program main

!*****************************************************************************80
!
!! MAIN is the main program for JACOBI_RULE.
!
!  Discussion:
!
!    This program computes a standard Gauss-Jacobi quadrature rule
!    and writes it to a file.
!
!    The user specifies:
!    * the ORDER (number of points) in the rule;
!    * ALPHA and BETA parameters;
!    * the root name of the output files.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    16 January 2008
!
!  Author:
!
!    John Burkardt
!
  implicit none

  real    ( kind = 8 ) alpha
  integer ( kind = 4 ) arg_num
  real    ( kind = 8 ) beta
  integer ( kind = 4 ) iarg
  integer ( kind = 4 ) iargc
  integer ( kind = 4 ) ierror
  integer ( kind = 4 ) last
  integer ( kind = 4 ) order
  character ( len = 80 ) output
  character ( len = 80 ) string

  call timestamp ( )
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'JACOBI_RULE'
  write ( *, '(a)' ) '  FORTRAN90 version'
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  Compute a Gauss-Jacobi rule for approximating'
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '    Integral ( -1 <= x <= +1 ) (1-x)^ALPHA (1+x)^BETA f(x) dx'
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  of order ORDER.'
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  The user specifies ORDER, ALPHA, BETA, and OUTPUT.'
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  OUTPUT is:'
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  "C++" for printed C++ output;'
  write ( *, '(a)' ) '  "F77" for printed Fortran77 output;'
  write ( *, '(a)' ) '  "F90" for printed Fortran90 output;'
  write ( *, '(a)' ) '  "MAT" for printed MATLAB output;'
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  or:'
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  "filename" to generate 3 files:'
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '    filename_w.txt - the weight file'
  write ( *, '(a)' ) '    filename_x.txt - the abscissa file.'
  write ( *, '(a)' ) '    filename_r.txt - the region file.'
!
!  Get the number of command line arguments.
!
  arg_num = iargc ( )
!
!  Get the order.
!
  if ( 1 <= arg_num ) then
  
    iarg = 1
    call getarg ( iarg, string )
    call s_to_i4 ( string, order, ierror, last )
    
  else
  
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) '  Enter the rule order ORDER:'
    read ( *, * ) order
    
  end if
!
!  Get ALPHA
!
  if ( 2 <= arg_num ) then

    iarg = 2
    call getarg ( iarg, string )
    call s_to_r8 ( string, alpha, ierror, last )

  else

    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) '  ALPHA is the exponent of (1-x) in the integral:'
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) '      Integral ( -1 <= x <= +1 ) (1-x)^ALPHA (1+x)^BETA f(x) dx'
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) '  Note that -1.0 < ALPHA is required.'
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) '  Enter the value of ALPHA:'
    read ( *, * ) alpha

  end if
!
!  Get BETA
!
  if ( 3 <= arg_num ) then

    iarg = 3
    call getarg ( iarg, string )
    call s_to_r8 ( string, beta, ierror, last )

  else

    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) '  BETA is the exponent of (1+x) in the integral:'
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) '      Integral ( -1 <= x <= +1 ) (1-x)^ALPHA (1+x)^BETA f(x) dx'
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) '  Note that -1.0 < BETA is required.'
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) '  Enter the value of BETA:'
    read ( *, * ) beta

  end if
!
!  Get the output option or quadrature file root name:
!
  if ( 4 <= arg_num ) then

    iarg = 4
    call getarg ( iarg, output )

  else

    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) '  Enter OUTPUT (one of C++, F77, F90, MAT,'
    write ( *, '(a)' ) '  or else the "root name" of the quadrature files).'

    read ( *, '(a)' ) output

  end if
!
!  Echo the input.
!
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  Input summary:'
  write ( *, '(a)' ) ' '
  write ( *, '(a,i8)'      ) '  ORDER =  ', order
  write ( *, '(a,g14.6)'   ) '  ALPHA =  ', alpha
  write ( *, '(a,g14.6)'   ) '  BETA =  ', beta
  write ( *, '(a)'         ) '  OUTPUT = "' // trim ( output ) // '".'
!
!  Construct the rule and output it.
!
  call jacobi_handle ( order, alpha, beta, output )

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'JACOBI_RULE:'
  write ( *, '(a)' ) '  Normal end of execution.'
  write ( *, '(a)' ) ' '
  call timestamp ( )

  stop
end
subroutine ch_cap ( c )

!*****************************************************************************80
!
!! CH_CAP capitalizes a single character.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    19 July 1998
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input/output, character C, the character to capitalize.
!
  implicit none

  character c
  integer ( kind = 4 ) itemp

  itemp = ichar ( c )

  if ( 97 <= itemp .and. itemp <= 122 ) then
    c = char ( itemp - 32 )
  end if

  return
end
function ch_eqi ( c1, c2 )

!*****************************************************************************80
!
!! CH_EQI is a case insensitive comparison of two characters for equality.
!
!  Example:
!
!    CH_EQI ( 'A', 'a' ) is .TRUE.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    28 July 2000
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, character C1, C2, the characters to compare.
!
!    Output, logical CH_EQI, the result of the comparison.
!
  implicit none

  logical ch_eqi
  character c1
  character c1_cap
  character c2
  character c2_cap

  c1_cap = c1
  c2_cap = c2

  call ch_cap ( c1_cap )
  call ch_cap ( c2_cap )

  if ( c1_cap == c2_cap ) then
    ch_eqi = .true.
  else
    ch_eqi = .false.
  end if

  return
end
subroutine ch_to_digit ( c, digit )

!*****************************************************************************80
!
!! CH_TO_DIGIT returns the integer value of a base 10 digit.
!
!  Example:
!
!     C   DIGIT
!    ---  -----
!    '0'    0
!    '1'    1
!    ...  ...
!    '9'    9
!    ' '    0
!    'X'   -1
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    04 August 1999
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, character C, the decimal digit, '0' through '9' or blank
!    are legal.
!
!    Output, integer ( kind = 4 ) DIGIT, the corresponding integer value.  
!    If C was 'illegal', then DIGIT is -1.
!
  implicit none

  character c
  integer ( kind = 4 ) digit

  if ( lge ( c, '0' ) .and. lle ( c, '9' ) ) then

    digit = ichar ( c ) - 48

  else if ( c == ' ' ) then

    digit = 0

  else

    digit = -1

  end if

  return
end
subroutine dtable_close_write ( output_unit )

!*****************************************************************************80
!
!! DTABLE_CLOSE_WRITE closes a file used to write a DTABLE.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    26 September 2006
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) OUTPUT_UNIT, the output unit that was used.
!
  implicit none

  integer ( kind = 4 ) output_unit

  close ( unit = output_unit )

  return
end
subroutine dtable_data_write ( output_unit, m, n, table )

