I edited some examples to make a simulation for the voltage superposition of 2 point charges and made a 3D surface plot, the code is the following:
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm
q1 = 2e-9
q2 = -2e-9
K = 9e9
#Charge1 position
x1 = 2.0
y1 = 4.0
#Charge2 position
x2 = 6.0
y2 = 4.0
x = np.linspace(0,8,50)
y = np.linspace(0,8,50)
x, y = np.meshgrid(x,y)
r1 = np.sqrt((x - x1)**2 + (y - y1)**2)
r2 = np.sqrt((x - x2)**2 + (y - y2)**2)
V = K*(q1/r1 + q2/r2)
fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(x, y, V, rstride=1, cstride=1, cmap=cm.rainbow,
linewidth=0, antialiased=False)
fig.colorbar(surf, shrink=0.5, aspect=5)
plt.show()
3D Surface
Now what I want to do is a contour plot with a vector (quiver) plot on top of it. I tried the following code, but I get a bunch of buggy vectors coming out of both charges, even the negative one:
fig2, ax2 = plt.subplots(1,1)
cp = ax2.contourf(x, y, V, cmap=cm.coolwarm)
fig2.colorbar(cp)
v,u = np.gradient(-V, 0.2, 0.2) #E = -∇V
ax2.quiver(x, y, u, v)
ax2.set_title("Point Charges")
plt.show()
Buggy vectors
I suspect that the long vectors are related to a division by zero. The vectors should come out of the positive charge and get into the negative one. But how would I go about fixing them? Thanks in advance.
Welcome to SO, very nice MWE. One option would be to exclude all vectors beyond a certain length by setting them to NaN. Here I use the 95th percentile.
r = np.sqrt(u**2 + v**2)
is_valid = r < np.percentile(r, 95)
u[~is_valid] = np.nan
v[~is_valid] = np.nan
x[~is_valid] = np.nan
y[~is_valid] = np.nan
fig2, ax2 = plt.subplots(1,1)
cp = ax2.contourf(x, y, V, cmap=cm.coolwarm)
fig2.colorbar(cp)
ax2.quiver(x, y, u, v)
ax2.set_title("Point Charges")
ax2.set_xlim(0, 8)
ax2.set_ylim(0, 8)
plt.show()
Related
I am facing a problem to plot the geometry in the python using matplotlib. I would like to have a plot which can have the equal lenth in all three axes (X, Y, Z). I have written below code but it does not show any equal axes in the obtained geometry.
How can I get the plot with equal axes?
def plotting(x, y, z, figname):
fig = plt.figure(figsize = (50,50))
ax = plt.axes(projection='3d')
ax.grid()
ax.scatter(x, y, z, c = 'r', s = 50)
ax.set_title(figname)
ax.set_xlabel('x', labelpad=20)
ax.set_ylabel('y', labelpad=20)
ax.set_zlabel('z', labelpad=20)
Matplotlib makes this very difficult. One way you could "achieve" that is by setting the same limits to xlim, ylim, zlim:
import numpy as np
import matplotlib.pyplot as plt
n = 1000
t = np.random.uniform(0, 2*np.pi, n)
p = np.random.uniform(0, 2*np.pi, n)
x = (4 + np.cos(t)) * np.cos(p)
y = (1.5 + np.cos(t)) * np.sin(p)
z = np.sin(t)
fig = plt.figure()
ax = fig.add_subplot(projection="3d")
ax.scatter(x, y, z)
ax.set_xlim(-4, 4)
ax.set_ylim(-4, 4)
ax.set_zlim(-4, 4)
plt.show()
Otherwise, your best bet is to use a different plotting library for 3D plots. Plotly allows to easily set equal aspect ratio. K3D-Jupyter and Mayavi uses equal aspect ratio by default.
I would like to plot a heatmap where the input data is not in the typical rectangularly spaced grid. Here is some sample data:
import numpy as np
xmin = 6
xmax= 12
ymin = 0
x = np.linspace(xmin, xmax, 100)
ymax = x**2
final = []
for i in range(len(ymax)):
yrange = np.linspace(0, ymax[i], 100)
for j in range(len(yrange)):
intensity = np.random.rand()
final.append([x[i], yrange[j], intensity])
data_for_plotting = np.asarray(final) # (10000, 3) shaped array
I would like to plot intensity (in the colorbar) as a function of (x,y) which represents the position and I would like to do this without interpolation.
