Fortran, LU method can't get it working fine - fortran

Question

I'm doing a fortran homework and i have to program the LU method, i have wrote some lines but i'm stuck because it's not working fine.
My program is doing well the array 1 and 2 and for U, and the col 1 and 2 for L but the 3 and 4 are wrong(L and U).
can you help me please?
this is the program:
program lu
implicit none
real*8 A(4,4),L(4,4),U(4,4)
integer i,j,n,k
open(unit=21,file='mat2.dat')
open(unit=22,file='L.dat')
open(unit=23,file='U.dat')
A=0.0d0
L=0.0d0
U=0.0d0
do i=1,4
read(21,*) (A(i,j),j=1,4) !read A matrix
end do
do i=1,4
L(i,1)=A(i,1) !creating array L(i,1)
U(1,i)=A(1,i)/L(1,1) !creating row U(1,i)
end do
do i=2,4
do j=2,4
if(i.eq.j) then
U(i,j)=1 !creating U diagonal=1, since U(1,1) is already created it can start from 2
end if
do n=1,j-1
if (i>=j) then
L(i,j)=A(i,j)-L(i,n)*U(n,j) !creating the L missing part, i think here is an error, but i can't find it
end if
end do
do n=1,i-1
if (i<j) then
U(i,j)=A(i,j)*1/L(i,i)-L(i,n)*U(n,j)*1/L(i,i) !creating the U missing part
end if
end do
end do
end do
do i=1,4
write(22,*) (L(i,j),j=1,4) !write to check if it's working fine
write(23,*) (U(i,j),j=1,4)
end do
end program
and this is the A matrix
3 -1 4 -1
-1 -1 3 1
2 3 -1 -1
7 1 1 2
L and U should looks like this picture
http://i.cubeupload.com/J6u1VN.png
sorry for my bad english :(

Answer 1

Usually, one stores L and U within a unique matrix, and, usually again, one just modifies the initial matrix which is used as input and output.
The algorithm is rather simple; Here is a variant without pivot search :
SUBROUTINE matrix_lu(matrix)
! decomposing a matrix as a product of two triangular matrices (lower and upper)
! the diagonal belongs to the upper triangular matrix (the diagonal of the lower
! triangular matrix is assumed to be equal to the identity matrix)
! Take care : the diagonal of U is already inversed
DOUBLE PRECISION, INTENT(inout) :: matrix(:,:)
INTEGER :: n,i,k,l
n=SIZE(matrix,1)
DO k = 1, n
matrix(k, k) = 1.d0/matrix(k, k)
DO i = k+1, n
matrix(i, k) = matrix(i, k)*matrix(k, k)
ENDDO
DO l = k+1, n
DO i = k+1, n
matrix(i, l) = matrix(i, l)-matrix(i, k)*matrix(k, l)
END DO
END DO
END DO
END SUBROUTINE
So I don't understand several things in your algorithm :
the second loop over j should be from i to n (or i+1 to n) :
there is no test within the loops
the global complexity (number of multiplications) is n^3/3. Your algorithm is in n^3