      -0.57377461458362246990957759635438D+00, &
      -0.51373173879402534769265540295112D+00, &
      -0.18600062141874083923383175875705D+00, &
      -0.52071016051529641903708216132188D+00, &
      -0.55471321549486532778867447040816D+00, &
       0.10940631576403911595307511796686D+01, &
      -0.44966761533984648209489215134754D+00, &
       0.65074263823985079600667000386443D+00, &
      -0.57266700781635460274026638478223D+00, &
      -0.19775702200253896797934274544035D+00, &
      -0.54145730613515149557950920114789D+00, &
      -0.40306833625953531748818108675870D+00, &
       0.11441448170815456331207001620839D+01, &
      -0.45699037409328199099206927354961D+00, &
       0.95123251126820600706088723471076D+00, &
      -0.45891721551063656195753394995739D+00, &
      -0.55254653716155075726305443495177D+00, &
      -0.50985596144990674077481289770119D+00, &
      -0.31858800667671763885666636445179D+00, &
      -0.46956784465504062728813836459427D+00, &
      -0.54683284777191952223714461151061D+00, &
      -0.57051260429903260207066265388305D+00, &
      -0.57227331670065037577673308824224D+00, &
      -0.57253866498558213253629629823534D+00, &
      -0.51790249949511235759270582432134D+00, &
       0.10252000964578561221300395045227D+01, &
       0.16568297477093707545432698117652D+00, &
      -0.38903470904529446210903397210864D+00, &
      -0.30137742399876299186434574375181D+00, &
      -0.55145765476506148518201936114546D+00, &
       0.43524327738107859551153511292157D+00, &
      -0.55031736573002371942681152441060D+00, &
      -0.51270307120416046582718931909697D+00, &
      -0.57221773164738784945037090035811D+00, &
      -0.57007049747206373797913896032469D+00, &
      -0.37942157065303255897465810627733D+00, &
      -0.38182236985847584746876547919066D+00, &
      -0.29988148386350240360102081846111D+00, &
      -0.55110081638940231919507254561012D+00, &
      -0.80478911639902275408961840267122D-01, &
      -0.45603365215790654433852111390607D+00, &
      -0.57138683817501246632052994868585D+00, &
      -0.51210804711263968662217366453516D+00, &
      -0.28983256020905742573818686292564D+00, &
      -0.55650931396143459003034201519312D+00, &
      -0.57683373408531432268827479475092D+00/
  data ws / &
       0.20820056888817244409479850097856D-02, &
       0.32704508067578457571759580719843D-02, &
       0.38571880274891361301769303800511D-02, &
       0.48648533235668256195606333219063D-02, &
       0.25862281661138416465531703526730D-02, &
       0.45760472370487254239987376847120D-03, &
       0.27293096561559624215019181897416D-02, &
       0.97008356269688197848677107128175D-02, &
       0.41132552385450103084160052046070D-02, &
       0.11925949669960168440297068927338D-02, &
       0.46027699181420719864281441155474D-03, &
       0.65746158861474390224655188929927D-02, &
       0.34233865355919380271157248680394D-02, &
       0.12182478611229097763044222506603D-02, &
       0.10899944052496863003448798018155D-01, &
       0.20225984312508308593119096478526D-02, &
       0.68735133627418967754698853779575D-02, &
       0.81627294555617067479425317996855D-04, &
       0.62097541317418902117276820215705D-02, &
       0.16492922508404918879311251694587D-02, &
       0.47406525818327189115185327580062D-02, &
       0.31194776872854070583692733919320D-02, &
       0.47516718437350612556088524941901D-02, &
       0.86077222408115445210495576178103D-02, &
       0.53685573833170132885235134226360D-02, &
       0.30607129436300396172490108601521D-02, &
       0.13236335711461000683695750999937D-02, &
       0.15044854999557370818299509578742D-02, &
       0.15641030619522655360987944091216D-02, &
       0.38234831557293443707212103289394D-02, &
       0.11236312245926095551123994880102D-02, &
       0.59128635891188981067020381172796D-02, &
       0.83264254588952817413009549759947D-02, &
       0.52233031594939664397142395297434D-02, &
       0.35872048025524414964720174624147D-02, &
       0.50988347474248667740715631552740D-02, &
       0.19977329387543947701265023377701D-02, &
       0.59507492016878607729260830919901D-02, &
       0.16966487646916691851186225113499D-02, &
       0.10748164815034162115762746127887D-02, &
       0.91437918154557240969683908824785D-02, &
       0.93423065980415739850720220419123D-02, &
       0.10123136480463870914740930355634D-01, &
       0.38498047327371845578787166272780D-02, &
       0.65645729720023034651464119787433D-02, &
       0.79710615214023377342492350020114D-02, &
       0.43918131172356037933829206838480D-03, &
       0.59611163393367252996223811895425D-02, &
       0.11058361133847283290469370750187D-01, &
       0.23833729931365671861610978427443D-02, &
       0.38466956567350313890347038963597D-03/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule39 ( x, y, w )

!*****************************************************************************80
!
!! RULE39 returns the rule of degree 39.
!
!  Discussion:
!
!    Order 39 (282 pts)
!    1/6 data for 39-th order quadrature with 54 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 54 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
     -0.51907510039262467181240723005295D+00, &
     -0.27085312542591789026981871557739D+00, &
     -0.62535084249163554801261088188681D-01, &
     -0.44171982481354024257677278787610D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.15015342269982087499746548552200D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.73242413817247197416912819947887D-01, &
     -0.61576635195673085768179561363787D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.48003862478268162304965734842567D+00, &
     -0.36508484113357361074797983209786D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.56713187575703966770973366858629D+00, &
     -0.14031613163580384457468777152879D+00, &
     -0.25349195822799364362686756031925D+00, &
     -0.23248267893550702450813771192708D+00, &
     -0.52163635975054715145448041789043D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.90690106293315290819021535664027D+00, &
     -0.12932342290720507011192674546810D+00, &
     -0.13784410422442617726158008200667D+00, &
     -0.66294103217865996758685557932486D+00, &
     -0.64122202646501331223433885902278D+00, &
     -0.81530008183876068918941172976357D+00, &
     -0.90238671492070698682084691210471D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.36521604921152885859291119415780D+00, &
     -0.81466971749275774599927221958440D-01, &
     -0.50100475560027347803268966859046D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.42538501367251799249997046103522D+00, &
     -0.40434782435372039643598964415201D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.16442016253358942481700772352343D+00, &
     -0.27207964379670182797824599426077D+00, &
     -0.31259592531293370325932513075940D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.23061575503872384396183209443032D+00, &
     -0.73174496781264133588838797582992D+00, &
     -0.55942199595539976634905924759128D+00, &
     -0.28187070033874590044167993901641D+00, &
     -0.63181925527793262592959928916708D+00, &
     -0.95845151882990183009015464856753D+00, &
     -0.83806929801903041855622721765482D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.73014202636963239486058389001507D+00, &
     -0.38481648423499752372487549629974D+00, &
     -0.74786883044034466526785200148550D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.82569754738333487928005814615627D+00, &
      0.00000000000000000000000000000000D+00/
  data ys / &
     -0.56977344334973953415009221378062D+00, &
     -0.11615238463710973900986144045138D+00, &
     -0.16841403059063582703799040319519D+00, &
     -0.57273896147926731246264811881990D+00, &
     -0.48177391174488216182747312872034D+00, &
     -0.21805432181592896862251556772349D+00, &
     -0.43015355484213642389086647596671D+00, &
     -0.55672301202474317753018700126839D+00, &
     -0.57361430082863865627675251023354D+00, &
     -0.71062437062144605538166336071450D-01, &
     -0.57425388147699645590520477695232D+00, &
     -0.39157484051927385758800981076725D+00, &
     -0.38260125928736646468021583934304D+00, &
      0.76210815817498206981551181976317D+00, &
     -0.37974002964326184444303529558949D+00, &
     -0.47005865572418340661540287763308D+00, &
     -0.36610435880584296669017948490237D+00, &
     -0.51041551846753395228797796020113D+00, &
     -0.54750015447026086336476242420687D+00, &
      0.11000415018640989305561291676418D+01, &
     -0.55212750394609514626346834644682D+00, &
     -0.31033539412300214897853090795097D+00, &
     -0.40217042416953081560570497781101D+00, &
     -0.45041551128090115382074323796237D+00, &
     -0.55393733579619755005613977870791D+00, &
     -0.50261462137952603540673793837763D+00, &
     -0.57241680160442647300899412288108D+00, &
      0.58655605653182625196365551350355D+00, &
     -0.26028645488038103161700300407634D+00, &
     -0.50737982602401753884163334078742D+00, &
     -0.52365228029452559568466482181594D+00, &
     -0.50930584971577307589941102218584D+00, &
     -0.35752411415512963812671499048932D+00, &
     -0.45339755648003318420528024155758D+00, &
     -0.30993099181146801236771669846609D+00, &
      0.10264156710616244871686286975762D+01, &
     -0.57254647239454006820290004274071D+00, &
     -0.27970449294975765316042730395238D+00, &
     -0.57171692937562625460547538450204D+00, &
      0.42124024273454953036405961333276D+00, &
     -0.54949681464841745643044481184475D+00, &
     -0.50173031881501531356011446242568D+00, &
     -0.45905866008218877559480919998558D+00, &
     -0.44792709733285852771474443606843D+00, &
     -0.51472732382392613411706398642860D+00, &
     -0.57244321215608923333186877139555D+00, &
     -0.54626015892447713295423347103218D+00, &
      0.16065133195264123594739464348022D+00, &
     -0.57182062792860608241992084882251D+00, &
     -0.54913090515973984664975730120048D+00, &
     -0.54631988756965195283384974383402D+00, &
      0.87522865731065508967027909558189D+00, &
     -0.57117161215160068889104816203223D+00, &
      0.11420800543675486817879702813617D+01/
  data ws / &
      0.10297002991753660501136103351341D-02, &
      0.71409200454957424138919555702907D-02, &
      0.84670476850581833366989493797193D-02, &
      0.10061525828127805509276236358357D-02, &
      0.25008518613742033230286581854602D-02, &
      0.82379503874691016163177015741387D-02, &
      0.31645234824978289216154005178556D-02, &
      0.28454670499457543125480683962546D-02, &
      0.90921496761479735112870080703174D-03, &
      0.53162773859582871544697296720480D-02, &
      0.55174868571100333634113037140252D-03, &
      0.57658467066484687646578171852548D-02, &
      0.64457871132908107545457606397354D-02, &
      0.24406168935034987856598180879293D-02, &
      0.58315103312031023476998033502050D-02, &
      0.61853878639532303634906561313174D-02, &
      0.74949719610539269221700456157038D-02, &
      0.49000462324377305053951530096155D-02, &
      0.29889444058930598950088528689227D-02, &
      0.43996809067738625074189199968923D-03, &
      0.12505146482203086295392343808630D-02, &
      0.97825105755546869735655412908223D-02, &
      0.81418004583935088155390428216798D-02, &
      0.50503317417279426125202432815639D-02, &
      0.24951091420867912577241746709087D-02, &
      0.30478657588270378768815691124488D-02, &
      0.64260046142092336339976252566979D-03, &
      0.38189427195873096307259859473584D-02, &
      0.50663628845451396008230346642253D-02, &
      0.51764441731398308561678437452717D-02, &
      0.49181464598226297253857270629541D-02, &
      0.46465662734804209629119572618546D-02, &
      0.44591898920056385785598751636219D-02, &
      0.64136254490796000834798012697594D-02, &
      0.79881644631115754408349534866859D-02, &
      0.10476275740484627938272086913711D-02, &
      0.14500024170436655618156678953819D-02, &
      0.96194255594278304779191550064611D-02, &
      0.15445701615508816200489059359044D-02, &
      0.46888846948789891123342520895612D-02, &
      0.37215235791213064892823990494283D-02, &
      0.37005626494781645355545034117062D-02, &
      0.57612742538281776709493292272587D-02, &
      0.76066250692246841971988592588158D-02, &
      0.43715876705429943949816550672880D-02, &
      0.42564655054254956754287557583451D-03, &
      0.20530208586099517375295895636913D-02, &
      0.57438263789397392552513701846135D-02, &
      0.11429571862723729149581721669044D-02, &
      0.36214122455131093638488339463188D-02, &
      0.26987232674585178812827363148936D-02, &
      0.24397941805574716783727001505373D-02, &
      0.10319996026161764514307891440984D-02, &
      0.11509579298275706789740693353329D-03/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule40 ( x, y, w )

!*****************************************************************************80
!
!! RULE40 returns the rule of degree 40.
!
!  Discussion:
!
!    Order 40 (295 pts)
!    1/6 data for 40-th order quadrature with 58 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 58 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
     -0.66411637423956578739874309909381D+00, &
     -0.24207197863738398306862447542249D+00, &
     -0.67514797177612497189134399646036D+00, &
     -0.87225015944191233374717005469166D+00, &
     -0.76868567879223402156192530043099D+00, &
     -0.30999131154608929623930725445334D+00, &
     -0.85323240841065682042462033708838D+00, &
     -0.53727030292133569609030595551578D+00, &
     -0.76757602207091515344003545816282D+00, &
     -0.41709706260058898440960904281784D+00, &
     -0.64250324642862691442102353901370D+00, &
     -0.73395730528035636744565078095249D+00, &
     -0.43310798704792516669286002220314D+00, &
     -0.84693242965372475993997325395966D+00, &
     -0.52988575538367881737400733664267D+00, &
     -0.81395203621001148192221956701526D+00, &
     -0.13262238321158207908085298608017D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.12565893500209059730381606002675D+00, &
     -0.25582836243545168466615122195358D+00, &
     -0.41982097163871183619680245728246D+00, &
     -0.39584244571866434364968812226225D+00, &
     -0.13831881077136084719064254716209D+00, &
     -0.55558835329547161475407470013715D+00, &
     -0.26904113625079335044301504651780D+00, &
     -0.38617376855258266995224135587201D+00, &
     -0.90712290003268365546639318057557D+00, &
     -0.13211254083412060410003056730975D+00, &
     -0.13532200006090754449420198166522D+00, &
     -0.51005162143835566342423604409501D+00, &
     -0.51567412876653561433770558683539D+00, &
     -0.72835797984670651201858245642167D+00, &
     -0.62260740206958077067832393367003D+00, &
     -0.63528538940605775324683142950171D+00, &
     -0.13545478402323854515885777980547D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.91834711208585899367680729069800D+00, &
     -0.26841456178680462127694701451016D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.29450956974500233083745593494225D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.15766005001997588398000791219776D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.39500420341927114646355151929679D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.26583541850389618832328064074218D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.96488163632640580772795528150790D+00/
  data ys / &
     -0.57470378380535839956317699309199D+00, &
     -0.55141831198597603831507286345131D+00, &
     -0.56556494724168897227639164041706D+00, &
     -0.51618467078933129623213777000412D+00, &
     -0.57460672418387407371421627702399D+00, &
     -0.54008229992950442561714306153720D+00, &
     -0.57384241303948358177304914166735D+00, &
     -0.55074388383078986548196008116722D+00, &
     -0.55974233776493979903089310270512D+00, &
     -0.52536474950509016897082596544373D+00, &
     -0.54449319151536051271909078020569D+00, &
     -0.53103387228266569983647483538750D+00, &
     -0.57587141183196674121843247917653D+00, &
     -0.55611797625038840229584838026927D+00, &
     -0.51296985906932015988541254967364D+00, &
     -0.52158827793142738546379723447015D+00, &
     -0.56187932687266342953378211324032D+00, &
      0.11003011687008237336733434466617D+01, &
      0.13663584323344421793456675059387D+00, &
     -0.12737340589454779203738364883373D+00, &
     -0.18929257322289204287244570649377D+00, &
     -0.25237212852983271455023246046020D+00, &
     -0.56044801444994193030345087522119D+00, &
     -0.47566799110898290470517971819636D+00, &
     -0.52410356380692977799609815127570D+00, &
     -0.57170940642241625229835788381429D+00, &
     -0.49908301034879271805709825139645D+00, &
     -0.31612494675971333985536967359669D+00, &
     -0.54847061860786860395005750661379D+00, &
     -0.29657575362028796765551235884180D+00, &
     -0.46558820109446506663286885353751D+00, &
     -0.37923882528380845099383801241958D+00, &
     -0.45684803758863608291625036678218D+00, &
     -0.48029591121869609066590186543256D+00, &
     -0.43603282267888446054028374651391D+00, &
     -0.50005009951296356150064101928238D+00, &
     -0.38891721146901775531494918295119D+00, &
      0.27933482596036362512959496310960D+00, &
     -0.57179705694461496519432143619911D+00, &
     -0.43363067211489722444853507200367D+00, &
      0.42523996391594593545924154391851D+00, &
      0.11441090108726184667750585003180D+01, &
     -0.24234470017351667426024672589549D+00, &
     -0.49681561132122740420073482664742D+00, &
     -0.57125217727233967706758863119402D+00, &
      0.93003191476975548336483377359380D+00, &
      0.56962631638217381356419889136285D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.57631399232172626259918827974601D+00, &
      0.82111436271392253740638163140260D+00, &
     -0.40469300239711789646100476636550D+00, &
     -0.54513955979531860983983136957607D+00, &
     -0.57203141564320759086953238463017D+00, &
     -0.35075660264700114997055999049565D+00, &
     -0.34273351742727767767145394888763D+00, &
      0.70353037724633104142734855780744D+00, &
     -0.42794958420782980247198112865939D+00, &
     -0.57216175902539330683834475050253D+00/
  data ws / &
      0.49688685986076335500813888089767D-03, &
      0.20421322651151844017762046611226D-02, &
      0.11376335398163363442669464305672D-02, &
      0.13123691749460771142584854517446D-02, &
      0.53837565018711308131679874030211D-03, &
      0.26896172405115405725156808433702D-02, &
      0.54307048276333835762068445369337D-03, &
      0.25198826411461542126409010399677D-02, &
      0.15319142782715693899177741951315D-02, &
      0.38411906228772124799394024016653D-02, &
      0.25562607929590933659755695536622D-02, &
      0.26896816019905783851160754457047D-02, &
      0.60036514084449199244017297704017D-03, &
      0.14715716460982722722064995019804D-02, &
      0.39962224319702302486375553437309D-02, &
      0.25534279525811038857142356722120D-02, &
      0.25201810346020069847466083850254D-02, &
      0.41167230724256272754400665111648D-03, &
      0.56555181082450911185900550967659D-02, &
      0.56586789117358307508299653903984D-02, &
      0.10834097702542315480967100797076D-01, &
      0.99225669815767172945689578107284D-02, &
      0.24415471132838240081093498781218D-02, &
      0.57970709422402784901464121587120D-02, &
      0.50105635706238936498550178535846D-02, &
      0.12758608174913493052074050132044D-02, &
      0.55592023555177532864401800823748D-02, &
      0.87115223434972838093595378352456D-02, &
      0.13179261092062112504683572450985D-02, &
      0.99446646389628687350930319624097D-02, &
      0.69734880107002948832233705466873D-02, &
      0.73103828906969970566980130701137D-02, &
      0.59302091834307146929707082953472D-02, &
      0.40971162551422433954212787599193D-02, &
      0.57773519974100858251570872273170D-02, &
      0.42621746164839825812632309788527D-02, &
      0.86522628980919465385085382556473D-02, &
      0.52900487244341074555301014519952D-02, &
      0.60794404513723632450482344169488D-03, &
      0.73967700759539224320693784348360D-02, &
      0.47456468096285949486134939736546D-02, &
      0.80914786877822581165281163168211D-04, &
      0.53082561926097671621877127564791D-02, &
      0.30789395107446736330440294150100D-02, &
      0.16224159778341893367110818294581D-02, &
      0.17880830179715579824918122606522D-02, &
      0.41061127743554988075477642960788D-02, &
      0.19270579632685484848497884675987D-02, &
      0.59093070603955750104585123796686D-03, &
      0.25603623606255944146797327158473D-02, &
      0.74860701764472599200155271263176D-02, &
      0.19931737634037231520593140572046D-02, &
      0.79295305880649344360913599297743D-03, &
      0.88807475399574394813610532572560D-02, &
      0.47542421811652855221590656198943D-02, &
      0.33799358355588133678392461897413D-02, &
      0.40037958142737030132660946973599D-02, &
      0.36660639965830984726685636110253D-03/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule41 ( x, y, w )

