Why would chol fail?

 I have a positive definite sparse array Ainv. When I do the chol like

 L=chol(Ainv);
 M = L*L';
 isequal(M,Ainv)

I find that M is not equal to Ainv. How can I use chol to get a right answer?

Answer 1

[Stephan]

Hi,

L*L'

is not the same as

L'*L

The way you do use chol will fulfill the second equation.

You can test with this little example:

A = [7 3; 3 7]
ev = eig(A)
Ch = chol(A)
B1 = Ch'*Ch
B2 = Ch * Ch'

EDIT:

Is Ainv symmetric? If it is, consider that we are dealing with double precision numbers and the operations you perform have rounding errors. See this example:

A = [7 3; 3 7]
Ch = chol(A)
B1 = Ch' * Ch
same = isequal(A,B1)
diff = A-B1
B2 = round(Ch' * Ch)
same2 = isequal(A,B2)
diff2 = A-B2

So there is not a problem with chol, since this is a normal behavior.

Best regards

Stephan

[SingHua Tsai]

Thank you for your help!

Answer 2

[SingHua Tsai]

Hi,Stephan, thank you for your help and advice. I already revise it as follow

 L=chol(Ainv);
 M = L'*L;
 isequal(M,Ainv)

But M is still not equal to Ainv. I have no idea how to modify it.

Thank for your time.

[Stephan]

See my edited answer