Note

Click here to download the full example code

Examples in 3D

This section contains several examples on how to generate 3D data with pyclugen. To run the examples we first need to import the clugen() function:

import numpy as np
from pyclugen import clugen

To plot these examples we use the plot_examples_3d function:

from plot_functions import plot_examples_3d

Manipulating the direction of cluster-supporting lines

Using the direction parameter

seed = 321

e043 = clugen(3, 4, 500, [1, 0, 0], 0, [10, 10, 10], 15, 1.5, 0.5, rng=seed)
e044 = clugen(3, 4, 500, [1, 1, 1], 0, [10, 10, 10], 15, 1.5, 0.5, rng=seed)
e045 = clugen(3, 4, 500, [0, 0, 1], 0, [10, 10, 10], 15, 1.5, 0.5, rng=seed)

plt = plot_examples_3d(
    e043, "e043: direction = [1, 0, 0]",
    e044, "e044: direction = [1, 1, 1]",
    e045, "e045: direction = [0, 0, 1]")

Changing the angle_disp parameter and using a custom angle_deltas_fn function

seed = 321

# Custom angle_deltas function: arbitrarily rotate some clusters by 90 degrees
def angdel_90_fn(nclu, astd, rng):
    return rng.choice([0, np.pi / 2], size=nclu)

e046 = clugen(3, 6, 1000, [1, 0, 0], 0, [10, 10, 10], 15, 1.5, 0.5, rng=seed)
e047 = clugen(3, 6, 1000, [1, 0, 0], np.pi / 8, [10, 10, 10], 15, 1.5, 0.5, rng=seed)
e048 = clugen(3, 6, 1000, [1, 0, 0], 0, [10, 10, 10], 15, 1.5, 0.5, rng=seed,
    angle_deltas_fn=angdel_90_fn)

plt = plot_examples_3d(
    e046, "e046: angle_disp = 0",
    e047, "e047: angle_disp = π / 8",
    e048, "e048: custom angle_deltas function")

Specifying a main direction for each cluster and changing angle_disp

seed = 123

# Define a main direction for each cluster
dirs = [[1, 1, 1], [0, 0, 1], [1, 0, 0], [0, 1, 0], [-1, 1, 1]]

e049 = clugen(3, 5, 1000, dirs, 0, np.zeros(3), 20, 0, 0.2, proj_dist_fn="unif", rng=seed)
e050 = clugen(3, 5, 1000, dirs, np.pi / 12, np.zeros(3), 20, 0, 0.2, proj_dist_fn="unif", rng=seed)
e051 = clugen(3, 5, 1000, dirs, np.pi / 4, np.zeros(3), 20, 0, 0.2, proj_dist_fn="unif", rng=seed)

plot_examples_3d(
    e049, "e049: angle_disp = 0",
    e050, "e050: angle_disp = π / 12",
    e051, "e051: angle_disp = π / 4")

Manipulating the length of cluster-supporting lines

Using the llength parameter

seed = 789

e052 = clugen(3, 5, 800, [1, 0, 0], np.pi / 10, [10, 10, 10], 0, 0, 0.5, rng=seed,
    point_dist_fn="n")
e053 = clugen(3, 5, 800, [1, 0, 0], np.pi / 10, [10, 10, 10], 10, 0, 0.5, rng=seed,
    point_dist_fn="n")
e054 = clugen(3, 5, 800, [1, 0, 0], np.pi / 10, [10, 10, 10], 30, 0, 0.5, rng=seed,
    point_dist_fn="n")

plt = plot_examples_3d(
    e052, "e052: llength = 0",
    e053, "e053: llength = 10",
    e054, "e054: llength = 30")

Changing the llength_disp parameter and using a custom llengths_fn function

seed = 765

# Custom llengths function: line lengths tend to grow for each new cluster
def llen_grow_fn(nclu, llen, llenstd, rng):
    return llen * np.arange(nclu) + rng.normal(scale=llenstd, size=nclu)

e055 = clugen(3, 5, 800, [1, 0, 0], np.pi / 10, [10, 10, 10], 15,  0.0, 0.5, rng=seed,
    point_dist_fn="n")
e056 = clugen(3, 5, 800, [1, 0, 0], np.pi / 10, [10, 10, 10], 15, 10.0, 0.5, rng=seed,
    point_dist_fn="n")
e057 = clugen(3, 5, 800, [1, 0, 0], np.pi / 10, [10, 10, 10], 10,  0.1, 0.5, rng=seed,
    point_dist_fn="n", llengths_fn=llen_grow_fn)

plt = plot_examples_3d(
    e055, "e055: llength_disp = 0.0",
    e056, "e056: llength_disp = 10.0",
    e057, "e057: custom llengths function")