!*****************************************************************************80
!
!! RULE41 returns the rule of degree 41.
!
!  Discussion:
!
!    Order 41 (309 pts)
!    1/6 data for 41-th order quadrature with 58 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 58 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.90707509366054513441839735030000D+00, &
      -0.83678266843431511046582515644399D+00, &
      -0.94247957093734042414919187055867D+00, &
      -0.47818348033753518695149771130636D+00, &
      -0.47786178727052685018858128857025D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.82977481051684242521921168766497D+00, &
      -0.80506207604730995380052139962066D+00, &
      -0.75892338634994084017742272212251D+00, &
      -0.66697937351822451848579519358950D-01, &
      -0.93039119591469919672730326618751D+00, &
      -0.10179246544689757723568411908004D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.11964378950220348999333477645940D+00, &
      -0.89370315180977679131356546281919D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.12537506708828195458087022987466D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.86060405291382569981156454363751D+00, &
      -0.37246528778512515239684348047261D+00, &
      -0.25224760836480194469992557046715D+00, &
      -0.77250795122178423033233897226693D+00, &
      -0.97281903597154664921569844697325D+00, &
      -0.20361834007684187876306722478542D+00, &
      -0.14229399114449109919839299325896D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.71543818078714833155329003431939D-01, &
       0.00000000000000000000000000000000D+00, &
      -0.34072584339074050558489837485303D+00, &
      -0.25420500317361023538457045471745D+00, &
      -0.13311178834618634999839119772768D+00, &
      -0.42835120414075877047497032365690D+00, &
      -0.28308678232916800143508359259067D+00, &
      -0.38982610581001483073643842554906D+00, &
      -0.71358109961060030283458818362239D+00, &
      -0.67177893900431715796469854575323D+00, &
      -0.75059812077502214633644715294448D+00, &
      -0.59464715111368400987629742768832D+00, &
      -0.55914730411574729626305044953771D+00, &
      -0.47513641482741620402395711593316D+00, &
      -0.55098939175943078591819138664469D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.66906775613675318713614198789292D+00, &
      -0.42086181836543388245829813956203D+00, &
      -0.21245173597369898203729302395941D+00, &
      -0.25800420807868548956655134212985D+00, &
      -0.29370336187542435095775000461405D+00, &
      -0.60047596226514389492291181185375D+00, &
      -0.64378659978871008420405373260754D+00, &
      -0.52124100620529880265092320687752D+00, &
      -0.35101185488933557658235806095652D+00, &
      -0.14878346974678461727537723668515D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00/
  data ys / &
       0.11484303236078189653199134730205D+01, &
       0.64867318675503157654602022450247D-01, &
      -0.13336487938297912910317293715113D+00, &
      -0.50914331749408594839577823579785D+00, &
      -0.54016766573740110842549247829795D+00, &
      -0.55659144758280954666377007954550D+00, &
      -0.41036116782557410608240092285442D+00, &
      -0.35568548495723222120621918256555D+00, &
      -0.51447322281830402728376303287297D+00, &
      -0.50391286234357388108253695826115D+00, &
      -0.55710779590286589800031532601371D+00, &
      -0.46781272099145912035205586389519D+00, &
      -0.55164499869306851582964960390351D+00, &
      -0.57416322708744445609317793776209D+00, &
      -0.13038223693758752754332823314062D+00, &
       0.66182123823402367862263609405308D+00, &
      -0.51461673052711459891571855445469D+00, &
      -0.55908758428750220767836487535657D+00, &
       0.54975195106341269371593215963727D+00, &
      -0.31822881181210445991186635948848D+00, &
      -0.31576402673138936793850567085049D+00, &
       0.42731758372108878724118641820065D+00, &
      -0.57305121360034517332191987171046D+00, &
      -0.30895554368016513106704832983371D+00, &
      -0.31414513744457014202355344166677D+00, &
      -0.57323223918730283416506419525826D+00, &
      -0.57206883390058007347834073977517D+00, &
      -0.55123879656195327272974224654403D+00, &
      -0.57235407491813576252917143617978D+00, &
       0.24454257138245059331980778970388D+00, &
      -0.39589172778651022907750111971765D+00, &
      -0.57251313359481391919877047590178D+00, &
      -0.55166089418268212499172347118887D+00, &
      -0.51370572700173861398292804694009D+00, &
      -0.22603324747774107959414273668825D+00, &
      -0.46374623851729501975734765797479D+00, &
      -0.57244266277976037743059136383490D+00, &
      -0.51490548014106772939857400939256D+00, &
      -0.55283101652348038522394903514786D+00, &
      -0.46689252269607195573705009252807D+00, &
      -0.51923400712748281983594166768317D+00, &
      -0.40487430456712229688846342248602D+00, &
      -0.46537465321601328935261456909651D+00, &
      -0.55154491728129470377025145643426D+00, &
      -0.57240622147657917252995100547841D+00, &
      -0.22943850805370712324762812120392D+00, &
      -0.57244722857070476735714053106836D+00, &
      -0.57243826525037158906984485750360D+00, &
      -0.39438908961583798768936375721498D+00, &
      -0.22157162536728802662765970391773D+00, &
      -0.46047385175478172230586878054650D+00, &
      -0.55148536852211283444706530727333D+00, &
      -0.51606114317066720323109583010886D+00, &
      -0.51455997052960895786677902884130D+00, &
      -0.39271417796087884909400497182759D+00, &
      -0.46204815328845467442262509683753D+00, &
      -0.46220719577895767618412315479348D+00, &
       0.79756730028191280539809974543073D+00/
  data ws / &
       0.34355666699665572908084305656243D-04, &
       0.42399098861468427455877995758264D-02, &
       0.37154110284138247834042735653067D-02, &
       0.12458404025090231132925565144087D-02, &
       0.14185150154704695672229773526671D-02, &
       0.72851462067084252604660686856037D-03, &
       0.49283298823596391034884407259565D-02, &
       0.53613423093296115706064365551043D-02, &
       0.19577303889005218175716306314385D-02, &
       0.23541334060017086291762687738959D-02, &
       0.13574312941869499732389430016423D-02, &
       0.33325721812546689467184010795628D-02, &
       0.29644284948173195699449497133337D-02, &
       0.37091902076730237290376100062468D-03, &
       0.80403871323958185654768572258748D-02, &
       0.27933379921942981118737786316620D-02, &
       0.43548510260672555779566602140770D-02, &
       0.98750346722284897815375163954063D-03, &
       0.33140399984357008523996740964860D-02, &
       0.39548685266133002402731823562045D-02, &
       0.81907961822989578237987369917385D-02, &
       0.39990415768416250914981967446877D-02, &
       0.64543016375148533251238361162029D-03, &
       0.77525238376409612296793051209554D-02, &
       0.82098277784420498504581064200822D-02, &
       0.77505992315050355696141616800802D-03, &
       0.31460954824696309149912473051966D-03, &
       0.30771570801706524162859379333622D-02, &
       0.13758671651214991382998623408107D-02, &
       0.44530286851553646989910342775063D-02, &
       0.78835322339101614146632253638963D-02, &
       0.67359298176593092050484809442566D-03, &
       0.30115058169438009830398484639718D-02, &
       0.47516681892344821461215335464754D-02, &
       0.92897161081570613163976545109188D-02, &
       0.57624992565964513866295347402457D-02, &
       0.13386293617916449653435311528237D-02, &
       0.45476733851440924400633719363253D-02, &
       0.21881299772745267054828351965957D-02, &
       0.44103886097359621239681297088827D-02, &
       0.31408957167973836083480622860722D-02, &
       0.54951077871372566664971370622657D-02, &
       0.50946823920529338224773265834011D-02, &
       0.28852806434905299950945859499645D-02, &
       0.12012233088773826615649104421917D-02, &
       0.47576797651663080029937010231751D-02, &
       0.10565898230048048225468444873170D-02, &
       0.12889097209731337671344489509095D-02, &
       0.78373349308822302058968405245672D-02, &
       0.88868099593492497317748964708364D-02, &
       0.64917648662630346100035827874498D-02, &
       0.26315125248814009986883523206499D-02, &
       0.37615631205534999461032753334140D-02, &
       0.42869570500049250611205071236900D-02, &
       0.77283572873216484561057801262313D-02, &
       0.67055003387097703603196736320573D-02, &
       0.33782766604571404544711257767029D-02, &
       0.26121233276609877149517818702563D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule42 ( x, y, w )

!*****************************************************************************80
!
!! RULE42 returns the rule of degree 42.
!
!  Discussion:
!
!    Order 42 (324 pts)
!    1/6 data for 42-th order quadrature with 62 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 62 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.33732186702983072527377866348931D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.96033929602597311557761977477877D+00, &
      -0.86369982899641926289375115271667D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.91964505433817813657264837251525D-01, &
      -0.66309355251219477483888932315586D+00, &
      -0.51372916997472296488281957020097D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.93438263780905817601029667101954D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.90377238041680626119957295786590D+00, &
      -0.97636560454756210194148963029962D+00, &
      -0.80976763015790175270655294347859D+00, &
      -0.11503943729553541704016281376984D+00, &
      -0.45642869772220040454862543963416D+00, &
      -0.26081632436550845472752474357332D+00, &
      -0.23737442933070842287301049364327D+00, &
      -0.48002697917900107156245025485608D+00, &
      -0.55650162501787387537981069378810D+00, &
      -0.12478176574417714212774268424213D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.57250293774060918335092055220851D+00, &
      -0.35082904042609762405060413462916D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.48329385573259627109084340701262D+00, &
      -0.60723425879311620189016063272093D+00, &
      -0.74479369220077260375364623234338D+00, &
      -0.88899121520171718881192636679144D-01, &
      -0.64093927012580804843536900337703D+00, &
      -0.72840614316212545054184733409861D+00, &
      -0.34632334976132410062989430769368D+00, &
      -0.29328359092418193020774881585849D+00, &
      -0.52075640841362497935400311743224D+00, &
      -0.60555027935120159340828726711903D+00, &
      -0.40905454399991287433613498814895D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.68384877689179067855591079553230D+00, &
      -0.71845211882128619528987877814782D+00, &
      -0.21667354415688649871182254929595D+00, &
      -0.78401417474182939603497549800273D+00, &
      -0.73829866676407222514323372659105D-01, &
      -0.13454529284893910979363670735151D+00, &
      -0.81224627731204864480024020247250D+00, &
      -0.21779874120415795023777409358666D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.42173742894104082835679644928203D+00, &
      -0.86724517518683599270071051238882D+00, &
      -0.35974948772649811066870719069685D+00, &
      -0.38462016485447150927117414922040D+00, &
      -0.14709579616219243877526898806227D+00, &
      -0.14236698354849056304093448822305D+00, &
       0.00000000000000000000000000000000D+00, &
      -0.21806859696894763488778637237838D+00, &
      -0.28058519641950796678974392628735D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00, &
       0.00000000000000000000000000000000D+00/
  data ys / &
      -0.23915669727967103118380139768186D+00, &
       0.11499706797515916998220806401861D+01, &
      -0.57463021225838519900335995927075D+00, &
      -0.56879992979770302521884041359830D+00, &
      -0.54196210567272946906489712244628D+00, &
      -0.53941219280079277870643403803930D+00, &
      -0.50772285124871792168226530442572D+00, &
       0.92445442054483368113851672487764D+00, &
      -0.57476336247113177371961348404936D+00, &
      -0.48132277490581309659947493263723D+00, &
      -0.37176697642006607510778844628504D+00, &
       0.10049252920684353614918795242733D+01, &
      -0.57493742331160895521040050048537D+00, &
      -0.54376585322681251262386416118604D+00, &
      -0.55951105488338182442194601355457D+00, &
      -0.57287342016015178837509330570583D+00, &
      -0.50897875397137854857739836711645D+00, &
      -0.55605671624505328368102486115945D+00, &
      -0.57286458799044539871933065364668D+00, &
      -0.51230069551399328623142182353309D+00, &
      -0.54774164573700082169258700885382D+00, &
      -0.42881250819630884111523888550059D+00, &
      -0.47691618600212933305894604508553D+00, &
      -0.51872351401291148614495359408056D+00, &
       0.10611738733054864308352869822745D+01, &
      -0.57297391133539792503817569661015D+00, &
      -0.55889259681253444754878375605606D+00, &
       0.67490581305685926714955055515407D+00, &
      -0.46308066751251361359457711328632D+00, &
      -0.55408939280498580695400859722506D+00, &
      -0.42433782075470535918840983649065D+00, &
      -0.52032748775510677492310958477448D+00, &
      -0.23994545417022376699165559718980D+00, &
      -0.52285819108589385499701905311092D+00, &
      -0.46066493316460819615558728243469D+00, &
      -0.25420978730877827119837106988602D+00, &
      -0.46670083015487351222116455572352D+00, &
      -0.52093525817617790107842375316544D+00, &
      -0.55435992266257116866227670316197D+00, &
      -0.34138644830088341585231904393856D+00, &
       0.78549511301950868330086537396862D+00, &
      -0.57282030241995550160692247503933D+00, &
      -0.55400012643472741059711642382680D+00, &
      -0.24499725128675631298290375529787D+00, &
      -0.57293824798152066163974973440469D+00, &
      -0.40234854190615793941968454639826D+00, &
      -0.14476929626336181753272157091150D+00, &
      -0.55359930548468954074315532763614D+00, &
      -0.57155725996820959476202397056243D+00, &
       0.74817466669102061182393603775266D-01, &
      -0.48091898059119731232834971500976D+00, &
      -0.57249401685345627316687746770457D+00, &
      -0.41046630772117739922581443734300D+00, &
      -0.52677593302205091340352395053193D+00, &
      -0.46723591737438723999494490231575D+00, &
      -0.32805865585485880306160348707314D+00, &
       0.30647862202829743938620359376295D+00, &
      -0.40551576066406470095805909037152D+00, &
      -0.33418952446785743728949888770460D+00, &
       0.54905382739186092457188995702651D+00, &
      -0.32644308263379735102228951317930D+00, &
      -0.14180931586841959084250934615779D+00/
  data ws / &
       0.23336887717611856261356883070280D-02, &
       0.22846739164921267903695204331260D-04, &
       0.70111433879772498743791597802441D-03, &
       0.66736115582873727562875088212462D-03, &
       0.57785786514264065438532593664687D-03, &
       0.13648017145261238754376858784678D-02, &
       0.18715796130141111886024261596391D-02, &
       0.12311750904528985305433912829374D-02, &
       0.73641178059201489942713406653212D-03, &
       0.33400912254975143418927736967276D-02, &
       0.53408360185582866807409529152528D-02, &
       0.87691656602387380470263190564516D-03, &
       0.29827840345921013265121144680296D-03, &
       0.14428656899060768897862657143696D-02, &
       0.89736946555330205057357879483966D-03, &
       0.24622832560853176787327086769666D-03, &
       0.22197294779296558696560399072253D-02, &
       0.25038963454662955321871600907872D-02, &
       0.10178082444714138863786539439139D-02, &
       0.41750972622189718039985200715331D-02, &
       0.28539390170943817441698264694008D-02, &
       0.53618401327742042860547051137744D-02, &
       0.44379187212093563379576658435829D-02, &
       0.43923515022689111826190793996648D-02, &
       0.62671836400915488143041776852213D-03, &
       0.97955449417192964190566775890366D-03, &
       0.23018208943548581359392383454856D-02, &
       0.28689426702522553567921914933795D-02, &
       0.29825739568587811806411249714095D-02, &
       0.25047104675084795836734599265446D-02, &
       0.52092111037958286914269299684586D-02, &
       0.28471024101248386546695067189237D-02, &
       0.82474954978823005019031886199947D-02, &
       0.31999957236382169770094914684218D-02, &
       0.37199859798352839350442391912941D-02, &
       0.85220480529686853126175155374059D-02, &
       0.55913173485803385482484428528564D-02, &
       0.38298884403760618569504568998379D-02, &
       0.23089127874100000149196844935704D-02, &
       0.70117980296802485289704436077025D-02, &
       0.24321512738535918412817989755737D-02, &
       0.93669661545711090880311728905074D-03, &
       0.20642879082447440946641719056348D-02, &
       0.90936551597467743554493293539138D-02, &
       0.79986620899126243521988101233587D-03, &
       0.77120700714742987371071118791067D-02, &
       0.10219559553814186449346549825429D-01, &
       0.17241106961996584893369591793848D-02, &
       0.13912182187991904328859295409100D-02, &
       0.53283478006725665670848896066726D-02, &
       0.53185152093575276335966863060532D-02, &
       0.68994902614553096607967297139181D-03, &
       0.68499915239657437963246941954227D-02, &
       0.39920622096982370641881855622790D-02, &
       0.64073752422181504921770295563876D-02, &
       0.86898690635024727222144915241917D-02, &
       0.47974852921883757762301535128063D-02, &
       0.74399462871562674711612756662098D-02, &
       0.81490368631924462501235690710386D-02, &
       0.39847607162807112945480365181103D-02, &
       0.44476356973374278433219749730315D-02, &
       0.52129984983515280965046257082396D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule43 ( x, y, w )

