program main

!*****************************************************************************80
!
!! MAIN is the main program for SGMGA_WEIGHT_TEST.
!
!  Discussion:
!
!    SGMGA_WEIGHT_TEST tests the SGMGA library.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    27 November 2009
!
!  Author:
!
!    John Burkardt
!
  implicit none

  call timestamp ( )
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'SGMGA_WEIGHT_TEST:'
  write ( *, '(a)' ) '  FORTRAN90 version'
  write ( *, '(a)' ) '  Test the SGMGA_WEIGHT function.'

  call sgmga_weight_tests ( )
!
!  Terminate.
!
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'SGMGA_WEIGHT_TEST:'
  write ( *, '(a)' ) '  Normal end of execution.'
  write ( *, '(a)' ) ' '
  call timestamp ( )

  stop 0
end
subroutine sgmga_weight_tests ( )

!****************************************************************************80
!
!! SGMGA_WEIGHT_TESTS calls SGMGA_WEIGHT_TEST with various arguments.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    20 June 2010
!
!  Author:
!
!    John Burkardt
!
!  Local Parameters:
!
!    Local, real ( kind = 8 ) TOL, a tolerance for point equality.
!    A value of sqrt ( eps ) is reasonable, and will allow the code to
!    consolidate points which are equal, or very nearly so.  A value of
!    -1.0, on the other hand, will force the code to use every point, regardless
!    of duplication.
!
  implicit none

  integer ( kind = 4 ) dim
  integer ( kind = 4 ) dim_num
  integer ( kind = 4 ), allocatable :: growth(:)
  real ( kind = 8 ), allocatable :: importance(:)
  integer ( kind = 4 ) level_max_max
  integer ( kind = 4 ) level_max_min
  real ( kind = 8 ), allocatable :: level_weight(:)
  integer ( kind = 4 ), allocatable :: np(:)
  integer ( kind = 4 ) np_sum
  integer ( kind = 4 ), allocatable :: order_1d(:)
  integer ( kind = 4 ) order_nd
  real ( kind = 8 ), allocatable :: p(:)
  real ( kind = 8 ) r8_epsilon
  integer ( kind = 4 ), allocatable :: rule(:)
  real ( kind = 8 ) tol

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'SGMGA_WEIGHT_TESTS'
  write ( *, '(a)' ) '  Call SGMGA_WEIGHT_TEST with various arguments.'
!
!  Set the point equality tolerance.
!
  tol = sqrt ( r8_epsilon ( ) )
  write ( *, '(a)' ) ' '
  write ( *, '(a,g14.6)' ) '  All tests will use a point equality tolerance of ', tol

  dim_num = 2
  allocate ( importance(1:dim_num) )
  do dim = 1, dim_num
    importance(dim) = 1.0D+00
  end do
  allocate ( level_weight(1:dim_num) )
  call sgmga_importance_to_aniso ( dim_num, importance, level_weight )
  level_max_min = 0
  level_max_max = 2
  allocate ( rule(1:dim_num) )
  rule = (/ 1, 1 /)
  allocate ( growth(1:dim_num) )
  growth = (/ 6, 6 /)
  allocate ( np(1:dim_num) )
  np = (/ 0, 0 /)
  np_sum = sum ( np(1:dim_num) )
  allocate ( p(1:np_sum) )
  call sgmga_weight_test ( dim_num, importance, level_weight, level_max_min, &
    level_max_max, rule, growth, np, p, tol )
  deallocate ( growth )
  deallocate ( importance )
  deallocate ( level_weight )
  deallocate ( np )
  deallocate ( p )
  deallocate ( rule )

