# pointpats.PointPattern¶

class pointpats.PointPattern(points, window=None, names=None, coord_names=None)[source]

Planar Point Pattern Class 2-D.

Parameters:
points: array

(n,p), n points with p >= 2 attributes on each point. Two attributes must comprise the spatial coordinate pair. Default is that the first two attributes are the x and y spatial coordinates.

window: :class:.Window

Bounding geometric object for the point pattern. If not specified, window will be set to the minimum bounding rectangle of the point pattern.

names: list

The names of the attributes.

coord_names: list

The names of the attributes defining the two spatial coordinates.

Examples

>>> from pointpats import PointPattern
>>> points = [[66.22, 32.54], [22.52, 22.39], [31.01, 81.21],
...           [9.47, 31.02], [30.78, 60.10], [75.21, 58.93],
...           [79.26,  7.68], [8.23, 39.93], [98.73, 77.17],
...           [89.78, 42.53], [65.19, 92.08], [54.46, 8.48]]
>>> pp = PointPattern(points)
>>> pp.n
12
>>> pp.mean_nnd
21.612139802089246
>>> pp.lambda_mbb
0.0015710507711240867
>>> pp.lambda_hull
0.0022667153468973137
>>> pp.hull_area
5294.00395
>>> pp.mbb_area
7638.200000000001

__init__(points, window=None, names=None, coord_names=None)[source]

Methods

 __init__(points[, window, names, coord_names]) add_marks(marks[, mark_names]) explode(mark) Explode a marked point pattern into a sequence of individual point patterns. Find all pairs of points in the pattern that are within r units of each other Flips the coordinates of a point pattern. Bounding geometry for the point pattern knn([k]) Find k nearest neighbors for each point in the pattern knn_other(other[, k]) Find k nearest neighbors in the pattern for each point in other plot([window, title, hull, get_ax]) Plot function for a point pattern. set_window(window) Description of the point pattern. superimpose(point_pattern) Returns a superimposed point pattern. Remove duplicate points in the point pattern.

Attributes

 hull Points defining convex hull in counterclockwise order hull_area Area of convex hull lambda_hull Intensity based on convex hull lambda_mbb Intensity based on minimum bounding box lambda_window Intensity estimate based on area of window max_nnd Max nearest neighbor distance mbb Minimum bounding box mbb_area Area of minimum bounding box mean_nnd Mean nearest neighbor distance min_nnd Min nearest neighbor distance n Number of points nnd Nearest neighbor distances rot Ripley's rule of thumb for distance range in plotting k and related functions tree window Bounding geometry for the point pattern
explode(mark)[source]

Explode a marked point pattern into a sequence of individual point patterns. If the mark has k unique values, then the sequence will be of length k.

Parameters:
mark: string

The label of the mark to use for the subsetting

Returns:
pps: list

sequence of PointPattern instances

find_pairs(r)[source]

Find all pairs of points in the pattern that are within r units of each other

Parameters:
r: float

diameter of pair circle

Returns:
s: set

pairs of points within r units of each other

flip_coordinates()[source]

Flips the coordinates of a point pattern.

Doesn’t change the structure of data frame. This function swaps _x and _y variables, which are used to represent coordinates.

get_window()[source]

Bounding geometry for the point pattern

window.Window

property hull

Points defining convex hull in counterclockwise order

property hull_area

Area of convex hull

knn(k=1)[source]

Find k nearest neighbors for each point in the pattern

Parameters:
k: int

number of nearest neighbors to find

Returns:
nn: array (n x k)

row i column j contains the id for i’s jth nearest neighbor

nnd: array(n x k)

row i column j contains the distance between i and its jth nearest neighbor

knn_other(other, k=1)[source]

Find k nearest neighbors in the pattern for each point in other

Parameters:
other: PointPattern

pointpats.PointPattern

k: int

number of nearest neighbors to find

Returns:
nn: array (n x k)

row i column j contains the id for i’s jth nearest neighbor

nnd: array(n x k)

row i column j contains the distance between i and its jth nearest neighbor

property lambda_hull

Intensity based on convex hull

property lambda_mbb

Intensity based on minimum bounding box

property lambda_window

Intensity estimate based on area of window

The intensity of a point process at point $$s_j$$ can be defined as:

$\lambda(s_j) = \lim \limits_{|\mathbf{A}s_j| \to 0} \left \{ \frac{E(Y(\mathbf{A}s_j)}{|\mathbf{A}s_j|} \right \}$

where $$\mathbf{A}s_j$$ is a small region surrounding location $$s_j$$ with area $$|\mathbf{A}s_j|$$, and $$E(Y(\mathbf{A}s_j))$$ is the expected number of event points in $$\mathbf{A}s_j$$.

The intensity is the mean number of event points per unit of area at point $$s_j$$.

property max_nnd

Max nearest neighbor distance

property mbb

Minimum bounding box

property mbb_area

Area of minimum bounding box

property mean_nnd

Mean nearest neighbor distance

property min_nnd

Min nearest neighbor distance

property n

Number of points

property nnd

Nearest neighbor distances

plot(window=False, title='Point Pattern', hull=False, get_ax=False)[source]

Plot function for a point pattern.

Parameters:
windowboolean

If window is True, plot window of the point pattern. If not, don’t plot window.

titlestring

Name of the figure.

hullboolean

If hull is True, plot convex hull of the point pattern. If not, don’t plot convex hull.

get_axboolean

If get_ax is True, return the current plot ax.

Returns:
axmatplotlib.axes._subplots.AxesSubplot

Current plot ax. Only return it when get_ax is True.

property rot

Ripley’s rule of thumb for distance range in plotting k and related functions

One-quarter the smallest side of the mbb.

set_window(window)[source]
summary()[source]

Description of the point pattern.

superimpose(point_pattern)[source]

Returns a superimposed point pattern.

Parameters:
point_pattern:

PointPattern instance

Returns:
superimposed

PointPattern instance

Examples

>>> from pointpats import PointPattern
>>> points1 = [[1, 3], [4, 5], [0, 0]]
>>> points2 = [[5, 6], [1, 4], [0, 0]]
>>> pp1 = PointPattern(points1)
>>> pp2 = PointPattern(points2)
>>> pp1.superimpose(pp2).points
x  y
0  1  3
1  4  5
2  0  0
0  5  6
1  1  4

property tree
unique()[source]

Remove duplicate points in the point pattern.

Two points in a point pattern are deemed to be identical if their coordinates are the same, and their marks are the same (if any)

Returns:
pp: list

A deduplicated PointPattern instance

Examples

>>> from pointpats import PointPattern
>>> points = [[1.2, 2.1], [1.2, 2.1], [0, 1], [1, 2]]
>>> pp = PointPattern(points)
>>> pp.unique().df
x    y
0  1.2  2.1
2  0.0  1.0
3  1.0  2.0

property window

Bounding geometry for the point pattern

window.Window