!*****************************************************************************80
!
!! RULE43 returns the rule of degree 43.
!
!  Discussion:
!
!    Order 43 (339 pts)
!    1/6 data for 43-th order quadrature with 65 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 65 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.39506733155766901012421952821161D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.24646837298065380013273617416435D+00, &
     -0.79575263644167424708927638836510D+00, &
     -0.48253886188633001772041546826783D+00, &
     -0.62546966261193450084215465475134D-01, &
     -0.30130814355531906520968875282228D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.35231165502281585353535246732493D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.12800312652182834294317879260650D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.75118628320269714215689196084969D+00, &
     -0.67034428298913296399375404066474D+00, &
     -0.77580876066209624496610974380034D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.12785487625900558619560024121639D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.71268785841843536059482927597042D+00, &
     -0.27040014117930207740167640614761D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.18478688196683115844840486556670D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.80938151535440202130076995993744D+00, &
     -0.31942848667068561771894552587106D+00, &
     -0.85468012516227660038415955640997D-01, &
     -0.25825613481914215491217537746903D+00, &
     -0.58279946491371434111606534307889D+00, &
     -0.87969623175882104649066373698787D+00, &
     -0.46561039262024648141549373583729D+00, &
     -0.93340399559638336764338113699127D+00, &
     -0.51396050819491791778081081792183D+00, &
     -0.61691723863061563788005694821551D+00, &
     -0.86363081428402156734207066959522D+00, &
     -0.97099189034945842829889245820946D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.62361278877871758607587901074940D+00, &
     -0.91989119779265366986023199875079D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.57692441054824302159307937523806D+00, &
     -0.50723010453494962638105205800859D+00, &
     -0.84394330147763359879321357561682D-01, &
     -0.72274543590291663139776270288902D+00, &
     -0.47250099165753816338998461789401D+00, &
     -0.35080029727614026576846631364065D+00, &
     -0.12275092202821139885819853243053D+00, &
     -0.38479753550946700083527634968480D+00, &
     -0.39605917796945196543812828983515D+00, &
     -0.84481754164315782828022282277629D+00, &
     -0.20507268425580293655253183641047D+00, &
     -0.52353562229447874684448906255323D+00, &
     -0.13693189087059081697918132267328D+00, &
     -0.62320689311818688506948006480502D+00, &
     -0.14379384782311729469209427032452D+00, &
     -0.27449236039881046467163004113221D+00, &
     -0.68227667429915713110204049156621D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.40313963669589460865080761368403D+00, &
     -0.22073052548745090606319136542233D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00/
  data ys / &
     -0.27174781657834587367794828403112D+00, &
     -0.49274259095938795471287794986388D+00, &
     -0.32541690542417216472121438315947D+00, &
     -0.57450914029685444604595657642940D+00, &
      0.12846740408215895203363603738439D+00, &
     -0.52120501981219468628421175620930D+00, &
     -0.55585048147520898296581708536554D+00, &
     -0.33857300476573982851491415786097D+00, &
     -0.34294121393179207633049958993479D+00, &
     -0.32875457338449147616580244617275D+00, &
     -0.68781371078380984368245670302187D-01, &
     -0.51594631133528140591593205811015D+00, &
     -0.56039688938398587880112568739761D+00, &
     -0.51600357027661430283719712442229D+00, &
      0.10406975917564771325612019382002D+01, &
     -0.48071245484494572753863498860590D+00, &
     -0.46654018005672172190079466787693D+00, &
     -0.52493394350877366855931608373780D+00, &
     -0.53080573778005055886715862589101D+00, &
     -0.55199717395419102378360697714430D+00, &
      0.93744923795883541057323646131539D+00, &
     -0.55378528333018398654846926976093D+00, &
     -0.57306164103038438002759473015017D+00, &
      0.65329413919843916560086065083107D+00, &
     -0.32979522157781538320615791050048D+00, &
      0.11084041345444688623805682120094D+01, &
     -0.57315735914007292751468298272925D+00, &
     -0.23933996521344827119141006030721D+00, &
     -0.46640357835051818210779901438991D+00, &
     -0.55450865650449884106657600267936D+00, &
     -0.47018294735939914621510849234674D+00, &
     -0.57282533435858176236473269144498D+00, &
     -0.51813075309225748766670475143277D+00, &
     -0.57275889464282222126170595591666D+00, &
     -0.57286153985489888900353792433004D+00, &
     -0.55262810787321224192869259072191D+00, &
     -0.55335026706806535430401211392438D+00, &
     -0.57303083539166774608654680411579D+00, &
      0.11458153208366305893213396871360D+01, &
      0.50423840889193913255432466884584D+00, &
     -0.40338147343700279281658672539043D+00, &
     -0.55362560310096266386701313905319D+00, &
     -0.17054110158363053238654111959974D+00, &
     -0.51821251917615874954294201331871D+00, &
     -0.55343995679985670491884892559641D+00, &
     -0.25432761855273552279988165105579D+00, &
     -0.57294781282937958180985481791538D+00, &
     -0.46817056136138252363928334992228D+00, &
     -0.46671221117152839234190202161524D+00, &
     -0.15827564830985659745747052529915D+00, &
     -0.55206358961559880212009617361087D+00, &
     -0.57246915152619833238307709646113D+00, &
     -0.51822758166184266566614267250055D+00, &
     -0.24244875862513978976057242564588D+00, &
     -0.40871265880657287984484480492628D+00, &
     -0.57252078775710633720596892661685D+00, &
     -0.57257680220856426874713292476538D+00, &
     -0.40790874923298185895067251523869D+00, &
     -0.40488358656967401446800162607396D+00, &
     -0.51826247883638312778785904937525D+00, &
     -0.41416427390059670796562799333653D+00, &
     -0.40328359141014275624720285726773D+00, &
     -0.47052810769116907040147328262294D+00, &
      0.83299965359609554712354240867349D+00, &
      0.28006707539158895931997168962991D+00/
  data ws / &
      0.20267313231941893676520332064545D-02, &
      0.16367671769150146246172346306318D-02, &
      0.51493216424315589396152049973413D-02, &
      0.40049166791821914724573044327252D-03, &
      0.38679957027277816063713365008715D-02, &
      0.34975453538986470037287749440995D-02, &
      0.13692247906521867994012332715043D-02, &
      0.50916564180668567506293917701109D-02, &
      0.71541887598019862130827731596776D-02, &
      0.67554356473948161976278050806714D-02, &
      0.45197199185406262459677900374973D-02, &
      0.35861506794982540830122357172132D-02, &
      0.10622739063192419924108232636689D-02, &
      0.40560451238345220270219217309857D-02, &
      0.71306365950803849055449621912648D-03, &
      0.28901178272685770916650253073937D-02, &
      0.35628382297785204095556205282981D-02, &
      0.23337289887646671489220572776197D-02, &
      0.17876266669191564461852559716746D-02, &
      0.27892998079816587686734710640336D-02, &
      0.13320835956879952672184157241896D-02, &
      0.18191641344329572250280779466083D-02, &
      0.10907352970205207235715895372753D-02, &
      0.27936513125358662464080516863599D-02, &
      0.75818102244409073466682226454199D-02, &
      0.31066065630647406501495742839881D-03, &
      0.64045511782145175218433235311442D-03, &
      0.79769491206495963710875582745134D-02, &
      0.52105480536968519556750471994035D-02, &
      0.25683586574526020251013582443614D-02, &
      0.41796721048381089538295214085205D-02, &
      0.54981489589321546105773135980457D-03, &
      0.36900063605190763288766065453592D-02, &
      0.40460366093556559458970343028029D-03, &
      0.99764710822395591487080703901083D-03, &
      0.21433057408916717136795809729450D-02, &
      0.13181554039184077697417192202970D-02, &
      0.24966385865177930712178241334390D-03, &
      0.56415208115924918653995444365333D-04, &
      0.35108086150369173319630529016857D-02, &
      0.51624236567181411900078094419075D-02, &
      0.96766243407032355999668290740009D-03, &
      0.45731471950392280996000615522500D-02, &
      0.34583136168620142190249880837043D-02, &
      0.24237265422044902192234994737096D-02, &
      0.77977816580077882796552949686740D-02, &
      0.80588323551714052775101742970255D-03, &
      0.50339349950361747376652268826760D-02, &
      0.54331525883336925722484960144977D-02, &
      0.88072094639810414255439357569340D-02, &
      0.26943758842246860082040659620724D-02, &
      0.11555336183140089850951172772477D-02, &
      0.20764819925413973070582238653112D-02, &
      0.83010524908151710705626972584161D-02, &
      0.56231102351940614439232706639500D-02, &
      0.12763777281762985620080832782995D-02, &
      0.97128666683373741323713272921117D-03, &
      0.69250253173029413525682166964403D-02, &
      0.69755502078755805652513910381880D-02, &
      0.32320158906108914651035701130350D-02, &
      0.35091833149609820457735281284170D-02, &
      0.66535574606795091616463991758331D-02, &
      0.58357235029408977357372091365790D-02, &
      0.21654064214107489596481597275945D-02, &
      0.48130202892800976037200791733793D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule44 ( x, y, w )

!*****************************************************************************80
!
!! RULE44 returns the rule of degree 44.
!
!  Discussion:
!
!    Order 44 (354 pts)
!    1/6 data for 44-th order quadrature with 67 nodes
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 67 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      0.0000000000000000000000000000000000D+00, &
     -0.9497329452118762389747014470132091D+00, &
     -0.8001862513364488071091260917428001D+00, &
     -0.6910725775767816500425682030963931D+00, &
     -0.7699895351147678691136080969564274D-01, &
     -0.9389616539760584684425697161489036D+00, &
     -0.3318014560907163140854925533609147D+00, &
      0.0000000000000000000000000000000000D+00, &
      0.0000000000000000000000000000000000D+00, &
     -0.7536007546194699584282605909703006D+00, &
     -0.6418838401483368830531210405780724D+00, &
     -0.8569413055073822333863570460181954D+00, &
     -0.4713099774418540641295127244304687D+00, &
     -0.4587710901095560036744622028451049D+00, &
     -0.3454684993219427932117970013334666D+00, &
     -0.5784975768218464125847982734150031D+00, &
     -0.9757061286693509772479542529554229D+00, &
     -0.9062217459170026624185611454216153D+00, &
     -0.6998855908781156060583940844630905D+00, &
      0.0000000000000000000000000000000000D+00, &
     -0.7828939494539899851949840039195377D+00, &
     -0.5976618502172688281903349218410519D+00, &
      0.0000000000000000000000000000000000D+00, &
     -0.2089756393930555645731581562882102D+00, &
     -0.7011575058845152681611414003803953D+00, &
     -0.5064990519200558712677355544916721D+00, &
     -0.6042610388710118243964657680731453D+00, &
     -0.2426529067325121256109910016105379D+00, &
     -0.4856256157498482835842484912328102D+00, &
      0.0000000000000000000000000000000000D+00, &
     -0.7004374206319495265033410739625405D-01, &
     -0.3757615711643657550148681484974144D+00, &
     -0.2919871922611893373479530841081256D+00, &
     -0.9994102280758133535657317453111649D-01, &
      0.0000000000000000000000000000000000D+00, &
     -0.7857254577834318544379545866687309D+00, &
     -0.3721620253239425678261695592905290D+00, &
      0.0000000000000000000000000000000000D+00, &
     -0.2824529226357365089257330994701188D+00, &
      0.0000000000000000000000000000000000D+00, &
      0.0000000000000000000000000000000000D+00, &
     -0.3953463775800016380774481750278100D+00, &
     -0.8361108176791535739269469385088765D+00, &
     -0.8814365377132475290846046360400148D+00, &
     -0.1406663437184717854538742687564680D+00, &
     -0.4650987866606519008128443728604466D+00, &
     -0.6964523670523666770018160868777266D+00, &
     -0.4113816477062986076261766146150044D+00, &
     -0.1610536446585760688667173579011407D+00, &
     -0.5028509942935229229810541094112460D+00, &
     -0.5448555197999273032450518681162338D+00, &
     -0.6058936424345374593927006219197785D+00, &
     -0.1081927332768446316060675202726035D+00, &
     -0.2295037521073542228709062704046674D+00, &
     -0.5898196614388808672207378844102958D-01, &
      0.0000000000000000000000000000000000D+00, &
      0.0000000000000000000000000000000000D+00, &
     -0.2324653629444445842929660552851472D+00, &
      0.0000000000000000000000000000000000D+00, &
     -0.1819171108132164261481020014379600D+00, &
      0.0000000000000000000000000000000000D+00, &
     -0.2500032323171110666706981553600442D+00, &
     -0.3375819432490318985102882332004112D+00, &
     -0.1161841402458460505963725617476231D+00, &
      0.0000000000000000000000000000000000D+00, &
      0.0000000000000000000000000000000000D+00, &
     -0.1381839808516535777015623012008872D+00/
  data ys / &
      0.1148768930925886262151310465623686D+01, &
     -0.5587190843946788319800702097639321D+00, &
     -0.5759982547513931308236141599939908D+00, &
     -0.5739929781026895530093619240854897D+00, &
     -0.5742565796637987766332210625225684D+00, &
     -0.5743118620654462339294955029963182D+00, &
     -0.5764542892494308227983752102621023D+00, &
      0.1053661869059013126390801025098173D+01, &
      0.9830543452221882010316337450645482D+00, &
     -0.5642804373589460086506076815201640D+00, &
     -0.5574445948250216759499998540402298D+00, &
     -0.5353255763542691825073068820035573D+00, &
     -0.5603801665927884443776809238750006D+00, &
     -0.5740608434639325204622941212626694D+00, &
     -0.5640573337469584267853102545754350D+00, &
     -0.5726612537821012774116991313991636D+00, &
     -0.5726626528471781321664603205600438D+00, &
     -0.5592282822642103798482359755790968D+00, &
     -0.5400889021600139741287112668257262D+00, &
     -0.5348248905002649083989599110468093D+00, &
     -0.5378170138107226759506693144865885D+00, &
     -0.4039918494468322341133479531414074D+00, &
     -0.5637079596777493822434797158628362D+00, &
     -0.5718777342221263057688087793323300D+00, &
     -0.5018890152406374639656521891734000D+00, &
     -0.4685508460352765972480529422854412D+00, &
     -0.5172633713942475966596304508297206D+00, &
     -0.5497203595501590605031193106499199D+00, &
     -0.5140166345967331496952227323818916D+00, &
      0.8893638105980905452621258664733128D+00, &
     -0.3645379523625655382701633893722455D+00, &
     -0.3659340829551636496622119107012566D+00, &
     -0.4252279065273847102094159009996268D+00, &
     -0.4635872615991260396686282785197555D+00, &
     -0.4940450202599493985592231391958893D+00, &
     -0.4981606513359721550788104276334523D+00, &
     -0.4858920787064337532175409440511338D+00, &
      0.7767824952808555984008258545514951D+00, &
     -0.5197375697152384646052054170576424D+00, &
      0.3536374193876506397331972717972702D+00, &
      0.4760546324939761283315701222537493D+00, &
     -0.5373555685767024547552789232104194D+00, &
     -0.5627800449469781889100343115674311D+00, &
     -0.5741358518948284514699798237494199D+00, &
     -0.3143189178536211088756277347160222D+00, &
     -0.3232690739017036811465453364851697D+00, &
     -0.4508096294389419700119239124729038D+00, &
     -0.4330349046242016037349211869278261D+00, &
     -0.4081806944417965784076695553371667D+00, &
     -0.4004602966965545264378386469600689D+00, &
     -0.5480091160789313012122431861765678D+00, &
     -0.4654469444625449906357368312464820D+00, &
     -0.2408240697048009236946195102972083D+00, &
     -0.4755237162067393099887086042912068D+00, &
     -0.1554487149960662937738036182401154D+00, &
     -0.3082651195390385495689250052901405D+00, &
     -0.4210560663521613009285800897713914D+00, &
     -0.2549706395457159319661921698363317D+00, &
      0.6562159018607634589554760136404371D+00, &
     -0.1645038009839102097914264096582779D+00, &
     -0.2390476568695849024278482393008327D+00, &
     -0.3500539054481347352752143235181112D+00, &
     -0.2855707593455760613475971357331510D+00, &
     -0.5546162891229904937801707067639082D+00, &
      0.1352301011214314104583760897705539D+00, &
     -0.6333228349610746330155009819900319D-01, &
     -0.5177444417481954592613791928463002D+00/
  data ws / &
      0.2915373135979705462354669962222584D-04, &
      0.5421904422449839736435313083383586D-03, &
      0.3596051767025996319384007236006714D-03, &
      0.7097961495022424493012412105851562D-03, &
      0.8830579864206354364504096263197627D-03, &
      0.2973426233859937360534817748447138D-03, &
      0.4238631002729904678977975696568931D-03, &
      0.7389606753338469971149288564795965D-03, &
      0.1148374312030633712597584302352535D-02, &
      0.1273653397793799775219820208340736D-02, &
      0.1772310668755885176871822523120592D-02, &
      0.1760259894656385175896251017077239D-02, &
      0.1591696809621534312060249900305618D-02, &
      0.7861912161306376969359324550937249D-03, &
      0.1932261265768957224441734639436218D-02, &
      0.1054246990932389772147217163517965D-02, &
      0.2442199620811447342051688108995863D-03, &
      0.9494447813509459504714159753943138D-03, &
      0.2016444809029372508564748979562772D-02, &
      0.1796212502278787821852696540715106D-02, &
      0.1985990719999202087365783713106505D-02, &
      0.4476918545924685844030658743575517D-02, &
      0.7926095313482192607115919198160405D-03, &
      0.1363437100111953041990336948238837D-02, &
      0.3128949768581953030780660470515785D-02, &
      0.4468586167117141199592656650169745D-02, &
      0.3558780448911060819562296812185439D-02, &
      0.2654525745999437126651160840433368D-02, &
      0.3674322205637929576474475378034387D-02, &
      0.1556779548166703629723862770843712D-02, &
      0.5659722156959053747811933867465999D-02, &
      0.6559124062355508037637436719411665D-02, &
      0.6124082302973937834781741237000250D-02, &
      0.5432590387902965678105625419649959D-02, &
      0.2310495765495803855211312734514998D-02, &
      0.2708245744720212530179525275012375D-02, &
      0.5124555916440916550164562572827943D-02, &
      0.1936910902435187766318955933882164D-02, &
      0.3646527070098702883931381699630589D-02, &
      0.4424142630723912210455942532277462D-02, &
      0.3276931385664301994721671259073124D-02, &
      0.3264053064814834336425695074922234D-02, &
      0.1135643135915063583134474479188575D-02, &
      0.4223718148997970920874463333812100D-03, &
      0.6555375990726206244644356106443562D-02, &
      0.6606136053977267350584211383354891D-02, &
      0.3644515347971302216660166325983147D-02, &
      0.4871554113050847936724114713691689D-02, &
      0.6679124914763547321632436773214387D-02, &
      0.5616578389429630050906029716034673D-02, &
      0.2275791117266683412259386884315207D-02, &
      0.4243996397034961679236635195585269D-02, &
      0.6959330566880718539247596084458503D-02, &
      0.5290070422157258189378060153617274D-02, &
      0.7976505080967100010251007180513698D-02, &
      0.3238093010218998159411476040299402D-02, &
      0.3304316395913585112942109463963793D-02, &
      0.7632093580324891025483614928517932D-02, &
      0.2926022905168081777270491914230688D-02, &
      0.8413855313504570550721436602221883D-02, &
      0.3057643153861432817013016432152174D-02, &
      0.7441970831021575269373809133451851D-02, &
      0.6989734119088538264792355031494924D-02, &
      0.2596917279271723848812657753581774D-02, &
      0.4228198393093499219382464343859585D-02, &
      0.4122988694755634966269440274723658D-02, &
      0.4679274136115308847400441526701599D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule45 ( x, y, w )

