I would like to create a 3D plot with the z axis in log scale. This is an example code.
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
def fun(x, y):
return x**2 + y
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
x = y = np.arange(-3.0, 3.0, 0.05)
X, Y = np.meshgrid(x, y)
zs = np.array([fun(x,y) for x,y in zip(np.ravel(X), np.ravel(Y))])
Z = zs.reshape(X.shape)
ax.plot_surface(X, Y, Z)
ax.set_xlabel('X Label')
ax.set_ylabel('Y Label')
ax.set_zlabel('Z Label')
plt.show()
I tried ax.set_zscale('log') and ax.zaxis.set_scale('log') but that is not working. It should be possible though. If I use ax.plot_surface(X, Y, np.log(Z)) the z ticks are off. I could not find an answer to this seemingly simple problem. I hope you can help.
Related
I am trying to visualize points on 3d surface.
For some reason only some points are shown in the plot.
When I start to move the plot around, some points suddenly appear. Is there a way to visualize points on a 3d surface?
This is the result I am getting right now:
And below the code used to generate it:
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import numpy as np
fig = plt.figure()
ax = fig.gca(projection='3d')
# Make data.
X = np.arange(-5, 5, 0.1)
Y = np.arange(-5, 5, 0.1)
X, Y = np.meshgrid(X, Y)
R = np.sqrt(X ** 2 + Y ** 2)
Z = np.sin(R)
# Plot the surface.
surf = ax.plot_surface(X, Y, Z, cmap=cm.coolwarm, linewidth=0, antialiased=False)
X = np.arange(-5, 5, 1)
Y = np.arange(-5, 5, 1)
X, Y = np.meshgrid(X, Y)
R = np.sqrt(X ** 2 + Y ** 2)
Z = np.sin(R)
ax.scatter(X, Y, Z, c='r', marker='o')
# Customize the z axis.
ax.set_zlim(-1.01, 1.01)
ax.zaxis.set_major_locator(LinearLocator(10))
ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
# Add a color bar which maps values to colors.
fig.colorbar(surf, shrink=0.5, aspect=5)
plt.show()
I want to plot the gravitational energy potential to highlight its extremums (the Lagrangian points around two celestial bodies).
Here is the function that returns the potential for each set of coordinates x and y:
def gravitational_potential(M,m,R,x,y):
G = 6.674*10**(-11)
omega2 = G*(M+m)/(R**3)
r = np.sqrt(x**2+y**2)
r2 = R*m/(M+m)
r1 = R-r2
phi = -G*(M/abs(r-r1)+m/abs(r-r2))-1/2*omega2*(x**2+y**2)
return phi
I want to use meshgrid and plot_surface to plot the surface and the contour of the potential but it doesn't work.
What am I doing wrong ?
PS: I managed to plot the potential with WolframAlpha so I know the math works.
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
from matplotlib import cm
import numpy as np
def gravitational_potential(M,m,R,x,y):
G = 6.674*10**(-11)
omega2 = G*(M+m)/(R**3)
r = np.sqrt(x**2+y**2)
r2 = R*m/(M+m)
r1 = R-r2
phi = -G*(M/abs(r-r1)+m/abs(r-r2))-1/2*omega2*(x**2+y**2)
return phi
fig = plt.figure()
ax = fig.gca(projection='3d')
X, Y = np.meshgrid(np.arange(-20, 20, 0.5), np.arange(-20, 20, 0.5))
M = 10
m = 1
R = 10
Z = gravitational_potential(M,m,R,X,Y)
ax.plot_surface(X, Y, Z, rstride=8, cstride=8, alpha=0.9)
cset = ax.contour(X, Y, Z, zdir='z', offset=-40, cmap=cm.coolwarm)
cset = ax.contour(X, Y, Z, zdir='x', offset=-20, cmap=cm.coolwarm)
cset = ax.contour(X, Y, Z, zdir='y', offset=20, cmap=cm.coolwarm)
ax.set_xlabel('X')
ax.set_xlim(-20, 20)
ax.set_ylabel('Y')
ax.set_ylim(-20, 20)
ax.set_zlabel('Z')
ax.set_zlim(-40, 40)
plt.show()
When I execute it I get the following:
runfile('C:/Users/python/Google Drive/lagrangepoint_maths/potential/gravitational_potential.py', wdir='C:/Users/python/Google Drive/lagrangepoint_maths/potential')
C:/Users/python/Google Drive/lagrangepoint_maths/potential/gravitational_potential.py:13: RuntimeWarning: divide by zero encountered in divide
phi = -G*(M/abs(r-r1)+m/abs(r-r2))-1/2*omega2*(x**2+y**2)
This is not really what I want. There is something wrong with Z. I want something like that:
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
from matplotlib import cm
fig = plt.figure()
ax = fig.gca(projection='3d')
X, Y, Z = axes3d.get_test_data(0.05)
ax.plot_surface(X, Y, Z, rstride=8, cstride=8, alpha=0.9)
cset = ax.contour(X, Y, Z, zdir='z', offset=-100, cmap=cm.coolwarm)
cset = ax.contour(X, Y, Z, zdir='x', offset=-40, cmap=cm.coolwarm)
cset = ax.contour(X, Y, Z, zdir='y', offset=40, cmap=cm.coolwarm)
ax.set_xlabel('X')
ax.set_xlim(-40, 40)
ax.set_ylabel('Y')
ax.set_ylim(-40, 40)
ax.set_zlabel('Z')
ax.set_zlim(-100, 100)
plt.show()
All of this are things one may just debug one by one:
Integer division in python 2 results in 0 if the nominator is smaller than the denominator. You may from __future__ import division or correct your code to divide by floats.
