Behavior of ctranspose.

[amitjamadagni]

ctranpose has the following behavior :

For Input :

m = [1+1im 2+2im 3+3im; 4+4im 5+5im 6+6im; 7+7im 8+8im 9+9im] qm = QuArray(m) qm 3x3 QuMatrix in QuBase.FiniteBasis{QuBase.Orthonormal,1}: ...original coefficients: Array{Complex{Int64},2} Complex{Int64}[1 + 1im 2 + 2im 3 + 3im 4 + 4im 5 + 5im 6 + 6im 7 + 7im 8 + 8im 9 + 9im]

c_qm = ctranspose(qm) c_qm 3x3 DualMatrix in QuBase.FiniteBasis{QuBase.Orthonormal,1}: ...original coefficients: Array{Complex{Int64},2} Complex{Int64}[1 + 1im 2 + 2im 3 + 3im 4 + 4im 5 + 5im 6 + 6im 7 + 7im 8 + 8im 9 + 9im]

In the above case the conjugate transpose is not performed.

The pull request aims to fix this. Hope my understanding of the ctranspose is right. Please do comment. Thanks.

[acroy]

Good thinking, but actually this is on purpose. The CTranspose type is basically just a label, which denotes a QuArray as "ctransposed". The actual transposition is only done when necessary, e.g. in getindex or in * (note the use of Ac_mul_B in *(::CTranspose, ::QuArray)).

The printing of the coefficients is broken though...

[jrevels]

This is intentional behavior. Our ctranspose is lazy, meaning that the actual conjugation and transposition on the coefficient array does not occur until the elements stored within are accessed (see how getindex and setindex! perform the eager ctranspose for access/mutation purposes, but do not perform the eager ctranspose on the underlying coefficient array).

For a majority of the operations we care about, it is enough to simply mark a QuArray as conjugate transposed rather than to actually perform the conjugate transpose, which requires a full copy of the array. A good example of this is all of the recently defined multiplication code, which uses Ac_mul_B and the like.

What you got caught up on here, I think, is that the current pretty-printing methods are just shoddy - the only indication that c_qm has been conjugate transposed is that it prints out DualMatrix instead of QuMatrix. The coefficients printed, however, are simply the original ones obtained by using rawcoeffs. This is confusing and should be fixed in the future, but it's been lower priority so far compared to getting most other basic functionality up and running.

Edit: @acroy you beat me to it!

[acroy]

@jrevels : only by 4 minutes :-)

[amitjamadagni]

@acroy @jrevels thanks for the explanation on this. But I have a doubt given an operator/vector how do we end up with the ctranspose of it in sense ket -> bra and bra -> ket and operator to a operator. I would like to do something like ctranspose(A) where A is an operator and end up with the result. Did I miss something really basic here ??

[acroy]

Well, it depends of course want you want to do, but for all practical purposes qt=qa' for qa::QuArray behaves like the dual of qa (at least that is the plan). For example if you access the coefficients via qt[indx] you will find that they are conjugated (and transposed). Also if you write qt*qa you will get a number if qa is a QuVector and so forth. What are you trying to do?

However, we should probably add

coeffs(qa::QuArray)=qa.coeffs
coeffs(qt::CTranspose)=rawcoeffs(qt)'

to make life a bit easier? (But we should avoid to use coeffs too much, since it spoils the lazy evaluation)

[amitjamadagni]

Yeah I was looking for the behavior of coeffs which has been implemented in the latest pull.