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DescriptionGaussian 2d 60 degrees.png |
English: Created in Python with Numpy and Matplotlib. |
Date | |
Source | Own work |
Author | Kopak999 |
This file was created with Python:
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
from matplotlib import cm
exp = np.exp
sqrt = np.sqrt
sin = np.sin
cos = np.cos
tau = 2 * np.pi
def ellipticalGaussian(
X, Y,
sigma_x = 1/sqrt(2),
sigma_y = 1/sqrt(2),
theta = 0,
):
"""
Returns values of a Gaussian surface whose bell curve is elliptical
instead of circular.
sigma_x: The standard deviation of the Gaussian in the X direction.
sigma_y: The standard deviation of the Gaussian in the Y direction.
sigma_x and sigma_y are comparable to the semimajor axes of an ellipse, and
affect the shape of the Gaussian mound.
theta: The angle the Gaussian is rotated about the Z-axis.
"""
a = cos(theta)**2 / (2*sigma_x**2) + sin(theta)**2 / (2*sigma_y**2)
b = -sin(2*theta) / (4*sigma_x**2) + sin(2*theta) / (4*sigma_y**2)
c = sin(theta)**2 / (2*sigma_x**2) + cos(theta)**2 / (2*sigma_y**2)
return exp(-(a*(X**2) + 2*b*(X*Y) + c*(Y**2)))
def plotGaussianSurface(
X, Y, Z,
colormap=cm.cividis,
title="",
filetype="png",
saveflag=False,
resolution=200,
dpi=300,
numticks_xy=7,
numticks_z=2,
numticks_xy_minor=25,
numticks_z_minor=5,
):
"""
Plots a 3D-surface of a 2D-Gaussian function.
X, Y: Meshgrids of x- and y-values for the Gaussian.
Z: The output of the Gaussian function.
colormap: The colormap for the surface, mapped to the Z-values of the
graph.
title: Title of the graph.
filetype: Three-letter extension of the image filetype for saving the
graph. Default is png.
saveflag: Boolean flag to check if the graph should be saved to a file.
Set to True if you want to save the graph to a file. Default is False.
resolution: Number of pixels to render along the x- and y-axes.
Default is 200, which gives a 200x200 grid.
dpi: Dots-per-inch of the image. Default is 300.
"""
plt.ioff()
# Set up kwargs:
limit = int(np.ceil(np.amax(X)))
zmin = int(np.floor(np.amin(Z)))
zmax = int(np.ceil(np.amax(Z)))
norm = mpl.colors.Normalize(vmin=zmin, vmax=zmax)
aspect = (limit*2 + 1, limit*2 + 1, zmax)
xy_major_params = dict(
direction = "in",
)
xy_minor_params = dict(
direction = "in",
which = "minor",
)
xy_major_ticks = dict(
ticks = np.linspace(-limit, limit, numticks_xy, endpoint=True,),
)
xy_minor_ticks = dict(
ticks = np.linspace(-limit, limit, numticks_xy_minor, endpoint=True,),
minor = True,
)
z_major_params = dict(
which = "major",
labelbottom = True,
labeltop = False,
)
z_minor_params = dict(
which = "minor",
)
z_major_ticks = dict(
ticks = np.linspace(0, zmax, numticks_z, endpoint=True,),
)
z_minor_ticks = dict(
ticks = np.linspace(0, zmax, numticks_z_minor, endpoint=True,),
minor = True,
)
tick_labelsize = 7
fig = plt.figure(dpi=dpi)
ax = fig.add_subplot(1, 1, 1, projection ='3d')
# Plot the surface
surf = ax.plot_surface(
X, Y, Z,
cmap = colormap,
linewidth=0,
antialiased=False,
vmin = zmin, vmax = zmax,
rcount = resolution,
ccount = resolution,
norm = norm,
)
# Customize the z axis.
ax.set_zlim(zmin, zmax)
# ax.zaxis.set_major_locator(LinearLocator(10))
ax.zaxis.set_major_formatter('{x:.1f}')
ax.set_title(
title,
fontdict = dict(verticalalignment = "bottom"),
)
ax.set_box_aspect(aspect)
# ax.proj_type("ortho")
ax.set_facecolor('none')
# Set tick parameters
ax.xaxis.set_tick_params(**xy_major_params)
ax.xaxis.set_tick_params(**xy_minor_params)
ax.yaxis.set_tick_params(**xy_major_params)
ax.yaxis.set_tick_params(**xy_minor_params)
ax.zaxis.set_tick_params(**z_major_params)
ax.zaxis.set_tick_params(**z_minor_params)
ax.set_xticks(**xy_major_ticks)
ax.set_xticks(**xy_minor_ticks)
ax.set_yticks(**xy_major_ticks)
ax.set_yticks(**xy_minor_ticks)
ax.set_zticks(**z_major_ticks)
ax.set_zticks(**z_minor_ticks)
ax.tick_params(labelsize=tick_labelsize)
cbar = fig.colorbar(
surf,
ax=ax,
orientation='vertical',
shrink=0.5,
aspect=12,
pad = 0.10,
)
cbar.ax.tick_params(labelsize=tick_labelsize)
if saveflag:
savePlot(colormap, filetype)
plt.tight_layout()
plt.show()
x = y = np.linspace(-7, 7, 2**10, endpoint=True)
X, Y = np.meshgrid(x, y)
plotargs = dict(
saveflag = False,
dpi = 400,
resolution = 200,
numticks_xy=3,
numticks_xy_minor=15,
numticks_z=2,
numticks_z_minor=3,
)
plotGaussianSurface(X, Y, ellipticalGaussian(X, Y, sigma_x=1, sigma_y=2, theta=tau/6,), **plotargs)
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 01:30, 17 December 2020 | 1,923 × 1,015 (178 KB) | Kopak999 | Uploaded own work with UploadWizard |
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