I have a matrix generated by parsing a file the numpy array is the size 101X101X41 and each entry has a value which represents the magnitude at each point.
Now what I want to do is to plot it in a 3d plot where the 4th dimension will be represented by color. so that I will be able to see the shape of the data points (represent molecular orbitals) and deduce its magnitude at that point.
If I plot each slice of data I get the desired outcome, but in a 2d with the 3rd dimension as the color.
Is there a way to plot this model in python using Matplotlib or equivalent library
Thanks
EDIT:
Im trying to get the question clearer to what I desire.
Ive tried the solution suggested but ive received the following plot:
as one can see, due to the fact the the mesh has lots of zeros in it it "hide" the 3d orbitals. in the following plot one can see a slice of the data, where I get the following plot:
So as you can see I have a certain structure I desire to show in the plot.
my question is, is there a way to plot only the structure and ignore the zeroes such that they won't "hide" the structure.
the code I used to generate the plots:
x = np.linspase(1,101,101)
y = np.linspase(1,101,101)
z = np.linspase(1,101,101)
xx,yy,zz = np.meshgrid(x,y,z)
fig=plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(xx, yy, zz, c=cube.calc_data.flatten())
plt.show()
plt.imshow(cube.calc_data[:,:,11],cmap='jet')
plt.show()
Hope that now the question is much clearer, and that you'd appreciate the question enough now to upvote
Thanks.
you can perform the following:
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
epsilon = 2.5e-2 # threshold
height, width, depth = data.shape
global_min = np.inf
global_max = -np.inf
for d in range(depth):
slice = data[:, :, d]
minima = slice.min()
if (minima < global_min): global_min = minima
maxima = slice.max()
if (maxima>global_max): global_max=maxima
norm = colors.Normalize(vmin=minima, vmax=maxima, clip=True)
mapper = cm.ScalarMappable(norm=norm, cmap=cm.jet)
points_gt_epsilon = np.where(slice >= epsilon)
ax.scatter(points_gt_epsilon[0], points_gt_epsilon[1], d,
c=mapper.to_rgba(data[points_gt_epsilon[0],points_gt_epsilon[1],d]), alpha=0.015, cmap=cm.jet)
points_lt_epsilon = np.where(slice <= -epsilon)
ax.scatter(points_lt_epsilon[0], points_lt_epsilon[1], d,
c=mapper.to_rgba(data[points_lt_epsilon[0], points_lt_epsilon[1], d]), alpha=0.015, cmap=cm.jet)
ax.set_xlabel('X Label')
ax.set_ylabel('Y Label')
ax.set_zlabel('Z Label')
plt.title('Electron Density Prob.')
norm = colors.Normalize(vmin=global_min, vmax=global_max, clip=True)
cax, _ = colorbar.make_axes(ax)
colorbar.ColorbarBase(cax, cmap=cm.jet,norm=norm)
plt.savefig('test.png')
plt.clf()
What this piece of code does is going slice by slice from the data matrix and for each scatter plot only the points desired (depend on epsilon).
in this case you avoid plotting a lot of zeros that 'hide' your model, using your words.
Hope this helps
You can adjust the color and size of the markers for the scatter. So for example you can filter out all markers below a certain threshold by putting their size to 0. You can also make the size of the marker adaptive to the field strength.
As an example:
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
f = lambda x,y,z: np.exp(-(x-3)**2-(y-3)**2-(z-1)**2) - \
np.exp(-(x+3)**2-(y+3)**2-(z+1)**2)
t1 = np.linspace(-6,6,101)
t2 = np.linspace(-3,3,41)
# Data of shape 101,101,41
data = f(*np.meshgrid(t1,t1,t2))
print(data.shape)
# Coordinates
x = np.linspace(1,101,101)
y = np.linspace(1,101,101)
z = np.linspace(1,101,41)
xx,yy,zz = np.meshgrid(x,y,z)
fig=plt.figure()
ax = fig.add_subplot(111, projection='3d')
s = np.abs(data/data.max())**2*25
s[np.abs(data) < 0.05] = 0
ax.scatter(xx, yy, zz, s=s, c=data.flatten(), linewidth=0, cmap="jet", alpha=.5)
plt.show()
Related
I currently have a scale problem with a heatmap:
As you can see at the beginning and at the end, there is a temperature variation, but as it is done on a very small distance and the scale is big, we can't see anything at all.
