program lu1
  implicit none
  call check( reshape([real(8)::1,2,1,3,4,1,5,7,0                  ],[3,3]) )
  call check( reshape([real(8)::11,1,3,2,9,5,17,5,24,2,18,7,2,6,1,1],[4,4]) )

contains

  subroutine check(a)
    real(8), intent(in)   :: a(:,:)
    integer               :: i,j,n
    real(8), allocatable  :: aa(:,:),l(:,:),u(:,:)
    integer, allocatable  :: p(:,:)
    integer, allocatable  :: ipiv(:)
    n = size(a,1)
    allocate(aa(n,n),l(n,n),u(n,n),p(n,n),ipiv(n))
    forall (j=1:n,i=1:n)
      aa(i,j) = a(i,j)
      u (i,j) = 0d0
      p (i,j) = merge(1  ,0  ,i.eq.j)
      l (i,j) = merge(1d0,0d0,i.eq.j)
    end forall
    call lu(aa, ipiv)
    do i = 1,n
       l(i, :i-1) = aa(ipiv(i), :i-1)
       u(i,i:   ) = aa(ipiv(i),i:   )
    end do
    p(ipiv,:) = p
    call mat_print('a',a)
    call mat_print('p',p)
    call mat_print('l',l)
    call mat_print('u',u)
    print *, "residual"
    print *, "|| P.A - L.U || =  ", maxval(abs(matmul(p,a)-matmul(l,u)))
  end subroutine

  subroutine lu(a,p)
!   in situ decomposition, corresponds to LAPACK's dgebtrf
    real(8), intent(inout) :: a(:,:)
    integer, intent(out  ) :: p(:)
    integer                :: n, i,j,k,kmax
    n = size(a,1)
    p = [ ( i, i=1,n ) ]
    do k = 1,n-1
        kmax = maxloc(abs(a(p(k:),k)),1) + k-1
        if (kmax /= k ) p([k, kmax]) = p([kmax, k])
        a(p(k+1:),k) = a(p(k+1:),k) / a(p(k),k)
        forall (j=k+1:n) a(p(k+1:),j) = a(p(k+1:),j) - a(p(k+1:),k) * a(p(k),j)
    end do
  end subroutine

  subroutine mat_print(amsg,a)
    character(*), intent(in) :: amsg
    class    (*), intent(in) :: a(:,:)
    integer                  :: i
    print*,' '
    print*,amsg
    do i=1,size(a,1)
      select type (a)
        type is (real(8)) ; print'(100f8.2)',a(i,:)
        type is (integer) ; print'(100i8  )',a(i,:)
      end select
    end do
    print*,' '
  end subroutine

end program