Error Programming Cholesky decomposition in FORTRAN 90

Question

Im struggling with my thesis on wave energy devices. Since I am a newbie to FORTRAN 90, I would like to improve my programming skills. Therefore, I just picked up an example from

http://rosettacode.org/wiki/Cholesky_decomposition

and tried to implement what is explained in the homepage. Basically it is about to program the Cholesky factorization of a 3x3 matrix A. I know there are already packages that do the decomposition for Fortran, but I would like to experience myself the effort in learning how to program.

There is no error in compilation, but the results do not match. I basically find out all the elements despite of the element L(3,3). Attached, you can find the code I've created from scratch in Fortran 90:

Program Cholesky_decomp

implicit none
!size of the matrix
INTEGER, PARAMETER :: m=3 !rows
INTEGER, PARAMETER :: n=3 !cols
REAL, DIMENSION(m,n) :: A, L

REAL :: sum1, sum2
INTEGER i,j,k

! Assign values to the matrix
A(1,:)=(/ 25,  15,  -5 /)   
A(2,:)=(/ 15,  18,   0 /)  
A(3,:)=(/ -5,   0,  11 /)

! Initialize values
L(1,1)=sqrt(A(1,1))
L(2,1)=A(2,1)/L(1,1)
L(2,2)=sqrt(A(2,2)-L(2,1)*L(2,1))
L(3,1)=A(3,1)/L(1,1)

sum1=0
sum2=0
do i=1,n
    do k=1,i
        do j=1,k-1
        if (i==k) then
            sum1=sum1+(L(k,j)*L(k,j))
            L(k,k)=sqrt(A(k,k)-sum1)    
        elseif (i > k) then
            sum2=sum2+(L(i,j)*L(k,j))
            L(i,k)=(1/L(k,k))*(A(i,k)-sum2)
        else
            L(i,k)=0
        end if
        end do
    end do
end do

!write output
do i=1,m
    print "(3(1X,F6.1))",L(i,:)
end do

End program Cholesky_decomp

Can you tell me what is the mistake in the code? I get L(3,3)=0 when it should be L(3,3)=3. I'm totally lost, and just for the record: on the Rosetta code homepage there is no solution for fortran, so any any hint is appreciated.

Thank you very much in advance.

Answer 1

You want to set sum1 and sum2 to zero for each iteration of the i and k loops.

Answer 2

I've finally found out how to solve the problem for greater order, 4x4 matrices, etc. as presented in the link I attached above. Here is the final code:

Program Cholesky_decomp
!*************************************************!
!LBH @ ULPGC 06/03/2014
!Compute the Cholesky decomposition for a matrix A
!after the attached 
!http://rosettacode.org/wiki/Cholesky_decomposition
!note that the matrix A is complex since there might
!be values, where the sqrt has complex solutions.
!Here, only the real values are taken into account
!*************************************************! 
implicit none

INTEGER, PARAMETER :: m=3 !rows
INTEGER, PARAMETER :: n=3 !cols
COMPLEX, DIMENSION(m,n) :: A 
REAL, DIMENSION(m,n) :: L
REAL :: sum1, sum2
INTEGER i,j,k

! Assign values to the matrix
A(1,:)=(/ 25,  15,  -5 /)   
A(2,:)=(/ 15,  18,   0 /)  
A(3,:)=(/ -5,   0,  11 /)
!!!!!!!!!!!!another example!!!!!!!
!A(1,:) = (/ 18,  22,   54,   42 /) 
!A(2,:) = (/ 22,  70,   86,   62 /) 
!A(3,:) = (/ 54,  86,  174,  134 /) 
!A(4,:) = (/ 42,  62,  134,  106 /)





! Initialize values
L(1,1)=real(sqrt(A(1,1)))
L(2,1)=A(2,1)/L(1,1)
L(2,2)=real(sqrt(A(2,2)-L(2,1)*L(2,1)))
L(3,1)=A(3,1)/L(1,1)
!for greater order than m,n=3 add initial row value
!for instance if m,n=4 then add the following line
!L(4,1)=A(4,1)/L(1,1)





do i=1,n
    do k=1,i
        sum1=0
        sum2=0
        do j=1,k-1
        if (i==k) then
            sum1=sum1+(L(k,j)*L(k,j))
            L(k,k)=real(sqrt(A(k,k)-sum1))  
        elseif (i > k) then
            sum2=sum2+(L(i,j)*L(k,j))
            L(i,k)=(1/L(k,k))*(A(i,k)-sum2)
        else
            L(i,k)=0
        end if
        end do
    end do
end do

!write output
do i=1,m
    print "(3(1X,F6.1))",L(i,:)
end do

End program Cholesky_decomp

Look forward to hear about comments, better ways to program it, corrections and any kind of feedback. Thanks 2 francescalus for answering so quickly!

Regards, lbh