I want to shade the surface and the contours of a specific function based on some constraint in the domain of the function. So far I have the following and I want to improve it.
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.ticker import LinearLocator, FormatStrFormatter
plt.figure(figsize=(8, 6))
plt.axes(projection="3d")
xdata = np.linspace(-3, 3, 20000)
ydata = np.linspace(-3, 3, 20000)
X, Y = np.meshgrid(xdata, ydata)
Z1 = X ** 2 + Y ** 2
Z2 = Z1.copy()
Z3 = Z1.copy()
Z1[np.multiply(X, Y) > 3] = np.nan
Z2[np.multiply(X, Y) <= 3] = np.nan
Z3[np.multiply(X, Y) == 3] = np.nan
ax3d = plt.axes(projection='3d')
ax3d.plot_surface(X, Y, Z1, cmap='Greys', antialiased=True, vmin=-np.nanmin(Z1), vmax=np.nanmax(Z1))
ax3d.plot_surface(X, Y, Z2, cmap='YlGnBu', antialiased=True, vmin=-np.nanmin(Z2), vmax=np.nanmax(Z2))
ax3d.contourf(X, Y, Z1, zdir='z', offset=0, cmap='Greys')
ax3d.contourf(X, Y, Z2, zdir='z', offset=0, cmap='Greys')
ax3d.set_title('Surface Plot in Matplotlib')
ax3d.set_xlabel('X')
ax3d.set_ylabel('Y')
ax3d.set_zlabel('Z')
plt.show()
Could you please someone help to solve the following problems:
The surface is over-imposed by the contour surface.
There are some gaps in the surface.
The contours of the two constraints are not continuous.
Is it possible to plot a line in the border of the two surfaces and contours?
Any help is highly appreciated.
The code below makes the following changes:
creating a custom colormap combining the two existing colormaps
using a TwoSlopeNorm to have the separation at z=3
setting antialiased=False (otherwise matplotlib creates a plot of antialiased lines instead of polygons)
xdata and ydata with 300 steps
using rstride=1, cstride=1 so every x and every y will be considered; this makes the surface smoother (but takes more time)
calling plt.axes(...) only once to prevent a dummy subplot
calling contourf before plot_surface; due to the painter's algorithm, matplotlib only minimally supports 3D overlaps
import matplotlib.pyplot as plt
from matplotlib.colors import TwoSlopeNorm, ListedColormap
import numpy as np
xdata = np.linspace(-3, 3, 300)
ydata = np.linspace(-3, 3, 300)
X, Y = np.meshgrid(xdata, ydata)
Z1 = X ** 2 + Y ** 2
cmap1 = plt.get_cmap('Greys')
cmap2 = plt.get_cmap('YlGnBu')
cmap = ListedColormap(np.r_[cmap1(np.linspace(0, 1, 128)), cmap2(np.linspace(0, 1, 128))])
norm = TwoSlopeNorm(vmin=np.nanmin(Z1), vmax=np.nanmax(Z1), vcenter=3)
plt.figure(figsize=(8, 6))
ax3d = plt.axes(projection='3d')
ax3d.contourf(X, Y, Z1, zdir='z', offset=0, cmap=cmap, norm=norm)
ax3d.plot_surface(X, Y, Z1, cmap=cmap, antialiased=False, norm=norm, rstride=1, cstride=1)
ax3d.set_title('Surface Plot in Matplotlib')
ax3d.set_xlabel('X')
ax3d.set_ylabel('Y')
ax3d.set_zlabel('Z')
plt.show()
xdata = np.linspace(-3, 3, 1000)
ydata = np.linspace(-3, 3, 1000)
X, Y = np.meshgrid(xdata, ydata)
Z1 = X ** 2 + Y ** 2
Z2 = Z1.copy()
Z3 = Z1.copy()
Z2[np.multiply(X, Y) <= 3] = np.nan
Z3[np.multiply(X, Y) == 3] = np.nan
plt.figure(figsize=(8, 6))
ax3d = plt.axes(projection='3d')
ax3d.contourf(X, Y, Z1, zdir='z', offset=0, cmap='Greys')
ax3d.contourf(X, Y, Z2, zdir='z', offset=0, cmap='YlGnBu')
ax3d.plot_surface(X, Y, Z1, cmap='Greys', antialiased=True, vmin=-np.nanmin(Z1), vmax=np.nanmax(Z1), alpha=.5)
ax3d.plot_surface(X, Y, Z2, cmap='YlGnBu', antialiased=True, vmin=-np.nanmin(Z2), vmax=np.nanmax(Z2), alpha=.5)
ax3d.set_title('Surface Plot in Matplotlib')
ax3d.set_xlabel('X')
ax3d.set_ylabel('Y')
ax3d.set_zlabel('Z')
plt.show()
Related
I am trying to surface fit 3d data (z is a function of x and y). I have assymetrical error bars for each point. I would like the fit to take this uncertainty into account.