So is there a way or a function to fix this problem and automatically apply a better scale to see better ? To apply a small scale where there is a variation and a big scale when it is not ?
Here is the code to generate this image :
x = np.linspace(0,L,Nx+1) #array for y-axis
t = np.linspace(0.0, t_fin,Nt+1) #array to plot the time in the title
x = np.round(x,2) #change decimals
t = np.round(t,5)
y = np.arange(T[Nt,:].shape[0]) #T[Nt,:] is an array that contains the temperature
my_yticks = x #change the number of points in the y-axis
frequency = 100
data = np.vstack(T[Nt,:]) #to use in imshow
df = pd.DataFrame(data)
fig = plt.figure(figsize=(3,9)) #plotting
titre = f"Température à {t[Nt]} s"
plt.ylabel('Profondeur en m')
plt.yticks(y[::frequency], my_yticks[::frequency])
im = plt.imshow(df, cmap='jet', aspect ='auto', interpolation='bilinear')
ax = plt.gca()
ax.get_xaxis().set_visible(False)
cb = plt.colorbar()
cb.set_label('Température en °C')
plt.title(titre)
If you have any questions, do not hesitate.
Thank you !
You could use a logit scale on the y-axis. This won't however work with imshow as the values must be between 0 and 1 exclusively. You could use a pcolormesh instead.
import matplotlib.pyplot as plt
import numpy as np
M,N = 100,20
a = np.array(M*[15])
a[:3] = [0,5,10]
a[-3:] = [20,25,30]
a = np.outer(a, np.ones(N))
fig, (axl,axr) = plt.subplots(ncols=2, figsize=(3,6))
axl.imshow(a, cmap='jet', aspect ='auto', interpolation='bilinear', extent=(N,0,M,0))
axl.yaxis.set_ticklabels([f'{t/M*10:.3g}' for t in axl.yaxis.get_ticklocs()])
axl.get_xaxis().set_visible(False)
axl.set_title('linear')
eps = 1e-3
X, Y = np.meshgrid(np.linspace(0, 1, N), np.linspace(1-eps, eps, M))
cm = axr.pcolormesh(X, Y, a, cmap='jet', shading='gouraud')
axr.set_yscale('logit')
axr.yaxis.set_ticklabels([f'{10*(1-t):.3g}' for t in axr.yaxis.get_ticklocs()])
axr.get_xaxis().set_visible(False)
axr.set_title('logit')
cb = plt.colorbar(cm, pad=0.2)
Warning: setting the y labels as fixed values is only useful if you don't want to pan/zoom your image.
You can set the y axis limit by ax.set_ylim([,])
I have some z=f(x,y) data which i would like to plot. The issue is that (x,y) are not part of a "nice" rectangle, but rather arbitrary parallelograms, as shown in the attached image (this particular one is also a rectangle, but you could think of more general cases). So I am having a hard time figuring out how I can use plot_surface in this case, as this usually will take x and y as 2d arrays, and here my x-and y-values are 1d. Thanks.
Abritrary points can be supplied as 1D arrays to matplotlib.Axes3D.plot_trisurf. It doesn't matter whether they follow a specific structure.
Other methods which would depend on the structure of the data would be
Interpolate the points on a regular rectangular grid. This can be accomplished using scipy.interpolate.griddata. See example here
Reshape the input arrays such that they live on a regular and then use plot_surface(). Depending on the order by which the points are supplied, this could be a very easy solution for a grid with "parallelogramic" shape.
As can be seen from the sphere example, plot_surface() also works in cases of very unequal grid shapes, as long as it's structured in a regular way.