  dim_num = 2
  allocate ( importance(1:dim_num) )
  do dim = 1, dim_num
    importance(dim) = real ( dim, kind = 8 )
  end do
  allocate ( level_weight(1:dim_num) )
  call sgmga_importance_to_aniso ( dim_num, importance, level_weight )
  level_max_min = 0
  level_max_max = 2
  allocate ( rule(1:dim_num) )
  rule = (/ 1, 1 /)
  allocate ( growth(1:dim_num) )
  growth = (/ 6, 6 /)
  allocate ( np(1:dim_num) )
  np = (/ 0, 0 /)
  np_sum = sum ( np(1:dim_num) )
  allocate ( p(1:np_sum) )
  call sgmga_weight_test ( dim_num, importance, level_weight, level_max_min, &
    level_max_max, rule, growth, np, p, tol )
  deallocate ( growth )
  deallocate ( importance )
  deallocate ( level_weight )
  deallocate ( np )
  deallocate ( p )
  deallocate ( rule )

  dim_num = 3
  allocate ( importance(1:dim_num) )
  do dim = 1, dim_num
    importance(dim) = 1.0D+00
  end do
  allocate ( level_weight(1:dim_num) )
  call sgmga_importance_to_aniso ( dim_num, importance, level_weight )
  level_max_min = 0
  level_max_max = 2
  allocate ( rule(1:dim_num) )
  rule = (/ 1, 1, 1 /)
  allocate ( growth(1:dim_num) )
  growth = (/ 6, 6, 6 /)
  allocate ( np(1:dim_num) )
  np = (/ 0, 0, 0 /)
  np_sum = sum ( np(1:dim_num) )
  allocate ( p(1:np_sum) )
  call sgmga_weight_test ( dim_num, importance, level_weight, level_max_min, &
    level_max_max, rule, growth, np, p, tol )
  deallocate ( growth )
  deallocate ( importance )
  deallocate ( level_weight )
  deallocate ( np )
  deallocate ( p )
  deallocate ( rule )

  dim_num = 3
  allocate ( importance(1:dim_num) )
  do dim = 1, dim_num
    importance(dim) = real ( dim, kind = 8 )
  end do
  allocate ( level_weight(1:dim_num) )
  call sgmga_importance_to_aniso ( dim_num, importance, level_weight )
  level_max_min = 0
  level_max_max = 2
  allocate ( rule(1:dim_num) )
  rule = (/ 1, 1, 1 /)
  allocate ( growth(1:dim_num) )
  growth = (/ 6, 6, 6 /)
  allocate ( np(1:dim_num) )
  np = (/ 0, 0, 0 /)
  np_sum = sum ( np(1:dim_num) )
  allocate ( p(1:np_sum) )
  call sgmga_weight_test ( dim_num, importance, level_weight, level_max_min, &
    level_max_max, rule, growth, np, p, tol )
  deallocate ( growth )
  deallocate ( importance )
  deallocate ( level_weight )
  deallocate ( np )
  deallocate ( p )
  deallocate ( rule )

  dim_num = 2
  allocate ( importance(1:dim_num) )
  do dim = 1, dim_num
    importance(dim) = real ( dim, kind = 8 )
  end do
  allocate ( level_weight(1:dim_num) )
  call sgmga_importance_to_aniso ( dim_num, importance, level_weight )
  level_max_min = 0
  level_max_max = 2
  allocate ( rule(1:dim_num) )
  rule = (/ 1, 3 /)
  allocate ( growth(1:dim_num) )
  growth = (/ 6, 6 /)
  allocate ( np(1:dim_num) )
  np = (/ 0, 0 /)
  np_sum = sum ( np(1:dim_num) )
  allocate ( p(1:np_sum) )
  call sgmga_weight_test ( dim_num, importance, level_weight, level_max_min, &
    level_max_max, rule, growth, np, p, tol )
  deallocate ( growth )
  deallocate ( importance )
  deallocate ( level_weight )
  deallocate ( np )
  deallocate ( p )
  deallocate ( rule )