I am using scipy.linalg.lstsq(). It does not have any option for uncertainties in its arguments.
I am trying to adapt some code found on this page.
import numpy as np
import scipy.linalg
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
# Create data with x and y random over [-2, 2], and z a Gaussian function of x and y.
np.random.seed(12345)
x = 2 * (np.random.random(500) - 0.5)
y = 2 * (np.random.random(500) - 0.5)
def f(x, y):
return np.exp(-(x + y ** 2))
z = f(x, y)
data = np.c_[x,y,z]
# regular grid covering the domain of the data
mn = np.min(data, axis=0)
mx = np.max(data, axis=0)
X,Y = np.meshgrid(np.linspace(mn[0], mx[0], 20), np.linspace(mn[1], mx[1], 20))
XX = X.flatten()
YY = Y.flatten()
# best-fit quadratic curve (2nd-order)
A = np.c_[np.ones(data.shape[0]), data[:,:2], np.prod(data[:,:2], axis=1), data[:,:2]**2]
C,_,_,_ = scipy.linalg.lstsq(A, data[:,2])
# evaluate it on a grid
Z = np.dot(np.c_[np.ones(XX.shape), XX, YY, XX*YY, XX**2, YY**2], C).reshape(X.shape)
# plot points and fitted surface using Matplotlib
fig = plt.figure(figsize=(10, 10))
ax = fig.gca(projection='3d')
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, alpha=0.2)
ax.scatter(data[:,0], data[:,1], data[:,2], c='r', s=50)
plt.xlabel('X')
plt.ylabel('Y')
ax.set_zlabel('Z')
ax.axis('equal')
ax.axis('tight')
My goal is to plot the probability distribution functions (pdfs) of two classes. Each class has Gaussian likelihood and equivalent covariance matrices, but different mean vectors. I want both pdfs on the same plane in the z-axis, with the x and y axes containing the projections of the pdfs.
The following code (mostly borrowed from here) plots one of the pdfs:
# Our 2-dimensional distribution will be over variables X and Y
N = 100
X = np.linspace(-10, 15, N)
Y = np.linspace(-10, 15, N)
X, Y = np.meshgrid(X, Y)
# Mean vector and covariance matrix
mu1 = np.array([8, 2])
mu2 = np.array([2,8])
Sigma1 = Sigma2 = np.array([[4.1,0],[0,2.8]])
# Pack X and Y into a single 3-dimensional array
pos = np.empty(X.shape + (2,))
pos[:, :, 0] = X
pos[:, :, 1] = Y
F1 = multivariate_normal(mu1, Sigma1)
F2 = multivariate_normal(mu2, Sigma2)
Z1 = F1.pdf(pos)
Z2 = F2.pdf(pos)
# Create a surface plot and projected filled contour plot under it.
fig1 = plt.figure(figsize=[10,10])
ax1 = fig1.gca(projection='3d')
ax1.plot_surface(X, Y, Z1, rstride=3, cstride=3, linewidth=1,
antialiased=True,cmap=cm.inferno)
cset = ax1.contourf(X, Y, Z1, zdir='z', offset=-0.15, cmap=cm.inferno)
# Adjust the limits, ticks and view angle
ax1.set_zlim(-0.15,0.2)
ax1.set_zticks(np.linspace(0,0.2,5))
ax1.view_init(27, -21)
plt.show()
This is the plot that results from the above code: plot_surfaces for plotting bivariate pdf. However, I need to plot both Z1 and Z2 on the same plane. If I try creating two plots, they overlap and the Z2 pdf cannot be seen. Tweaking the code slightly, I get roughly what I want:
ax1 = fig1.gca(projection='3d')
ax2 = fig1.gca(projection='3d')
ax1.plot_wireframe(X, Y, Z1, rstride=3, cstride=3, linewidth=1,
antialiased=True,cmap=cm.inferno)
ax2.plot_wireframe(X,Y,Z2,rstride=3, cstride=3, linewidth=1,
antialiased=True,cmap=cm.inferno)
the resulting plot of which can be found here: wireframe method to plot 2 bivariate pdfs. But these plots are still overlapping. How can I get around this issue? I want the result to be styled as the first plot, with the surface_plot method and projections on the x-y plane.