!*****************************************************************************80
!
!! DTABLE_DATA_WRITE writes DTABLE data to a file.
!
!  Discussion:
!
!    This routine writes a single line of output for each point,
!    containing its spatial coordinates.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    07 September 2004
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) OUTPUT_UNIT, the output unit.
!
!    Input, integer ( kind = 4 ) M, the spatial dimension.
!
!    Input, integer ( kind = 4 ) N, the number of points.
!
!    Input, real ( kind = 8 ) TABLE(M,N), the table data.
!
  implicit none

  integer ( kind = 4 ) m
  integer ( kind = 4 ) n

  integer ( kind = 4 ) output_unit
  integer ( kind = 4 ) j
  character ( len = 30 ) string
  real    ( kind = 8 ) table(m,n)
!
!  Create the format string.
!
  write ( string, '(a1,i8,a1,i8,a1,i8,a1)' ) '(', m, 'g', 24, '.', 16, ')'
  call s_blank_delete ( string )

  do j = 1, n
    write ( output_unit, string ) table(1:m,j)
  end do

  return
end
subroutine dtable_header_write ( output_file_name, output_unit, m, n )

!*****************************************************************************80
!
!! DTABLE_HEADER_WRITE writes the header to a DTABLE file.
!
!  Discussion:
!
!    The file must already be open before this routine is called.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    07 September 2004
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, character ( len = * ) OUTPUT_FILE_NAME, the output file name.
!
!    Input, integer ( kind = 4 ) OUTPUT_UNIT, the output unit.
!
!    Input, integer ( kind = 4 ) M, the spatial dimension.
!
!    Input, integer ( kind = 4 ) N, the number of points.
!
  implicit none

  integer ( kind = 4 ) m
  integer ( kind = 4 ) n
  character ( len = * ) output_file_name
  integer ( kind = 4 ) output_unit
  character ( len = 40 ) string
  real    ( kind = 8 ), parameter :: x = 1.0D+00

  call timestring ( string )

  write ( output_unit, '(a)'       ) '#  ' // trim ( output_file_name )
  write ( output_unit, '(a)'       ) '#  created by TABLE_IO.F90'
  write ( output_unit, '(a)'       ) '#  at ' // trim ( string )
  write ( output_unit, '(a)'       ) '#'
  write ( output_unit, '(a,i8)'    ) '#  Spatial dimension M = ', m
  write ( output_unit, '(a,i8)'    ) '#  Number of points N = ', n
  write ( output_unit, '(a,g14.6)' ) '#  EPSILON (unit roundoff) = ', &
    epsilon ( x )
  write ( output_unit, '(a)'       ) '#'

  return
end
subroutine dtable_open_write ( output_file_name, output_unit )

!*****************************************************************************80
!
!! DTABLE_OPEN_WRITE opens a file to write a DTABLE.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    26 September 2006
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, character ( len = * ) OUTPUT_FILE_NAME, the output file name.
!
!    Output, integer ( kind = 4 ) OUTPUT_UNIT, the output unit to be used.
!
  implicit none

  character ( len = * ) output_file_name
  integer ( kind = 4 ) output_status
  integer ( kind = 4 ) output_unit

  call get_unit ( output_unit )

  open ( unit = output_unit, file = output_file_name, &
    status = 'replace', iostat = output_status )

  if ( output_status /= 0 ) then
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) 'DTABLE_OPEN_WRITE - Fatal error!'
    write ( *, '(a,i8)' ) '  Could not open the output file "' // &
      trim ( output_file_name ) // '" on unit ', output_unit
    output_unit = -1
    stop
  end if

  return
end
subroutine dtable_write ( output_file_name, m, n, table, header )

!*****************************************************************************80
!
!! DTABLE_WRITE writes a DTABLE to a file.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    27 September 2006
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, character ( len = * ) OUTPUT_FILE_NAME, the output file name.
!
!    Input, integer ( kind = 4 ) M, the spatial dimension.
!
!    Input, integer ( kind = 4 ) N, the number of points.
!
!    Input, real ( kind = 8 ) TABLE(M,N), the table data.
!
!    Input, logical HEADER, is TRUE if the header is to be included.
!
  implicit none

  integer ( kind = 4 ) m
  integer ( kind = 4 ) n

  logical header
  character ( len = * ) output_file_name
  integer ( kind = 4 ) output_unit
  real    ( kind = 8 ) table(m,n)

  call dtable_open_write ( output_file_name, output_unit )

  if ( header ) then
    call dtable_header_write ( output_file_name, output_unit, m, n )
  end if

  call dtable_data_write ( output_unit, m, n, table )

  call dtable_close_write ( output_unit )

  return
end
subroutine get_unit ( iunit )

!*****************************************************************************80
!
!! GET_UNIT returns a free FORTRAN unit number.
!
!  Discussion:
!
!    A "free" FORTRAN unit number is an integer 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 an integer 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:
!
!    18 September 2005
!
!  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 jacobi_compute ( order, alpha, beta, xtab, weight )

!*****************************************************************************80
!
!! JACOBI_COMPUTE computes a Gauss-Jacobi quadrature rule.
!
!  Discussion:
!
!    The integral to approximate:
!
!      Integral ( -1 <= X <= 1 ) (1-X)**ALPHA * (1+X)**BETA * F(X) dX
!
!    The quadrature rule:
!
!      Sum ( 1 <= I <= ORDER ) WEIGHT(I) * F ( XTAB(I) )
!
!    Thanks to Xu Xiang of Fudan University for pointing out that
!    an earlier implementation of this routine was incorrect!
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    14 May 2007
!
!  Author:
!
!    FORTRAN77 original version by Arthur Stroud, Don Secrest
!    FORTRAN90 version by John Burkardt
!
!  Reference:
!
!    Arthur Stroud, Don Secrest,
!    Gaussian Quadrature Formulas,
!    Prentice Hall, 1966,
!    LC: QA299.4G3S7.
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) ORDER, the order of the quadrature rule
!    to be computed.
!
!    Input, real ( kind = 8 ) ALPHA, BETA, the exponents of (1-X) and
!    (1+X) in the quadrature rule.  For simple Gauss-Legendre quadrature,
!    set ALPHA = BETA = 0.0.  -1.0 < ALPHA and -1.0 < BETA are required.
!
!    Output, real ( kind = 8 ) XTAB(ORDER), the abscissas.
!
!    Output, real ( kind = 8 ) WEIGHT(ORDER), the weights.
!
  implicit none

