Single column cases

To debug the codes which you generalized for cI(), cJ(), L(), and O(), simply rerun your Poisson solver (don't forget to run ``setup.m'' first!) and verify that you have the same results. This verifies that these operators function properly in the case of a single column.

To verify the new operators cIdag() and cJdag(), you should check the identities which actually define the mathematic meaning of the Hermitian conjugate of an operator,

$$\begin{eqnarray*} \left( a^\dagger {\cal I}b \right)^* & = & b^\dagger {\cal I}^... ...^\dagger {\cal J}b \right)^* & = & b^\dagger {\cal J}^\dagger a, \end{eqnarray*}$$

for all vectors $a$ and $b$. Cut and paste the fragment below into the octave prompt to check the above identities:

a=randn(prod(S),1)+i*randn(prod(S),1); %# Single columns of random complex data
b=randn(prod(S),1)+i*randn(prod(S),1);

conj(a'*cI(b))
b'*cIdag(a)

conj(a'*cJ(b))
b'*cJdag(a)