Here is my solution which uses matplotlib's griddata and linear interpolation.
import matplotlib.pyplot as plt
from matplotlib.mlab import griddata
total_length = 100
x1 = np.linspace(min(data_for_plotting[:,0]), max(data_for_plotting[:,0]), total_length)
y1 = np.linspace(min(data_for_plotting[:,1]), max(data_for_plotting[:,1]), total_length)
z1 = griddata(data_for_plotting[:,0], data_for_plotting[:,1], data_for_plotting[:,2], x1, y1, interp='linear')
p=plt.pcolormesh(x1, y1, z1, vmin = 0. , vmax=1.0, cmap='viridis')
clb = plt.colorbar(p)
plt.show()
I am looking for an alternate solution without interpolation as I would like to see the smallest unit of measurement in my x and y position (pixel size/rectangle). Based on the sample data given above I expect the height of the pixel to increase for large values of x.
I'm unsure what matplotlib.mlab.griddata is about. Maybe some very old version?
You could use scipy.interpolate.griddata which needs its parameters in a slightly different format. method='nearest' switches off the interpolation (default method='linear').
Here is how it could look with your test data (see griddata's documentation for more explanation and examples):
import matplotlib.pyplot as plt
from scipy.interpolate import griddata
import numpy as np
xmin = 6
xmax = 12
ymin = 0
x = np.linspace(xmin, xmax, 100)
ymax = x ** 2
final = []
for i in range(len(ymax)):
yrange = np.linspace(0, ymax[i], 100)
for j in range(len(yrange)):
intensity = np.random.rand()
final.append([x[i], yrange[j], intensity])
data_for_plotting = np.asarray(final) # (10000, 3) shaped array
total_length = 100
x1 = np.linspace(min(data_for_plotting[:, 0]), max(data_for_plotting[:, 0]), total_length)
y1 = np.linspace(min(data_for_plotting[:, 1]), max(data_for_plotting[:, 1]), total_length)
grid_x, grid_y = np.meshgrid(x1, y1)
z1 = griddata(data_for_plotting[:, :2], data_for_plotting[:, 2], (grid_x, grid_y), method='nearest')
img = plt.imshow(z1, extent=[x1[0], x1[-1], y1[0], y1[-1]], origin='lower',
vmin=0, vmax=1, cmap='inferno', aspect='auto')
cbar = plt.colorbar(img)
plt.show()
An alernative, is to create one rectangle for each of the prolonged pixels. Beware that this can be a rather slow operation. If really needed, one could create a pcolormesh for each column.
import matplotlib.pyplot as plt
from matplotlib.cm import ScalarMappable
import numpy as np
# ... create x and data_for_plotting as before
fig, ax = plt.subplots()
cmap = plt.get_cmap('inferno')
norm = plt.Normalize(0, 1)
x_step = x[1] - x[0]
y_step = 0
for i, (xi, yi, intensity_i) in enumerate(data_for_plotting):
if i + 1 < len(data_for_plotting) and data_for_plotting[i + 1, 0] == xi: # when False, the last y_step is reused
y_step = data_for_plotting[i + 1, 1] - yi
ax.add_artist(plt.Rectangle((xi, yi), x_step, y_step, color=cmap(norm(intensity_i))))
cbar = plt.colorbar(ScalarMappable(cmap=cmap, norm=norm))
ax.set_xlim(x[0], x[-1])
ax.set_ylim(0, data_for_plotting[:, 1].max())
plt.tight_layout()
plt.show()
The figure above is a great artwork showing the wind speed, wind direction and temperature simultaneously. detailedly:
The X axes represent the date
The Y axes shows the wind direction(Southern, western, etc)
The variant widths of the line were stand for the wind speed through timeseries
The variant colors of the line were stand for the atmospheric temperature
This simple figure visualized 3 different attribute without redundancy.
So, I really want to reproduce similar plot in matplotlib.
My attempt now
## Reference 1 http://stackoverflow.com/questions/19390895/matplotlib-plot-with-variable-line-width
## Reference 2 http://stackoverflow.com/questions/17240694/python-how-to-plot-one-line-in-different-colors
def plot_colourline(x,y,c):
c = plt.cm.jet((c-np.min(c))/(np.max(c)-np.min(c)))
lwidths=1+x[:-1]
ax = plt.gca()
for i in np.arange(len(x)-1):
ax.plot([x[i],x[i+1]], [y[i],y[i+1]], c=c[i],linewidth = lwidths[i])# = lwidths[i])
return
x=np.linspace(0,4*math.pi,100)
y=np.cos(x)
lwidths=1+x[:-1]
fig = plt.figure(1, figsize=(5,5))
ax = fig.add_subplot(111)
plot_colourline(x,y,prop)
ax.set_xlim(0,4*math.pi)
ax.set_ylim(-1.1,1.1)
Does someone has a more interested way to achieve this? Any advice would be appreciate!