Here are some examples:
For completeness, find here the code that produces the above image:
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
f = lambda x,y: np.sin(x+0.4*y)*0.23+1
fig = plt.figure(figsize=(5,6))
plt.subplots_adjust(left=0.1, top=0.95,wspace=0.01)
ax0 = fig.add_subplot(322, projection="3d")
ma = 6*(np.random.rand(100)-0.5)
mb = 6*(np.random.rand(100)-0.5)
phi = np.pi/4
x = 1.7*ma*np.cos(phi) + 1.7*mb*np.sin(phi)
y = -1.2*ma*np.sin(phi) +1.2* mb*np.cos(phi)
z = f(x,y)
ax0.plot_trisurf(x,y,z)
ax1 = fig.add_subplot(321)
ax0.set_title("random plot_trisurf()")
ax1.set_aspect("equal")
ax1.scatter(x,y, marker="+", alpha=0.4)
for i in range(len(x)):
ax1.text(x[i],y[i], i , ha="center", va="center", fontsize=6)
n = 10
a = np.linspace(-3, 3, n)
ma, mb = np.meshgrid(a,a)
phi = np.pi/4
xm = 1.7*ma*np.cos(phi) + 1.7*mb*np.sin(phi)
ym = -1.2*ma*np.sin(phi) +1.2* mb*np.cos(phi)
shuf = np.c_[xm.flatten(), ym.flatten()]
np.random.shuffle(shuf)
x = shuf[:,0]
y = shuf[:,1]
z = f(x,y)
ax2 = fig.add_subplot(324, projection="3d")
ax2.plot_trisurf(x,y,z)
ax3 = fig.add_subplot(323)
ax2.set_title("unstructured plot_trisurf()")
ax3.set_aspect("equal")
ax3.scatter(x,y, marker="+", alpha=0.4)
for i in range(len(x)):
ax3.text(x[i],y[i], i , ha="center", va="center", fontsize=6)
x = xm.flatten()
y = ym.flatten()
z = f(x,y)
X = x.reshape(10,10)
Y = y.reshape(10,10)
Z = z.reshape(10,10)
ax4 = fig.add_subplot(326, projection="3d")
ax4.plot_surface(X,Y,Z)
ax5 = fig.add_subplot(325)
ax4.set_title("regular plot_surf()")
ax5.set_aspect("equal")
ax5.scatter(x,y, marker="+", alpha=0.4)
for i in range(len(x)):
ax5.text(x[i],y[i], i , ha="center", va="center", fontsize=6)
for axes in [ax0, ax2,ax4]:
axes.set_xlim([-3.5,3.5])
axes.set_ylim([-3.5,3.5])
axes.set_zlim([0.9,2.0])
axes.axis("off")
plt.savefig(__file__+".png")
plt.show()
If your data is in order, and you know the size of the parallgram, a reshape will probably suffice:
ax.surface(x.reshape(10, 10), y.reshape(10, 10), z.reshape(10, 10))
Will work if the parallelogram has 10 points on each side, and the points are ordered in a zigzag pattern
I got a problem when I was plotting a 3d figure using matplotlib of python. Using the following python function, I got this figure:
Here X, Y are meshed grids and Z and Z_ are functions of X and Y. C stands for surface color.
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import matplotlib.pyplot as plt
def plot(X, Y, Z, Z_, C):
fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(
X, Y, Z, rstride=1, cstride=1,
facecolors=cm.jet(C),
linewidth=0, antialiased=False, shade=False)
surf_ = ax.plot_surface(
X, Y, Z_, rstride=1, cstride=1,
facecolors=cm.jet(C),
linewidth=0, antialiased=False, shade=False)
ax.view_init(elev=7,azim=45)
plt.show()
But now I want to cut this figure horizontally and only the part whose z is between -1 and 2 remain.
What I want, plotted with gnuplot, is this:
I have tried ax.set_zlim3d and ax.set_zlim, but neither of them give me the desired figure. Does anybody know how to do it using python?