!*****************************************************************************80
!
!! RULE45 returns the rule of degree 45.
!
!  Discussion:
!
!    Order 45 (370 pts)
!    1/6 data for 45-th order quadrature with 70 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 70 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
     -0.96749796278768431752695073746986D+00, &
     -0.98943904955500689467050133968185D+00, &
     -0.85724783085411714050106137680522D+00, &
     -0.86009422327718343131869480185428D+00, &
     -0.54678180057409276098388610849729D-01, &
     -0.49732663296837674567709737943128D+00, &
     -0.96239582473679000067551742403253D+00, &
     -0.27961070235673144034368245271631D+00, &
     -0.40402890296751249677645751975093D+00, &
     -0.29442839410535855309352484266892D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.43275119028613663914670241562698D+00, &
     -0.44044389245586822931301266425545D+00, &
     -0.61279883033232538372205093469042D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.40788451897774191002745407172850D+00, &
     -0.69268856593560823389350549597623D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.76676405679321178282204182266112D+00, &
     -0.88142494556619689489685668224494D+00, &
     -0.30788563677170870686746228513001D+00, &
     -0.51690806387591814992569974157337D+00, &
     -0.36522335396393722816446107730499D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.54085071215301248177693480228527D+00, &
     -0.83755436630162203436831978893993D+00, &
     -0.39400450916939910389752569327788D+00, &
     -0.33507526831923579205690213103223D+00, &
     -0.93207383259146302186264561603832D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.24725397282679600089234012793255D+00, &
     -0.59548295462739307737882050980714D+00, &
     -0.21190291318947065883045380978784D+00, &
     -0.48065853549210622637194679384859D+00, &
     -0.58563257009522274955669451569327D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.36489263643259686426301607599478D+00, &
     -0.10662122389563936276094546991520D+00, &
     -0.63098646216816865329341790460037D+00, &
     -0.10951950034472544896736583276610D+00, &
     -0.14147353942031966219611357193348D+00, &
     -0.32195104149719150226124582347371D+00, &
     -0.79909003824949698793707745791143D+00, &
     -0.10582426030688274991436338221365D+00, &
     -0.11204595369159801121778549049946D+00, &
     -0.61200208537203979332083793516425D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.69310856751575954320818550365882D+00, &
     -0.52182537044957879662933711116161D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.21330305926164315152747136574011D+00, &
     -0.76353151836479030982601065330425D+00, &
     -0.67884482751176626602735151717562D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.71309872195622120220433316560504D+00, &
     -0.23702202213867019459513762948482D+00, &
     -0.49629255197942964513516871846921D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.21703474679150985775348937929931D+00, &
     -0.12791164301131482078856717349660D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.91918133084949909274827769251893D+00, &
     -0.78297196007811101735741996204489D+00, &
     -0.14461283051109006329463020198732D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.26734836171405202882645924901152D+00, &
      0.00000000000000000000000000000000D+00/
  data ys / &
     -0.56471941069694844856954469658100D+00, &
     -0.57501200548013563442214533934183D+00, &
     -0.56546982796685102989871197087213D+00, &
     -0.57522024853914446403759310165459D+00, &
     -0.56214268954647688248601400572909D+00, &
     -0.57443518202158385272046704794250D+00, &
     -0.57430537135662979697492111738520D+00, &
     -0.57479443137000535377443032432917D+00, &
     -0.31119792517448315773562579509789D+00, &
     -0.18309182975606309835985477370170D+00, &
      0.70503710102613623076996776216914D+00, &
     -0.37954480542530077301394984603928D+00, &
     -0.43813658252872489137658216590349D+00, &
     -0.52431770764693138795353125680755D+00, &
      0.43988432838417361094660056896797D+00, &
      0.54818973150740130019484360782211D+00, &
     -0.53068517830945825690351866312342D+00, &
     -0.52054382897965220831059074194035D+00, &
     -0.57563407311774753488214306675980D+00, &
     -0.52066524714991149578624581683571D+00, &
     -0.55109220346610688251784303249678D+00, &
     -0.28136936804129377678526074056198D+00, &
     -0.52770400117212017756160700268800D+00, &
     -0.55536072100117397125270524523176D+00, &
      0.96341139552317968299064589061772D+00, &
     -0.42510034407525727010496874963780D+00, &
     -0.52414106878540363881135726636148D+00, &
     -0.57247532448088443486712017171738D+00, &
     -0.43906434358617035923094688491037D+00, &
     -0.55427727760435318351185124343632D+00, &
      0.11840495907177995488840441336373D+00, &
     -0.56071879514252223550399956253037D+00, &
     -0.57301592049564293598812570618238D+00, &
     -0.22794222552637819257304990263196D+00, &
     -0.48610984701993063250622405741056D+00, &
     -0.48075527463104237978284559370263D+00, &
     -0.11656336099177678980294986355914D+00, &
     -0.49380185173253747396240691815876D+00, &
     -0.17257418086954546445487547770085D+00, &
     -0.41685471639662622825619311565566D+00, &
     -0.27691779802002702321949855249422D+00, &
     -0.54643161443323592717327912197685D+00, &
     -0.36959650358697796007635862331191D+00, &
     -0.55312820158517175524163271806254D+00, &
     -0.37061655711808016877061539071484D+00, &
     -0.44989790809755280647980798667131D+00, &
     -0.55532421580891103975772368666732D+00, &
      0.23698504908978765362861518397758D+00, &
     -0.57312340633371483370089991608323D+00, &
     -0.35237310557002597123601067611590D+00, &
     -0.22563680509593199790438697496259D+00, &
     -0.32814170713377593953818022888866D+00, &
     -0.47540208897837744967251438098628D+00, &
     -0.47291221034981050011352430482453D+00, &
     -0.41322179544695816391477350068005D+00, &
     -0.55444311333444255226437372754811D+00, &
     -0.47815353791871963047978697256372D+00, &
     -0.55841263605812562308032038707870D+00, &
     -0.32398951274847599369007130866498D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.41120300953009715133424788540273D+00, &
     -0.50863906936384494919608030957095D+00, &
      0.82709200615759949176722321241391D+00, &
     -0.48378305160084771830753762022321D+00, &
     -0.57250910447612774904686920854490D+00, &
     -0.57273156232313427034131360506698D+00, &
     -0.57295167407019810131965208299179D+00, &
      0.10366261458457849101902218371190D+01, &
     -0.52758606695132708413591860408544D+00, &
     -0.53231347309540434406510538720317D+00/
  data ws / &
      0.25572163619669275347030002593120D-03, &
      0.78130681960434454688570462017890D-04, &
      0.63262191626397677725423132811818D-03, &
      0.30286144471206534618188349487863D-03, &
      0.17036087426692587176471947445535D-02, &
      0.60607958666190953424951755070468D-03, &
      0.20408229164689422092414467361640D-03, &
      0.69282349702782943622699287812265D-03, &
      0.53664270813767778699249041260574D-02, &
      0.35893775549966510288707779886923D-02, &
      0.21073089951061989088486797402699D-02, &
      0.50245578513041966694332486164703D-02, &
      0.42688044135583548301459101168732D-02, &
      0.24807543972727024276437592523865D-02, &
      0.30515471493979938480916234139891D-02, &
      0.26894370339966747219062415099150D-02, &
      0.28699920637932601309100432329669D-02, &
      0.24144446935100309739631679872824D-02, &
      0.31790657648418738011813407939271D-03, &
      0.21416996150124135443929791578456D-02, &
      0.10904105148236371090982266813776D-02, &
      0.67218349746074238515473176347085D-02, &
      0.29468389036919417335879077316037D-02, &
      0.21585882255773739347679137982008D-02, &
      0.11138001100223078504096300255199D-02, &
      0.48321913046622933674773381791937D-02, &
      0.18596190838124657102588736539343D-02, &
      0.10060622517439881677085687475045D-02, &
      0.52037982694409060390307613806173D-02, &
      0.84864867119809259804133052600579D-03, &
      0.44968639304153501776835069862992D-02, &
      0.20461751558888743165348782978731D-02, &
      0.82449377452441123159564369966813D-03, &
      0.78856598384631329009983207242156D-02, &
      0.40251042064986514657905454665344D-02, &
      0.39434945748613745276711516127143D-02, &
      0.45355232247853231691788919927919D-02, &
      0.42553589471708845699257172105916D-02, &
      0.87471074213636353080888215779404D-02, &
      0.42047313560550802314674632374969D-02, &
      0.81096371219963978174715168622098D-02, &
      0.28740657651753097232044695511438D-02, &
      0.63674671313288725555458273689796D-02, &
      0.15410483366597558629474357722504D-02, &
      0.71166660878827645405484492115954D-02, &
      0.59662756163675577400108631767509D-02, &
      0.20094402952755521669759725025506D-02, &
      0.41552779846196640707863828648633D-02, &
      0.78774367939671502747274922841800D-03, &
      0.55555924933787222053248810519126D-02, &
      0.43156090349809314605947306977033D-02, &
      0.72575720454752208315574044802253D-02, &
      0.30758989792726489058477276759038D-02, &
      0.36691998090203889068724774157613D-02, &
      0.33012791980584823111731500154720D-02, &
      0.18827425749868378780107906069778D-02, &
      0.52275015728844655248822057721928D-02, &
      0.21360163256866199017108940749397D-02, &
      0.38709086959575945186011536418464D-02, &
      0.15225813039724090290900702612314D-02, &
      0.63577625651425152836180330975545D-02, &
      0.46584793041288563398185969929494D-02, &
      0.20643564927291033331571316680505D-02, &
      0.26933883371835105597852952390420D-02, &
      0.48308600971180510860882325582472D-03, &
      0.75143865994468267960236104870498D-03, &
      0.11530302612959225729996460632643D-02, &
      0.82341136968804111621935856491347D-03, &
      0.40628665291981280528823925473427D-02, &
      0.20108332814602822754605793773821D-02/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule46 ( x, y, w )