  integer ( kind = 4 ) order

  real    ( kind = 8 ) alpha
  real    ( kind = 8 ) an
  real    ( kind = 8 ) b(order)
  real    ( kind = 8 ) beta
  real    ( kind = 8 ) bn
  real    ( kind = 8 ) c(order)
  real    ( kind = 8 ) cc
  real    ( kind = 8 ) delta
  real    ( kind = 8 ) dp2
  integer ( kind = 4 ) i
  real    ( kind = 8 ) p1
  real    ( kind = 8 ) r1
  real    ( kind = 8 ) r2
  real    ( kind = 8 ) r3
  real    ( kind = 8 ) r8_gamma
  real    ( kind = 8 ) weight(order)
  real    ( kind = 8 ) x
  real    ( kind = 8 ) xtab(order)
!
!  Check ALPHA and BETA.
!
  if ( alpha <= -1.0D+00 ) then
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) 'JACOBI_COMPUTE - Fatal error!'
    write ( *, '(a)' ) '  -1.0 < ALPHA is required.'
    stop
  end if

  if ( beta <= -1.0D+00 ) then
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) 'JACOBI_COMPUTE - Fatal error!'
    write ( *, '(a)' ) '  -1.0 < BETA is required.'
    stop
  end if
!
!  Set the recursion coefficients.
!
  do i = 1, order

    if ( alpha + beta == 0.0D+00 .or. beta - alpha == 0.0D+00 ) then

      b(i) = 0.0D+00

    else

      b(i) = ( alpha + beta ) * ( beta - alpha ) / &
            ( ( alpha + beta + real ( 2 * i, kind = 8 ) ) &
            * ( alpha + beta + real ( 2 * i - 2, kind = 8 ) ) )

    end if

    if ( i == 1 ) then

      c(i) = 0.0D+00

    else

      c(i) = 4.0D+00 * real ( i - 1, kind = 8 ) &
            * ( alpha + real ( i - 1, kind = 8 ) ) &
            * ( beta + real ( i - 1, kind = 8 ) ) &
            * ( alpha + beta + real ( i - 1, kind = 8 ) ) / &
            ( ( alpha + beta + real ( 2 * i - 1, kind = 8 ) ) &
            * ( alpha + beta + real ( 2 * i - 2, kind = 8 ) )**2 &
            * ( alpha + beta + real ( 2 * i - 3, kind = 8 ) ) )

    end if

  end do

  delta = r8_gamma ( alpha        + 1.0D+00 ) &
        * r8_gamma (         beta + 1.0D+00 ) &
        / r8_gamma ( alpha + beta + 2.0D+00 )

  cc = delta * 2.0D+00**( alpha + beta + 1.0D+00 ) * product ( c(2:order) )

  do i = 1, order

    if ( i == 1 ) then

      an = alpha / real ( order, kind = 8 )
      bn = beta / real ( order, kind = 8 )

      r1 = ( 1.0D+00 + alpha ) &
        * ( 2.78D+00 / ( 4.0D+00 + real ( order**2, kind = 8 ) ) &
        + 0.768D+00 * an / real ( order, kind = 8 ) )

      r2 = 1.0D+00 + 1.48D+00 * an + 0.96D+00 * bn &
        + 0.452D+00 * an**2 + 0.83D+00 * an * bn

      x = ( r2 - r1 ) / r2

    else if ( i == 2 ) then

      r1 = ( 4.1D+00 + alpha ) / &
        ( ( 1.0D+00 + alpha ) * ( 1.0D+00 + 0.156D+00 * alpha ) )

      r2 = 1.0D+00 + 0.06D+00 * ( real ( order, kind = 8 ) - 8.0D+00 ) * &
        ( 1.0D+00 + 0.12D+00 * alpha ) / real ( order, kind = 8 )

      r3 = 1.0D+00 + 0.012D+00 * beta * &
        ( 1.0D+00 + 0.25D+00 * abs ( alpha ) ) / real ( order, kind = 8 )

      x = x - r1 * r2 * r3 * ( 1.0D+00 - x )

    else if ( i == 3 ) then

      r1 = ( 1.67D+00 + 0.28D+00 * alpha ) / ( 1.0D+00 + 0.37D+00 * alpha )

      r2 = 1.0D+00 + 0.22D+00 * ( real ( order, kind = 8 ) - 8.0D+00 ) &
        / real ( order, kind = 8 )

      r3 = 1.0D+00 + 8.0D+00 * beta / &
        ( ( 6.28D+00 + beta ) * real ( order**2, kind = 8 ) )

      x = x - r1 * r2 * r3 * ( xtab(1) - x )

    else if ( i < order - 1 ) then

      x = 3.0D+00 * xtab(i-1) - 3.0D+00 * xtab(i-2) + xtab(i-3)

    else if ( i == order - 1 ) then

      r1 = ( 1.0D+00 + 0.235D+00 * beta ) / ( 0.766D+00 + 0.119D+00 * beta )

      r2 = 1.0D+00 / ( 1.0D+00 + 0.639D+00 &
        * ( real ( order, kind = 8 ) - 4.0D+00 ) &
        / ( 1.0D+00 + 0.71D+00 * ( real ( order, kind = 8 ) - 4.0D+00 ) ) )

      r3 = 1.0D+00 / ( 1.0D+00 + 20.0D+00 * alpha / ( ( 7.5D+00 + alpha ) * &
        real ( order**2, kind = 8 ) ) )

      x = x + r1 * r2 * r3 * ( x - xtab(i-2) )

    else if ( i == order ) then

      r1 = ( 1.0D+00 + 0.37D+00 * beta ) / ( 1.67D+00 + 0.28D+00 * beta )

      r2 = 1.0D+00 / &
        ( 1.0D+00 + 0.22D+00 * ( real ( order, kind = 8 ) - 8.0D+00 ) &
        / real ( order, kind = 8 ) )

      r3 = 1.0D+00 / ( 1.0D+00 + 8.0D+00 * alpha / &
        ( ( 6.28D+00 + alpha ) * real ( order**2, kind = 8 ) ) )

      x = x + r1 * r2 * r3 * ( x - xtab(i-2) )

    end if

    call jacobi_root ( x, order, alpha, beta, dp2, p1, b, c )

    xtab(i) = x
    weight(i) = cc / ( dp2 * p1 )

  end do
!
!  Reverse the order of the data.
!
  xtab(1:order) = xtab(order:1:-1)
  weight(1:order) = weight(order:1:-1)

  return
end
subroutine jacobi_handle ( order, alpha, beta, output )