  dim_num = 2
  allocate ( importance(1:dim_num) )
  do dim = 1, dim_num
    importance(dim) = real ( dim, kind = 8 )
  end do
  allocate ( level_weight(1:dim_num) )
  call sgmga_importance_to_aniso ( dim_num, importance, level_weight )
  level_max_min = 0
  level_max_max = 2
  allocate ( rule(1:dim_num) )
  rule = (/ 1, 4 /)
  allocate ( growth(1:dim_num) )
  growth = (/ 6, 3 /)
  allocate ( np(1:dim_num) )
  np = (/ 0, 0 /)
  np_sum = sum ( np(1:dim_num) )
  allocate ( p(1:np_sum) )
  call sgmga_weight_test ( dim_num, importance, level_weight, level_max_min, &
    level_max_max, rule, growth, np, p, tol )
  deallocate ( growth )
  deallocate ( importance )
  deallocate ( level_weight )
  deallocate ( np )
  deallocate ( p )
  deallocate ( rule )

  dim_num = 2
  allocate ( importance(1:dim_num) )
  do dim = 1, dim_num
    importance(dim) = real ( dim, kind = 8 )
  end do
  allocate ( level_weight(1:dim_num) )
  call sgmga_importance_to_aniso ( dim_num, importance, level_weight )
  level_max_min = 0
  level_max_max = 2
  allocate ( rule(1:dim_num) )
  rule = (/ 1, 7 /)
  allocate ( growth(1:dim_num) )
  growth = (/ 6, 3 /)
  allocate ( np(1:dim_num) )
  np = (/ 0, 0 /)
  np_sum = sum ( np(1:dim_num) )
  allocate ( p(1:np_sum) )
  call sgmga_weight_test ( dim_num, importance, level_weight, level_max_min, &
    level_max_max, rule, growth, np, p, tol )
  deallocate ( growth )
  deallocate ( importance )
  deallocate ( level_weight )
  deallocate ( np )
  deallocate ( p )
  deallocate ( rule )

  dim_num = 2
  allocate ( importance(1:dim_num) )
  do dim = 1, dim_num
    importance(dim) = real ( dim, kind = 8 )
  end do
  allocate ( level_weight(1:dim_num) )
  call sgmga_importance_to_aniso ( dim_num, importance, level_weight )
  level_max_min = 0
  level_max_max = 2
  allocate ( rule(1:dim_num) )
  rule = (/ 1, 8 /)
  allocate ( growth(1:dim_num) )
  growth = (/ 6, 3 /)
  allocate ( np(1:dim_num) )
  np = (/ 0, 1 /)
  np_sum = sum ( np(1:dim_num) )
  allocate ( p(1:np_sum) )
  p(1) = 1.5D+00
  call sgmga_weight_test ( dim_num, importance, level_weight, level_max_min, &
    level_max_max, rule, growth, np, p, tol )
  deallocate ( growth )
  deallocate ( importance )
  deallocate ( level_weight )
  deallocate ( np )
  deallocate ( p )
  deallocate ( rule )

  dim_num = 2
  allocate ( importance(1:dim_num) )
  do dim = 1, dim_num
    importance(dim) = real ( dim, kind = 8 )
  end do
  allocate ( level_weight(1:dim_num) )
  call sgmga_importance_to_aniso ( dim_num, importance, level_weight )
  level_max_min = 0
  level_max_max = 2
  allocate ( rule(1:dim_num) )
  rule = (/ 2, 9 /)
  allocate ( growth(1:dim_num) )
  growth = (/ 6, 3 /)
  allocate ( np(1:dim_num) )
  np = (/ 0, 2 /)
  np_sum = sum ( np(1:dim_num) )
  allocate ( p(1:np_sum) )
  p(1) = 0.5D+00
  p(2) = 1.5D+00
  call sgmga_weight_test ( dim_num, importance, level_weight, level_max_min, &
    level_max_max, rule, growth, np, p, tol )
  deallocate ( growth )
  deallocate ( importance )
  deallocate ( level_weight )
  deallocate ( np )
  deallocate ( p )
  deallocate ( rule )