!*****************************************************************************80
!
!! RULE46 returns the rule of degree 46.
!
!  Discussion:
!
!    Order 46 (385 pts)
!    1/6 data for 46-th order quadrature with 73 nodes
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 73 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      0.00000000000000000000000000000000D+00, &
     -0.49937321552503064883212174284696D-01, &
     -0.58248078099624925941940739070475D-01, &
     -0.26752517246704927261140630108639D+00, &
     -0.43867813853252091527068916646400D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.23976542950787972353232922301146D+00, &
     -0.87549594799702810906321628660430D+00, &
     -0.41617075719872941659009240564594D+00, &
     -0.54326121142564273632982220217311D+00, &
     -0.49334938461621505385336504601822D+00, &
     -0.98141250190288778713761374334280D+00, &
     -0.65605474425672036542123830767580D-01, &
     -0.16097654175693748178184943252463D+00, &
     -0.32922143422069145595634871480200D+00, &
     -0.23167087272607281619362898673378D+00, &
     -0.32291103943378255878422004279321D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.79135174960542667310417788753063D-01, &
     -0.79501562539103118019172171437469D+00, &
     -0.43520622836381734705078227452941D+00, &
     -0.64094592211243916763929215200559D+00, &
     -0.31732449637355273069551804224371D+00, &
     -0.19862767910431307864204482880642D+00, &
     -0.12403617126406631952361500698963D+00, &
     -0.43416110602837889188093965553450D+00, &
     -0.38864284496138298848368820422816D+00, &
     -0.49742313896156865617690862094750D+00, &
     -0.65506909060071668258633513435152D-01, &
     -0.54046107587222447376898336935916D+00, &
     -0.19374430311448627449139164957895D+00, &
     -0.21797347584325374123660718055068D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.19584532512471844401439133027531D+00, &
     -0.63168655681204850681563549874707D+00, &
     -0.90233030436033463513181070921112D+00, &
     -0.60642348255765936124722001014165D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.80972189677200294143541375522637D+00, &
     -0.58209787586990173647256990544253D+00, &
     -0.83686548692344391617162664381025D+00, &
     -0.10243921312001814379582985121977D+00, &
     -0.52704295544169988915202539886442D+00, &
     -0.71820502549667139042476315500771D+00, &
     -0.78211800995999025958688636663884D+00, &
     -0.85578878348643964344785103905108D+00, &
     -0.26080043841003711556582180762586D+00, &
     -0.13061737230200327923828027514913D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.44521414457403926773317497715994D+00, &
     -0.69780908932146560679288082039321D+00, &
     -0.66899206817769503267088297222047D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.72891023006189965013712326310293D+00, &
     -0.37024530768151522800672063932221D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.32275953620672120686976828661180D+00, &
     -0.66470762672695841262017667178171D+00, &
     -0.32306760913108771241386793073162D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.13683702205917657289237473998807D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.55947816484895364063783653823836D+00, &
     -0.75690025149534103382015622011351D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.92282620861069337654871187945177D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.94945587611159447764356569726866D+00, &
      0.00000000000000000000000000000000D+00/
  data ys / &
     -0.50516777744773643918214212704283D+00, &
     -0.31040114421146323467610402783791D+00, &
     -0.38139174632823850428680564625081D+00, &
     -0.45087881559146180751303614188317D+00, &
     -0.38716524171664208079585405722511D+00, &
      0.98605740376479278980387642403069D+00, &
     -0.53179537383682808117522612094495D+00, &
     -0.39923330820610651661243817919637D+00, &
     -0.55924165141919532170843072337147D+00, &
     -0.32183421694439171166523920516920D+00, &
     -0.48706522111890310455837522078968D+00, &
     -0.43864037323932895072146723439064D+00, &
     -0.57360768783134360345778307830250D+00, &
     -0.55766758615272760217178705034940D+00, &
     -0.35256727255257676283714405416718D+00, &
     -0.49258841625772331573291383409050D+00, &
     -0.30296300817765420709023711921593D+00, &
     -0.27337520447762240864886970930914D+00, &
      0.47471537268435794928244865456278D+00, &
      0.58035693653140731668646213878644D+00, &
     -0.48533267753756863676915233617052D+00, &
     -0.48917333384362543356099193333710D+00, &
     -0.55808744003610720897481815391397D+00, &
     -0.55694713731397587210816279802739D+00, &
     -0.55689799448943849551272945603815D+00, &
     -0.48859325854023263980525452506683D+00, &
     -0.26117953849550246736508673038521D+00, &
     -0.48398948921467227547423443087059D+00, &
     -0.52999026102693285956849576671356D+00, &
     -0.52583495263659649090093095454021D+00, &
     -0.57355483546767908414270209478254D+00, &
     -0.55557204112323420607295734852969D+00, &
     -0.55739761697092742823342363228578D+00, &
     -0.21246252441995259506958905076888D+00, &
      0.36139661177510802837475693850211D+00, &
      0.11582303928093664478281478578489D+00, &
     -0.57359024620476593895960903232245D+00, &
     -0.48075999227146968059407118917937D+00, &
     -0.57371658547584443139058969065517D+00, &
     -0.52698535358924523864722032814143D+00, &
     -0.11344215054773373022279305101957D+00, &
     -0.55728798211338842288776835769559D+00, &
     -0.42586101506138965898586810863037D+00, &
     -0.57375019535379531179673731067538D+00, &
     -0.16775873288237485180210443333935D+00, &
     -0.36463881029295166822714518212865D+00, &
     -0.48207876525200853027431004337685D+00, &
     -0.52747840671084502211591497419342D+00, &
     -0.53180888262584484912774717875574D+00, &
     -0.52832053993193271018974971786141D+00, &
     -0.52863298211428052722594126999808D+00, &
      0.10481124042981156776747972952527D+01, &
     -0.57371140175475285675686432495456D+00, &
     -0.52448444053919330486337551923650D+00, &
     -0.42468204214393876878868764552758D+00, &
      0.86891668006615384049718425264833D+00, &
     -0.55555967179393677106465759845972D+00, &
     -0.43207267925178557569834574602145D+00, &
     -0.44163717527386104241934308216581D+00, &
     -0.36120487686156226967665052805572D+00, &
     -0.57348736410677225487636160697833D+00, &
     -0.57339310967499044449513445911666D+00, &
      0.23111663125846296538268627177402D+00, &
      0.70977328433019335226869776419213D+00, &
     -0.43325524227150080894750839759120D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.57318116904317379016261023974720D+00, &
     -0.57316379219729504712466298101902D+00, &
     -0.22231995200693748608468315007358D+00, &
     -0.55502955244943758240255763984666D+00, &
      0.11100839542250144489340222725729D+01, &
     -0.57286876316098503074069033064773D+00, &
      0.11529930056431959330783131719851D+01/
  data ws / &
      0.99124219640185234470989336544560D-03, &
      0.58614096060962842645487250845942D-02, &
      0.56854522710881067383564039723551D-02, &
      0.40625620962929522664929908767625D-02, &
      0.45144310543124329374817531802773D-02, &
      0.82088088596127442161702412322479D-03, &
      0.14407828064975009824715695382818D-02, &
      0.49783947422097924090273775604626D-02, &
      0.88233634287350469355364288087551D-03, &
      0.54934439723781169400547752605367D-02, &
      0.33669998728502865263960539461844D-02, &
      0.41903624852692709261378072222874D-02, &
      0.17334944288966619414269024913119D-03, &
      0.21658266572394104793711645431275D-02, &
      0.60479958760001231392858259471875D-02, &
      0.37756322991798540494330453652444D-02, &
      0.62207318637145172822591743503502D-02, &
      0.63286469162156006735700584173533D-02, &
      0.29826294052344452485495959644700D-02, &
      0.27059360522727772191971339645741D-02, &
      0.42019177882590680248910223133272D-02, &
      0.23015042374454809666901890875641D-02, &
      0.18828680455513843606219753257332D-02, &
      0.16690125284755693166888299832115D-02, &
      0.20781252759372409612923667460460D-02, &
      0.42317638788900425084313484715466D-02, &
      0.71037803619188976533554128557295D-02, &
      0.40307467270170115306414668368486D-02, &
      0.30522630792848607523818935976199D-02, &
      0.30218379230350043130768695564237D-02, &
      0.96574870847494658906685789105858D-03, &
      0.19000953811516758513791103731380D-02, &
      0.21829276451288062623559064112356D-02, &
      0.73314920756006735071788427464883D-02, &
      0.35114723476610777601133441893946D-02, &
      0.42611988684563371970090214166312D-02, &
      0.94946505946997602521228000171027D-03, &
      0.34509142883519454104321786989457D-02, &
      0.39953322686081774873355011018233D-03, &
      0.27638699271507528771931724478937D-02, &
      0.42958741400998447897262423018398D-02, &
      0.12717205008773558943510641599495D-02, &
      0.42175860264852262389840957601069D-02, &
      0.51628931464429952176360586413594D-03, &
      0.82354400118366882096718549841164D-02, &
      0.49763923773181868425612339373364D-02, &
      0.30353430462986957072339039682070D-02, &
      0.21010204804081172094616080287391D-02, &
      0.16435606239301717159637463528701D-02, &
      0.33633961349195807382580363482430D-02, &
      0.35248211978801784050294560000961D-02, &
      0.63942094224216359477928434782097D-03, &
      0.84411673200603475386814798360338D-03, &
      0.25146454557737862996260311126641D-02, &
      0.39858155043769138905211326067054D-02, &
      0.16047534667867884438074054540413D-02, &
      0.15714180013667609459726436385097D-02, &
      0.52508538616460060672169443423580D-02, &
      0.27559932699033631806510178138074D-02, &
      0.62831477470730771167890815345462D-02, &
      0.74766335440469584911791085907174D-03, &
      0.95979934038783073189952725536941D-03, &
      0.39391900179981746067668114449212D-02, &
      0.24830895862025367863318765158069D-02, &
      0.57901415438434356432649769437734D-02, &
      0.14553688489280240366387824569707D-02, &
      0.89356029388787655872574198511159D-03, &
      0.69941978699045079847532710585071D-03, &
      0.42651637563773055644827276665484D-02, &
      0.85219038226410641706285284477815D-03, &
      0.29568676410262965948870235894266D-03, &
      0.34392691859187999137468851025595D-03, &
      0.92751764638845732676762722810718D-05/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule47 ( x, y, w )

!*****************************************************************************80
!
!! RULE47 returns the rule of degree 47.
!
!  Discussion:
!
!    Order 47 (399 pts)
!    1/6 data for 47-th order quadrature with 75 nodes
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 75 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      0.00000000000000000000000000000000D+00, &
     -0.96663742233248238790417222682341D+00, &
     -0.55421586636589606362103864964496D+00, &
     -0.61264177937586419170392244079506D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.79684085415639357802005234937672D+00, &
     -0.97128586885482393995603476389312D+00, &
     -0.93648904794849557432223757784636D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.53945273449791007382233425306043D-01, &
     -0.10288337054182960580026068100176D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.73248213764906407079372614104364D+00, &
     -0.68426811117296314009035410342951D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.11259199413113422069683485156813D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.87984784872866267520426458088785D+00, &
     -0.23123809819906032963749193832378D+00, &
     -0.46889550912339936686025371549248D+00, &
     -0.11739233105524143722624127853417D+00, &
     -0.10992961573914339919329881126213D+00, &
     -0.16204920039724447196768977188244D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.56792554236958167052318250024853D+00, &
     -0.36310842599378440119880946169444D+00, &
     -0.46903656396230065793902775073785D+00, &
     -0.33803039308384563532443360051617D+00, &
     -0.12603730801931571541242657552702D+00, &
     -0.44018371642510357125560685343620D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.20847045004866279897685055766704D+00, &
     -0.22797318474342093841199473155967D+00, &
     -0.81969334154814590110268106658620D+00, &
     -0.24826155062103396453153632431776D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.12427095901943726054227825242898D+00, &
     -0.26070189438266727648706156956545D+00, &
     -0.56248468735254147016623038597020D+00, &
     -0.66071472756340151327417396690268D+00, &
     -0.82669686777638652733059075709640D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.88966644367593888841875654650478D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.34452655299507786176572793372419D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.65494542725425338003061612036810D+00, &
     -0.93012524112428256602193934913638D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.66785089424544850131055902834174D-01, &
     -0.41597899021645575618793010361463D+00, &
     -0.24627705576691568442688105699070D+00, &
     -0.74973726200095632101264662967133D+00, &
     -0.74550793444160419487461731848021D+00, &
     -0.45718177804191062450002601345813D+00, &
     -0.31237691698758109357216488302742D+00, &
     -0.36244609664691797249270623595478D+00, &
     -0.32616646260370706311727811093441D+00, &
     -0.53784292001756868772192703221020D+00, &
     -0.55851533886826749020734059929719D+00, &
     -0.66003657270757138896159641690619D+00, &
     -0.44695335875345503292611264014711D+00, &
     -0.19870749346215743992312176932942D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.80239000604949848720107906069622D+00, &
     -0.13449553992786908006612921402555D+00, &
     -0.71709284775736678626288283834417D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.51015724874008600140209964145657D+00, &
     -0.87380123018010155280547358512783D+00, &
     -0.39184908288647526514367672290932D+00, &
     -0.61920375973213862119233932838043D+00, &
     -0.26594843220537421747193002664485D+00, &
      0.00000000000000000000000000000000D+00/
  data ys / &
     -0.54885817731744273760020596669005D-01, &
     -0.56535389802881173311914125214849D+00, &
     -0.43595283427447394280235040784487D+00, &
     -0.42805378386933825639851755340423D+00, &
      0.10543613068074012401800062516168D+00, &
     -0.49023992523710045116805254072657D+00, &
     -0.57553352291636312128177900316235D+00, &
     -0.55999425828931551781156236993222D+00, &
      0.97965289344360951855945358784080D+00, &
     -0.22457611472173417062464887127478D+00, &
     -0.30138835771850783413933825956514D+00, &
     -0.30545083028762013017508143191825D+00, &
     -0.48491296481354098368779641623556D+00, &
     -0.42961315180326213617646939344682D+00, &
     -0.48945570323521847726831699400261D+00, &
     -0.48818031348608414902160574354381D+00, &
      0.87905212764608203798450778699722D+00, &
     -0.52962597960343054791384488347290D+00, &
     -0.37175232717159904337497914590613D+00, &
     -0.43001929575977665531448764589702D+00, &
     -0.37274742279795921566656912482601D+00, &
     -0.13964656636214571305124861250780D+00, &
     -0.22098784556599346718036712899788D+00, &
      0.10726698183580133144561578611120D+01, &
     -0.52773439710278615552647179725219D+00, &
     -0.52763898191178919130394070654322D+00, &
     -0.52697835910181444235797110038292D+00, &
     -0.36648653111336403999140387539267D+00, &
     -0.52894478654176106374465306810932D+00, &
     -0.36579746792427023484428727362546D+00, &
      0.24344631435472381136691814975209D+00, &
     -0.29950682881818228902768609651588D+00, &
     -0.48721710760636867571802595633338D+00, &
     -0.52883882159690679649594382117023D+00, &
     -0.52822203489770240968743803141947D+00, &
     -0.37667277468535763242146591083137D+00, &
     -0.52940747517054265256495756528320D+00, &
     -0.43564261027324440083824439259671D+00, &
     -0.20992358276179358318845033026211D+00, &
     -0.48651251086220905025316938031502D+00, &
     -0.52681305116132787774755531194190D+00, &
     -0.55712806420844685964294934833455D+00, &
      0.59300989346090695220519494616955D+00, &
     -0.55768637399333409575145201865462D+00, &
     -0.13980368807481589507662723468431D+00, &
     -0.48599981614691996341237894437611D+00, &
      0.41840134446650681930079926553608D+00, &
     -0.48392971086401977797578179121298D+00, &
     -0.57383958132479530247972005058149D+00, &
     -0.43820483878434062239610080574033D+00, &
     -0.55764972588734990620416241805372D+00, &
     -0.29204731777806559769068818139152D+00, &
     -0.43448156854177003457395184650007D+00, &
     -0.55679770960375493548218080656374D+00, &
     -0.52714057557693106272153869645905D+00, &
     -0.48449632102066625308448025105653D+00, &
     -0.29161853684292105771088446811658D+00, &
     -0.43162684421663934029018768245950D+00, &
     -0.55705385397930168896131546768592D+00, &
     -0.36980700529962546759999533399443D+00, &
     -0.55689739217360638744554116629651D+00, &
     -0.55674192040916277835962510290896D+00, &
     -0.55682962368161313519342300149308D+00, &
     -0.55738068167530312022049700934039D+00, &
     -0.57360394426682101478744320464048D+00, &
     -0.57345366439244921550225256351043D+00, &
     -0.57357771856416956297048773459624D+00, &
     -0.57343681973260213887282500888328D+00, &
      0.72177614769930334697640951850176D+00, &
     -0.57345497171610556737079624481070D+00, &
     -0.57352108080599339578631706071895D+00, &
     -0.57345327364010964490936936951959D+00, &
     -0.57342883815744037296971547838128D+00, &
     -0.57351635407928127465513028410519D+00, &
      0.11456762187114260229690797261936D+01/
  data ws / &
      0.28392039488336948310179896994156D-02, &
      0.28003686921136784757704775202544D-03, &
      0.29631179312114912348720642679995D-02, &
      0.29809999165091017111077408004804D-02, &
      0.30922285699322994610269077138085D-02, &
      0.18460959404365729590181431759235D-02, &
      0.12872508972618665537965952389878D-03, &
      0.53151358172545237088027219688402D-03, &
      0.81365776381310603141873461966954D-03, &
      0.67825918391732126919840300376994D-02, &
      0.59347976694683184123957244470317D-02, &
      0.29716933960007650620912395217221D-02, &
      0.25197407852253980023714633624274D-02, &
      0.34300378782082533220752669591608D-02, &
      0.19375775064770987319833820229901D-02, &
      0.40484506484434265904918087580818D-02, &
      0.13706927206297658573031048360427D-02, &
      0.13592574447542674909853690088402D-02, &
      0.57306616583541857081486048497868D-02, &
      0.44642387582970339954371597118078D-02, &
      0.59659697355700592641664212659135D-02, &
      0.70669480375351196705523756968934D-02, &
      0.65951783851403357899976425662021D-02, &
      0.43628370961428043795773932668710D-03, &
      0.25708114420998187417114840014581D-02, &
      0.29876897524925467219456452120523D-02, &
      0.28146519351937002714666355261641D-02, &
      0.56303412225285581963359647583548D-02, &
      0.32994230091903712639399659211836D-02, &
      0.52297242356955663867894660142373D-02, &
      0.36838585883225044871577564370140D-02, &
      0.62387352632335361474645491103618D-02, &
      0.41599811873456112930679098763696D-02, &
      0.17194415272340685412270563416839D-02, &
      0.31880794971043660654134886269745D-02, &
      0.29952623965446603243032973139989D-02, &
      0.16498839143299521006632241989400D-02, &
      0.54403322566293624509259954994073D-02, &
      0.67187331124535844522324030229043D-02, &
      0.35502719665898356713324365688902D-02, &
      0.24754883633746269136218392735926D-02, &
      0.12031798815691044211245980202696D-02, &
      0.26745453014501257900256883065918D-02, &
      0.92265422131087006168788486251726D-03, &
      0.36225684350627313248590370760841D-02, &
      0.41984151428468319683013713735675D-02, &
      0.32537703172163361922509390986613D-02, &
      0.32030949415312354270600565161129D-02, &
      0.33013381207853754356962435323648D-03, &
      0.26754401539508943172771916930207D-02, &
      0.22515566984635737794357729457255D-02, &
      0.59591990991400095363194619176182D-02, &
      0.52750078810945658157831528545914D-02, &
      0.14733980267684772821583690219304D-02, &
      0.21789567303724062164154906204501D-02, &
      0.40463448470928386904872275539629D-02, &
      0.63567301660162872416841128607952D-02, &
      0.51309743375347267914123716886908D-02, &
      0.21660630347248746919200853426513D-02, &
      0.48851415391794237971659363471398D-02, &
      0.18669504929149491480935586903022D-02, &
      0.16964959923743123037357734611633D-02, &
      0.20550364827452665795472373860314D-02, &
      0.22311032805628682468829744578561D-02, &
      0.49275841826369605327759276116059D-03, &
      0.59592130393246716586641585985888D-03, &
      0.98092238248484605161450626802125D-03, &
      0.70060956245054444684115888791512D-03, &
      0.23900824377240423856080438652344D-02, &
      0.86547617602673961987264272734724D-03, &
      0.47650966908745127742574114884819D-03, &
      0.92916397453096297560102228965669D-03, &
      0.79211481322285497661392660284067D-03, &
      0.96420760486050977248262575972495D-03, &
      0.58732212176584084295881188275225D-04/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule48 ( x, y, w )

