# squidpy.gr.ripley

squidpy.gr.ripley(adata, cluster_key, mode='F', spatial_key='spatial', metric='euclidean', n_neigh=2, n_simulations=100, n_observations=1000, max_dist=None, n_steps=50, seed=None, copy=False)[source]

Calculate various Ripley’s statistics for point processes.

According to the ‘mode’ argument, it calculates one of the following Ripley’s statistics: ‘F’, ‘G’ or ‘L’ statistics.

‘F’, ‘G’ are defined as:

$F(t),G(t)=P( d_{i,j} \le t )$

Where $$d_{i,j}$$ represents:

• distances to a random Spatial Poisson Point Process for ‘F’.

• distances to any other point of the dataset for ‘G’.

‘L’ we first need to compute $$K(t)$$, which is defined as:

$K(t) = \frac{1}{\lambda} \sum_{i \ne j} \frac{I(d_{i,j}<t)}{n}$

and then we apply a variance-stabilizing transformation:

$L(t) = (\frac{K(t)}{\pi})^{1/2}$
Parameters:
• adata () – Annotated data object.

• cluster_key (str) – Key in anndata.AnnData.obs where clustering is stored.

• mode (Literal['F', 'G', 'L']) – Which Ripley’s statistic to compute.

• spatial_key (str) – Key in anndata.AnnData.obsm where spatial coordinates are stored.

• metric (str) – Which metric to use for computing distances. For available metrics, check out sklearn.neighbors.DistanceMetric.

• n_neigh (int) – Number of neighbors to consider for the KNN graph.

• n_simulations (int) – How many simulations to run for computing p-values.

• n_observations (int) – How many observations to generate for the Spatial Poisson Point Process.

• max_dist () – Maximum distances for the support. If None, max_dist=$$\sqrt{area \over 2}$$.

• n_steps (int) – Number of steps for the support.

• seed () – Random seed for reproducibility.

• copy (bool) – If True, return the result, otherwise save it to the adata object.

Return type:

dict[str, DataFrame | ndarray[Any, dtype[Any]]]

Returns:

: If copy = True, returns a dict with following keys:

• ’{mode}_stat’ - pandas.DataFrame containing the statistics of choice for the real observations.

• ’sims_stat’ - pandas.DataFrame containing the statistics of choice for the simulations.

• ’bins’ - numpy.ndarray containing the support.

• ’pvalues’ - numpy.ndarray containing the p-values for the statistics of interest.

Otherwise, modifies the adata object with the following key:

Statistics and p-values are computed for each cluster anndata.AnnData.obs ['{cluster_key}'] separately.

References

For reference, check out Wikipedia or .