  dim_num = 2
  allocate ( importance(1:dim_num) )
  do dim = 1, dim_num
    importance(dim) = real ( dim, kind = 8 )
  end do
  allocate ( level_weight(1:dim_num) )
  call sgmga_importance_to_aniso ( dim_num, importance, level_weight )
  level_max_min = 0
  level_max_max = 2
  allocate ( rule(1:dim_num) )
  rule = (/ 6, 10 /)
  allocate ( growth(1:dim_num) )
  growth = (/ 3, 4 /)
  allocate ( np(1:dim_num) )
  np = (/ 1, 0 /)
  np_sum = sum ( np(1:dim_num) )
  allocate ( p(1:np_sum) )
  p(1) = 2.0D+00
  call sgmga_weight_test ( dim_num, importance, level_weight, level_max_min, &
    level_max_max, rule, growth, np, p, tol )
  deallocate ( growth )
  deallocate ( importance )
  deallocate ( level_weight )
  deallocate ( np )
  deallocate ( p )
  deallocate ( rule )
!
!  LEVEL_MAX 0 to 5
!
  dim_num = 2
  allocate ( importance(1:dim_num) )
  do dim = 1, dim_num
    importance(dim) = real ( dim, kind = 8 )
  end do
  allocate ( level_weight(1:dim_num) )
  call sgmga_importance_to_aniso ( dim_num, importance, level_weight )
  level_max_min = 0
  level_max_max = 5
  allocate ( rule(1:dim_num) )
  rule = (/ 1, 1 /)
  allocate ( growth(1:dim_num) )
  growth = (/ 6, 6 /)
  allocate ( np(1:dim_num) )
  np = (/ 0, 0 /)
  np_sum = sum ( np(1:dim_num) )
  allocate ( p(1:np_sum) )
  call sgmga_weight_test ( dim_num, importance, level_weight, level_max_min, &
    level_max_max, rule, growth, np, p, tol )
  deallocate ( growth )
  deallocate ( importance )
  deallocate ( level_weight )
  deallocate ( np )
  deallocate ( p )
  deallocate ( rule )
!
!  Dimension 3
!
  dim_num = 3
  allocate ( importance(1:dim_num) )
  do dim = 1, dim_num
    importance(dim) = real ( dim, kind = 8 )
  end do
  allocate ( level_weight(1:dim_num) )
  call sgmga_importance_to_aniso ( dim_num, importance, level_weight )
  level_max_min = 0
  level_max_max = 2
  allocate ( rule(1:dim_num) )
  rule = (/ 1, 4, 5 /)
  allocate ( growth(1:dim_num) )
  growth = (/ 6, 3, 3 /)
  allocate ( np(1:dim_num) )
  np = (/ 0, 0, 0 /)
  np_sum = sum ( np(1:dim_num) )
  allocate ( p(1:np_sum) )
  call sgmga_weight_test ( dim_num, importance, level_weight, level_max_min, &
    level_max_max, rule, growth, np, p, tol )
  deallocate ( growth )
  deallocate ( importance )
  deallocate ( level_weight )
  deallocate ( np )
  deallocate ( p )
  deallocate ( rule )
!
!  Try a case with a dimension of "0 importance".
!
  dim_num = 3
  allocate ( importance(1:dim_num) )
  importance = (/ 1.0D+00, 0.0D+00, 1.0D+00 /)
  allocate ( level_weight(1:dim_num) )
  call sgmga_importance_to_aniso ( dim_num, importance, level_weight )
  level_max_min = 0
  level_max_max = 3
  allocate ( rule(1:dim_num) )
  rule = (/ 1, 1, 1 /)
  allocate ( growth(1:dim_num) )
  growth = (/ 6, 6, 6 /)
  allocate ( np(1:dim_num) )
  np = (/ 0, 0, 0 /)
  np_sum = sum ( np(1:dim_num) )
  allocate ( p(1:np_sum) )
  call sgmga_weight_test ( dim_num, importance, level_weight, level_max_min, &
    level_max_max, rule, growth, np, p, tol )
  deallocate ( growth )
  deallocate ( importance )
  deallocate ( level_weight )
  deallocate ( np )
  deallocate ( p )
  deallocate ( rule )

  return
end
subroutine sgmga_weight_test ( dim_num, importance, level_weight, &
  level_max_min, level_max_max, rule, growth, np, p, tol )