!*****************************************************************************80
!
!! JACOBI_HANDLE computes the requested rule and outputs it.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    02 September 2007
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, integer ( kind = 4 ) ORDER, the order of the rule.
!
!    Input, real ( kind = 8 ) ALPHA, BETA, the parameters.
!
!    Input, character ( len = * ) OUTPUT, specifies the output.
!    * 'C++', print as C++ code.
!    * 'F77', print as FORTRAN77 code.
!    * 'F90', print as FORTRAN90 code.
!    * 'MAT', print as MATLAB code.
!    * file,  write files 'file_w.txt', 'file_x.txt', 'file_r.txt' defining weights,
!             abscissas, and region.
! 
  implicit none

  real    ( kind = 8 ) alpha
  real    ( kind = 8 ) beta
  logical header
  integer ( kind = 4 ) i
  integer ( kind = 4 ) order
  character ( len = * ) output
  character ( len = 80 ) output_r
  character ( len = 80 ) output_w
  character ( len = 80 ) output_x
  real    ( kind = 8 ) r(2)
  real    ( kind = 8 ), allocatable, dimension ( : ) :: w
  real    ( kind = 8 ), allocatable, dimension ( : ) :: x

  r(1) = -1.0D+00
  r(2) = +1.0D+00

  allocate ( w(order) )
  allocate ( x(order) )

  call jacobi_compute ( order, alpha, beta, x, w )

  if ( output(1:3) == 'C++' .or. output(1:3) == 'c++' ) then
  
    write ( *, '(a)'       ) '//'
    write ( *, '(a)'       ) '//  Weights W, abscissas X and range R'
    write ( *, '(a)'       ) '//  for a Gauss-Jacobi quadrature rule'
    write ( *, '(a,i8)'    ) '//  ORDER = ', order
    write ( *, '(a,g14.6)' ) '//  ALPHA = ', alpha
    write ( *, '(a,g14.6)' ) '//  BETA  = ', beta
    write ( *, '(a)'       ) '//'
    write ( *, '(a)'       ) '//  Standard rule:'
    write ( *, '(a)'       ) '//    Integral ( -1 <= x <= +1 ) (1-x)^ALPHA (1+x)^BETA f(x) dx'
    write ( *, '(a)'       ) '//    is to be approximated by'
    write ( *, '(a)'       ) '//    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).'
    write ( *, '(a)'       ) '//'

    do i = 1, order
      write ( *, '(a,i2,a,g24.16,a)' ) '  w[', i-1, '] = ', w(i), ';'
    end do
    write ( *, '(a)' ) ' '
    do i = 1, order
      write ( *, '(a,i2,a,g24.16,a)' ) '  x[', i-1, '] = ', x(i), ';'
    end do
    write ( *, '(a)' ) ' '
    do i = 1, 2
      write ( *, '(a,i2,a,g24.16,a)' ) '  r[', i-1, '] = ', r(i), ';'
    end do

   else if ( output(1:3) == 'F77' .or. output(1:3) == 'f77' ) then
  
    write ( *, '(a)'       ) 'c'
    write ( *, '(a)'       ) 'c  Weights W, abscissas X and range R'
    write ( *, '(a)'       ) 'c  for a Gauss-Jacobi quadrature rule'
    write ( *, '(a,i8)'    ) 'c  ORDER = ', order
    write ( *, '(a,g14.6)' ) 'c  ALPHA = ', alpha
    write ( *, '(a,g14.6)' ) 'c  BETA  = ', beta
    write ( *, '(a)'       ) 'c'
    write ( *, '(a)'       ) 'c  Standard rule:'
    write ( *, '(a)'       ) 'c    Integral ( -1 <= x <= +1 ) (1-x)^ALPHA (1+x)^BETA f(x) dx'
    write ( *, '(a)'       ) 'c    is to be approximated by'
    write ( *, '(a)'       ) 'c    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).'
    write ( *, '(a)'       ) 'c'

    do i = 1, order
      write ( *, '(a,i2,a,g24.16)' ) '      w(', i, ') = ', w(i)
    end do
    write ( *, '(a)' ) ' '
    do i = 1, order
      write ( *, '(a,i2,a,g24.16)' ) '      x(', i, ') = ', x(i)
    end do
    write ( *, '(a)' ) ' '
    do i = 1, 2
      write ( *, '(a,i2,a,g24.16)' ) '      r(', i, ') = ', r(i)
    end do

  else if ( output(1:3) == 'F90' .or. output(1:3) == 'f90' ) then
  
    write ( *, '(a)'       ) '!'
    write ( *, '(a)'       ) '!  Weights W, abscissas X and range R'
    write ( *, '(a)'       ) '!  for a Gauss-Jacobi quadrature rule'
    write ( *, '(a,i8)'    ) '!  ORDER = ', order
    write ( *, '(a,g14.6)' ) '!  ALPHA = ', alpha
    write ( *, '(a,g14.6)' ) '!  BETA =  ', beta
    write ( *, '(a)'       ) '!'
    write ( *, '(a)'       ) '!  Standard rule:'
    write ( *, '(a)'       ) '!    Integral ( -1 <= x <= +1 ) (1-x)^ALPHA (1+x)^BETA f(x) dx'
    write ( *, '(a)'       ) '!    is to be approximated by'
    write ( *, '(a)'       ) '!    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).'
    write ( *, '(a)'       ) '!'

    do i = 1, order
      write ( *, '(a,i2,a,g24.16)' ) '  w(', i, ') = ', w(i)
    end do
    write ( *, '(a)' ) ' '
    do i = 1, order
      write ( *, '(a,i2,a,g24.16)' ) '  x(', i, ') = ', x(i)
    end do
    write ( *, '(a)' ) ' '
    do i = 1, 2
      write ( *, '(a,i2,a,g24.16)' ) '  r(', i, ') = ', r(i)
    end do
    
  else if ( output(1:3) == 'MAT' ) then
  
    write ( *, '(a)'       ) '%'
    write ( *, '(a)'       ) '%  Weights W, abscissas X and range R'
    write ( *, '(a)'       ) '%  for a Gauss-Jacobi quadrature rule'
    write ( *, '(a,i8)'    ) '%  ORDER = ', order
    write ( *, '(a,g14.6)' ) '%  ALPHA = ', alpha
    write ( *, '(a,g14.6)' ) '%  BETA  = ', beta
    write ( *, '(a)'       ) '%'
    write ( *, '(a)'       ) '%  Standard rule:'
    write ( *, '(a)'       ) '%    Integral ( -1 <= x <= +1 ) (1-x)^ALPHA (1+x)^BETA f(x) dx'
    write ( *, '(a)'       ) '%    is to be approximated by'
    write ( *, '(a)'       ) '%    sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).'
    write ( *, '(a)'       ) '%'

    do i = 1, order
      write ( *, '(a,i2,a,g24.16,a)' ) '  w(', i, ') = ', w(i), ';'
    end do
    write ( *, '(a)' ) ' '
    do i = 1, order
      write ( *, '(a,i2,a,g24.16,a)' ) '  x(', i, ') = ', x(i), ';'
    end do
    write ( *, '(a)' ) ' '
    do i = 1, 2
      write ( *, '(a,i2,a,g24.16,a)' ) '  r(', i, ') = ', r(i), ';'
    end do
    
  else
  
    output_w = trim ( output ) // '_w.txt'
    output_x = trim ( output ) // '_x.txt'
    output_r = trim ( output ) // '_r.txt'

