subroutine i4vec_transpose_print ( n, a, title )

c*********************************************************************72
c
cc i4vec_transpose_print() prints an I4VEC "transposed".
c
c  Discussion:
c
c    An I4VEC is a vector of I4's.
c
c  Example:
c
c    A = (/ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 /)
c    TITLE = 'My vector:  '
c
c    My vector:
c
c        1    2    3    4    5
c        6    7    8    9   10
c       11
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    31 August 2008
c
c  Author:
c
c    John Burkardt
c
c  Parameters:
c
c    Input, integer N, the number of components of the vector.
c
c    Input, integer A(N), the vector to be printed.
c
c    Input, character ( len = * ) TITLE, a title.
c
      implicit none

      integer n

      integer a(n)
      integer i
      integer ihi
      integer ilo
      character ( len = * ) title

      write ( *, '(a)' ) ' '
      write ( *, '(a)' ) trim ( title )
      write ( *, '(a)' ) ' '
      do ilo = 1, n, 5
        ihi = min ( ilo + 5 - 1, n )
        write ( *, '(5i12)' ) ( a(i), i = ilo, ihi)
      end do

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

c*********************************************************************72
c
cc I4VEC_UNIFORM_AB returns a scaled pseudorandom I4VEC.
c
c  Discussion:
c
c    An I4VEC is a vector of I4's.
c
c    The pseudorandom numbers should be uniformly distributed
c    between A and B.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    12 November 2006
c
c  Author:
c
c    John Burkardt
c
c  Parameters:
c
c    Input, integer N, the dimension of the vector.
c
c    Input, integer A, B, the limits of the interval.
c
c    Input/output, integer SEED, the "seed" value, which should NOT be 0.
c    On output, SEED has been updated.
c
c    Output, integer X(N), a vector of numbers between A and B.
c
      implicit none

      integer n

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

      if ( seed .eq. 0 ) then
        write ( *, '(a)' ) ' '
        write ( *, '(a)' ) 'I4VEC_UNIFORM_AB - 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 .lt. 0 ) then
          seed = seed + 2147483647
        end if

        r = real ( seed ) * 4.656612875E-10
c
c  Scale R to lie between A-0.5 and B+0.5.
c
        r = ( 1.0E+00 - r ) * ( real ( min ( a, b ) ) - 0.5E+00 )
     &    +             r   * ( real ( max ( a, b ) ) + 0.5E+00 )
c
c  Use rounding to convert R to an integer between A and B.
c
        value = nint ( r )

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

        x(i) = value

      end do

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

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

      integer m
      integer n

      integer e(m)
      integer i
      integer j
      double precision v(n)
      double precision x(m,n)

      do j = 1, n
        v(j) = 1.0D+00
      end do

      do i = 1, m
        if ( 0 .ne. e(i) ) then
          do j = 1, n
            v(j) = v(j) * x(i,j) ** e(i)
          end do
        end if
      end do

      return
      end
      subroutine r8mat_nint ( m, n, a )

c*********************************************************************72
c
cc R8MAT_NINT rounds the entries of an R8MAT.
c
c  Discussion:
c
c    An R8MAT is an array of R8 values.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    22 November 2011
c
c  Author:
c
c    John Burkardt
c
c  Parameters:
c
c    Input, integer M, N, the number of rows and columns of A.
c
c    Input/output, double precision A(M,N), the matrix to be NINT'ed.
c
      implicit none
   
      integer m
      integer n

      double precision a(m,n)
      integer i
      integer j

      do j = 1, n
        do i = 1, m
          a(i,j) = dble ( nint ( a(i,j) ) )
        end do
      end do

      return
      end
      subroutine r8mat_uniform_ab ( m, n, a, b, seed, r )

c*********************************************************************72
c
cc R8MAT_UNIFORM_AB returns a scaled pseudorandom R8MAT.
c
c  Discussion:
c
c    A <= R(I,J) <= B.
c
c  Licensing:
c
c    This code is distributed under the MIT license. 
c
c  Modified:
c
c    05 February 2005
c
c  Author:
c
c    John Burkardt
c
c  Reference:
c
c    Paul Bratley, Bennett Fox, Linus Schrage,
c    A Guide to Simulation,
c    Second Edition,
c    Springer, 1987,
c    ISBN: 0387964673,
c    LC: QA76.9.C65.B73.
c
c    Bennett Fox,
c    Algorithm 647:
c    Implementation and Relative Efficiency of Quasirandom
c    Sequence Generators,
c    ACM Transactions on Mathematical Software,
c    Volume 12, Number 4, December 1986, pages 362-376.
c
c    Pierre L'Ecuyer,
c    Random Number Generation,
c    in Handbook of Simulation,
c    edited by Jerry Banks,
c    Wiley, 1998,
c    ISBN: 0471134031,
c    LC: T57.62.H37.
c
c    Peter Lewis, Allen Goodman, James Miller,
c    A Pseudo-Random Number Generator for the System/360,
c    IBM Systems Journal,
c    Volume 8, Number 2, 1969, pages 136-143.
c
c  Parameters:
c
c    Input, integer M, N, the number of rows and columns in the array.
c
c    Input, double precision A, B, the lower and upper limits.
c
c    Input/output, integer SEED, the "seed" value, which should NOT be 0.
c    On output, SEED has been updated.
c
c    Output, double precision R(M,N), the array of pseudorandom values.
c
      implicit none

      integer m
      integer n

      double precision a
      double precision b
      integer i
      integer i4_huge
      parameter ( i4_huge = 2147483647 )
      integer j
      integer k
      integer seed
      double precision r(m,n)

      if ( seed .eq. 0 ) then
        write ( *, '(a)' ) ' '
        write ( *, '(a)' ) 'R8MAT_UNIFORM_AB - Fatal error!'
        write ( *, '(a)' ) '  Input value of SEED = 0.'
        stop 1
      end if

      do j = 1, n

        do i = 1, m

          k = seed / 127773

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

          if ( seed .lt. 0 ) then
            seed = seed + i4_huge
          end if

          r(i,j) = a + ( b - a ) * dble ( seed ) * 4.656612875D-10

        end do
      end do

      return
      end
      subroutine timestamp ( )

c*********************************************************************72
c
cc TIMESTAMP prints out the current YMDHMS date as a timestamp.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    12 January 2007
c
c  Author:
c
c    John Burkardt
c
c  Parameters:
c
c    None
c
      implicit none

      character * ( 8 ) ampm
      integer d
      character * ( 8 ) date
      integer h
      integer m
      integer mm
      character * ( 9 ) month(12)
      integer n
      integer s
      character * ( 10 ) time
      integer 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 .lt. 12 ) then
        ampm = 'AM'
      else if ( h .eq. 12 ) then
        if ( n .eq. 0 .and. s .eq. 0 ) then
          ampm = 'Noon'
        else
          ampm = 'PM'
        end if
      else
        h = h - 12
        if ( h .lt. 12 ) then
          ampm = 'PM'
        else if ( h .eq. 12 ) then
          if ( n .eq. 0 .and. s .eq. 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