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examples.py
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examples.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
This file
"""
# For Travis CI
import matplotlib
matplotlib.use("Agg")
import time
import os
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm
from KDEpy import NaiveKDE, TreeKDE, FFTKDE
def main():
here = os.path.abspath(os.path.dirname(__file__))
save_path = os.path.join(here, r"_static/img/")
# -----------------------------------------------------------------------------
# ------ ADVERTISEMENT PLOT: Create the plot that is shown in the README ------
# -----------------------------------------------------------------------------
plt.figure(figsize=(12, 5.5))
np.random.seed(42)
FONTSIZE = 15
plt.subplot(2, 3, 1)
n = 15
plt.title("Automatic bandwidth,\nrobust w.r.t multimodality", fontsize=FONTSIZE)
data = np.concatenate((np.random.randn(n), np.random.randn(n) + 10))
plt.scatter(data, np.zeros_like(data), marker="|", color="red", label="Data")
x, y = FFTKDE(bw="ISJ").fit(data)()
plt.plot(x, y, label="FFTKDE")
plt.yticks([])
plt.xticks([])
plt.grid(True, ls="--", zorder=-15)
plt.subplot(2, 3, 2)
plt.title("9+ kernel functions", fontsize=FONTSIZE)
for kernel in FFTKDE._available_kernels.keys():
x, y = FFTKDE(kernel=kernel).fit([0])()
plt.plot(x, y, label=kernel)
plt.yticks([])
plt.xticks([])
plt.grid(True, ls="--", zorder=-15)
plt.subplot(2, 3, 3)
plt.title("Fast 2D computations\nusing binning and FFT", fontsize=FONTSIZE)
n = 16
gen_random = lambda n: np.random.randn(n).reshape(-1, 1)
data1 = np.concatenate((gen_random(n), gen_random(n)), axis=1)
data2 = np.concatenate((gen_random(n) + 1, gen_random(n) + 4), axis=1)
data = np.concatenate((data1, data2))
grid_points = 2**7 # Grid points in each dimension
N = 8 # Number of contours
x, z = FFTKDE(bw=1).fit(data)((grid_points, grid_points))
x, y = np.unique(x[:, 0]), np.unique(x[:, 1])
z = z.reshape(grid_points, grid_points).T
plt.contour(x, y, z, N, linewidths=0.8, colors="k")
plt.contourf(x, y, z, N, cmap="PuBu")
plt.plot(data[:, 0], data[:, 1], "ok", ms=2)
plt.yticks([])
plt.xticks([])
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.colors import LightSource
from matplotlib import cm
ax = plt.subplot(2, 3, 4, projection="3d")
plt.title("Kernels normalized in any\ndimension for any $p$-norm", fontsize=FONTSIZE)
data = np.array([[0, 0]])
grid_points = 2**6 # Grid points in each dimension
x, z = FFTKDE(kernel="gaussian", bw=1, norm=2).fit(data)((grid_points, grid_points))
x, y = np.unique(x[:, 0]), np.unique(x[:, 1])
x, y = np.meshgrid(x, y)
z = z.reshape(grid_points, grid_points).T + 0.1
ls = LightSource(350, 45)
rgb = ls.shade(z, cmap=cm.PuBu, vert_exag=0.1, blend_mode="soft")
surf = ax.plot_surface(
x,
y,
z,
rstride=1,
cstride=1,
facecolors=rgb,
linewidth=0,
antialiased=False,
shade=True,
)
ax.view_init(30, 65)
plt.yticks([])
plt.xticks([])
ax.set_zticks([])
plt.subplot(2, 3, 5)
plt.title("Individual data points\nmay be weighted", fontsize=FONTSIZE)
np.random.seed(123)
n = 5
data = np.random.randn(n) * 2
weights = np.random.randn(n) ** 2 + 1
kernel = "triweight"
x, y = TreeKDE(kernel=kernel).fit(data, weights)()
plt.plot(x, y)
plt.scatter(data, np.zeros_like(data), s=weights * 20, color="red")
for d, w in zip(data, weights):
y = TreeKDE(kernel=kernel).fit([d], weights=[w])(x) * w / np.sum(weights)
plt.plot(x, y, "--k", zorder=-15, alpha=0.75)
plt.yticks([])
plt.xticks([])
plt.grid(True, ls="--", zorder=-15)
