I am a beginner for data analysis or analytics,
My question here is, I have grid points (x and y) of a grid or a mesh and I have a corresponding temperature value for every grid point, I have to generate a 2D contour plot of temperature using that data which is present in an excel, Any idea on how to start on this topic, this would be of great help to me.
Here is an example of contour map from here
import matplotlib.pyplot as plt
plt.style.use('seaborn-white')
import numpy as np
def f(x, y):
return np.sin(x) ** 10 + np.cos(10 + y * x)
x = np.linspace(0, 5, 50)
y = np.linspace(0, 5, 40)
X, Y = np.meshgrid(x, y)
Z = f(X, Y) # temperature
plt.contourf(X, Y, Z, 20, cmap='RdGy')
plt.colorbar()
output :
matplotlib is good, but plotly is powerful and easier, you should try it.
Related
I have a large set of measurements that I want to visualize in 4D using matplotlib in Python.
Currently, my variables are arranged in this way:
x = np.array(range(0, v1))
y = np.array(range(0, v2))
z = np.array(range(0, v3))
I have C which is a 3D array containing measurement values for each combination of the previous variables. So it has a dimension of v1*v2*v3.
Currently, I visualize my measurements using contourf function and I plot that for each z value. This results in 3D contour plot i.e. 2D + color map for the values. Now, I want to combine all the variables and look at the measurements in 4D dimensions (x, y, z, and color corresponding to the measurement value). What is the most efficient way to do this in python?
Regarding to #Sameeresque answer, I think the question was about a 4D graph like this (three coordinates x, y, z and a color as the fourth coordinate):
import numpy as np
import matplotlib.pyplot as plt
# only for example, use your grid
z = np.linspace(0, 1, 15)
x = np.linspace(0, 1, 15)
y = np.linspace(0, 1, 15)
X, Y, Z = np.meshgrid(x, y, z)
# Your 4dimension, only for example (use yours)
U = np.exp(-(X/2) ** 2 - (Y/3) ** 2 - Z ** 2)
# Creating figure
fig = plt.figure()
ax = plt.axes(projection="3d")
# Creating plot
ax.scatter3D(X, Y, Z, c=U, alpha=0.7, marker='.')
plt.show()
A 4D plot with (x,y,z) on the axis and the fourth being color can be obtained like so:
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
x = np.array(range(0, 50))
y = np.array(range(0, 50))
z = np.array(range(0, 50))
colors = np.random.standard_normal(len(x))
img = ax.scatter(x, y, z, c=colors, cmap=plt.hot())
fig.colorbar(img)
plt.show()
A simple way to visualize your 4D function, call it W(x, y, z), could be producing a gif of the cross-section contour plots along the z-axis.
Package plot4d could help you do it. An example plotting an isotropic 4D function:
from plot4d import plotter
import numpy as np
plotter.plot4d(lambda x,y,z:x**2+y**2+z**2, np.linspace(0,1,20), wbounds=(0,3), fps=5)
The code above generates this gif:
I have this function:
z = 0.000855995633558468*x**2 + 0.0102702516120239*x + 0.00451027901725375*y**2 - 2.23785431578513*y + 251.029058292935
I also have lists (X, Y, Z) of the coordinates of the points from this function. Then I made this code to do a plot, of that coordinates:
fig = plt.figure()
ax = fig.gca(projection='3d')
plt.plot(X, Y, Z)
plt.show()
As you can see, with this code, I join the points by segments. How can I plot the curve that passes through those points?
In short, Python does not know how all xyz points need to be connected to each other to create a surface, so it just plots lines between them.
If you want to plot a surface whose z-coordinates are a function of its x and y coordinates you need to create a grid of all the possible combinations of xy coordinates and get the resulting z-grid. Then you can plot the grids.
