kups.observables.radial_distribution_function ¶

@no_jax_tracing
def offline_radial_distribution_function(
    positions: Array,
    cell: Cell[Periodic3D],
    rmax: float,
    bins: int,
    *,
    batch_size: int | None = None,
) -> Array:
    """Compute RDF from trajectory data with automatic capacity management.

    Processes large trajectory datasets efficiently by:
    1. Automatically determining neighbor list capacity via trial runs
    2. Processing frames in batches using `jax.lax.map`
    3. Handling assertion failures and retrying with increased capacity

    This function is **not JIT-compilable** and intended for **offline analysis**
    of stored trajectories (e.g., from HDF5 files). For on-the-fly computation,
    use [RadialDistributionFunction][kups.observables.radial_distribution_function.RadialDistributionFunction].

    Args:
        positions: Particle positions, shape `(..., n_frames, n_particles, 3)`.
            Batch dimensions are preserved in output.
        cell: Cell for periodic boundary conditions (shared across frames)
        rmax: Maximum distance for RDF calculation (cutoff radius)
        bins: Number of histogram bins
        batch_size: Number of frames to process simultaneously in jax.lax.map.
            Lower values reduce memory usage. Defaults to None (process all at once).

    Returns:
        RDF array, shape `(..., n_frames, bins)`. Preserves all batch dimensions
        from input positions.

    Example:
        ```python
        import h5py
        from kups.observables.radial_distribution_function import offline_radial_distribution_function

        # Load trajectory from file
        with h5py.File("trajectory.h5", "r") as f:
            positions = f["positions"][:]  # Shape: (n_frames, n_particles, 3)
            cell = PeriodicCell(TriclinicFrame.from_matrix(f["cell"][()]))

        # Compute time-averaged RDF
        g_r = offline_radial_distribution_function(
            positions, cell, rmax=10.0, bins=200, batch_size=100
        )  # Shape: (n_frames, 200)

        # Average over trajectory
        g_r_avg = g_r.mean(axis=0)  # Shape: (200,)

        # Plot
        import matplotlib.pyplot as plt
        r = jnp.linspace(0.025, 9.975, 200)
        plt.plot(r, g_r_avg)
        plt.xlabel("r (Å)")
        plt.ylabel("g(r)")
        ```

    Note:
        - Automatically retries with increased capacity if neighbor list is too small
        - Memory usage scales with `n_frames * batch_size * n_particles²`
        - For very large trajectories, use smaller batch_size to avoid OOM errors
    """

    _SystemData = namedtuple("_SystemData", ["cell", "cutoff"])
    systems = Table.arange(
        _SystemData(cell, jnp.array([rmax])),
        label=SystemId,
    )
    cutoffs = Table((SystemId(0),), jnp.array([rmax]))
    particles_per_system = Table((SystemId(0),), jnp.array([positions.shape[-2]]))

    @dataclass
    class _NeighborListState:
        neighborlist_params: UniversalNeighborlistParameters

    @jit
    @as_result_function
    def rdf_with_capacity(nnlist: DenseNearestNeighborList) -> Array:
        def rdf(pos: Array) -> Array:
            _RDFParticles = namedtuple("_RDFParticles", ["positions", "system"])
            n = pos.shape[0]
            system = Index((SystemId(0),), jnp.zeros(n, dtype=int))
            particles = Table.arange(
                _RDFParticles(jnp.asarray(pos), system),
                label=ParticleId,
            )
            return radial_distribution_function(
                particles,
                systems,
                rmax=rmax,
                bins=bins,
                neighborlist=nnlist,
            )

        return jax.lax.map(
            rdf, positions.reshape(-1, *positions.shape[-2:]), batch_size=batch_size
        )

    params = UniversalNeighborlistParameters.estimate(
        particles_per_system, systems, cutoffs
    )
    capacity = DenseNearestNeighborList.from_state(_NeighborListState(params), cutoffs)
    while (out := rdf_with_capacity(capacity)).failed_assertions:
        capacity = out.fix_or_raise(capacity)
    result = out.value
    result = result.reshape(*positions.shape[:-2], *result.shape[-2:])
    return result

def radial_distribution_function(
    positions: Table[ParticleId, HasPositionsAndSystemIndex],
    systems: Table[SystemId, NeighborListSystems],
    rmax: float,
    bins: int,
    neighborlist: NeighborList[Literal[2]],
) -> Array:
    """Compute radial distribution function $g(r)$ from particle positions.

    Calculates the pair correlation function by:

    1. Finding all particle pairs within rmax using neighbor lists
    2. Computing pairwise distances
    3. Binning distances into histogram
    4. Normalizing by ideal gas distribution: $4\\pi r^2 \\rho dr$

    The normalization includes a finite bin width correction:

    $$g(r) = \\frac{n(r)}{4\\pi r^2 \\rho N \\Delta r} \\cdot \\frac{1}{1 + (\\Delta r)^2/(12r^2)}$$

    where $n(r)$ is the pair count in bin at $r$, $\\rho$ is number density, $N$ is particle
    count, and $\\Delta r$ is bin width.

    Args:
        positions: Indexed particle positions with system assignments.
        systems: Indexed system data with cells.
        rmax: Maximum distance to consider (cutoff radius).
        bins: Number of histogram bins for $g(r)$.
        neighborlist: Cutoff-bound neighbor list algorithm for finding pairs.

    Returns:
        RDF array, shape `(n_systems, bins)`. The $r$-values for each bin are
        centered at $r_i = (i + 0.5) \times dr$ where $dr = r_{\text{max}} / \text{bins}$.

    Note:
        - Excludes self-pairs automatically via neighbor list construction
        - Uses periodic boundary conditions from cell
        - Assumes uniform density within each system
    """
    nnl_positions = _to_nnlist_points(positions)
    edge_result = neighborlist(nnl_positions, systems)
    diffs = edge_result.difference_vectors(positions, systems)
    dists = jnp.linalg.norm(diffs, axis=(-2, -1))
    dr = rmax / bins
    bin_indices = jnp.ceil(dists / dr).astype(int)
    system_index = positions.data.system
    n_sys = system_index.num_labels
    batch_id = system_index.indices[edge_result.indices.indices[:, 0]]
    rdf = jnp.zeros((n_sys, bins + 1), dtype=dists.dtype)
    rdf = rdf.at[batch_id, bin_indices].add(1, mode="drop")

    rr = jnp.linspace(dr / 2, rmax - dr / 2, bins)
    segment_sizes = system_index.counts.data
    phi = segment_sizes / systems.data.cell.volume
    norm = 4.0 * jnp.pi * dr * phi * segment_sizes
    rdf = rdf[:, 1:] / (norm[:, None] * (rr * rr + (dr * dr / 12)))
    return rdf