    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) '  Creating quadrature files.'
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) '  "Root" file name is   "' // trim ( output ) // '".'
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) '  Weight file will be   "' // trim ( output_w ) // '".'
    write ( *, '(a)' ) '  Abscissa file will be "' // trim ( output_x ) // '".'
    write ( *, '(a)' ) '  Region file will be   "' // trim ( output_r ) // '".'

    header = .false.
            
    call dtable_write ( output_w, 1, order, w, header )
    call dtable_write ( output_x, 1, order, x, header )
    call dtable_write ( output_r, 1, 2,     r, header )
    
  end if
  
  deallocate ( w )
  deallocate ( x )

  return
end
subroutine jacobi_recur ( p2, dp2, p1, x, order, alpha, beta, b, c )

!*****************************************************************************80
!
!! JACOBI_RECUR finds the value and derivative of a Jacobi polynomial.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    19 February 2008
!
!  Author:
!
!    FORTRAN77 original version by Arthur Stroud, Don Secrest
!    FORTRAN90 version by John Burkardt
!
!  Reference:
!
!    Arthur Stroud, Don Secrest,
!    Gaussian Quadrature Formulas,
!    Prentice Hall, 1966,
!    LC: QA299.4G3S7.
!
!  Parameters:
!
!    Output, real ( kind = 8 ) P2, the value of J(ORDER)(X).
!
!    Output, real ( kind = 8 ) DP2, the value of J'(ORDER)(X).
!
!    Output, real ( kind = 8 ) P1, the value of J(ORDER-1)(X).
!
!    Input, real ( kind = 8 ) X, the point at which polynomials are evaluated.
!
!    Input, integer ( kind = 4 ) ORDER, the order of the polynomial 
!    to be computed.
!
!    Input, real ( kind = 8 ) ALPHA, BETA, the exponents of (1+X) and
!    (1-X) in the quadrature rule.
!
!    Input, real ( kind = 8 ) B(ORDER), C(ORDER), the recursion
!    coefficients.
!
  implicit none

  integer ( kind = 4 ) order

  real    ( kind = 8 ) alpha
  real    ( kind = 8 ) b(order)
  real    ( kind = 8 ) beta
  real    ( kind = 8 ) c(order)
  real    ( kind = 8 ) dp0
  real    ( kind = 8 ) dp1
  real    ( kind = 8 ) dp2
  integer ( kind = 4 ) i
  real    ( kind = 8 ) p0
  real    ( kind = 8 ) p1
  real    ( kind = 8 ) p2
  real    ( kind = 8 ) x

  p1 = 1.0D+00
  dp1 = 0.0D+00

  p2 = x + ( alpha - beta ) / ( alpha + beta + 2.0D+00 )
  dp2 = 1.0D+00

  do i = 2, order

    p0 = p1
    dp0 = dp1

    p1 = p2
    dp1 = dp2

    p2 = ( x - b(i) ) * p1 - c(i) * p0
    dp2 = ( x - b(i) ) * dp1 + p1 - c(i) * dp0

  end do

  return
end
subroutine jacobi_root ( x, order, alpha, beta, dp2, p1, b, c )

!*****************************************************************************80
!
!! JACOBI_ROOT improves an approximate root of a Jacobi polynomial.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    19 February 2008
!
!  Author:
!
!    FORTRAN77 original version by Arthur Stroud, Don Secrest
!    FORTRAN90 version by John Burkardt
!
!  Reference:
!
!    Arthur Stroud, Don Secrest,
!    Gaussian Quadrature Formulas,
!    Prentice Hall, 1966,
!    LC: QA299.4G3S7.
!
!  Parameters:
!
!    Input/output, real ( kind = 8 ) X, the approximate root, which
!    should be improved on output.
!
!    Input, integer ( kind = 4 ) ORDER, the order of the polynomial 
!    to be computed.
!
!    Input, real ( kind = 8 ) ALPHA, BETA, the exponents of (1+X) and
!    (1-X) in the quadrature rule.
!
!    Output, real ( kind = 8 ) DP2, the value of J'(ORDER)(X).
!
!    Output, real ( kind = 8 ) P1, the value of J(ORDER-1)(X).
!
!    Input, real ( kind = 8 ) B(ORDER), C(ORDER), the recursion coefficients.
!
  implicit none

  integer ( kind = 4 ) order

  real    ( kind = 8 ) alpha
  real    ( kind = 8 ) b(order)
  real    ( kind = 8 ) beta
  real    ( kind = 8 ) c(order)
  real    ( kind = 8 ) d
  real    ( kind = 8 ) dp2
  real    ( kind = 8 ) eps
  real    ( kind = 8 ) p1
  real    ( kind = 8 ) p2
  real    ( kind = 8 ) r8_epsilon
  integer ( kind = 4 ) step
  integer ( kind = 4 ), parameter :: step_max = 10
  real    ( kind = 8 ) x

  eps = r8_epsilon ( )

  do step = 1, step_max

    call jacobi_recur ( p2, dp2, p1, x, order, alpha, beta, b, c )

    d = p2 / dp2
    x = x - d

    if ( abs ( d ) <= eps * ( abs ( x ) + 1.0D+00 ) ) then
      return
    end if

  end do

  return
end
function r8_epsilon ( )

!*****************************************************************************80
!
!! R8_EPSILON returns the R8 roundoff unit.
!
!  Discussion:
!
!    The roundoff unit is a number R which is a power of 2 with the
!    property that, to the precision of the computer's arithmetic,
!      1 < 1 + R
!    but
!      1 = ( 1 + R / 2 )
!
!    FORTRAN90 provides the superior library routine
!
!      EPSILON ( X )
!
!  Modified:
!
!    15 April 2004
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Output, real ( kind = 8 ) R8_EPSILON, the R8 round-off unit.
!
  implicit none

  real    ( kind = 8 ) d
  real    ( kind = 8 ) d_test
  real    ( kind = 8 ) r8_epsilon

  d = 1.0D+00
  d_test = 1.0D+00 + d / 2.0D+00

  do while ( 1.0D+00 < d_test )
    d = d / 2.0D+00
    d_test = 1.0D+00 + d / 2.0D+00
  end do

  r8_epsilon = d

  return
end
function r8_gamma ( x )

