# tree_d_3d.kernels.fmm_m2l.fmm_m2l_numpy

*module*

The version of the ``fmm_m2l`` kernel for machines without Pyccel.

There is no vectorized form (the translation of each pair is a short loop over the expansion order): this is the algorithm of
``fmm_m2l_pyccel.py``, run by the Python interpreter.

[View source](https://github.com/max-models/tree-d-3d/blob/devel/src/tree_d_3d/kernels/fmm_m2l/fmm_m2l_numpy.py#L1-L1)

## tree_d_3d.kernels.fmm_m2l.fmm_m2l_numpy.fmm_m2l

*function*

```python
def fmm_m2l(pairs: int64[:, :], count: int, node_center: float[:, :], moment_re: float[:, :], moment_im: float[:, :], binomial: float[:, :], symmetric: int, inv_re: float[:], inv_im: float[:], local_re: float[:, :], local_im: float[:, :]) -> None
```

Re-exported from: `tree_d_3d.kernels.fmm_m2l.fmm_m2l_pyccel`

Add each pair's multipole of one cell to the other's local expansion.

``symmetric`` nonzero truncates the translated series by total degree
(``k + l <= p``, Dehnen's symmetric truncation) instead of ``k <= p`` and
``l <= p``: the pair interaction then depends on ``z_i - z_j`` only, so the
forces of a mutual pair are exactly antisymmetric. ``inv_re``/``inv_im`` are
scratch buffers of length 2 p + 2.

[View source](https://github.com/max-models/tree-d-3d/blob/devel/src/tree_d_3d/kernels/fmm_m2l/fmm_m2l_pyccel.py#L17-L112)