You can play with alpha:
ax1.plot_surface(X, Y, Z1, rstride=3, cstride=3, linewidth=1,
antialiased=True,cmap=cm.inferno, alpha = 0.5)
ax1.plot_surface(X, Y, Z2, rstride=3, cstride=3, linewidth=1,
antialiased=True,cmap=cm.inferno, alpha = 1)
cset = ax1.contourf(X, Y, Z1, zdir='z', offset=-0.15, cmap=cm.inferno, alpha=1)
cset = ax1.contourf(X, Y, Z2, zdir='z', offset=-0.15, cmap=cm.inferno, alpha=0.5)
But in some cases you can get the same results by just summing your pdf's
ax1.plot_surface(X, Y, Z1 + Z2, rstride=3, cstride=3, linewidth=1, antialiased=True,cmap=cm.inferno)
cset = ax1.contourf(X, Y, Z1 + Z2, zdir='z', offset=-0.15, cmap=cm.inferno)
I am trying to visualise a multivariate normal distribution with matplotlib. I would like to produce something like this:
I use the following code:
from mpl_toolkits import mplot3d
x = np.linspace(-1, 3, 100)
y = np.linspace(0, 4, 100)
X, Y = np.meshgrid(x, y)
Z = np.random.multivariate_normal(mean = [1, 2], cov = np.array([[0.5, 0.25],[0.25, 0.50]]), size = 100000)
ax = plt.axes(projection='3d')
ax.plot_surface(X, Y, Z, rstride=1, cstride=1,
cmap='viridis', edgecolor='none')
ax.set_title('surface');
But I get the following error message:
...
7 ax.plot_surface(X, Y, Z, rstride=1, cstride=1,
----> 8 cmap='viridis', edgecolor='none')
...
ValueError: shape mismatch: objects cannot be broadcast to a single shape
What is the reason of the error and how my code could be corrected?
In the past I have done this with scipy.stats.multivariate_normal, specifically using the pdf method to generate the z values. As #Piinthesky pointed out the numpy implementation returns the x and y values for a given distribution. An example using the spicy version would be (another can be found in (Python add gaussian noise in a radius around a point [closed]):
from mpl_toolkits import mplot3d
import matplotlib.pyplot as plt
from scipy.stats import multivariate_normal
x = np.linspace(-1, 3, 100)
y = np.linspace(0, 4, 100)
X, Y = np.meshgrid(x, y)
pos = np.dstack((X, Y))
mu = np.array([1, 2])
cov = np.array([[.5, .25],[.25, .5]])
rv = multivariate_normal(mu, cov)
Z = rv.pdf(pos)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X, Y, Z)
fig.show()
I am trying to 'paint' the faces of a cube with a contourf function using Python Matplotlib. Is this possible?
This is similar idea to what was done here but obviously I cannot use patches. Similarly, I don't think I can use add_collection3d like this as it only supports PolyCollection, LineColleciton and PatchCollection.
I have been trying to use contourf on a fig.gca(projection='3d'). Toy example below.
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
plt.close('all')
fig = plt.figure()
ax = fig.gca(projection='3d')
############################################
# plotting the 'top' layer works okay... #
############################################
X = np.linspace(-5, 5, 43)
Y = np.linspace(-5, 5, 28)
X, Y = np.meshgrid(X, Y)
varone=np.random.rand(75,28,43)
Z=varone[0,:,:]
cset = ax.contourf(X, Y, Z, zdir='z', offset=1,
levels=np.linspace(np.min(Z),np.max(Z),30),cmap='jet')
#see [1]
plt.show()
#################################################
# but now trying to plot a vertical slice.... #
#################################################
plt.close('all')
fig = plt.figure()
ax = fig.gca(projection='3d')
Z=varone[::-1,:,-1]
X = np.linspace(-5, 5, 28)
Y = np.linspace(-5, 5, 75)
X, Y = np.meshgrid(X, Y)
#this 'projection' doesn't result in what I want, I really just want to rotate it
cset = ax.contourf(X, Y, Z, offset=5,zdir='x',
levels=np.linspace(np.min(Z),np.max(Z),30),cmap='jet')
#here's what it should look like....
ax=fig.add_subplot(1, 2,1)
cs1=ax.contourf(X,Y,Z,levels=np.linspace(np.min(Z),np.max(Z),30),cmap='jet')
#see [2]
plt.show()
1 From the example, the top surface comes easily:
2 But I'm not sure how to do the sides. Left side of this plot is what the section should look like (but rotated)...
Open to other python approaches. The data I'm actually plotting are geophysical netcdf files.
You have to assign the data to the right axis. The zig-zag results from the fact that now you are at x = const and have your oscillation in the z-direction (from the random data, which is generated between 0 and 1).