!*****************************************************************************80
!
!! R8_GAMMA evaluates Gamma(X) for a real argument.
!
!  Discussion:
!
!    This function was originally named DGAMMA.
!
!    However, a number of Fortran compilers now include a library 
!    function of this name.  To avoid conflicts, this function was
!    renamed R8_GAMMA.
!
!    This routine calculates the GAMMA function for a real argument X.
!    Computation is based on an algorithm outlined in reference 1.
!    The program uses rational functions that approximate the GAMMA
!    function to at least 20 significant decimal digits.  Coefficients
!    for the approximation over the interval (1,2) are unpublished.
!    Those for the approximation for 12 <= X are from reference 2.
!
!  Modified:
!
!    11 February 2008
!
!  Author:
!
!    FORTRAN77 original version by William Cody, Laura Stoltz
!    FORTRAN90 version by John Burkardt
!
!  Reference:
!
!    William Cody,
!    An Overview of Software Development for Special Functions,
!    in Numerical Analysis Dundee, 1975,
!    edited by GA Watson,
!    Lecture Notes in Mathematics 506,
!    Springer, 1976.
!
!    John Hart, Ward Cheney, Charles Lawson, Hans Maehly,
!    Charles Mesztenyi, John Rice, Henry Thatcher,
!    Christoph Witzgall,
!    Computer Approximations,
!    Wiley, 1968,
!    LC: QA297.C64.
!
!  Parameters:
!
!    Input, real ( kind = 8 ) X, the argument of the function.
!
!    Output, real ( kind = 8 ) R8_GAMMA, the value of the function.
!
  implicit none
!
!  Coefficients for minimax approximation over (12, INF).
!
  real    ( kind = 8 ), dimension ( 7 ) :: c = (/ &
   -1.910444077728D-03, &
    8.4171387781295D-04, &
   -5.952379913043012D-04, &
    7.93650793500350248D-04, &
   -2.777777777777681622553D-03, &
    8.333333333333333331554247D-02, &
    5.7083835261D-03 /)
  real    ( kind = 8 ), parameter :: eps = 2.22D-16
  real    ( kind = 8 ) fact
  real    ( kind = 8 ), parameter :: half = 0.5D+00
  integer ( kind = 4 ) i
  integer ( kind = 4 ) n
  real    ( kind = 8 ), parameter :: one = 1.0D+00
  real    ( kind = 8 ), dimension ( 8 ) :: p = (/ &
    -1.71618513886549492533811D+00, &
     2.47656508055759199108314D+01, &
    -3.79804256470945635097577D+02, &
     6.29331155312818442661052D+02, &
     8.66966202790413211295064D+02, &
    -3.14512729688483675254357D+04, &
    -3.61444134186911729807069D+04, &
     6.64561438202405440627855D+04 /)
  logical parity
  real    ( kind = 8 ), parameter :: pi = 3.1415926535897932384626434D+00
  real    ( kind = 8 ), dimension ( 8 ) :: q = (/ &
    -3.08402300119738975254353D+01, &
     3.15350626979604161529144D+02, &
    -1.01515636749021914166146D+03, &
    -3.10777167157231109440444D+03, &
     2.25381184209801510330112D+04, &
     4.75584627752788110767815D+03, &
    -1.34659959864969306392456D+05, &
    -1.15132259675553483497211D+05 /)
  real    ( kind = 8 ) r8_gamma
  real    ( kind = 8 ) res
  real    ( kind = 8 ), parameter :: sqrtpi = 0.9189385332046727417803297D+00
  real    ( kind = 8 ) sum
  real    ( kind = 8 ), parameter :: twelve = 12.0D+00
  real    ( kind = 8 ), parameter :: two = 2.0D+00
  real    ( kind = 8 ) x
  real    ( kind = 8 ), parameter :: xbig = 171.624D+00
  real    ( kind = 8 ) xden
  real    ( kind = 8 ), parameter :: xinf = 1.0D+30
  real    ( kind = 8 ), parameter :: xminin = 2.23D-308
  real    ( kind = 8 ) xnum
  real    ( kind = 8 ) y
  real    ( kind = 8 ) y1
  real    ( kind = 8 ) ysq
  real    ( kind = 8 ) z
  real    ( kind = 8 ), parameter :: zero = 0.0D+00

  parity = .false.
  fact = one
  n = 0
  y = x
!
!  Argument is negative.
!
  if ( y <= zero ) then

    y = - x
    y1 = aint ( y )
    res = y - y1

    if ( res /= zero ) then

      if ( y1 /= aint ( y1 * half ) * two ) then
        parity = .true.
      end if

      fact = - pi / sin ( pi * res )
      y = y + one

    else

      res = xinf
      r8_gamma = res
      return

    end if

  end if
!
!  Argument is positive.
!
  if ( y < eps ) then
!
!  Argument < EPS.
!
    if ( xminin <= y ) then
      res = one / y
    else
      res = xinf
      r8_gamma = res
      return
    end if

  else if ( y < twelve ) then

    y1 = y
!
!  0.0 < argument < 1.0.
!
    if ( y < one ) then

      z = y
      y = y + one
!
!  1.0 < argument < 12.0.
!  Reduce argument if necessary.
!
    else

      n = int ( y ) - 1
      y = y - real ( n, kind = 8 )
      z = y - one

    end if
!
!  Evaluate approximation for 1.0 < argument < 2.0.
!
    xnum = zero
    xden = one
    do i = 1, 8
      xnum = ( xnum + p(i) ) * z
      xden = xden * z + q(i)
    end do

    res = xnum / xden + one
!
!  Adjust result for case  0.0 < argument < 1.0.
!
    if ( y1 < y ) then

      res = res / y1
!
!  Adjust result for case 2.0 < argument < 12.0.
!
    else if ( y < y1 ) then

      do i = 1, n
        res = res * y
        y = y + one
      end do

    end if

  else
!
!  Evaluate for 12.0 <= argument.
!
    if ( y <= xbig ) then

      ysq = y * y
      sum = c(7)
      do i = 1, 6
        sum = sum / ysq + c(i)
      end do
      sum = sum / y - y + sqrtpi
      sum = sum + ( y - half ) * log ( y )
      res = exp ( sum )

    else

      res = xinf
      r8_gamma = res
      return

    end if

  end if
!
!  Final adjustments and return.
!
  if ( parity ) then
    res = - res
  end if

  if ( fact /= one ) then
    res = fact / res
  end if

  r8_gamma = res

  return
end
subroutine s_blank_delete ( s )

!*****************************************************************************80
!
!! S_BLANK_DELETE removes blanks from a string, left justifying the remainder.
!
!  Discussion:
!
!    All TAB characters are also removed.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    26 July 1998
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input/output, character ( len = * ) S, the string to be transformed.
!
  implicit none

  character c
  integer ( kind = 4 ) get
  integer ( kind = 4 ) put
  integer ( kind = 4 ) nchar
  character ( len = * ) s
  character, parameter :: TAB = char ( 9 )

  put = 0
  nchar = len_trim ( s )

  do get = 1, nchar

    c = s(get:get)

    if ( c /= ' ' .and. c /= TAB ) then
      put = put + 1
      s(put:put) = c
    end if

  end do

  s(put+1:nchar) = ' '

  return
end
subroutine s_to_i4 ( s, ival, ierror, length )