!*****************************************************************************80
!
!! RULE48 returns the rule of degree 48.
!
!  Discussion:
!
!    Order 48 (423 pts)
!    1/6 data for 48-th order quadrature with 78 nodes
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 78 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      0.00000000000000000000000000000000D+00, &
     -0.45164772650050731682068089766497D-01, &
     -0.27473470409127158336658796332646D+00, &
     -0.32601858877976093934124855013368D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.99490990154620226158720849494482D+00, &
     -0.32465958030201586136906707429503D+00, &
     -0.84012618143751376567667347453966D-01, &
     -0.68050562893254251474678136205112D+00, &
     -0.55412485218420527438896911621850D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.33038679441849822366871793787534D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.72722633108802342397155155606768D+00, &
     -0.23810041415405527504557089888405D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.76837647852811595992367941824138D+00, &
     -0.39481835688065754917935872570598D+00, &
     -0.35808200103666623461734551126576D+00, &
     -0.70743720676693189266156017090859D+00, &
     -0.97010789493490351143718625991234D-01, &
     -0.22510606888237807083444019159841D+00, &
     -0.89142246128908740222364354150092D+00, &
     -0.11231501558393124954330372677768D+00, &
     -0.24247749198133974832677108412529D+00, &
     -0.83724014027395502676007507010710D+00, &
     -0.13318347049091707247482863126316D+00, &
     -0.72689161196677377776022254195996D+00, &
     -0.64034267680893964392473256901576D+00, &
     -0.68321717220184284728388581404162D+00, &
     -0.83839805257724055363465708705911D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.59225145333921036546705814041242D+00, &
     -0.36426477146050005896562735592106D+00, &
     -0.64466682188081663940279587210100D+00, &
     -0.18326940651609773666251309353216D+00, &
     -0.64024696057757473624745250904559D-01, &
     -0.46015923358724641317739926182026D+00, &
     -0.62850907517187595403082243802386D+00, &
     -0.93449067868256757675651398163129D+00, &
     -0.49718634910646430159295459732375D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.76477834359061656278550903563318D+00, &
     -0.86560964360183956199073793066554D+00, &
     -0.80347270468749417960796064245399D+00, &
     -0.12053965097836346999960081953107D+00, &
     -0.61721699934178919899314762692642D-01, &
     -0.94600280954375241238529550780606D+00, &
     -0.20973158081832926767896749904045D+00, &
     -0.53588808819149533597940929507170D+00, &
     -0.89909074000354327737143587267527D+00, &
     -0.14226265688360420003675348239732D+00, &
     -0.58106813824728181662821714714662D+00, &
     -0.43230361497566010923448640099201D+00, &
     -0.54615078926623396814736475110416D+00, &
     -0.79506240679562089185948571554395D+00, &
     -0.25184574558858296991088593038170D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.97712556750745254153359066235566D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.26607245123060807138658601473649D+00, &
     -0.12724847472110119640623202948370D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.30727380337735402963322838421622D+00, &
     -0.58589180790116215572933101719513D+00, &
     -0.17860222460692283965662443246084D+00, &
     -0.43751879768235861761962323575309D+00, &
     -0.48056445088740205085548935531431D+00, &
     -0.48038610507302961545832372554540D+00, &
     -0.41788380954447150618204025259598D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.36944533995870546586326908358313D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.72247744117483068359801481921580D-01, &
     -0.23245589269716346191888401881117D+00/
  data ys / &
     -0.49852320663764975836658715881651D-01, &
     -0.20374579426251387086718546231968D+00, &
     -0.38976656878879817546660173662947D+00, &
     -0.51725511617300734515148746244054D+00, &
     -0.13890333151925469882109904912617D+00, &
     -0.57319686228940163286673996687428D+00, &
     -0.54414549714157621787319018880544D+00, &
     -0.98677996812038879657787374589079D-01, &
     -0.57450768223436031703493865457993D+00, &
     -0.48499178896207101508248204799370D+00, &
     -0.54041966741780855485936015475384D+00, &
     -0.43371331113028682857825644993170D+00, &
      0.98700017550217162316302585294308D+00, &
      0.87701971609267538163224358348922D+00, &
     -0.53696054670467352362246242651342D+00, &
     -0.33709214277689455129828382991245D+00, &
     -0.50491682572683646092981172306082D+00, &
     -0.46179620632104391793324280621199D+00, &
     -0.55909334619049486411241922583373D+00, &
     -0.55942830548805619506092139545342D+00, &
     -0.48419731762996786439303530812544D+00, &
     -0.45652178474401761799466199325239D+00, &
     -0.55049949314164685016946873588734D+00, &
     -0.50872207349408828698853958022725D+00, &
     -0.55689353511683902690020296113291D+00, &
     -0.51622984675368820169968858727220D+00, &
     -0.46526044009365978341053361548518D+00, &
     -0.55929784568894692081450974794614D+00, &
     -0.18399301337776744727308882527111D+00, &
     -0.50260381043912900882119219273873D+00, &
     -0.49252317057731876434255148922154D+00, &
     -0.56097451023259417695151253611004D+00, &
     -0.57406923516192628548625680508365D+00, &
      0.11141547030632238086479160754135D+01, &
     -0.55651660365661076171303549417789D+00, &
     -0.57405163423686233358717892168751D+00, &
     -0.53196149015755170375584796642517D+00, &
     -0.41372183327215987269752027182733D+00, &
     -0.41051333470792190295409628981832D+00, &
     -0.48470232197639096590316447145498D+00, &
     -0.43960983180755192818725222543803D+00, &
     -0.55824444146228311378010225156953D+00, &
     -0.55624309454314381245877434541105D+00, &
      0.22685299762337478108310204018125D+00, &
     -0.57369006779153222884968212905112D+00, &
     -0.53020559443910391226024877057732D+00, &
     -0.53187309456333599368352110014477D+00, &
     -0.46914022619776744572721261875474D+00, &
     -0.27636104453730623282084492698214D+00, &
     -0.57380107877191676765658650529341D+00, &
     -0.54463175727474219404497175590015D+00, &
     -0.43425004501953381185987824757432D+00, &
     -0.57340126819590793499251738305266D+00, &
     -0.56908448605073339254550804081805D+00, &
     -0.37608188392552828091032473401365D+00, &
     -0.42921616619109235112346077631242D+00, &
     -0.52577535892830112703001792903022D+00, &
     -0.49030858978345230828266827255943D+00, &
     -0.20270732080067755549950587581872D+00, &
      0.41636790443295163120820765376968D+00, &
     -0.57333501569761494464853713844014D+00, &
     -0.34742627962761774860725212273245D+00, &
     -0.56621285723554951319184951691942D+00, &
     -0.34679505484408231261353167027046D+00, &
      0.60078752240377683267001545331127D+00, &
      0.10574851563475822963976796065719D+01, &
     -0.28592841602633954760583222174030D+00, &
     -0.57323206949747451195434362599767D+00, &
     -0.26683655423740594471342520417422D+00, &
     -0.52805029804391126423728142010436D+00, &
     -0.57349391506508209544925398288834D+00, &
     -0.36887306566949226352897864054757D+00, &
     -0.29271463211375329134525196252490D+00, &
      0.78041430345998157811281878081512D+00, &
     -0.36277089606217184970553665226938D+00, &
     -0.56756638958566119435478459622114D+00, &
     -0.57707312306547335610792852443827D+00, &
     -0.57716232573911703125929908613260D+00/
  data ws / &
      0.28724228383926440358132669094431D-02, &
      0.48957050616893594998704796075844D-02, &
      0.39911404555441563247326888994291D-02, &
      0.24308030008482638440637786996581D-02, &
      0.26118640649911296596022610648512D-02, &
      0.31286906542800058837727462589604D-04, &
      0.20332915152781863944904896111764D-02, &
      0.66223356940445958324045825592685D-02, &
      0.51160504059193445246422419150521D-03, &
      0.30177173547108975416398128210504D-02, &
      0.11990187952425307052673011943937D-02, &
      0.42890959944533322728503697326550D-02, &
      0.79717712193663934454694268352422D-03, &
      0.12706395119960644037665264677177D-02, &
      0.17101518366924235948036417308251D-02, &
      0.53225083732062422101624101122955D-02, &
      0.17372337371711722394712009961994D-02, &
      0.21611199292316263486466123355414D-02, &
      0.11377184875874711922363652238389D-02, &
      0.16661121086858607539082516065793D-02, &
      0.36094495784172349233648222679572D-02, &
      0.27840329081828913602050362052188D-02, &
      0.21361914923668763800444433760586D-02, &
      0.33445043203334672620049150278461D-02, &
      0.81943436438923681400473901191879D-03, &
      0.34768574704553087820389981511291D-02, &
      0.42973989829883201728563607299665D-02, &
      0.10074738530685819860190968486265D-02, &
      0.67963853132839489825520666772776D-02, &
      0.24418950258761731688970926384011D-02, &
      0.30003987104228644513285637413249D-02, &
      0.13513377123312761519271287419019D-02, &
      0.43804618210474632627816499919792D-03, &
      0.21250973370504179328882832139026D-03, &
      0.16000160750664913858277795560230D-02, &
      0.77557764662015942773935106392613D-03, &
      0.22824221568478339384080338386456D-02, &
      0.53299353429123467214358800295839D-02, &
      0.56252060523420948976026938340142D-02, &
      0.37291069649491200558250666737351D-02, &
      0.36110603880506100367942684638801D-02, &
      0.62253124627782549500409494910883D-03, &
      0.18073877946168386060665209809962D-02, &
      0.35738294519148201788176936416809D-02, &
      0.55709543451833858845707308928538D-03, &
      0.14035418542487990820244339057528D-02, &
      0.18193421280631652518829218910697D-02, &
      0.48148722968830507266694307528103D-02, &
      0.68567519968462246935420491727088D-02, &
      0.27283604140411874997242863942056D-03, &
      0.25772891742822183465897792887364D-02, &
      0.42231795512038431505510095354369D-02, &
      0.41379361426485253173206620037588D-03, &
      0.14194049785849893147037237210493D-02, &
      0.47384283794563909094585996951638D-02, &
      0.48183988814673540748933494366651D-02, &
      0.28449733997703946018961571694460D-02, &
      0.23703233612168300918965933073201D-02, &
      0.71693912212143004097243510739388D-02, &
      0.33905755163797439812159959659759D-02, &
      0.18396767112155352948407062614303D-03, &
      0.32855821621882024772752035184439D-02, &
      0.15742892940985067189187325607995D-02, &
      0.65179431778550066437367125243887D-02, &
      0.27923790445661769025995748763738D-02, &
      0.58407401612327712992571037001792D-03, &
      0.66530250807598734354239162260138D-02, &
      0.79700265904184871610937261087522D-03, &
      0.70512484634479567571833106295500D-02, &
      0.31132194356885414154457811749791D-02, &
      0.83725477449697097193875164230539D-03, &
      0.54179864271945087535990988436145D-02, &
      0.62428841652845444519001502321154D-02, &
      0.20885623095275804800293379629396D-02, &
      0.60569245588953023785142088907429D-02, &
      0.85221050803831089796247049975189D-03, &
      0.30928913568865192645879463322352D-03, &
      0.31569151523254203691074928546368D-03/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule49 ( x, y, w )

!*****************************************************************************80
!
!! RULE49 returns the rule of degree 49.
!
!  Discussion:
!
!    Order 49 (435 pts)
!    1/6 data for 49-th order quadrature with 82 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 82 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
     -0.61057213632871754777556178617093D+00, &
     -0.21740746844089577030217736555995D+00, &
     -0.74657702398083537596708720880628D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.18652159062065316394708803878930D+00, &
     -0.88761825157466116267033225250300D-01, &
      0.00000000000000000000000000000000D+00, &
     -0.48639838036980400557648362218933D+00, &
     -0.37022598751812238568894342780029D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.55660589033253986016354022616185D+00, &
     -0.23093959523489028823297605424361D+00, &
     -0.12830890012394010891659450444936D+00, &
     -0.63417236502579470761226709395580D+00, &
     -0.36128311243234453339020706484578D+00, &
     -0.24458985250678919382029730465663D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.76440468282859730372500804391987D+00, &
     -0.43881396034292203335647632860058D+00, &
     -0.29031421623299546923298899864555D+00, &
     -0.11022106138867966101881171838643D+00, &
     -0.82697827385445359866410833664403D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.22649962118473459738073399292893D+00, &
     -0.34409570678022498852315838982214D+00, &
     -0.75185639971866986636651769262636D+00, &
     -0.53461908075309836850101213437195D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.67842852868361945529379240804657D+00, &
     -0.98128049170705739598259613001700D-01, &
     -0.81198101881640100102568599136862D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.38816954030832809949204934487173D+00, &
     -0.51214253977457617025282281965566D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.89378361429922217289759901811815D+00, &
     -0.20438937977062137351398598793386D+00, &
     -0.29077462427214531822794640367537D+00, &
     -0.45530327016209634617378737911148D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.50049811961058966626537547990924D+00, &
     -0.59653316717651885600358396085261D+00, &
     -0.18241222915476293063943966605377D+00, &
     -0.17504275018488792290118428567192D+00, &
     -0.87027029250770403203069802318185D+00, &
     -0.25906638561252602666842654816923D+00, &
     -0.25389417516222969869856982682409D+00, &
     -0.63924734492284199961203241117988D-01, &
     -0.32336677856616207857128015137548D+00, &
     -0.45933867955078441295151086540347D+00, &
     -0.73910550014397140051390907061818D+00, &
     -0.11606977913379114755850687691385D+00, &
     -0.65577583679224655444244929369890D+00, &
     -0.83552616064107205337213906126893D+00, &
     -0.67748842104198500405815554991182D+00, &
     -0.37231932331276101094567014835110D+00, &
     -0.93676060044306703638748111096616D+00, &
     -0.66619173394165069756523303173151D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.80515347766473982936691157759254D+00, &
     -0.94025356560109772303978498971830D+00, &
     -0.55800138185704783040837528977761D+00, &
     -0.33515583932564482010856277294034D+00, &
     -0.72304850966873315163769622529180D+00, &
     -0.46826261407944706264024812254397D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.11247883641677583766316101770443D+00, &
     -0.41172923406071229009367773338534D+00, &
     -0.89091288563351724918827721227521D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.70999559860544022018934170422900D-01, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.13798316432331004899182819510688D+00, &
     -0.57133871576000905289179002614761D+00, &
     -0.97448997895894366957466437859893D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.58709342896187276256324804582086D+00/
  data ys / &
     -0.50805411191391851523789864972562D+00, &
     -0.56234652242839114914654701128374D+00, &
     -0.57509668203848429431038797517268D+00, &
      0.53679828476119178289324025007759D+00, &
     -0.15190921808712561549658969393441D+00, &
     -0.14305301576398435281760117117876D+00, &
      0.90237311257497758569938319452643D+00, &
     -0.57473532714413321696267840291545D+00, &
     -0.38858551748024275977250958169595D+00, &
     -0.33135871726650782696587314579878D+00, &
     -0.40073527072101794974371578083120D+00, &
     -0.54310366079605492812547381587275D+00, &
     -0.57500475146778529513914433479050D+00, &
     -0.42554839571165244196875402232376D+00, &
     -0.44153050231697094128484412680053D+00, &
     -0.46866793891867074878457016677705D+00, &
     -0.16570704844176947394320757260228D+00, &
     -0.56504278301868705651681263115196D+00, &
     -0.50652589028067622329647801023762D+00, &
     -0.52106748079988378853417843443633D+00, &
     -0.56223112097793733954156361308556D+00, &
     -0.57462270717388530892162623588585D+00, &
      0.45932243496595672349082629601422D+00, &
     -0.22828624984036516968491608086478D+00, &
     -0.48829139755087173802506438507515D+00, &
     -0.54439150942275613023935368560183D+00, &
     -0.50670327829951912727787293959844D+00, &
      0.99438807073001743653229293189603D+00, &
      0.12536668432105287250159280886041D+00, &
     -0.52796151262664728760570958076544D+00, &
     -0.31111906291100543384916079312981D+00, &
     -0.53473260414787373087982349525345D+00, &
      0.11171423268477136498973199720050D+01, &
     -0.53658558406526073583077834124086D+00, &
     -0.33881791091529569834478815622842D+00, &
      0.79840597283762599147168675735209D+00, &
     -0.55834047448625304405740354168855D+00, &
     -0.29941559804457568276715427694835D+00, &
     -0.34707538263885206082450977546688D+00, &
     -0.56218624883920679775484228539619D+00, &
     -0.52252588465952329020710730711399D+00, &
     -0.54142101949433652578422629700355D+00, &
     -0.54312444348452881138890792354339D+00, &
     -0.50297724458337249430337647089853D+00, &
     -0.37315461111231110867297450418990D+00, &
     -0.53339994853211595567498621491810D+00, &
     -0.41535262741815023278680392917739D+00, &
     -0.57390850498838587799366720382219D+00, &
     -0.38909332692463915420277441179215D+00, &
     -0.27441054007776771321877791597838D+00, &
     -0.46136190485467458900510307928511D+00, &
     -0.50637232744855604509324845495701D+00, &
     -0.53497319519919178836708838160351D+00, &
     -0.47916361999904640273373623874426D+00, &
     -0.56063167758821432142013730704571D+00, &
     -0.55812525411705885484285303911831D+00, &
     -0.57393107655513157172595640909445D+00, &
     -0.55819574918551185878858176169832D+00, &
     -0.57308501713419226805469571310331D+00, &
     -0.55400636586589158164274508913012D+00, &
     -0.49699174948588019440752603403060D+00, &
     -0.57375002851113489476058869278243D+00, &
     -0.45895888627009702143807907926916D+00, &
     -0.55885836769979743482431579044375D+00, &
     -0.45754555590751383576718554173853D+00, &
     -0.40298677651135379575927050935698D+00, &
     -0.25079797310498966721630314170512D+00, &
     -0.22883057799614009961932750289238D+00, &
     -0.32888195428957532835127033424983D+00, &
     -0.57366938316409890583305452094740D+00, &
      0.70290670754518056713385541693329D+00, &
     -0.48828388229492647796479685307693D+00, &
     -0.44375651708543360206049930519612D+00, &
      0.10591815381653453969290932401725D+01, &
      0.35157474889658538587578359215421D+00, &
     -0.63699436116132156076951185465648D-01, &
      0.11470364861459781695524661983521D+01, &
     -0.44198593821724404560352142656255D+00, &
     -0.56609726595635302503750770819831D+00, &
     -0.57372975226826569608034581860957D+00, &
     -0.57315719828247563816289202130035D+00, &
     -0.57710801847006901827791738420396D+00/
  data ws / &
      0.19977337356156323426514692597692D-02, &
      0.12687431336688509410843998391028D-02, &
      0.37027790592768656352817137656994D-03, &
      0.21253790361811728001071706475289D-02, &
      0.61674141211813126477419858184194D-02, &
      0.59458894649162451804820476952354D-02, &
      0.10391008318227642432772429159470D-02, &
      0.56119170151050531358685160135421D-03, &
      0.42730773131837205407382425934036D-02, &
      0.25866812740239429576418384733441D-02, &
      0.35683371351746158116269879423198D-02, &
      0.21488306719133579150142490513559D-02, &
      0.63043916628928240061101412753203D-03, &
      0.34221501813368796618088746749049D-02, &
      0.40453583847800237927752889872429D-02, &
      0.39321920602677497806251470735232D-02, &
      0.32874602491734720571848038384576D-02, &
      0.91150147690764261925763826535926D-03, &
      0.29798409559495009891833524489293D-02, &
      0.28537247963181996687266646898085D-02, &
      0.16586934600140952309818245115017D-02, &
      0.39735960174484489743453114770676D-03, &
      0.26834215475038735697529994323634D-02, &
      0.60034335233209257724964806936636D-02, &
      0.34785715040962553678932832030749D-02, &
      0.14890850096270047389519178852968D-02, &
      0.27754331998416555843944854095898D-02, &
      0.77107891245567947444663501212492D-03, &
      0.33454955156733941459045360333934D-02, &
      0.20541529314760399047675461654284D-02, &
      0.60945428068954117127542229222828D-02, &
      0.15330127901593561414098039723028D-02, &
      0.19148445202446191652573211720709D-03, &
      0.25108686300732809342950959448632D-02, &
      0.47651564692312408698835096361491D-02, &
      0.16240239076313059324667223643076D-02, &
      0.79583774233079393748085634291181D-03, &
      0.58849276406227123448983694298859D-02, &
      0.56877909758060890782274443197947D-02, &
      0.15575024842219775881243735068023D-02, &
      0.16105816942358188547189746892777D-02, &
      0.22502840437046037026372796523992D-02, &
      0.20084168279399749118935611766491D-02, &
      0.36230228738241653515806389685717D-02, &
      0.57423299789474669137183051012294D-02, &
      0.12717030464342037309770710927106D-02, &
      0.49768031950563028511667619620966D-02, &
      0.79434188752183035723354695167328D-03, &
      0.56001107097121521065256828080448D-02, &
      0.63817130650436342049602870849597D-02, &
      0.39817711545630631406587510631784D-02, &
      0.24087654021930613127612933755615D-02, &
      0.30418302126603186311999594057584D-02, &
      0.30238355103351015420463768411162D-02, &
      0.10183025304896036412292516963758D-02, &
      0.14596718890771209157014286627469D-02, &
      0.77875785285251059052497877539906D-03, &
      0.61372358148713085688282377971969D-03, &
      0.66600519529457007903113678794478D-03, &
      0.11077863336612002623045984707220D-02, &
      0.20349205397800009217113402131491D-02, &
      0.29455943798576609790138160596699D-03, &
      0.38905584979980386058934940581983D-02, &
      0.18807248411144958164960089336880D-02, &
      0.28241228846436807197405817934160D-02, &
      0.47178192432261121880126220071801D-02, &
      0.35306465870984426703979784223797D-02, &
      0.71762038572211377060639788033076D-02, &
      0.57665964607857117382384704479685D-02, &
      0.40426442422356089657524686097409D-03, &
      0.23026478604784709918110573713097D-02, &
      0.42616806207016132242718913366787D-02, &
      0.26058395691911076244778888792290D-02, &
      0.54745447246951839739615843265097D-03, &
      0.35299796865257136122691199548024D-02, &
      0.40316437640725431828744499609816D-02, &
      0.42516711921106531477513916666353D-04, &
      0.54029876938551540928891230894040D-02, &
      0.14060391641463104982472631429696D-02, &
      0.18730351088069459968645316638647D-03, &
      0.51889848051624996463295221022567D-03, &
      0.21130683065318872697498930840672D-03/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine rule50 ( x, y, w )