Using as inspiration another question.
One option would be to use fill_between. But perhaps not in the way it was intended. Instead of using it to create your line, use it to mask everything that is not the line. Under it you can have a pcolormesh or contourf (for example) to map color any way you want.
Look, for instance, at this example:
import matplotlib.pyplot as plt
import numpy as np
from scipy.interpolate import interp1d
def windline(x,y,deviation,color):
y1 = y-deviation/2
y2 = y+deviation/2
tol = (y2.max()-y1.min())*0.05
X, Y = np.meshgrid(np.linspace(x.min(), x.max(), 100), np.linspace(y1.min()-tol, y2.max()+tol, 100))
Z = X.copy()
for i in range(Z.shape[0]):
Z[i,:] = c
#plt.pcolormesh(X, Y, Z)
plt.contourf(X, Y, Z, cmap='seismic')
plt.fill_between(x, y2, y2=np.ones(x.shape)*(y2.max()+tol), color='w')
plt.fill_between(x, np.ones(x.shape) * (y1.min() - tol), y2=y1, color='w')
plt.xlim(x.min(), x.max())
plt.ylim(y1.min()-tol, y2.max()+tol)
plt.show()
x = np.arange(100)
yo = np.random.randint(20, 60, 21)
y = interp1d(np.arange(0, 101, 5), yo, kind='cubic')(x)
dv = np.random.randint(2, 10, 21)
d = interp1d(np.arange(0, 101, 5), dv, kind='cubic')(x)
co = np.random.randint(20, 60, 21)
c = interp1d(np.arange(0, 101, 5), co, kind='cubic')(x)
windline(x, y, d, c)
, which results in this:
The function windline accepts as arguments numpy arrays with x, y , a deviation (like a thickness value per x value), and color array for color mapping. I think it can be greatly improved by messing around with other details but the principle, although not perfect, should be solid.
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.collections import LineCollection
x = np.linspace(0,4*np.pi,10000) # x data
y = np.cos(x) # y data
r = np.piecewise(x, [x < 2*np.pi, x >= 2*np.pi], [lambda x: 1-x/(2*np.pi), 0]) # red
g = np.piecewise(x, [x < 2*np.pi, x >= 2*np.pi], [lambda x: x/(2*np.pi), lambda x: -x/(2*np.pi)+2]) # green
b = np.piecewise(x, [x < 2*np.pi, x >= 2*np.pi], [0, lambda x: x/(2*np.pi)-1]) # blue
a = np.ones(10000) # alpha
w = x # width
fig, ax = plt.subplots(2)
ax[0].plot(x, r, color='r')
ax[0].plot(x, g, color='g')
ax[0].plot(x, b, color='b')
# mysterious parts
points = np.array([x, y]).T.reshape(-1, 1, 2)
segments = np.concatenate([points[:-1], points[1:]], axis=1)
# mysterious parts
rgba = list(zip(r,g,b,a))
lc = LineCollection(segments, linewidths=w, colors=rgba)
ax[1].add_collection(lc)
ax[1].set_xlim(0,4*np.pi)
ax[1].set_ylim(-1.1,1.1)
fig.show()
I notice this is what I suffered.
The issue is that this script is not able to plot a sphere for example while it is able to plot several cones such as the one in the script.
I have changes the shape and tried finding the lines from which the error comes from using the error message given when plotting a sphere.
import sympy as sy
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits import mplot3d
# Plot Figure
nd = 50 # Number of points in graph
ax = plt.axes(projection='3d') # Adds 3d axis to figure
x1 = np.linspace(-15, 15, nd)
y1 = np.linspace(-15, 15, nd)
X, Y = np.meshgrid(x1, y1) # Create 2D grid with x1 and y1
i = 0
a = 0
b = 0
Z = np.array([])
x = sy.Symbol('x')
y = sy.Symbol('y')
z = (x**2+y**2)**0.5 # Function goes here
for i in range(nd): # Iterate over rows
b = 0
xv1 = X[a, :]
yv1 = Y[a, :]
for i in range(nd): # Iterate over elements in one row
xv = xv1[b]
yv = yv1[b]
z1 = z.subs([(x, xv), (y, yv)])
Z = np.append(Z, z1) # Append values to array just a row
b = b + 1
a = a + 1
Z = np.reshape(Z, (nd, nd))
print(Z.dtype)
print(Y.dtype)
print(X.dtype)
Z = Z.astype(float)
Y = Y.astype(float)
X = X.astype(float)
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap='viridis', edgecolor='none')
plt.show()
The result with a sphere function is that the script crashes. I would hope this script should be able to graph this kind of 3D shapes.