If you you assign the matrixes differently in your example, you end up with the desired result:
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
plt.close('all')
fig = plt.figure()
ax = fig.gca(projection='3d')
X = np.linspace(-5, 5, 43)
Y = np.linspace(-5, 5, 28)
X, Y = np.meshgrid(X, Y)
varone=np.random.rand(75,28,43) * 5.0 - 10.0
Z=varone[0,:,:]
cset = [[],[],[]]
# this is the example that worked for you:
cset[0] = ax.contourf(X, Y, Z, zdir='z', offset=5,
levels=np.linspace(np.min(Z),np.max(Z),30),cmap='jet')
# now, for the x-constant face, assign the contour to the x-plot-variable:
cset[1] = ax.contourf(Z, Y, X, zdir='x', offset=5,
levels=np.linspace(np.min(Z),np.max(Z),30),cmap='jet')
# likewise, for the y-constant face, assign the contour to the y-plot-variable:
cset[2] = ax.contourf(X, Z, Y, zdir='y', offset=-5,
levels=np.linspace(np.min(Z),np.max(Z),30),cmap='jet')
# setting 3D-axis-limits:
ax.set_xlim3d(-5,5)
ax.set_ylim3d(-5,5)
ax.set_zlim3d(-5,5)
plt.show()
The result looks like this:
The answer given below is not fully satisfying. Indeed, planes in x, y and z direction reproduce the same field.
Hereafter, a function that allows to represent the correct field in each of the planes.
import numpy as np
import matplotlib.pyplot as plt
def plot_cube_faces(arr, ax):
"""
External faces representation of a 3D array with matplotlib
Parameters
----------
arr: numpy.ndarray()
3D array to handle
ax: Axes3D object
Axis to work with
"""
x0 = np.arange(arr.shape[0])
y0 = np.arange(arr.shape[1])
z0 = np.arange(arr.shape[2])
x, y, z = np.meshgrid(x0, y0, z0)
xmax, ymax, zmax = max(x0), max(y0), max(z0)
vmin, vmax = np.min(arr), np.max(arr)
ax.contourf(x[:, :, 0], y[:, :, 0], arr[:, :, -1].T,
zdir='z', offset=zmax, vmin=vmin, vmax=vmax)
ax.contourf(x[0, :, :].T, arr[:, 0, :].T, z[0, :, :].T,
zdir='y', offset=0, vmin=vmin, vmax=vmax)
ax.contourf(arr[-1, :, :].T, y[:, 0, :].T, z[:, 0, :].T,
zdir='x', offset=xmax, vmin=vmin, vmax=vmax)
x0 = np.arange(30)
y0 = np.arange(20)
z0 = np.arange(10)
x, y, z = np.meshgrid(x0, y0, z0)
arr = (x + y + z) // 10
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
plot_cube_faces(arr, ax)
plt.show()
I'm looking to plot a 2D probability distribution with one of its marginals in a single plot using Python and matplotlib. I'm almost there, but the line in the plot is always drawn in front of the surface, instead of being occluded properly. How do I fix this?
import numpy as np
import scipy.stats as stats
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import axes3d
fig = plt.figure()
ax = fig.gca(projection='3d')
delta = 0.05
f = 0.5
X, Y = np.meshgrid(np.arange(-3.0, 3.0, delta),
np.arange(-3.0, 3.0, delta))
xy = np.hstack((X.flatten()[:, None], Y.flatten()[:, None]))
p1 = stats.multivariate_normal.pdf(xy, mean=[1, -1], cov=(np.eye(2) * 0.28 * f))
p2 = stats.multivariate_normal.pdf(xy, mean=[-1, 1], cov=(np.eye(2) * 0.5 * f))
p = 0.3 * p1 + 0.7 * p2
Z = p.reshape(len(X), len(X))
plt.plot(X[0, :], np.zeros(len(X)) + 3, np.sum(Z, 0) * 0.05) # , color='red')
ax.plot_surface(X, Y, Z, alpha=1.0, cmap='jet', linewidth=0.1, rstride=2, cstride=2)
ax.set_xlabel('Object colour')
ax.set_ylabel('Illumination colour')
ax.set_zlabel('Probability density')
ax.set_zlim(min(cont_offset, np.min(Z)), max(np.max(Z), cont_offset))
plt.show()
The built-in contour function at least gets the z-order right; if you don't want the full thing, you could cheat with a calculated Z. To start, replacing your call to plt.plot with this:
from matplotlib import cm
cset = ax.contour(X, Y, Z, zdir='y', offset=3, cmap='binary')
cset = ax.contour(X, Y, Z, zdir='x', offset=-3, cmap='Blues')
Faking up Z's for the contours, one way:
from matplotlib import cm
Zys = np.zeros_like(Z)
Zys[60,:] = Z.max(0)
cset = ax.contour(X, Y, Zys, zdir='y', offset=3, cmap='binary')
Zys = np.zeros_like(Z)
Zys[:,60] = Z.max(1)
cset = ax.contour(X, Y, Zys, zdir='x', offset=-3, cmap='Blues')
More ambitiously, somewhere in the contour code they're calculating the z-order...