!*****************************************************************************80
!
!! RULE50 returns the rule of degree 50.
!
!  Discussion:
!
!    Order 50 (453 pts)
!    1/6 data for 50-th order quadrature with 84 nodes.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) X(*), Y(*), the coordinates of the nodes.
!
!    Output, real ( kind = 8 ) W(*), the weights.
!
  implicit none

  integer ( kind = 4 ) n
  parameter ( n = 84 )

  real ( kind = 8 ) w(n)
  real ( kind = 8 ) ws(n)
  real ( kind = 8 ) x(n)
  real ( kind = 8 ) xs(n)
  real ( kind = 8 ) y(n)
  real ( kind = 8 ) ys(n)

  save xs
  save ys
  save ws

  data xs / &
      0.00000000000000000000000000000000D+00, &
     -0.11243137017724544706384538604138D+00, &
     -0.92568822098610615625930541796974D+00, &
     -0.29692106117972817002503164575225D+00, &
     -0.70777454997646828139185546400833D+00, &
     -0.90907207527032819051622115148967D+00, &
     -0.17776222920358422699613435141006D+00, &
     -0.63358007216059497217331539880521D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.48639150346057012854861946724002D+00, &
     -0.67960972311168179219672603013974D+00, &
     -0.80987858028162034515744403376905D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.10197291667485080764243827190062D+00, &
     -0.63905313551409030298179847776955D+00, &
     -0.54848856966069179497342801711918D+00, &
     -0.28743291564930093738030476563064D+00, &
     -0.25853575380565982943550456940571D+00, &
     -0.85293311497853524347068807827847D+00, &
     -0.69117532096345247573444072455055D-01, &
      0.00000000000000000000000000000000D+00, &
     -0.56115415639613667473122134344096D-01, &
     -0.24397413927543615902606748562471D+00, &
     -0.27325078883205130181299635420966D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.16627205471955132096796330738419D+00, &
     -0.93789271474578126741505762079105D+00, &
     -0.11930506754016075016780500019251D+00, &
     -0.90151108565688587759737165100797D+00, &
     -0.32049535943729789391066639033515D+00, &
     -0.59104204439569195659289399130103D+00, &
     -0.21751462540323724688100842714558D+00, &
     -0.15800907798262943177922632788479D+00, &
     -0.34192996428318888182680259909761D+00, &
     -0.50348314662449992878796511382845D+00, &
     -0.72296664168698516928824798397709D+00, &
     -0.83410412765541264189179663045556D+00, &
     -0.45220969294953177503238310311635D+00, &
     -0.89091508745388259553341479950777D+00, &
     -0.43793566633133321281524272450307D+00, &
     -0.54799008713988301043149151643902D+00, &
     -0.20885455826291604847376889739060D+00, &
     -0.19653261626463977858040946368613D+00, &
     -0.34026425560719830519871252095558D+00, &
     -0.30334121141262021200705945773916D+00, &
     -0.49535294281864462436231396682347D+00, &
     -0.54967499236570302852186466340436D-01, &
     -0.79641981144983823490340768373671D+00, &
     -0.77252621434083133665996549756551D+00, &
     -0.22122265719250289382440633768970D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.63310729924221124505794362578563D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.38407586571187361708454487843458D+00, &
     -0.53170841252843484837013141905012D+00, &
     -0.17511720551530423320716712387413D+00, &
     -0.30063413976092480084347753701585D+00, &
     -0.10868692205689496593149118515046D+00, &
     -0.41113970829952388068679218228879D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.69178376289359713732790198931403D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.97953562628985148065013964889033D+00, &
     -0.95090315064315556393142498648752D+00, &
     -0.11195104828353529165299273055927D+00, &
     -0.39218251627345475097146235231760D+00, &
     -0.48703846544346851999956533815843D+00, &
     -0.74320583688319031979489348519293D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.69393567486204502934677097789401D+00, &
     -0.59416809204083916290436093693814D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.59168695264172826158307513888901D+00, &
     -0.42226270556224588488343911175678D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.77777971180155417861382042517561D+00, &
      0.00000000000000000000000000000000D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.37473331227815313999612621965198D+00, &
      0.00000000000000000000000000000000D+00, &
     -0.77988920685466297897759157424588D-01, &
      0.00000000000000000000000000000000D+00, &
     -0.84965569809328811423376218283034D+00/
  data ys / &
      0.26665777797796383627973623253967D+00, &
     -0.57575252834615965036824127302641D+00, &
     -0.53848652830351311098524847745854D+00, &
     -0.19146540832960751941458046699634D+00, &
     -0.53730488391129554992245069202693D+00, &
     -0.57586628305377182252547466076703D+00, &
     -0.56902146444580641033160663668216D+00, &
     -0.53665917816023464212621359008944D+00, &
      0.11490520500034347586508846660531D+01, &
     -0.41558253110498620541881452613918D+00, &
     -0.50495637092434172779930285170762D+00, &
     -0.49186089726616651601947223505482D+00, &
     -0.54384156132974709175980042825510D+00, &
     -0.31266847173129537509553966714426D+00, &
     -0.46456703619309813450876313794865D+00, &
     -0.53671264515430239685282775620237D+00, &
     -0.48722771965406562202415837416678D+00, &
     -0.57476168616596147470350970491546D+00, &
     -0.55648988758506322732625931002792D+00, &
     -0.47916934061220515500684077992539D+00, &
     -0.30918435458414123508211511701385D+00, &
     -0.37840666740342688089437456064073D+00, &
     -0.52319798442392801521139581532973D+00, &
     -0.40025389355433590091307180243175D+00, &
     -0.51006243855179098239070640229809D+00, &
     -0.49360682183497845303635246898716D+00, &
     -0.56006513490944252779041221120332D+00, &
     -0.43200879236359204554404676070914D+00, &
     -0.56569680324298668363410710315288D+00, &
     -0.27024376159027951510165751092348D+00, &
     -0.50341926055772996189589528959240D+00, &
     -0.44849821522859359956466291790167D+00, &
     -0.15547647645906741636976279609852D+00, &
     -0.44503618911963343982519208289006D+00, &
     -0.36218696833371919155331150775928D+00, &
     -0.56041252984416499585686185156419D+00, &
     -0.52895122351604286441157165271526D+00, &
     -0.53438108768101891752999282805610D+00, &
     -0.54075896308780913586275538622291D+00, &
     -0.45931123138039248803011481724000D+00, &
     -0.45819330231577922836160500737553D+00, &
     -0.30653810287769073602767881586011D+00, &
     -0.55000331539356022007925762637213D+00, &
     -0.53673989933539527787145346842252D+00, &
     -0.34191292599382455707842137133247D+00, &
     -0.49993522428841323273059831641668D+00, &
     -0.15116834147609688134917263547298D+00, &
     -0.55870738754201772527722045828665D+00, &
     -0.53093517049471556661138723835977D+00, &
     -0.23111044337275539896270189389374D+00, &
     -0.43735474019364034368275094309953D+00, &
     -0.56061901718698357069687788950861D+00, &
      0.76210269896315505375472989314401D+00, &
     -0.50180464055963906570282323273135D+00, &
     -0.56066404582769439179312259695008D+00, &
     -0.37564082456563228243592800723225D+00, &
     -0.56093583647028840530479402530989D+00, &
     -0.52891066884917480700076516219948D+00, &
     -0.32227834482125130031233025928199D+00, &
      0.11168066855539393695052411427936D+01, &
     -0.57411035226075729901604357841345D+00, &
      0.88226154891869896377217079959897D+00, &
     -0.57376987737405061910707525396861D+00, &
     -0.57387511563190780439997792525620D+00, &
     -0.23684295020028737262235915750548D+00, &
     -0.39119141236066998475482225138722D+00, &
     -0.57412552079576272088571038657122D+00, &
     -0.49038868751056796001858236250926D+00, &
      0.56490646899011486213357544715935D+00, &
     -0.44034718635067890842582839203872D+00, &
     -0.57418257398341738868103015579407D+00, &
      0.46314994945504571565754224755338D+00, &
     -0.40847798164087445421263923221521D+00, &
     -0.55956030132080839871226342430982D+00, &
     -0.23325735799867068880579964798512D+00, &
      0.66759979014975408805793640512288D+00, &
     -0.57398131471203676458813819810279D+00, &
     -0.61858570316929177810688167413239D-01, &
      0.10083409893504061073884069251960D+01, &
     -0.57386414467099150410234406203086D+00, &
     -0.57279115920674012280479926283406D+00, &
     -0.56023791168005362040639295690520D+00, &
      0.12766415047174134768367989248219D+00, &
     -0.57349445987280550794758489384318D+00/
  data ws / &
      0.21904046082402179331777860407172D-02, &
      0.45710956467466776333595601564413D-03, &
      0.39488814170737652484817523330772D-03, &
      0.35934111950642942202851471876703D-02, &
      0.14910742851108025176218601254730D-02, &
      0.17967284713619579793465412642966D-03, &
      0.10125558476824481605944822924240D-02, &
      0.17069127169250074598843709053414D-02, &
      0.24079695740395151054526221911175D-04, &
      0.36927130629621416994224679037866D-02, &
      0.22489391525853586565409506926398D-02, &
      0.19524312574849497675486111229175D-02, &
      0.10866799154497416799396832774298D-02, &
      0.55988347396351114436180639136753D-02, &
      0.28924669217577866067492578922788D-02, &
      0.20380484585475350431644792897213D-02, &
      0.34261098541603004157722338638113D-02, &
      0.61351457019749324652202710478653D-03, &
      0.86542020701437739404493838669357D-03, &
      0.36671947134331494740326630077914D-02, &
      0.28026432284100394242484806225548D-02, &
      0.54349341984383407453878533427381D-02, &
      0.28351957640421590232032942807150D-02, &
      0.45746103628843216234268299714345D-02, &
      0.15952659260343677779327391072587D-02, &
      0.35621046832988029971593531686097D-02, &
      0.50771409433251890919140609918512D-03, &
      0.45268556007289308320192321203838D-02, &
      0.57647586887781341017507334442447D-03, &
      0.57986412207422415390596586269670D-02, &
      0.26551803851187666770994169697277D-02, &
      0.42618143181478615021232589520584D-02, &
      0.61410787717774668691311895702589D-02, &
      0.41577749997957744966853239679784D-02, &
      0.45714943165212042708880269013658D-02, &
      0.11784033012900141932339284269968D-02, &
      0.14219896538536742581747920401589D-02, &
      0.23860085586204575770728358003760D-02, &
      0.10070034152583604416622993805894D-02, &
      0.37609206282914322618831855234874D-02, &
      0.34952452756601121036043544579388D-02, &
      0.58926392977540359306346878698652D-02, &
      0.21761510975303425549110319628113D-02, &
      0.25597503150258418017093231009733D-02, &
      0.53360452230413602215172989866309D-02, &
      0.30890849879669851554048232262039D-02, &
      0.71328535685235871693729072620986D-02, &
      0.10810483517258989817564835528970D-02, &
      0.17544886347878652397548372765366D-02, &
      0.61494904649466669709635349908104D-02, &
      0.23575565603961950228417434213703D-02, &
      0.13783891229758136398436483499410D-02, &
      0.18290788738495703825316717211575D-02, &
      0.33652181243651173378348463861955D-02, &
      0.15184413550438083995525042414313D-02, &
      0.55587775921145309411995749989960D-02, &
      0.17601404353050383171865064267571D-02, &
      0.31341293249895626259540265265832D-02, &
      0.56365508134121191078584408821979D-02, &
      0.19737963916342285028504669269696D-03, &
      0.57998586649655338308131100175788D-03, &
      0.13607360815822191768414153771193D-02, &
      0.15219771844702045466850220251726D-03, &
      0.24008493579443378017998981782239D-03, &
      0.67581925200909458799817643884140D-02, &
      0.51393423392662772922503829588641D-02, &
      0.69517340368258314203719954545839D-03, &
      0.24993080895095462395459033935751D-02, &
      0.26503828818360718009873158711194D-02, &
      0.30717948054284111140681604233590D-02, &
      0.63523033610323033970102101013160D-03, &
      0.30076725635797333204424140098894D-02, &
      0.42759500648291081429579191318110D-02, &
      0.17369109423123418439135661109544D-02, &
      0.33989953518860807286401877670786D-02, &
      0.22934322638873487811005284243824D-02, &
      0.52212507063839734314031356362762D-03, &
      0.38540006507433082413851188895204D-02, &
      0.78895266863538848229357197934055D-03, &
      0.77068430988334312857080924995683D-03, &
      0.49308164137002449756423311284903D-03, &
      0.18435234238175567747584066472141D-02, &
      0.37992680605946786583823819678412D-02, &
      0.48761272444903304947626163241666D-03/

  x(1:n) = xs(1:n)
  y(1:n) = ys(1:n)
  w(1:n) = ws(1:n)

  return
end
subroutine simplex_to_triangle ( tvert1, tvert2, tvert3, s, t )