!****************************************************************************80
!
!! SGMGA_WEIGHT_TEST checks the sum of the quadrature weights.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license.
!
!  Modified:
!
!    07 June 2010
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) DIM_NUM, the spatial dimension.
!
!    Input, real ( kind = 8 ) IMPORTANCE(DIM_NUM), the anisotropic
!    importance for each dimension.
!
!    Input, real ( kind = 8 ) LEVEL_WEIGHT(DIM_NUM), the anisotropic weight
!    for each dimension.
!
!    Input, integer ( kind = 4 ) LEVEL_MAX_MIN, LEVEL_MAX_MAX, the minimum and
!    maximum values of LEVEL_MAX.
!
!    Input, integer ( kind = 4 ) RULE(DIM_NUM), the rule in each dimension.
!     1, "CC",  Clenshaw Curtis, Closed Fully Nested.
!     2, "F2",  Fejer Type 2, Open Fully Nested.
!     3, "GP",  Gauss Patterson, Open Fully Nested.
!     4, "GL",  Gauss Legendre, Open Weakly Nested.
!     5, "GH",  Gauss Hermite, Open Weakly Nested.
!     6, "GGH", Generalized Gauss Hermite, Open Weakly Nested.
!     7, "LG",  Gauss Laguerre, Open Non Nested.
!     8, "GLG", Generalized Gauss Laguerre, Open Non Nested.
!     9, "GJ",  Gauss Jacobi, Open Non Nested.
!    10, "HGK", Hermite Genz-Keister, Open Fully Nested.
!    11, "UO",  User supplied Open, presumably Non Nested.
!    12, "UC",  User supplied Closed, presumably Non Nested.
!
!    Input, integer ( kind = 4 ) GROWTH(DIM_NUM), the growth in each dimension.
!    0, "DF", default growth associated with this quadrature rule;
!    1, "SL", slow linear, L+1;
!    2  "SO", slow linear odd, O=1+2((L+1)/2)
!    3, "ML", moderate linear, 2L+1;
!    4, "SE", slow exponential;
!    5, "ME", moderate exponential;
!    6, "FE", full exponential.
!
!    Input, integer ( kind = 4 ) NP(DIM_NUM), the number of parameters
!    used by each rule.
!
!    Input, real ( kind = 8 ) P(*), the parameters needed by each rule.
!
!    Input, real ( kind = 8 ) TOL, a tolerance for point equality.
!
  implicit none

  integer ( kind = 4 ) dim_num

  real ( kind = 8 ) alpha
  real ( kind = 8 ) arg1
  real ( kind = 8 ) arg2
  real ( kind = 8 ) arg3
  real ( kind = 8 ) arg4
  real ( kind = 8 ) beta
  integer ( kind = 4 ) dim
  integer ( kind = 4 ) growth(dim_num)
  real ( kind = 8 ) importance(dim_num)
  integer ( kind = 4 ) level_max
  integer ( kind = 4 ) level_max_max
  integer ( kind = 4 ) level_max_min
  real ( kind = 8 ) level_weight(dim_num)
  integer ( kind = 4 ) np(dim_num)
  real ( kind = 8 ) p(*)
  integer ( kind = 4 ) p_index
  real ( kind = 8 ), parameter :: pi = 3.141592653589793D+00
  integer ( kind = 4 ) point_num
  integer ( kind = 4 ) point_total_num
  real ( kind = 8 ) r8_gamma
  integer ( kind = 4 ) rule(dim_num)
  integer ( kind = 4 ), allocatable, dimension(:) :: sparse_unique_index
  real ( kind = 8 ), allocatable, dimension(:) :: sparse_weight
  real ( kind = 8 ) tol
  real ( kind = 8 ) value1
  real ( kind = 8 ) value2
  real ( kind = 8 ) weight_sum
  real ( kind = 8 ) weight_sum_error
  real ( kind = 8 ) weight_sum_exact

