DFSolver
========

Overview
--------
DFSolver represents an operator that applies the inverse (or an approximate
inverse) of the auxiliary metric matrix V. It is a thin C++/pybind11 wrapper
exposed to Python for efficient dense transformations.

Constructor
-----------

.. code-block:: python

   DFSolver(basis, mtx, type='cholesky', device='cuda', gpu_mem_fraction=0.5)

Parameters
----------
* **basis** *(libintx.Basis)* - basis associated with the matrix.
* **mtx** *(ndarray, shape (n,n))* - square metric matrix.
* **type** *(str)* - solver type (``"cholesky"``, ``"lu"``, ...).
* **device** *(str)* - ``"cuda"`` or ``"host"``.
* **gpu_mem_fraction** *(float)* - GPU memory fraction for CUDA runs.

Methods
-------
* ``solve(vec)`` - apply the transformation in-place (:math:`V^{-1} \ \mathrm{vec}`).

Notes
-----
* The Python binding creates a DFSolver by validating the dimension and then
  calling into the C++ helper that returns a solver object potentially backed
  by GPU resources. See the Python bindings for exact behavior.