plt.subplot(2, 3, 6)
data = np.random.gamma(10, 100, size=(10**6))
st = time.perf_counter()
x, y = FFTKDE(kernel="gaussian", bw=100).fit(data)(2**10)
timed = (time.perf_counter() - st) * 1000
plt.plot(x, y)
plt.title(
("One million observations on\n1024 grid" + " points in {} ms".format(int(round(timed, 0)))),
fontsize=FONTSIZE,
)
data = np.random.choice(data, size=100, replace=False)
plt.scatter(data, np.zeros_like(data), marker="|", color="red", label="Data", s=3)
plt.yticks([])
plt.xticks([])
plt.grid(True, ls="--", zorder=-15)
plt.tight_layout()
plt.savefig(os.path.join(save_path, r"showcase.png"))
# -----------------------------------------------------------------------------
# ------ MINIMAL WORKING EXAMPLE: Showing a simle way to create a plot --------
# -----------------------------------------------------------------------------
plt.figure(figsize=(6, 3))
##############################
np.random.seed(42)
data = norm(loc=0, scale=1).rvs(2**3)
x, y = TreeKDE(kernel="gaussian", bw="silverman").fit(data).evaluate()
plt.plot(x, y, label="KDE estimate")
##############################
plt.plot(x, norm(loc=0, scale=1).pdf(x), label="True distribution")
plt.scatter(data, np.zeros_like(data), marker="|", color="red", label="Data")
plt.legend(loc="best")
plt.tight_layout()
plt.savefig(os.path.join(save_path, r"mwe.png"))
# -----------------------------------------------------------------------------
# ------ COMPARING BANDWIDTHS: Different bandwidths on the same data set ------
# -----------------------------------------------------------------------------
plt.figure(figsize=(6, 3))
##############################
data = norm(loc=0, scale=1).rvs(2**6)
for bw in [0.1, "silverman", 1.5]:
x, y = FFTKDE(kernel="triweight", bw=bw).fit(data).evaluate()
plt.plot(x, y, label="KDE estimate, bw={}".format(bw))
##############################
plt.scatter(data, np.zeros_like(data), marker="|", color="red", label="Data")
plt.legend(loc="best")
plt.tight_layout()
# plt.savefig(os.path.join(save_path, r'example2.png'))
# -----------------------------------------------------------------------------
# ------ EVERY ESTIMATOR: Comparing the different algorithms ------------------
# -----------------------------------------------------------------------------
plt.figure(figsize=(6, 3))
np.random.seed(42)
data = norm(loc=0, scale=1).rvs(2**3)
for kde in [NaiveKDE, TreeKDE, FFTKDE]:
x, y = kde(kernel="gaussian", bw="silverman").fit(data).evaluate()
plt.plot(x, y + np.random.randn() / 100, label=kde.__name__ + " estimate")
plt.plot(x, norm(loc=0, scale=1).pdf(x), label="True distribution")
plt.scatter(data, np.zeros_like(data), marker="|", color="red", label="Data")
plt.legend(loc="best")
plt.tight_layout()
if __name__ == "__main__":
# main()
np.random.seed(123)
x = [0, 0.1, 0.2, 0.3, 0.4, 1, 2, 3, 4, 5, 7, 9, 14, 19]
x = np.array(x)
x = np.linspace(0, 5) ** 2
y = np.sin(x)
plt.plot(x, y)
y += np.random.randn(len(y)) / 2
plt.scatter(x, y, label="Points")
x_interpol = np.linspace(min(x) - 1, max(x) + 1, num=2**6)
y_interpol = np.interp(x_interpol, x, y)
plt.plot(x_interpol, y_interpol, "--", label="Interpol")
kernel = FFTKDE._available_kernels["box"]
kernel_grid = np.linspace(-kernel.support, kernel.support, num=2**6)
bw = 0.02
kernel_weights = kernel(kernel_grid, bw=bw)
kernel_weights /= np.sum(kernel_weights)
print(kernel_weights)
from scipy.signal import convolve
evaluated = convolve(y_interpol, kernel_weights, mode="same").reshape(-1, 1)
plt.plot(x_interpol, evaluated)
plt.legend()