How to get started#
This section cover the xfac c++ API, which is very similar to it python binding xfacpy.
Simple use cases can be found in the Tutorials, while
more advanced use cases and explicit examples for the C++ API are found in the testcases, which cover the full scope of the library.
The testcases can be found in the test folder of the source-code repository.
A detailed description of the algorithms, which contains the mathematical definitions and further usescases in form of explicit code examples,
can be found in the main article on xfac.
The main components of the library are represented below:
To factorize a discrete tensor function \(F\),
xfacintroduces the classTensorCI2(orTensorCI1for legacy reasons). Its main output is the tensor train, stored in the classTensorTrain, which represents a list of 3-leg tensors.To factorize a function on the continuous \(f:\mathcal{R}^N\rightarrow\mathcal{C}\),
xfacintroduces the helper classCTensorCI2. TheCTensorCI2is aTensorCI2that can be constructed from a multidimensional function \(f\) by providing also the grid of points for each component. The main output ofCTensorCI2is a continuous tensor trainCTensorTrain, which can be evaluated at any point in \(\mathcal{R}^N\) including those outside the original grid.To factorize a function on the continuous using quantics,
xfacintroduces the helper classQTensorCI. Again, theQTensorCIis aTensorCI2that can be constructed from a multidimensional function \(f\) by providing also the quantics grid. The main output ofQTensorCIis a quantics tensor trainQTensorTrain, which is a cheap representation of the function \(f\) that can be evaluated, and saved/loaded to file.As an independent topic, to build a tensor train for operators, also known as matrix product operator,
xfacintroduces classes to collect sum of rank-1 operators, in such a way that the Hamiltonian definitions can be written easily. The posterior conversion toTensorTraindoesn’t loss any information, similar to the SVD method for autompo.