Nice conical intersections you have there:)
What you're trying to do should be achieved by setting the Z data you want to ignore to NaN. Using graphene's tight binding band structure as an example:
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
# generate dummy data (graphene tight binding band structure)
kvec = np.linspace(-np.pi,np.pi,101)
kx,ky = np.meshgrid(kvec,kvec)
E = np.sqrt(1+4*np.cos(3*kx/2)*np.cos(np.sqrt(3)/2*ky) + 4*np.cos(np.sqrt(3)/2*ky)**2)
# plot full dataset
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(kx,ky,E,cmap='viridis',vmin=-E.max(),vmax=E.max(),rstride=1,cstride=1)
ax.plot_surface(kx,ky,-E,cmap='viridis',vmin=-E.max(),vmax=E.max(),rstride=1,cstride=1)
# focus on Dirac cones
Elim = 1 #threshold
E[E>Elim] = np.nan
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
#ax.plot_surface(kx2,ky2,E2,cmap='viridis',vmin=-Elim,vmax=Elim)
#ax.plot_surface(kx2,ky2,-E2,cmap='viridis',vmin=-Elim,vmax=Elim)
ax.plot_surface(kx,ky,E,cmap='viridis',rstride=1,cstride=1,vmin=-Elim,vmax=Elim)
ax.plot_surface(kx,ky,-E,cmap='viridis',rstride=1,cstride=1,vmin=-Elim,vmax=Elim)
plt.show()
The results look like this:
Unfortunately, there are problems with the rendering of the second case: the apparent depth order of the data is messed up in the latter case: cones in the background are rendered in front of the front ones (this is much clearer in an interactive plot). The problem is that there are more holes than actual data, and the data is not connected, which confuses the renderer of plot_surface. Matplotlib has a 2d renderer, so 3d visualization is a bit of a hack. This means that for complex overlapping surfaces you'll more often than not get rendering artifacts (in particular, two simply connected surfaces are either fully behind or fully in front of one another).
We can get around the rendering bug by doing a bit more work: keeping the data in a single surface by not using nans, but instead colouring the the surface to be invisible where it doesn't interest us. Since the surface we're plotting now includes the entire original surface, we have to set the zlim manually in order to focus on our region of interest. For the above example:
from matplotlib.cm import get_cmap
# create a color mapping manually
Elim = 1 #threshold
cmap = get_cmap('viridis')
colors_top = cmap((E + Elim)/2/Elim) # listed colormap that maps E from [-Elim, Elim] to [0.0, 1.0] for color mapping
colors_bott = cmap((-E + Elim)/2/Elim) # same for -E branch
colors_top[E > Elim, -1] = 0 # set outlying faces to be invisible (100% transparent)
colors_bott[-E < -Elim, -1] = 0
# in nature you would instead have something like this:
#zmin,zmax = -1,1 # where to cut the _single_ input surface (x,y,z)
#cmap = get_cmap('viridis')
#colors = cmap((z - zmin)/(zmax - zmin))
#colors[(z < zmin) | (z > zmax), -1] = 0
# then plot_surface(x, y, z, facecolors=colors, ...)
# or for your specific case where you have X, Y, Z and C:
#colors = get_cmap('viridis')(C)
#colors[(z < zmin) | (z > zmax), -1] = 0
# then plot_surface(x, y, z, facecolors=colors, ...)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
# pass the mapped colours as the facecolors keyword arg
s1 = ax.plot_surface(kx, ky, E, facecolors=colors_top, rstride=1, cstride=1)
s2 = ax.plot_surface(kx, ky, -E, facecolors=colors_bott, rstride=1, cstride=1)
# but now we need to manually hide the invisible part of the surface:
ax.set_zlim(-Elim, Elim)
plt.show()
Here's the output:
Note that it looks a bit different from the earlier figures because 3 years have passed in between and the current version of matplotlib (3.0.2) has very different (and much prettier) default styles. In particular, edges are now transparent in surface plots. But the main point is that the rendering bug is gone, which is evident if you start rotating the surface around in an interactive plot.