!*****************************************************************************80
!
!! S_TO_I4 reads an I4 from a string.
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    28 June 2000
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, character ( len = * ) S, a string to be examined.
!
!    Output, integer ( kind = 4 ) IVAL, the integer value read from the string.
!    If the string is blank, then IVAL will be returned 0.
!
!    Output, integer ( kind = 4 ) IERROR, an error flag.
!    0, no error.
!    1, an error occurred.
!
!    Output, integer ( kind = 4 ) LENGTH, the number of characters of S 
!    used to make IVAL.
!
  implicit none

  character c
  integer ( kind = 4 ) i
  integer ( kind = 4 ) ierror
  integer ( kind = 4 ) isgn
  integer ( kind = 4 ) istate
  integer ( kind = 4 ) ival
  integer ( kind = 4 ) length
  character ( len = * ) s

  ierror = 0
  istate = 0
  isgn = 1
  ival = 0

  do i = 1, len_trim ( s )

    c = s(i:i)
!
!  Haven't read anything.
!
    if ( istate == 0 ) then

      if ( c == ' ' ) then

      else if ( c == '-' ) then
        istate = 1
        isgn = -1
      else if ( c == '+' ) then
        istate = 1
        isgn = + 1
      else if ( lle ( '0', c ) .and. lle ( c, '9' ) ) then
        istate = 2
        ival = ichar ( c ) - ichar ( '0' )
      else
        ierror = 1
        return
      end if
!
!  Have read the sign, expecting digits.
!
    else if ( istate == 1 ) then

      if ( c == ' ' ) then

      else if ( lle ( '0', c ) .and. lle ( c, '9' ) ) then
        istate = 2
        ival = ichar ( c ) - ichar ( '0' )
      else
        ierror = 1
        return
      end if
!
!  Have read at least one digit, expecting more.
!
    else if ( istate == 2 ) then

      if ( lle ( '0', c ) .and. lle ( c, '9' ) ) then
        ival = 10 * ival + ichar ( c ) - ichar ( '0' )
      else
        ival = isgn * ival
        length = i - 1
        return
      end if

    end if

  end do
!
!  If we read all the characters in the string, see if we're OK.
!
  if ( istate == 2 ) then
    ival = isgn * ival
    length = len_trim ( s )
  else
    ierror = 1
    length = 0
  end if

  return
end
subroutine s_to_r8 ( s, dval, ierror, length )

!*****************************************************************************80
!
!! S_TO_R8 reads an R8 from a string.
!
!  Discussion:
!
!    The routine will read as many characters as possible until it reaches
!    the end of the string, or encounters a character which cannot be
!    part of the number.
!
!    Legal input is:
!
!       1 blanks,
!       2 '+' or '-' sign,
!       2.5 blanks
!       3 integer part,
!       4 decimal point,
!       5 fraction part,
!       6 'E' or 'e' or 'D' or 'd', exponent marker,
!       7 exponent sign,
!       8 exponent integer part,
!       9 exponent decimal point,
!      10 exponent fraction part,
!      11 blanks,
!      12 final comma or semicolon,
!
!    with most quantities optional.
!
!  Example:
!
!    S                 DVAL
!
!    '1'               1.0
!    '     1   '       1.0
!    '1A'              1.0
!    '12,34,56'        12.0
!    '  34 7'          34.0
!    '-1E2ABCD'        -100.0
!    '-1X2ABCD'        -1.0
!    ' 2E-1'           0.2
!    '23.45'           23.45
!    '-4.2E+2'         -420.0
!    '17d2'            1700.0
!    '-14e-2'         -0.14
!    'e2'              100.0
!    '-12.73e-9.23'   -12.73 * 10.0**(-9.23)
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    07 September 2004
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, character ( len = * ) S, the string containing the
!    data to be read.  Reading will begin at position 1 and
!    terminate at the end of the string, or when no more
!    characters can be read to form a legal real.  Blanks,
!    commas, or other nonnumeric data will, in particular,
!    cause the conversion to halt.
!
!    Output, real ( kind = 8 ) DVAL, the value read from the string.
!
!    Output, integer ( kind = 4 ) IERROR, error flag.
!    0, no errors occurred.
!    1, 2, 6 or 7, the input number was garbled.  The
!    value of IERROR is the last type of input successfully
!    read.  For instance, 1 means initial blanks, 2 means
!    a plus or minus sign, and so on.
!
!    Output, integer ( kind = 4 ) LENGTH, the number of characters read
!    to form the number, including any terminating
!    characters such as a trailing comma or blanks.
!
  implicit none

  logical ch_eqi
  character c
  real    ( kind = 8 ) dval
  integer ( kind = 4 ) ierror
  integer ( kind = 4 ) ihave
  integer ( kind = 4 ) isgn
  integer ( kind = 4 ) iterm
  integer ( kind = 4 ) jbot
  integer ( kind = 4 ) jsgn
  integer ( kind = 4 ) jtop
  integer ( kind = 4 ) length
  integer ( kind = 4 ) nchar
  integer ( kind = 4 ) ndig
  real    ( kind = 8 ) rbot
  real    ( kind = 8 ) rexp
  real    ( kind = 8 ) rtop
  character ( len = * ) s

  nchar = len_trim ( s )

  ierror = 0
  dval = 0.0D+00
  length = -1
  isgn = 1
  rtop = 0
  rbot = 1
  jsgn = 1
  jtop = 0
  jbot = 1
  ihave = 1
  iterm = 0

  do

    length = length + 1

    if ( nchar < length+1 ) then
      exit
    end if

    c = s(length+1:length+1)
!
!  Blank character.
!
    if ( c == ' ' ) then

      if ( ihave == 2 ) then

      else if ( ihave == 6 .or. ihave == 7 ) then
        iterm = 1
      else if ( 1 < ihave ) then
        ihave = 11
      end if
!
!  Comma.
!
    else if ( c == ',' .or. c == ';' ) then

      if ( ihave /= 1 ) then
        iterm = 1
        ihave = 12
        length = length + 1
      end if
!
!  Minus sign.
!
    else if ( c == '-' ) then

      if ( ihave == 1 ) then
        ihave = 2
        isgn = -1
      else if ( ihave == 6 ) then
        ihave = 7
        jsgn = -1
      else
        iterm = 1
      end if
!
!  Plus sign.
!
    else if ( c == '+' ) then

      if ( ihave == 1 ) then
        ihave = 2
      else if ( ihave == 6 ) then
        ihave = 7
      else
        iterm = 1
      end if
!
!  Decimal point.
!
    else if ( c == '.' ) then