If you want to show numbers between -2 x 10^-8 and +2 x 10^-8 it is not useful to set the z_limits to -40 to 40.
If you want to show small features in the plot, you should not set the plotting resolution coarsely to rstride=8, cstride=8.
In total you would arrive at something like this:
I used Matplotlib to plot a 3D potential energy surface.
But, I also want to show a reaction path with the lowest potential barrier between the minima of a potential energy surface by arrows.
Can any one help me with this: this is the my code for the 3D surface:
#!/usr/bin/python
INPUT='input.txt'
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.mlab import griddata
from matplotlib import cm
from pylab import *
from matplotlib.ticker import LinearLocator, FormatStrFormatter
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
data = np.genfromtxt(INPUT)
x = data[:,0]
y = data[:,1]
z = data[:,2]
xi = np.linspace(min(x), max(x))
yi = np.linspace(min(y), max(y))
X, Y = np.meshgrid(xi, yi)
Z = griddata(x, y, z, xi, yi, interp='linear')
ax.contourf(X, Y, Z, 30, zdir='z', offset=-7, linewidth=0.2, cmap=cm.jet, antialiased=False, shade=True)
C = ax.contour(X, Y, Z, 30, colors='k', linewidths=0.2)
surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.jet, linewidth=0, antialiased=False, shade=False)
fig.colorbar(surf)
ax.clabel(C, inline=1, fontsize=10)
ax.set_xlabel(r"$d$$_{3}$ ($\AA$)")
ax.set_ylabel(r"$d$$_{4}$ ($\AA$)")
ax.set_zlabel(r"$\Delta$$E$$_{e}$ (kcal/mol)")
plt.show()
I want a graph like the one below:
3D surface
Source: http://pubs.acs.org/doi/abs/10.1021/ja801727k
I am trying to add legend to a surface plot but unable to do so. Here is the code.
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import random
def fun(x, y):
return 0.063*x**2 + 0.0628*x*y - 0.15015876*x + 96.1659*y**2 - 74.05284306*y + 14.319143466051
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
x = y = np.arange(-1.0, 1.0, 0.05)
X, Y = np.meshgrid(x, y)
zs = np.array([fun(x,y) for x,y in zip(np.ravel(X), np.ravel(Y))])
Z = zs.reshape(X.shape)
ax.plot_surface(X, Y, Z)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
plt.plot(color='red',label='Lyapunov function on XY plane',linewidth=4) # Adding legend
plt.show()
Kindly help. Thanks in advance.
It is not trivial to make a legend in a 3D axis. You can use the following hack:
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import matplotlib as mpl
import random
def fun(x, y):
return 0.063*x**2 + 0.0628*x*y - 0.15015876*x + 96.1659*y**2 - 74.05284306*y + 14.319143466051
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
x = y = np.arange(-1.0, 1.0, 0.05)
X, Y = np.meshgrid(x, y)
zs = np.array([fun(x,y) for x,y in zip(np.ravel(X), np.ravel(Y))])
Z = zs.reshape(X.shape)
ax.plot_surface(X, Y, Z)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
fake2Dline = mpl.lines.Line2D([0],[0], linestyle="none", c='b', marker = 'o')
ax.legend([fake2Dline], ['Lyapunov function on XY plane'], numpoints = 1)
plt.show()
I would say a title is more appropriate than a legend in this case.
According to this question, the issue is ongoing, and there is a relatively simple workaround. You can manually set the two missing attributes that would allow legend to automatically create the patch for you:
surf = ax.plot_surface(X, Y, Z, label='Lyapunov function on XY plane')
surf._edgecolors2d = surf._edgecolor3d
surf._facecolors2d = surf._facecolor3d
ax.legend()
The attribute names on the right hand side of the assignment are surf._edgecolors3d and surf.facecolors3d for matplotlib < v3.3.3.
I have 2 1D arrays with the values of x and y, and also a 2D array with the values of z for each point where the columns correspond to the x values and the rows to the y values. Is there any way to get a plot_surface with this data? when I try to do it it returns me no plot. Here is the code: (calculate_R is a function I made for the program)
x=np.arange(0,10,1)
y=np.arange(0,1,0.2)
lx= len(x)
ly=len(y)
z=np.zeros((lx,ly))
for i in range(lx):
for j in range(ly):
z[i,j]=calculate_R(y[j],x[i])
fig = plt.figure()
ax = Axes3D(fig)
x, y = np.meshgrid(x, y)
ax.plot_surface(x, y, z, rstride=1, cstride=1, cmap='hot')
You forgot to call plt.show() to display your plot.
Note that you might be able to exploit numpy vectorization to speed up the calculation of z:
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.axes3d import Axes3D
x = np.arange(0,10,1)
y = np.arange(0,1,0.2)
xs, ys = np.meshgrid(x, y)
# z = calculate_R(xs, ys)
zs = xs**2 + ys**2
fig = plt.figure()
ax = Axes3D(fig)
ax.plot_surface(xs, ys, zs, rstride=1, cstride=1, cmap='hot')
plt.show()
Here, I used a simple function, since you didn't supply a fully working example.