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'SGMGA_WEIGHT_TEST:'
  write ( *, '(a)' ) '  Compute the weights of a sparse grid.'
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  Each sparse grid is of spatial dimension DIM_NUM,'
  write ( *, '(a)' ) '  and is made up of product grids of levels up to LEVEL_MAX.'
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  IMPORTANCE:'
  write ( *, '(5g14.6)' ) importance(1:dim_num)
  write ( *, '(a)' ) '  LEVEL_WEIGHT:'
  write ( *, '(5g14.6)' ) level_weight(1:dim_num)
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) ' Dimension      Rule       Growth     Parameters'
  write ( *, '(a)' ) ' '

  p_index = 1

  do dim = 1, dim_num

    if ( rule(dim) == 1 ) then
      write ( *, '(2x,i8,2x,i8,2x,i11,2x,g14.6,2x,g14.6)' ) &
        dim, rule(dim), growth(dim)
    else if ( rule(dim) ==  2 ) then
      write ( *, '(2x,i8,2x,i8,2x,i11,2x,g14.6,2x,g14.6)' ) &
        dim, rule(dim), growth(dim)
    else if ( rule(dim) ==  3 ) then
      write ( *, '(2x,i8,2x,i8,2x,i11,2x,g14.6,2x,g14.6)' ) &
        dim, rule(dim), growth(dim)
    else if ( rule(dim) ==  4 ) then
      write ( *, '(2x,i8,2x,i8,2x,i11,2x,g14.6,2x,g14.6)' ) &
        dim, rule(dim), growth(dim)
    else if ( rule(dim) ==  5 ) then
      write ( *, '(2x,i8,2x,i8,2x,i11,2x,g14.6,2x,g14.6)' ) &
        dim, rule(dim), growth(dim)
    else if ( rule(dim) ==  6 ) then
      write ( *, '(2x,i8,2x,i8,2x,i11,2x,g14.6,2x,g14.6)' ) &
        dim, rule(dim), growth(dim), p(p_index)
    else if ( rule(dim) ==  7 ) then
      write ( *, '(2x,i8,2x,i8,2x,i11,2x,g14.6,2x,g14.6)' ) &
        dim, rule(dim), growth(dim)
    else if ( rule(dim) ==  8 ) then
      write ( *, '(2x,i8,2x,i8,2x,i11,2x,g14.6,2x,g14.6)' ) &
        dim, rule(dim), growth(dim), p(p_index)
    else if ( rule(dim) ==  9 ) then
      write ( *, '(2x,i8,2x,i8,2x,i11,2x,g14.6,2x,g14.6)' ) &
        dim, rule(dim), growth(dim), p(p_index), p(p_index+1)
    else if ( rule(dim) == 10 ) then
      write ( *, '(2x,i8,2x,i8,2x,i11,2x,g14.6,2x,g14.6)' ) &
        dim, rule(dim), growth(dim)
    else if ( rule(dim) == 11 ) then
      write ( *, '(2x,i8,2x,i8,2x,i11,2x,g14.6,2x,g14.6)' ) &
        dim, rule(dim), growth(dim)
    else if ( rule(dim) == 12 ) then
      write ( *, '(2x,i8,2x,i8,2x,i11,2x,g14.6,2x,g14.6)' ) &
        dim, rule(dim), growth(dim)
    end if

    p_index = p_index + np(dim)