Is this the error you are getting by any chance?
TypeError: can't convert complex to float
The way this is formulated you are asking for an imaginary number back. If you define this as your sphere equation:
z = (x**2+y**2-1)**0.5
you will end up asking for sqrt(-1) when x=y=0, which will not work. Try parameterizing with spherical coordinates like in this example: Python/matplotlib : plotting a 3d cube, a sphere and a vector?
I would like to plot a grid of 3 variables (same min, same max, same spacing) in 3D and I would like each point on the grid to have a specific color according to a function f which is a function of these 3 variables except for when the values of the function are superior to a specific threshold for which I assign another color.
The code below as what I have tried so far:
from mpl_toolkits.mplot3d import axes3d
import matplotlib.colors
import matplotlib.pyplot as plt
from matplotlib import cm
import numpy as np
import math
from matplotlib.colors import ListedColormap, LinearSegmentedColormap
%matplotlib notebook
x = np.arange(0.001, 0.175, 0.01)
y = np.arange(0.001, 0.175, 0.01)
z = np.arange(0.001, 0.175, 0.01)
X, Y, Z = np.meshgrid(x, y, z)
def function(X,Y,Z):
'''function of (X,Y,Z) going from 0 to high values'''
return(f)
f=function(X,Y,Z)
#flatten the f array (I think there is a function to flatten an array but I have seen it to late)
fflat=[]
for l in f:
for p in l:
for t in p:
fflat.append(t)
#masking high values with the highest interesting value: maxV
mfflat = ma.masked_greater(fflat, maxV)
mfflat = mfflat.filled(maxV)
#normalizing values and mapping to veridis cmap:
cmap = matplotlib.cm.get_cmap('viridis')
norm = matplotlib.colors.Normalize(vmin=min(mfflat), vmax=maxV) #(vmax=maxV=max(mfflat))
colors = [cmap(norm(value)) for value in mfflat]
#plot
ax.scatter(X, Y, Z, color=colors, s=10, alpha=1)
cax, _ = matplotlib.colorbar.make_axes(ax)
cbar = matplotlib.colorbar.ColorbarBase(cax, cmap=cmap, norm=norm)
The problem is that now all the "unwanted high values", i.e. values > maxV have the same colors as my "maximal wanted values", i.e. maxV ...
I would like all my "unwanted values" outside of my veridis colorscale and giving them another unique color.
Thanks for your help !
Cheers
Thanks to ImportanceOfBeingErnest for the answer, I just had to use: cmap.set_over, here is the corrected code:
x = np.arange(0.001, 0.175, 0.01)
y = np.arange(0.001, 0.175, 0.01)
z = np.arange(0.001, 0.175, 0.01)
X, Y, Z = np.meshgrid(x, y, z)
def function(X,Y,Z):
'''function of (X,Y,Z) going from 0 to high values'''
return(f)
f=function(X,Y,Z)
#flatten the f array (I think there is a function to flatten an array but I have seen it to late)
fflat=[]
for l in f:
for p in l:
for t in p:
fflat.append(t)
cmap = plt.cm.get_cmap('viridis')
cmap.set_over(color=(0,0,0), alpha=0.5)
norm = matplotlib.colors.Normalize(vmin=minV, vmax=maxV)
colors = [cmap(norm(value)) for value in fflat]
#plot
ax.scatter(X, Y, Z, color=colors, s=10, alpha=1)
cax, _ = matplotlib.colorbar.make_axes(ax)
cbar = matplotlib.colorbar.ColorbarBase(cax, cmap=cmap, norm=norm)
In the meantime I have found a workaround by creating the "colors" list selectively which is of course not as clean as using cmap.set_over:
colors=[]
for value in fflat:
if minV <= value <= maxV:
colors.append(cmap(norm(value)))
else:
colors.append((255/258,255/258,255/258,0))