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
def z_func(x, y):
z = 0.000855995633558468 * x ** 2 + 0.0102702516120239 * x + \
0.00451027901725375 * y ** 2 - 2.23785431578513 * y + \
251.029058292935
return z
# Creates a 1D array of all possible x and y coordinates
x_coords = np.linspace(-30, 30, 100)
y_coords = np.linspace(180, 220, 100)
# Creates 2D array with all possible combinations of x and y coordinates,
# so x_grid.shape = (100, 100) and y_grid.shape = (100, 100)
[x_grid, y_grid] = np.meshgrid(x_coords, y_coords)
# Evaluates z at all grid points
z_grid = z_func(x_grid, y_grid)
# Plotting
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(x_grid,y_grid,z_grid)
plt.show()
I'm trying to create a plot a bit like this:
Where there are spheres above all the minima.
The surface can be approximated with a sin(x)*sin(y) plot:
import numpy as np
import matplotlib.pyplot as plt
def func(x, y):
return np.sin(2*np.pi*x)*np.sin(2*np.pi*y) / 3
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([func(x,y) for x,y in zip(np.ravel(X), np.ravel(Y))])
Z = zs.reshape(X.shape)
ax.plot_surface(X, Y, Z, color="grey")
ax.set_zlim3d(-1,1)
plt.show()
However I'm unsure how to add evenly spaced spheres into this. Would anyone be able to help?
Using matplotlib one will inevitably run into problems of objects being hidden behind others. This is also stated in the matplotlib 3d FAQ and the recommendation is to use mayavi.
In mayavi the solution would look like this:
from mayavi import mlab
import numpy as np
### SURFACE '''
x,y = np.meshgrid(np.linspace(-2.5,2), np.linspace(-2,2))
f = lambda x,y: .4*np.sin(2*np.pi*x)*np.sin(2*np.pi*y)
z=f(x,y)
mlab.surf(x.T,y.T,z.T, colormap="copper")
### SPHERES '''
px,py = np.meshgrid(np.arange(-2,2)+.25, np.arange(-2,2)+.75)
px,py = px.flatten(),py.flatten()
pz = np.ones_like(px)*0.05
r = np.ones_like(px)*.4
mlab.points3d(px,py,pz,r, color=(0.9,0.05,.3), scale_factor=1)
mlab.show()
You need to determine the minima of the function, which are (with your parametrization) at (x = integer + 0.25, y=integer + 0.75) or the other way round. Then you can simply parametrize the spheres using spherical coordinates (for example as done here: python matplotlib: drawing 3D sphere with circumferences) and plot the spheres.
Now comes some good news and some bad news:
1.) The good news is that the minima are correctly determined and that the spheres are created. In the below plot you can see that they are right above the blue parts of the surface plot (where the blue parts show indeed the minima).
2.) The bad news is that you will have a hard time looking for another angle where the spheres are actually correctly rendered. I do not know a solution to this rather annoying behaviour, therefore you will probably have to play around until you have found the right angle. Have fun!
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
def func(x, y):
return np.sin(2*np.pi*x)*np.sin(2*np.pi*y) / 3
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
x = y = np.arange(-2.0, 2.0, 0.05)
# Get the minima of the function.
minsx1 = np.arange(int(np.amin(x)) + 0.25, int(np.amax(x)) + 0.25 + 1, 1)
minsy1 = np.arange(int(np.amin(y)) + 0.75, int(np.amax(y)) + 0.75 + 1, 1)
minsx2 = np.arange(int(np.amin(x)) + 0.75, int(np.amax(x)) + 0.75 + 1, 1)
minsy2 = np.arange(int(np.amin(y)) + 0.25, int(np.amax(y)) + 0.25 + 1, 1)
X, Y = np.meshgrid(x, y)
zs = np.array([func(x,y) for x,y in zip(np.ravel(X), np.ravel(Y))])
Z = zs.reshape(X.shape)
# Color map for better detection of minima (blue)
ax.plot_surface(X, Y, Z, cmap="viridis")
ax.set_zlim3d(-1,1)
# Spherical coordinates
r = 0.15
phi = np.linspace(0, 2 * np.pi, 30)
theta = np.linspace(0, np.pi, 30)