  end do

  weight_sum_exact = 1.0D+00

  p_index = 1

  do dim = 1, dim_num

    if ( rule(dim) == 1 ) then
      weight_sum_exact = weight_sum_exact * 2.0D+00
    else if ( rule(dim) == 2 ) then
      weight_sum_exact = weight_sum_exact * 2.0D+00
    else if ( rule(dim) == 3 ) then
      weight_sum_exact = weight_sum_exact * 2.0D+00
    else if ( rule(dim) == 4 ) then
      weight_sum_exact = weight_sum_exact * 2.0D+00
    else if ( rule(dim) == 5 ) then
      weight_sum_exact = weight_sum_exact * sqrt ( pi )
    else if ( rule(dim) == 6 ) then
      alpha = p(p_index)
      weight_sum_exact = weight_sum_exact * r8_gamma ( 0.5D+00 * ( alpha + 1.0D+00 ) )
    else if ( rule(dim) == 7 ) then
      weight_sum_exact = weight_sum_exact * 1.0D+00
    else if ( rule(dim) == 8 ) then
      alpha = p(p_index)
      weight_sum_exact = weight_sum_exact * r8_gamma ( alpha + 1.0D+00 )
    else if ( rule(dim) == 9 ) then
      alpha = p(p_index)
      beta = p(p_index+1)
      arg1 = - alpha
      arg2 = 1.0D+00
      arg3 = beta + 2.0D+00
      arg4 = - 1.0D+00
      call r8_hyper_2f1 ( arg1, arg2, arg3, arg4, value1 )
      arg1 = - beta
      arg2 = 1.0D+00
      arg3 = alpha + 2.0D+00
      arg4 = - 1.0D+00
      call r8_hyper_2f1 ( arg1, arg2, arg3, arg4, value2 )
      weight_sum_exact = weight_sum_exact * ( &
        value1 / ( beta + 1.0D+00 ) + value2 / ( alpha + 1.0D+00 ) )
    else if ( rule(dim) == 10 ) then
      weight_sum_exact = weight_sum_exact * sqrt ( pi )
    else if ( rule(dim) == 11 ) then
      write ( *, '(a)' ) ' '
      write ( *, '(a)' ) 'SGMGA_WEIGHT_TEST - Fatal error!'
      write ( *, '(a)' ) '  Unexpected value of RULE = 11.'
      stop
    else if ( rule(dim) == 12 ) then
      write ( *, '(a)' ) ' '
      write ( *, '(a)' ) 'SGMGA_WEIGHT_TEST - Fatal error!'
      write ( *, '(a)' ) '  Unexpected value of RULE = 12.'
      stop
    else
      write ( *, '(a)' ) ' '
      write ( *, '(a)' ) 'SGMGA_WEIGHT_TEST - Fatal error!'
      write ( *, '(a,i8)' ) '  Unexpected value of RULE = ', rule(dim)
      stop
    end if

    p_index = p_index + np(dim)

  end do

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  As a simple test, sum these weights.'
  write ( *, '(a,g14.6)' ) '  They should sum to exactly ', weight_sum_exact
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '     Level      Weight sum  Expected sum    Difference'
  write ( *, '(a)' ) ' '

  do level_max = level_max_min, level_max_max

    call sgmga_size_total ( dim_num, level_weight, level_max, rule, growth, &
      point_total_num )

    call sgmga_size ( dim_num, level_weight, level_max, rule, growth, np, &
      p, tol, point_num )

    allocate ( sparse_unique_index(1:point_total_num) )

    call sgmga_unique_index ( dim_num, level_weight, level_max, &
      rule, growth, np, p, tol, point_num, point_total_num, sparse_unique_index )

    allocate ( sparse_weight(1:point_num) )

    call sgmga_weight ( dim_num, level_weight, level_max, rule, growth, &
      np, p, point_num, point_total_num, sparse_unique_index, sparse_weight )

    weight_sum = sum ( sparse_weight(1:point_num) )

    weight_sum_error = abs ( weight_sum - weight_sum_exact )

    write ( *, '(2x,i8,2x,g14.6,2x,g14.6,2x,g14.6)' ) &
      level_max, weight_sum, weight_sum_exact, weight_sum_error

    deallocate ( sparse_unique_index )
    deallocate ( sparse_weight )

  end do

  return
end