subroutine mgs ( m, n, c, r, q )

c*********************************************************************72
c
cc mgs() does ... something.  The student is encouraged to figure this out.
c
      integer m
      integer n

      real c(m,n)
      real q(m,n)
      real r(n,n)
      real x(m)
      real xn

      do k = 1, n
      do j = 1, m
      x(j) = c(j,k)
      end do
      xn = 0
      do j = 1, m
      xn = xn + x(j)*x(j)
      end do
      r(k,k) = sqrt(xn)
      if ( 0.0 .lt. r(k,k) ) then
      do j = 1, m
      q(j,k) = c(j,k)/r(k,k)
      end do
      else
      do j = 1, m
      q(j,k) = 0.0
      end do
      end if
      do j = k+1, n
      r(k,j) = 0
      do i=1, m
      r(k,j) = r(k,j) + q(i,k)*c(i,j)
      end do
      do i=1,m
      c(i,j) = c(i,j) - q(i,k)*r(k,j)
      end do
      end do
      end do

      return
      end