!*****************************************************************************80
!
!! SIMPLEX_TO_TRIANGLE maps points from the simplex to a triangle.
!
!  Discussion:
!
!    The simplex has vertices:
!
!      (  0, 0 )
!      (  1, 0 )
!      (  0, 1 )
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, real ( kind = 8 ) TVERT1(2), TVERT2(2), TVERT3(2), the coordinates
!    of the vertices of the triangle.  These vertices will be taken
!    to be the images of (0,0), (1,0) and (0,1) respectively.
!
!    Input, real ( kind = 8 ) S(2), the coordinates of the point in the simplex.
!
!    Output, real ( kind = 8 ) T(2), the coordinates of the point in
!    the triangle.
!
  implicit none

  integer ( kind = 4 ) n

  integer ( kind = 4 ) i
  real ( kind = 8 ) s(2)
  real ( kind = 8 ) t(2)
  real ( kind = 8 ) tvert1(2)
  real ( kind = 8 ) tvert2(2)
  real ( kind = 8 ) tvert3(2)

  do i = 1, 2
    t(i) = tvert1(i) * ( 1.0D+00 - s(1) - s(2) ) &
         + tvert2(i) * s(1) &
         + tvert3(i) * s(2)
  end do

  return
end
subroutine timestamp ( )

!*****************************************************************************80
!
!! TIMESTAMP prints out the current YMDHMS date as a timestamp.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    12 January 2007
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    None
!
  implicit none

  character * ( 8 ) ampm
  integer ( kind = 4 ) d
  character * ( 8 ) date
  integer ( kind = 4 ) h
  integer ( kind = 4 ) m
  integer ( kind = 4 ) mm
  character * ( 9 ) month(12)
  integer ( kind = 4 ) n
  integer ( kind = 4 ) s
  character * ( 10 ) time
  integer ( kind = 4 ) y

  save month

  data month / &
    'January  ', 'February ', 'March    ', 'April    ', &
    'May      ', 'June     ', 'July     ', 'August   ', &
    'September', 'October  ', 'November ', 'December ' /

  call date_and_time ( date, time )

  read ( date, '(i4,i2,i2)' ) y, m, d
  read ( time, '(i2,i2,i2,1x,i3)' ) h, n, s, mm

  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, month(m), y, h, ':', n, ':', s, '.', mm, ampm

  return
end
function triangle_area ( vert1, vert2, vert3 )

!*****************************************************************************80
!
!! TRIANGLE_AREA returns the area of a triangle.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, real ( kind = 8 ) VERT1(2), VERT2(2), VERT3(2), the vertices of
!    the triangle.
!
!    Output, real ( kind = 8 ) TRIANGLE_AREA, the area of the triangle.
!
  real ( kind = 8 ) triangle_area
  real ( kind = 8 ) vert1(2)
  real ( kind = 8 ) vert2(2)
  real ( kind = 8 ) vert3(2)

  triangle_area = 0.5D+00 * &
    ( &
        ( vert2(1) - vert1(1) ) * ( vert3(2) - vert1(2) ) &
      - ( vert3(1) - vert1(1) ) * ( vert2(2) - vert1(2) ) &
    )

  return
end
subroutine triangle_to_ref ( tvert1, tvert2, tvert3, t, r )

!*****************************************************************************80
!
!! TRIANGLE_TO_REF maps points from any triangle to the reference triangle.
!
!  Discussion:
!
!    The reference triangle has vertices:
!
!      ( -1, -1/sqrt(3) )
!      ( +1, -1/sqrt(3) )
!      (  0, +2/sqrt(3) )
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, real ( kind = 8 ) TVERT1(2), TVERT2(2), TVERT3(2), the coordinates
!    of the vertices of the triangle.  These vertices will be taken
!    to be the images of (0,0), (1,0) and (0,1) respectively.
!
!    Input, real ( kind = 8 ) T(2), the coordinates of a point in the triangle.
!
!    Output, real ( kind = 8 ) R(2), the coordinates of a point in the
!    reference triangle.
!
  implicit none

  real ( kind = 8 ) r(2)
  real ( kind = 8 ) rvert1(2)
  real ( kind = 8 ) rvert2(2)
  real ( kind = 8 ) rvert3(2)
  real ( kind = 8 ) s(2)
  real ( kind = 8 ) t(2)
  real ( kind = 8 ) tvert1(2)
  real ( kind = 8 ) tvert2(2)
  real ( kind = 8 ) tvert3(2)

  call triangle_to_simplex ( tvert1, tvert2, tvert3, t, s )

  rvert1(1) = - 1.0D+00
  rvert1(2) = - 1.0D+00 / sqrt ( 3.0D+00 )
  rvert2(1) = + 1.0D+00
  rvert2(2) = - 1.0D+00 / sqrt ( 3.0D+00 )
  rvert3(1) =   0.0D+00
  rvert3(2) =   2.0D+00 / sqrt ( 3.0D+00 )

  call simplex_to_triangle ( rvert1, rvert2, rvert3, s, r )

  return
end
subroutine triangle_to_simplex ( tvert1, tvert2, tvert3, t, s )

!*****************************************************************************80
!
!! TRIANGLE_TO_SIMPLEX maps points from any triangle to the simplex.
!
!  Discussion:
!
!    The simplex has vertices:
!
!      (  0, 0 )
!      (  1, 0 )
!      (  0, 1 )
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, real ( kind = 8 ) TVERT1(2), TVERT2(2), TVERT3(2), the coordinates
!    of the vertices of the triangle.  These vertices will be taken
!    to be the images of (0,0), (1,0) and (0,1) respectively.
!
!    Input, real ( kind = 8 ) T(2), the coordinates of a point in the triangle.
!
!    Output, real ( kind = 8 ) S(2), the coordinates of the
!    point in the simplex.
!
  implicit none

  integer ( kind = 4 ) j
  real ( kind = 8 ) s(2)
  real ( kind = 8 ) t(2)
  real ( kind = 8 ) tvert1(2)
  real ( kind = 8 ) tvert2(2)
  real ( kind = 8 ) tvert3(2)

  s(1) = ( ( tvert3(2) - tvert1(2) ) * ( t(1)      - tvert1(1) ) &
         - ( tvert3(1) - tvert1(1) ) * ( t(2)      - tvert1(2) ) ) &
       / ( ( tvert3(2) - tvert1(2) ) * ( tvert2(1) - tvert1(1) ) &
         - ( tvert3(1) - tvert1(1) ) * ( tvert2(2) - tvert1(2) ) )

  s(2) = ( ( tvert2(1) - tvert1(1) ) * ( t(2)      - tvert1(2) ) &
         - ( tvert2(2) - tvert1(2) ) * ( t(1)      - tvert1(1) ) ) &
       / ( ( tvert3(2) - tvert1(2) ) * ( tvert2(1) - tvert1(1) ) &
         - ( tvert3(1) - tvert1(1) ) * ( tvert2(2) - tvert1(2) ) )

  return
end
subroutine trianmap ( numnodes, vert1, vert2, vert3, rnodes, whts )

!*****************************************************************************80
!
!! TRIANMAP maps rules from the reference triangle to the user triangle.
!
!  Discussion:
!
!    This routine maps the quadrature nodes on the reference
!    triangle into a user-defined triangle specified by its vertices.
!
!    The weights are rescaled accordingly, so that
!    the resulting quadrature will integrate correctly constants, i.e.
!    the sum of the weights is the area of the user-defined triangle.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) NUMNODES, the number of nodes.
!
!    Input, real ( kind = 8 ) VERT1(2), VERT2(2), VERT3(2), the vertices of
!    the triangle on which the quadrature rule is to be constructed.
!
!    Input/output, real ( kind = 8 ) RNODES(2,NUMNODES), the nodes.
!
!    Input/output, real ( kind = 8 ) WHTS(NUMNODES), the weights.
!
  implicit none

  integer ( kind = 4 ) numnodes

  real ( kind = 8 ) area
  integer ( kind = 4 ) j
  real ( kind = 8 ) rnodes(2,numnodes)
  real ( kind = 8 ) scale
  real ( kind = 8 ) triangle_area
  real ( kind = 8 ) u
  real ( kind = 8 ) v
  real ( kind = 8 ) vert1(2)
  real ( kind = 8 ) vert2(2)
  real ( kind = 8 ) vert3(2)
  real ( kind = 8 ) whts(numnodes)
  real ( kind = 8 ) x
  real ( kind = 8 ) y

  area = abs ( triangle_area ( vert1, vert2, vert3 ) )

  scale = sum ( whts(1:numnodes) )

  scale = area / scale

  do j = 1, numnodes
    call triasimp ( rnodes(1,j), rnodes(2,j), u, v )
    x = ( vert2(1) - vert1(1) ) * u &
      + ( vert3(1) - vert1(1) ) * v + vert1(1)
    y = ( vert2(2) - vert1(2) ) * u &
      + ( vert3(2) - vert1(2) ) * v + vert1(2)
    rnodes(1,j) = x
    rnodes(2,j) = y
    whts(j) = whts(j) * scale
  end do

  return
end
subroutine triasimp ( x, y, uout, vout )

!*****************************************************************************80
!
!! TRIASIMP maps a point from the reference triangle to the simplex.
!
!  Discussion:
!
!    Map the reference triangle with vertices
!      (-1,-1/sqrt(3)), (1,-1/sqrt(3)), (0,2/sqrt(3))
!    to the simplex with vertices
!      (0,0), (1,0), (0,1).
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, real ( kind = 8 ) X, Y, the coordinates of a point in the
!    reference triangle.
!
!    Output, real ( kind = 8 ) UOUT, VOUT, the coordinates of the corresponding
!    point in the simplex.
!
  implicit none

  real ( kind = 8 ) scale
  real ( kind = 8 ) uout
  real ( kind = 8 ) vout
  real ( kind = 8 ) x
  real ( kind = 8 ) y

  scale = 1.0D+00 / sqrt ( 3.0D+00 )

  uout = 0.5D+00 * ( x + 1.0D+00 ) &
    - 0.5D+00 * scale * ( y + scale )

  vout = 1.0D+00 * scale * ( y + scale )

  return
end
subroutine triasymq ( n, vert1, vert2, vert3, rnodes, weights, numnodes )

!*****************************************************************************80
!
!! TRIASYMQ returns a symmetric quadrature formula for a user triangle.
!
!  Discussion:
!
!    This routine constructs (or rather retrieves) a symmetric
!    quadrature formula on the user-defined triangle in the plane
!    specified by its vertices (vert1,vert2,vert3).
!
!    The total number of nodes and weights to be created is numnodes.
!
!      n       1     2     3     4     5     6     7     8     9    10
!     -----------------------------------------------------------------
!    nodes     1     3     6     6     7    12    15    16    19    25
!
!
!      n      11    12    13    14    15    16    17    18    19    20
!     -----------------------------------------------------------------
!    nodes    28    33    37    42    49    55    60    67    73    79
!
!
!      n      21    22    23    24    25    26    27    28    29    30
!     -----------------------------------------------------------------
!    nodes    87    96   103   112   120   130   141   150   159   171
!
!
!      n      31    32    33    34    35    36    37    38    39    40
!     -----------------------------------------------------------------
!    nodes   181   193   204   214   228   243   252   267   282   295
!
!
!      n      41    42    43    44    45    46    47    48    49    50
!     -----------------------------------------------------------------
!    nodes   309   324   339   354   370   385   399   423   435   453
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    26 June 2014
!
!  Author:
!
!    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
!    This FORTRAN90 version by John Burkardt.
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) N, the degree of the quadrature (must not 
!    exceed 50).
!
!    Input, real ( kind = 8 ) VERT1(2), VERT2(2), VERT3(2), the vertices of
!    the triangle on which the quadrature rule is to be constructed.
!
!    Output, real ( kind = 8 ) RNODES(2,NUMNODES), the nodes in the plane
!    (all inside the user-supplied triangle)
!
!    Output, real ( kind = 8 ) WEIGHTS(NUMNODES), the quadrature weights.
!
!    Input, integer ( kind = 4 ) NUMNODES, the number of nodes.
!
  implicit none

  integer ( kind = 4 ) numnodes

  integer ( kind = 4 ) itype
  integer ( kind = 4 ) n
  real ( kind = 8 ) rnodes(2,numnodes)
  real ( kind = 8 ) vert1(2)
  real ( kind = 8 ) vert2(2)
  real ( kind = 8 ) vert3(2)
  real ( kind = 8 ) weights(numnodes)

  itype = 0

  call quaequad ( itype, n, rnodes, weights, numnodes )

  call trianmap ( numnodes, vert1, vert2, vert3, rnodes, weights )

  return
end
subroutine triasymq_gnuplot ( vert1, vert2, vert3, numnodes, rnodes, header )

!*****************************************************************************80
!
!! TRIASYMQ_GNUPLOT: set up a GNUPLOT plot of the triangle quadrature rule.
!
!  Licensing:
!
!    This code is distributed under the GNU GPL license.
!
!  Modified:
!
!    11 July 2014
!
!  Author:
!
!    John Burkardt
!
!  Reference:
!
!    Hong Xiao, Zydrunas Gimbutas,
!    A numerical algorithm for the construction of efficient quadrature
!    rules in two and higher dimensions,
!    Computers and Mathematics with Applications,
!    Volume 59, 2010, pages 663-676.
!
!  Parameters:
!
!    Input, real ( kind = 8 ) VERT1(2), VERT2(2), VERT3(2), the vertices
!    of the triangle.
!
!    Input, real ( kind = 8 ) NUMNODES, the number of nodes.
!
!    Input, real ( kind = 8 ) RNODES(2,NUMNODES), the coordinates of
!    the nodes.
!
!    Input, character * ( * ) HEADER, a string to be used to identify
!    the files created.
!
  implicit none

  integer ( kind = 4 ) numnodes

  character * ( 255 ) command_filename
  integer ( kind = 4 ) command_unit
  character * ( * ) header
  integer ( kind = 4 ) i
  integer ( kind = 4 ) j
  integer ( kind = 4 ) l
  integer ( kind = 4 ) n
  character * ( 255 ) node_filename
  integer ( kind = 4 ) node_unit
  character * ( 255 ) plot_filename
  real ( kind = 8 ) rnodes(2,numnodes)
  real ( kind = 8 ) vert1(2)
  real ( kind = 8 ) vert2(2)
  real ( kind = 8 ) vert3(2)
  character * ( 255 ) vertex_filename
  integer ( kind = 4 ) vertex_unit
!
!  Create the vertex file.
!
  call get_unit ( vertex_unit )
  vertex_filename = trim ( header ) // '_vertices.txt'
  open ( unit = vertex_unit, file = vertex_filename, &
    status = 'replace' )
  write ( vertex_unit, '(g14.6,2x,g14.6)' ) vert1(1), vert1(2)
  write ( vertex_unit, '(g14.6,2x,g14.6)' ) vert2(1), vert2(2)
  write ( vertex_unit, '(g14.6,2x,g14.6)' ) vert3(1), vert3(2)
  write ( vertex_unit, '(g14.6,2x,g14.6)' ) vert1(1), vert1(2)
  close ( unit = vertex_unit )
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  Created vertex file "' // &
    trim ( vertex_filename ) // '".'
!
!  Create node file.
!
  call get_unit ( node_unit )
  node_filename = trim ( header ) // '_nodes.txt'
  open ( unit = node_unit, file = node_filename, &
    status = 'replace' )
  do j = 1, numnodes
    write ( node_unit, '(g14.6,2x,g14.6)' ) rnodes(1:2,j)
  end do
  close ( unit = node_unit )
  write ( *, '(a)' ) '  Created node file "' // &
    trim ( node_filename ) // '".'
!
!  Create graphics command file.
!
  call get_unit ( command_unit )
  command_filename = trim ( header ) // '_commands.txt'
  open ( unit = command_unit, file = command_filename, &
    status = 'replace' )
  write ( command_unit, '(a)' ) '# ' // trim ( command_filename )
  write ( command_unit, '(a)' ) '#'
  write ( command_unit, '(a)' ) '# Usage:'
  write ( command_unit, '(a)' ) '#  gnuplot < ' // &
    trim ( command_filename )
  write ( command_unit, '(a)' ) '#'
  write ( command_unit, '(a)' ) 'set term png'
  plot_filename = trim ( header ) // '.png'
  write ( command_unit, '(a)' ) 'set output "' // &
    trim ( plot_filename ) // '"'
  write ( command_unit, '(a)' ) 'set xlabel "<--- X --->"'
  write ( command_unit, '(a)' ) 'set ylabel "<--- Y --->"'
  write ( command_unit, '(a)' ) &
    'set title "' // trim ( header ) // '"'
  write ( command_unit, '(a)' ) 'set grid'
  write ( command_unit, '(a)' ) 'set key off'
  write ( command_unit, '(a)' ) 'set size ratio -1'
  write ( command_unit, '(a)' ) 'set style data lines'
  write ( command_unit, '(a)' ) 'set timestamp'
  write ( command_unit, '(a)' ) 'plot "' // &
    trim ( vertex_filename ) // &
    '" with lines lw 3, \'
  write ( command_unit, '(a)' ) '     "' // &
    trim ( node_filename ) // '" with points pt 7 lt 0'
  close ( unit = command_unit )

  write ( *, '(a)' ) &
    '  Created command file "' // trim ( command_filename ) // '".'

  return
end