I am creating a histogram for my data. Interestingly, when I plot my raw data and their histogram together on one plot, they are a "y-flipped" version of each other as follows:
I failed to find out the reason and fix it. My code snippet is as follows:
import math as mt
import numpy as np
import matplotlib.pylab as plt
x = np.random.randn(50)
y = np.random.randn(50)
w = np.random.randn(50)
leftBound, rightBound, topBound, bottomBound = min(x), max(x), max(y), min(y)
# parameters for histogram
x_edges = np.linspace(int(mt.floor(leftBound)), int(mt.ceil(rightBound)), int(mt.ceil(rightBound))-int(mt.floor(leftBound))+1)
y_edges = np.linspace(int(mt.floor(bottomBound)), int(mt.ceil(topBound)), int(mt.ceil(topBound))-int(mt.floor(bottomBound))+1)
# construct the histogram
wcounts = np.histogram2d(x, y, bins=(x_edges, y_edges), normed=False, weights=w)[0]
# wcounts is a 2D array, with each element representing the weighted count in a bins
# show histogram
extent = x_edges[0], x_edges[-1], y_edges[0], y_edges[-1]
fig = plt.figure()
axes = fig.add_axes([0.1, 0.1, 0.8, 0.8]) # left, bottom, width, height (range 0 to 1)
axes.set_xlabel('x (m)')
axes.set_ylabel('y (m)')
histogram = axes.imshow(np.transpose(wcounts), extent=extent, alpha=1, vmin=0.5, vmax=5, cmap=cm.binary) # alpha controls the transparency
fig.colorbar(histogram)
# show data
axes.plot(x, y, color = '#99ffff')
Since the data here are generated randomly for demonstration, I don't think it helps much, if the problem is with that particular data set. But anyway, if it is something wrong with the code, it still helps.
By default, axes.imshow(z) places array element z[0,0] in the top left corner of the axes (or the extent in this case). You probably want to either add the origin="bottom" argument to your imshow() call or pass a flipped data array, i.e., z[:,::-1].
I have one question about the grid lines matplotlib.
I am not sure if this is possible to do or not.
I am plotting the following graph as shown in the image.
I won't give the entire code, since it is involving reading of files.
However the important part of code is here -
X, Y = np.meshgrid(smallX, smallY)
Z = np.zeros((len(X),len(X[0])))
plt.contourf(X, Y, Z, levels, cmap=cm.gray_r, zorder = 1)
plt.colorbar()
...
# Set Border width zero
[i.set_linewidth(0) for i in ax.spines.itervalues()]
gridLineWidth=0.1
ax.set_axisbelow(False)
gridlines = ax.get_xgridlines()+ax.get_ygridlines()
#ax.set_axisbelow(True)
plt.setp(gridlines, 'zorder', 5)
ax.yaxis.grid(True, linewidth=gridLineWidth, linestyle='-', color='0.6')
ax.xaxis.grid(False)
ax.xaxis.set_ticks_position('none')
ax.yaxis.set_ticks_position('none')
Now, my questions is like this -
If I put the grid lines below the contour, they disappear since they are below it.
If I put the grid line above the contour, they looks like what they are looking now.
However, what I would like to have is the grid lines should be visible, but should be below the black portion of the contour. I am not sure if that is possible.
Thank You !
In addition to specifying the z-order of the contours and the gridlines, you could also try masking the zero values of your contoured data.
Here's a small example:
import numpy as np
import matplotlib.pyplot as plt
x = np.arange(-2*np.pi, 2*np.pi, 0.1)
y = np.arange(-2*np.pi, 2*np.pi, 0.1)
X, Y = np.meshgrid(x, y)
Z = np.sin(X) - np.cos(Y)
Z = np.ma.masked_less(Z, 0) # you use mask_equal(yourData, yourMagicValue)
fig, ax = plt.subplots()
ax.contourf(Z, zorder=5, cmap=plt.cm.coolwarm)
ax.xaxis.grid(True, zorder=0)
ax.yaxis.grid(True, zorder=0)
And the output: