subroutine r8mat_fs ( n, a, b, x )

c*********************************************************************72
c
cc r8mat_fs() factors and solves a system with one right hand side.
c
c  Discussion:
c
c    An R8MAT is an MxN array of R8's, stored by (I,J) -> [I+J*M].
c
c    This routine differs from R8MAT_FSS in two ways:
c    * only one right hand side is allowed;
c    * the input matrix A is not modified.
c
c    This routine uses partial pivoting, but no pivot vector is required.
c
c  Licensing:
c
c    This code is distributed under the MIT license. 
c
c  Modified:
c
c    20 January 2013
c
c  Author:
c
c    John Burkardt
c
c  Parameters:
c
c    Input, integer N, the order of the matrix.
c    N must be positive.
c
c    Input, double precision A(N,N), the coefficient matrix.
c
c    Input, double precision B(N), the right hand side of the linear system.
c
c    Output, double precision X(N), the solution of the linear system.
c
      implicit none

      integer n

      double precision a(n,n)
      double precision a2(n,n)
      double precision b(n)
      integer i
      integer info
      integer ipiv
      integer j
      integer jcol
      integer k
      double precision piv
      double precision temp
      double precision x(n)
c
c  Copy the matrix.
c
      do j = 1, n
        do i = 1, n
          a2(i,j) = a(i,j)
        end do
      end do

      do i = 1, n
        x(i) = b(i)
      end do

      info = 0

      do jcol = 1, n
c
c  Find the maximum element in column I.
c
        piv = abs ( a2(jcol,jcol) )
        ipiv = jcol
        do i = jcol + 1, n
          if ( piv .lt. abs ( a2(i,jcol) ) ) then
            piv = abs ( a2(i,jcol) )
            ipiv = i
          end if
        end do

        if ( piv .eq. 0.0D+00 ) then
          info = jcol
          write ( *, '(a)' ) ' '
          write ( *, '(a)' ) 'R8MAT_FS - Fatal error!'
          write ( *, '(a,i8)' ) '  Zero pivot on step ', info
          stop 1
        end if
c
c  Switch rows JCOL and IPIV, and B.
c
        if ( jcol .ne. ipiv ) then

          do j = 1, n
            temp = a2(jcol,j)
            a2(jcol,j) = a2(ipiv,j)
            a2(ipiv,j) = temp
          end do

          temp = x(jcol)
          x(jcol) = x(ipiv)
          x(ipiv) = temp

        end if
c
c  Scale the pivot row.
c
        do j = jcol + 1, n
          a2(jcol,j) = a2(jcol,j) / a2(jcol,jcol)
        end do
        x(jcol) = x(jcol) / a2(jcol,jcol)
        a2(jcol,jcol) = 1.0D+00
c
c  Use the pivot row to eliminate lower entries in that column.
c
        do i = jcol + 1, n
          if ( a2(i,jcol) .ne. 0.0D+00 ) then
            temp = - a2(i,jcol)
            a2(i,jcol) = 0.0D+00
            do j = jcol + 1, n
              a2(i,j) = a2(i,j) + temp * a2(jcol,j)
            end do
            x(i) = x(i) + temp * x(jcol)
          end if
        end do

      end do
c
c  Back solve.
c
      do k = n, 2, -1
        do i = 1, k - 1
          x(i) = x(i) - a2(i,k) * x(k)
        end do
      end do

      return
      end
      subroutine r8mat_print ( m, n, a, title )

c*********************************************************************72
c
cc R8MAT_PRINT prints an R8MAT.
c
c  Discussion:
c
c    An R8MAT is an array of R8's.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    20 May 2004
c
c  Author:
c
c    John Burkardt
c
c  Parameters:
c
c    Input, integer M, the number of rows in A.
c
c    Input, integer N, the number of columns in A.
c
c    Input, double precision A(M,N), the matrix.
c
c    Input, character * ( * ) TITLE, a title.
c
      implicit none

      integer m
      integer n

      double precision a(m,n)
      character * ( * ) title

      call r8mat_print_some ( m, n, a, 1, 1, m, n, title )

      return
      end
      subroutine r8mat_print_some ( m, n, a, ilo, jlo, ihi, jhi,
     &  title )

c*********************************************************************72
c
cc R8MAT_PRINT_SOME prints some of an R8MAT.
c
c  Discussion:
c
c    An R8MAT is an array of R8's.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    25 January 2007
c
c  Author:
c
c    John Burkardt
c
c  Parameters:
c
c    Input, integer M, N, the number of rows and columns.
c
c    Input, double precision A(M,N), an M by N matrix to be printed.
c
c    Input, integer ILO, JLO, the first row and column to print.
c
c    Input, integer IHI, JHI, the last row and column to print.
c
c    Input, character * ( * ) TITLE, a title.
c
      implicit none

      integer incx
      parameter ( incx = 5 )
      integer m
      integer n

      double precision a(m,n)
      character * ( 14 ) ctemp(incx)
      integer i
      integer i2hi
      integer i2lo
      integer ihi
      integer ilo
      integer inc
      integer j
      integer j2
      integer j2hi
      integer j2lo
      integer jhi
      integer jlo
      character * ( * ) title

      write ( *, '(a)' ) ' '
      write ( *, '(a)' ) trim ( title )

      if ( m .le. 0 .or. n .le. 0 ) then
        write ( *, '(a)' ) ' '
        write ( *, '(a)' ) '  (None)'
        return
      end if

      do j2lo = max ( jlo, 1 ), min ( jhi, n ), incx

        j2hi = j2lo + incx - 1
        j2hi = min ( j2hi, n )
        j2hi = min ( j2hi, jhi )

        inc = j2hi + 1 - j2lo

        write ( *, '(a)' ) ' '

        do j = j2lo, j2hi
          j2 = j + 1 - j2lo
          write ( ctemp(j2), '(i7,7x)') j
        end do

        write ( *, '(''  Col   '',5a14)' ) ( ctemp(j), j = 1, inc )
        write ( *, '(a)' ) '  Row'
        write ( *, '(a)' ) ' '

        i2lo = max ( ilo, 1 )
        i2hi = min ( ihi, m )

        do i = i2lo, i2hi

          do j2 = 1, inc

            j = j2lo - 1 + j2

            write ( ctemp(j2), '(g14.6)' ) a(i,j)

          end do

          write ( *, '(i5,a,5a14)' ) i, ':', ( ctemp(j), j = 1, inc )

        end do

      end do

      return
      end
      subroutine r8vec_print ( n, a, title )

c*********************************************************************72
c
cc R8VEC_PRINT prints an R8VEC.
c
c  Discussion:
c
c    An R8VEC is a vector of R8's.
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    Input, integer N, the number of components of the vector.
c
c    Input, double precision A(N), the vector to be printed.
c
c    Input, character * ( * ) TITLE, a title.
c
      implicit none

      integer n

      double precision a(n)
      integer i
      character * ( * ) title

      write ( *, '(a)' ) ' '
      write ( *, '(a)' ) trim ( title )
      write ( *, '(a)' ) ' '
      do i = 1, n
        write ( *, '(2x,i8,a,1x,g16.8)' ) i, ':', a(i)
      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