# Write spherical coordinates in cartesian coordinates.
x = r * np.outer(np.cos(phi), np.sin(theta))
y = r * np.outer(np.sin(phi), np.sin(theta))
z = r * np.outer(np.ones(np.size(phi)), np.cos(theta))
# Plot the spheres.
for xp in minsx1:
for yp in minsy1:
sphere = ax.plot_surface(x+xp, y+yp, z+0.35, color='r')
for xp in minsx2:
for yp in minsy2:
sphere = ax.plot_surface(x+xp, y+yp, z+0.35, color='r')
ax.view_init(elev=90, azim=0)
plt.savefig('test.png')
plt.show()
This question already has answers here:
Make contour of scatter
(3 answers)
Closed 5 years ago.
I have 3 lots of data. These are x and y values as well as a temperature value for each xy point. I would like to plot each point and interpolate the area between points to get a continuous surface. The issue I have is specifying the temperature values. I can't get it to work with an equal number of x,y and z (temperature) values and all the examples I can find online use a function of x and y to create z or have z values for every point on an xy grid.
Is there a simple way to do this?
import numpy as np
import matplotlib.pyplot as plt
fig, axs = plt.subplots()
x = np.linspace(0, 1, 100)
y = np.linspace(0,1,100)
X, Y = np.meshgrid(x, y)
#Z = np.sin(X)*np.sin(Y) # want to specify not an equation
Z = np.linspace(1,2,100)
levels = np.linspace(-1, 1, 40)
cs = axs.contourf(X, Y, Z, levels=levels)
fig.colorbar(cs, ax=axs, format="%.2f")
plt.show()
Update:
Here is what I have so far. I still need to work out a good method to fill in the area between points. Does anyone have any ideas?
import numpy as np
import matplotlib.pyplot as plt
fig, axs = plt.subplots()
# create a grid in the correct shape / size
x = np.linspace(0, 1, 3)
y = np.linspace(0,1,3)
X, Y = np.meshgrid(x, y)
# specify and change the relevent areas
y = [1,2,0] # location of point in x direction
x =[2,1,1] #location of point in y direction
z = [40,30,20] #temperature
Z = np.arange(1,10).reshape((3,3))
Z[y,x] = z
levels = np.linspace(0, 40, 40)
cs = axs.contourf(X, Y, Z, levels=levels)
fig.colorbar(cs, ax=axs, format="%.2f")
plt.show()
The reason people use a function of x and y is because your Z value has to be a function of x and y. In your test code Z is 1D but it needs to be 2D to plot the contours.
If you have Z (temperature) values that have the same shape as your x and y coordinates then it should work.
x = np.linspace(0, 1, 100)
y = np.linspace(0,1,100)
X, Y = np.meshgrid(x, y)
#Z = np.sin(X)*np.sin(Y) # want to specify not an equation
Z = np.linspace(1,2,100)
print X.shape
print Z.shape
(100L,100L)
(100L)
Provided we have a contour on the xy plane, how can we plot "a curtain" raised from the contour to the limiting surface?
An example:
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
def figure():
fig = plt.figure(figsize=(8,6))
axes = fig.gca(projection='3d')
x = np.linspace(-2, 2, 100)
y = np.linspace(-2, 2, 100)
x, y = np.meshgrid(x, y)
t1 = np.linspace(0, 8/9, 100)
x1 = t1
y1 = (2*t1)**0.5
f1 = lambda x, y: y
plt.plot(x1, y1)
axes.plot_surface(x, y, f1(x, y),color ='red', alpha=0.1)
axes.set_xlim(-2,2)
axes.set_ylim(-2,2)
figure()
How to plot a surface from the given line to the limiting surface?
Somebody wanted help plotting an intersection here cylinder "cuts" a sphere in python you could use the vertical cylinder part. It uses u, v parameters to generate x, y, z values