Calculate inverse of an operator

[M Cotrufo]

Hi all,

Is there any function in QuTIP to calculate the inverse of an hermitian operator?

I checked both in the docs and in this group but I didnt find anything about it...

[Paul Nation]

Nope.  But you most likely do not need to calculate the actual inverse.  Often times you are looking at an equation of the form A^-1 * x = y, which can be recast as A * y = x.  Thus you just need to do a linear solve.

-P

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[M Cotrufo]

Hi Paul,

thanks for your very quick answer (as usual!)

Unfortunately for this specific case I probably need to explicit calculate the inverse. In case you have access to PRL, what I'm trying to do is to costruct the operator Q_j defined in eq. 9 of this paper http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.76.1055 , which means that I need to calculate the operator 1/sqrt(a.dag()* a) , where a is the annihilation operator of a harmonic oscillator.

I was wondering: is there a way to convert an operator to a regular matrix, and then to convert a matrix to an operator? In this way, I could just calculate the inverse of the matrix and then convert it to an operator.

Michele

[M Cotrufo]

Ok, I found the method "full()" to get the matrix corresponding to an operator, and I see that you can create an operator by just passsing the numerical values. I will try and see if it works!

[Paul Nation]

Yes, that returns a dense array.  Or, you can access the sparse matrix using Q.data.  In your case, I think the full() method is probably better as the inverse is likely dense anyway.  Note however that by converting to a dense matrix, your Hilbert space dimensions will be quite restricted.

-P