Manipulating relative cluster positions

Using the cluster_sep parameter

seed = 765

e058 = clugen(3, 8, 1000, [1, 1, 1], np.pi / 4, [30, 10, 10], 25, 4, 3, rng=seed)
e059 = clugen(3, 8, 1000, [1, 1, 1], np.pi / 4, [10, 30, 10], 25, 4, 3, rng=seed)
e060 = clugen(3, 8, 1000, [1, 1, 1], np.pi / 4, [10, 10, 30], 25, 4, 3, rng=seed)

plt = plot_examples_3d(
    e058, "e058: cluster_sep = [30, 10, 10]",
    e059, "e059: cluster_sep = [10, 30, 10]",
    e060, "e060: cluster_sep = [10, 10, 30]")

Changing the cluster_offset parameter and using a custom clucenters_fn function

# Custom clucenters function: places clusters in a diagonal
def centers_diag_fn(nclu, csep, coff, rng):
    return np.ones((nclu, len(csep))) * np.arange(1, nclu + 1)[:, None] * np.max(csep) + coff

e061 = clugen(3, 8, 1000, [1, 1, 1], np.pi / 4, [10, 10, 10], 12, 3, 2.5, rng=seed)
e062 = clugen(3, 8, 1000, [1, 1, 1], np.pi / 4, [10, 10, 10], 12, 3, 2.5, rng=seed,
    cluster_offset=[30, -30, 30])
e063 = clugen(3, 8, 1000, [1, 1, 1], np.pi / 4, [10, 10, 10], 12, 3, 2.5, rng=seed,
    cluster_offset=[-40, -40, -40], clucenters_fn=centers_diag_fn)

plt = plot_examples_3d(
    e061, "e061: default",
    e062, "e062: cluster_offset=[30, -30, 30]",
    e063, "e063: custom clucenters function")

Lateral dispersion and placement of point projections on the line

Normal projection placement (default): proj_dist_fn="norm"

seed = 246

e064 = clugen(3, 4, 1000, [1, 0, 0], np.pi / 2, [20, 20, 20], 13, 2, 0.0, rng=seed)
e065 = clugen(3, 4, 1000, [1, 0, 0], np.pi / 2, [20, 20, 20], 13, 2, 1.0, rng=seed)
e066 = clugen(3, 4, 1000, [1, 0, 0], np.pi / 2, [20, 20, 20], 13, 2, 3.0, rng=seed)

plt = plot_examples_3d(
    e064, "e064: lateral_disp = 0",
    e065, "e065: lateral_disp = 1",
    e066, "e066: lateral_disp = 3")

Uniform projection placement: proj_dist_fn="unif"

seed = 246

e067 = clugen(3, 4, 1000, [1, 0, 0], np.pi / 2, [20, 20, 20], 13, 2, 0.0, rng=seed,
    proj_dist_fn="unif")
e068 = clugen(3, 4, 1000, [1, 0, 0], np.pi / 2, [20, 20, 20], 13, 2, 1.0, rng=seed,
    proj_dist_fn="unif")
e069 = clugen(3, 4, 1000, [1, 0, 0], np.pi / 2, [20, 20, 20], 13, 2, 3.0, rng=seed,
    proj_dist_fn="unif")

plt = plot_examples_3d(
    e067, "e067: lateral_disp = 0",
    e068, "e068: lateral_disp = 1",
    e069, "e069: lateral_disp = 3")

Custom projection placement using the Laplace distribution

seed = 246

# Custom proj_dist_fn: point projections placed using the Laplace distribution
def proj_laplace(len, n, rng):
    return rng.laplace(scale=len / 6, size=n)

e070 = clugen(3, 4, 1000, [1, 0, 0], np.pi / 2, [20, 20, 20], 13, 2, 0.0, rng=seed,
    proj_dist_fn=proj_laplace)
e071 = clugen(3, 4, 1000, [1, 0, 0], np.pi / 2, [20, 20, 20], 13, 2, 1.0, rng=seed,
    proj_dist_fn=proj_laplace)
e072 = clugen(3, 4, 1000, [1, 0, 0], np.pi / 2, [20, 20, 20], 13, 2, 3.0, rng=seed,
    proj_dist_fn=proj_laplace)

plt = plot_examples_3d(
    e070, "e070: lateral_disp = 0",
    e071, "e071: lateral_disp = 1",
    e072, "e072: lateral_disp = 3")

Controlling final point positions from their projections on the cluster-supporting line

Points on hyperplane orthogonal to cluster-supporting line (default): point_dist_fn="n-1"

seed = 840

# Custom proj_dist_fn: point projections placed using the Laplace distribution
def proj_laplace(len, n, rng):
    return rng.laplace(scale=len / 6, size=n)

e073 = clugen(3, 5, 1500, [1, 0, 0], np.pi / 3, [20, 20, 20], 22, 3, 2, rng=seed)
e074 = clugen(3, 5, 1500, [1, 0, 0], np.pi / 3, [20, 20, 20], 22, 3, 2, rng=seed,
    proj_dist_fn="unif")
e075 = clugen(3, 5, 1500, [1, 0, 0], np.pi / 3, [20, 20, 20], 22, 3, 2, rng=seed,
    proj_dist_fn=proj_laplace)

plt = plot_examples_3d(
    e073, "e073: proj_dist_fn=\"norm\" (default)",
    e074, "e074: proj_dist_fn=\"unif\"",
    e075, "e075: custom proj_dist_fn (Laplace)")