      if ( ihave < 4 ) then
        ihave = 4
      else if ( 6 <= ihave .and. ihave <= 8 ) then
        ihave = 9
      else
        iterm = 1
      end if
!
!  Scientific notation exponent marker.
!
    else if ( ch_eqi ( c, 'E' ) .or. ch_eqi ( c, 'D' ) ) then

      if ( ihave < 6 ) then
        ihave = 6
      else
        iterm = 1
      end if
!
!  Digit.
!
    else if (  ihave < 11 .and. lle ( '0', c ) .and. lle ( c, '9' ) ) then

      if ( ihave <= 2 ) then
        ihave = 3
      else if ( ihave == 4 ) then
        ihave = 5
      else if ( ihave == 6 .or. ihave == 7 ) then
        ihave = 8
      else if ( ihave == 9 ) then
        ihave = 10
      end if

      call ch_to_digit ( c, ndig )

      if ( ihave == 3 ) then
        rtop = 10.0D+00 * rtop + real ( ndig, kind = 8 )
      else if ( ihave == 5 ) then
        rtop = 10.0D+00 * rtop + real ( ndig, kind = 8 )
        rbot = 10.0D+00 * rbot
      else if ( ihave == 8 ) then
        jtop = 10 * jtop + ndig
      else if ( ihave == 10 ) then
        jtop = 10 * jtop + ndig
        jbot = 10 * jbot
      end if
!
!  Anything else is regarded as a terminator.
!
    else
      iterm = 1
    end if
!
!  If we haven't seen a terminator, and we haven't examined the
!  entire string, go get the next character.
!
    if ( iterm == 1 ) then
      exit
    end if

  end do
!
!  If we haven't seen a terminator, and we have examined the
!  entire string, then we're done, and LENGTH is equal to NCHAR.
!
  if ( iterm /= 1 .and. length+1 == nchar ) then
    length = nchar
  end if
!
!  Number seems to have terminated.  Have we got a legal number?
!  Not if we terminated in states 1, 2, 6 or 7!
!
  if ( ihave == 1 .or. ihave == 2 .or. ihave == 6 .or. ihave == 7 ) then
    ierror = ihave
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) 'S_TO_R8 - Serious error!'
    write ( *, '(a)' ) '  Illegal or nonnumeric input:'
    write ( *, '(a)' ) '    ' // trim ( s )
    return
  end if
!
!  Number seems OK.  Form it.
!
  if ( jtop == 0 ) then
    rexp = 1.0D+00
  else
    if ( jbot == 1 ) then
      rexp = 10.0D+00 ** ( jsgn * jtop )
    else
      rexp = 10.0D+00 ** ( real ( jsgn * jtop, kind = 8 ) &
        / real ( jbot, kind = 8 ) )
    end if
  end if

  dval = real ( isgn, kind = 8 ) * rexp * rtop / rbot

  return
end
subroutine timestamp ( )

!*****************************************************************************80
!
!! TIMESTAMP prints the current YMDHMS date as a time stamp.
!
!  Example:
!
!    May 31 2001   9:45:54.872 AM
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    31 May 2001
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    None
!
  implicit none

  character ( len = 8 ) ampm
  integer ( kind = 4 ) d
  character ( len = 8 ) date
  integer ( kind = 4 ) h
  integer ( kind = 4 ) m
  integer ( kind = 4 ) mm
  character ( len = 9 ), parameter, dimension(12) :: month = (/ &
    'January  ', 'February ', 'March    ', 'April    ', &
    'May      ', 'June     ', 'July     ', 'August   ', &
    'September', 'October  ', 'November ', 'December ' /)
  integer ( kind = 4 ) n
  integer ( kind = 4 ) s
  character ( len = 10 )  time
  integer ( kind = 4 ) values(8)
  integer ( kind = 4 ) y
  character ( len = 5 ) zone

  call date_and_time ( date, time, zone, values )

  y = values(1)
  m = values(2)
  d = values(3)
  h = values(5)
  n = values(6)
  s = values(7)
  mm = values(8)

  if ( h < 12 ) then
    ampm = 'AM'
  else if ( h == 12 ) then
    if ( n == 0 .and. s == 0 ) then
      ampm = 'Noon'
    else
      ampm = 'PM'
    end if
  else
    h = h - 12
    if ( h < 12 ) then
      ampm = 'PM'
    else if ( h == 12 ) then
      if ( n == 0 .and. s == 0 ) then
        ampm = 'Midnight'
      else
        ampm = 'AM'
      end if
    end if
  end if

  write ( *, '(a,1x,i2,1x,i4,2x,i2,a1,i2.2,a1,i2.2,a1,i3.3,1x,a)' ) &
    trim ( month(m) ), d, y, h, ':', n, ':', s, '.', mm, trim ( ampm )

  return
end
subroutine timestring ( string )

!*****************************************************************************80
!
!! TIMESTRING writes the current YMDHMS date into a string.
!
!  Example:
!
!    STRING = 'May 31 2001   9:45:54.872 AM'
!
!  Licensing:
!
!    This code is distributed under the GNU LGPL license. 
!
!  Modified:
!
!    15 March 2003
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Output, character ( len = * ) STRING, contains the date information.
!    A character length of 40 should always be sufficient.
!
  implicit none

  character ( len = 8 ) ampm
  integer ( kind = 4 ) d
  character ( len = 8 ) date
  integer ( kind = 4 ) h
  integer ( kind = 4 ) m
  integer ( kind = 4 ) mm
  character ( len = 9 ), parameter, dimension(12) :: month = (/ &
    'January  ', 'February ', 'March    ', 'April    ', &
    'May      ', 'June     ', 'July     ', 'August   ', &
    'September', 'October  ', 'November ', 'December ' /)
  integer ( kind = 4 ) n
  integer ( kind = 4 ) s
  character ( len = * ) string
  character ( len = 10 )  time
  integer ( kind = 4 ) values(8)
  integer ( kind = 4 ) y
  character ( len = 5 ) zone

  call date_and_time ( date, time, zone, values )

  y = values(1)
  m = values(2)
  d = values(3)
  h = values(5)
  n = values(6)
  s = values(7)
  mm = values(8)

  if ( h < 12 ) then
    ampm = 'AM'
  else if ( h == 12 ) then
    if ( n == 0 .and. s == 0 ) then
      ampm = 'Noon'
    else
      ampm = 'PM'
    end if
  else
    h = h - 12
    if ( h < 12 ) then
      ampm = 'PM'
    else if ( h == 12 ) then
      if ( n == 0 .and. s == 0 ) then
        ampm = 'Midnight'
      else
        ampm = 'AM'
      end if
    end if
  end if

  write ( string, '(a,1x,i2,1x,i4,2x,i2,a1,i2.2,a1,i2.2,a1,i3.3,1x,a)' ) &
    trim ( month(m) ), d, y, h, ':', n, ':', s, '.', mm, trim ( ampm )

  return
end