Points around projection on cluster-supporting line: point_dist_fn="n"

seed = 840

# Custom proj_dist_fn: point projections placed using the Laplace distribution
def proj_laplace(len, n, rng):
    return rng.laplace(scale=len / 6, size=n)

e076 = clugen(3, 5, 1500, [1, 0, 0], np.pi / 3, [20, 20, 20], 22, 3, 2, rng=seed,
    point_dist_fn="n")
e077 = clugen(3, 5, 1500, [1, 0, 0], np.pi / 3, [20, 20, 20], 22, 3, 2, rng=seed,
    point_dist_fn="n", proj_dist_fn="unif")
e078 = clugen(3, 5, 1500, [1, 0, 0], np.pi / 3, [20, 20, 20], 22, 3, 2, rng=seed,
    point_dist_fn="n", proj_dist_fn=proj_laplace)

plt = plot_examples_3d(
    e076, "e076: proj_dist_fn=\"norm\" (default)",
    e077, "e077: proj_dist_fn=\"unif\"",
    e078, "e078: custom proj_dist_fn (Laplace)")

Custom point placement using the exponential distribution

For this example we require the clupoints_n_1_template() helper function:

from pyclugen import clupoints_n_1_template

seed = 840

# Custom point_dist_fn: final points placed using the Exponential distribution
def clupoints_n_1_exp(projs, lat_std, len, clu_dir, clu_ctr, rng):
    def dist_exp(npts, lstd, rg):
        return lstd * rg.exponential(scale=2 / lstd, size=npts)
    return clupoints_n_1_template(projs, lat_std, clu_dir, dist_exp, rng=rng)

# Custom proj_dist_fn: point projections placed using the Laplace distribution
def proj_laplace(len, n, rng):
    return rng.laplace(scale=len / 6, size=n)

e079 = clugen(3, 5, 1500, [1, 0, 0], np.pi / 3, [20, 20, 20], 22, 3, 2, rng=seed,
    point_dist_fn=clupoints_n_1_exp)
e080 = clugen(3, 5, 1500, [1, 0, 0], np.pi / 3, [20, 20, 20], 22, 3, 2, rng=seed,
    point_dist_fn=clupoints_n_1_exp, proj_dist_fn="unif")
e081 = clugen(3, 5, 1500, [1, 0, 0], np.pi / 3, [20, 20, 20], 22, 3, 2, rng=seed,
    point_dist_fn=clupoints_n_1_exp, proj_dist_fn=proj_laplace)

plt = plot_examples_3d(
    e079, "e079: proj_dist_fn=\"norm\" (default)",
    e080, "e080: proj_dist_fn=\"unif\"",
    e081, "e081: custom proj_dist_fn (Laplace)")

Manipulating cluster sizes

seed = 555

# Custom clusizes_fn (e083): cluster sizes determined via the uniform distribution,
# no correction for total points
def clusizes_unif(nclu, npts, ae, rng):
    return rng.integers(low=1, high=2 * npts / nclu + 1, size=nclu)

# Custom clusizes_fn (e084): clusters all have the same size, no correction for total points
def clusizes_equal(nclu, npts, ae, rng):
    return (npts // nclu) * np.ones(nclu, dtype=int)

# Custom clucenters_fn (all): yields fixed positions for the clusters
def centers_fixed(nclu, csep, coff, rng):
    return np.array([
        [-csep[0], -csep[1], -csep[2]],
        [csep[0], -csep[1], -csep[2]],
        [-csep[0], csep[1], csep[2]],
        [csep[0], csep[1], csep[2]]])

e082 = clugen(3, 4, 1500, [1, 1, 1], np.pi, [20, 20, 20], 0, 0, 5, rng=seed,
    clucenters_fn=centers_fixed, point_dist_fn="n")
e083 = clugen(3, 4, 1500, [1, 1, 1], np.pi, [20, 20, 20], 0, 0, 5, rng=seed,
    clucenters_fn=centers_fixed, clusizes_fn=clusizes_unif, point_dist_fn="n")
e084 = clugen(3, 4, 1500, [1, 1, 1], np.pi, [20, 20, 20], 0, 0, 5, rng=seed,
    clucenters_fn=centers_fixed, clusizes_fn=clusizes_equal, point_dist_fn="n")

plt = plot_examples_3d(
    e082, "e082: normal dist. (default)",
    e083, "e083: unif. dist. (custom)",
    e084, "e084: equal size (custom)")

Total running time of the script: ( 0 minutes 5.724 seconds)

Download Python source code: plot_3_3d_examples.py

Download Jupyter notebook: plot_3_3d_examples.ipynb

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