I have a numpy array of xyz coordinates. All but one is representing ground level. I want to interpolate the ground level to a surface and find height above the Surface of one point:
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
arr = np.array([[0,0,0,2,2,4,5,5,2],
[0,3,5,0,5,2,0,5,2],
[80,70,50,90,40,75,60,46,220]])
x,y,z = arr
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(x, y, z, zdir='z', c= 'red')
plt.show()
Im looking for the nomenclatur for this kind of problem, not a solution. I dont know what to search for to be able to make an attempt at a solution.
Solution:
#Rebuild arr without the point which is to be measured:
arr = np.array([[0,0,0,2,2,4,5,5],
[0,3,5,0,5,2,0,5],
[80,70,50,90,40,75,60,46]])
x,y,z = arr
groundlvl = scipy.interpolate.LinearNDInterpolator(list(zip(x,y)),z)
groundlvl(2,2)
#Outputs
array(76.)
Since your ground level data does not seem to be on a grid you could use
LinearNDInterpolator. It uses Delaunay triangulation and is quite robust.
Another algorithm that I can recommend is Rbf (radial basis function).
Both are available in scipy and work on n-dimensional data.
Use one of these two to interpolate the ground level and then calculate the difference to the single value.
Related
I have two data sets index_list and frequency_list which I plot in a loglog plot by plt.loglog(index_list, freq_list). Now I'm trying to fit a power law a*x^(-b) with linear regression. I expect the curve to follow the initial curve closely but the following code seems to output a similar curve but mirrored on the y-axis.
I suspect I am using curve_fit badly.
why is this curve mirrored on the x-axis and how I can get it to properly fit my inital curve?
Using this data
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
f = open ("input.txt", "r")
index_list = []
freq_list = []
index = 0
for line in f:
split_line = line.split()
freq_list.append(int(split_line[1]))
index_list.append(index)
index += 1
plt.loglog(index_list, freq_list)
def power_law(x, a, b):
return a * np.power(x, -b)
popt, pcov = curve_fit(power_law, index_list, freq_list)
plt.plot(index_list, power_law(freq_list, *popt))
plt.show()
The code below made the following changes:
For the scipy functions to work, it is best that both index_list and freq_list are numpy arrays, not Python lists. Also, for the power not to overflow too rapidly, these arrays should be of float type (not of int).
As 0 to a negative power causes a divide-by-zero problem, it makes sense to start the index_list with 1.
Due to the powers, also for floats an overflow can be generated. Therefore, it makes sense to add bounds to curve_fit. Especially b should be limited not to cross about 50 (the highest value is about power(100000, b) giving an overflow when be.g. is100). Also setting initial values helps to direct the fitting process (p0=...).
Drawing a plot with index_list as x and power_law(freq_list, ...) as y would generate a very weird curve. It is necessary that the same x is used for the plot and for the function.
Note that calling plt.loglog() changes both axes of the plot to logarithmic. All subsequent plots on the same axes will continue to use the logarithmic scale.
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
import pandas as pd
import numpy as np
def power_law(x, a, b):
return a * np.power(x, -b)
df = pd.read_csv("https://norvig.com/google-books-common-words.txt", delim_whitespace=True, header=None)
index_list = df.index.to_numpy(dtype=float) + 1
freq_list = df[1].to_numpy(dtype=float)
plt.loglog(index_list, freq_list, label='given data')
popt, pcov = curve_fit(power_law, index_list, freq_list, p0=[1, 1], bounds=[[1e-3, 1e-3], [1e20, 50]])
plt.plot(index_list, power_law(index_list, *popt), label='power law')
plt.legend()
plt.show()
I'd like to make a streamplot with lines that don't stop when they get too close together. I'd rather each streamline be calculated in both directions until it hits the edge of the window. The result is there'd be some areas where they'd all jumble up. But that's what I want.
I there anyway to do this in matplotlib? If not, is there another tool I can use for this that could interface with python/numpy?
import numpy as np
import matplotlib.pyplot as plt
Y,X = np.mgrid[-10:10:.01, -10:10:.01]
U, V = Y**2, X**2
plt.streamplot(X,Y, U,V, density=1)
plt.show(False)
Ok, I've figured out I can get mostly what I want by turning up the density a lot and using custom start points. I'm still interested if there is a better or alternate way to do this.
Here's my solution. Doesn't it look so much better?
import numpy as np
import matplotlib.pyplot as plt
Y,X = np.mgrid[-10:10:.01, -10:10:.01]
y,x = Y[:,0], X[0,:]
U, V = Y**2, X**2
stream_points = np.array(zip(np.arange(-9,9,.5), -np.arange(-9,9,.5)))
plt.streamplot(x,y, U,V, start_points=stream_points, density=35)
plt.show(False)
Edit: By the way, there seems to be some bug in streamplot such that start_points keyword only works if you use 1d arrays for the grid data. See Python Matplotlib Streamplot providing start points
As of Matplotlib version 3.6.0, an optional parameter broken_streamlines has been added for disabling streamline breaks.
Adding it to your snippet produces the following result:
import numpy as np
import matplotlib.pyplot as plt
Y,X = np.mgrid[-10:10:.01, -10:10:.01]
U, V = Y**2, X**2
plt.streamplot(X,Y, U,V, density=1, broken_streamlines=False)
plt.show(False)
Note
This parameter just extends the streamlines which were originally drawn (as in the question). This means that the streamlines in the modified plot above are much more uneven than the result obtained in the other answer, with custom start_points. The density of streamlines on any stream plot does not represent the magnitude of U or V at that point, only their direction. See the documentation for the density parameter of matplotlib.pyplot.streamplot for more details on how streamline start points are chosen by default, when they aren't specified by the optional start_points parameter.
For accurate streamline density, consider using matplotlib.pyplot.contour, but be aware that contour does not show arrows.
Choosing start points automatically
It may not always be easy to choose a set of good starting points automatically. However, if you know the streamfunction corresponding to the flow you wish to plot you can use matplotlib.pyplot.contour to produce a contour plot (which can be hidden from the output), and then extract a suitable starting point from each of the plotted contours.
In the following example, psi_expression is the streamfunction corresponding to the flow. When modifying this example for your own needs, make sure to update both the line defining psi_expression, as well as the one defining U and V. Ensure these both correspond to the same flow.
The density of the streamlines can be altered by changing contour_levels. Here, the contours are uniformly distributed.
import numpy as np
import matplotlib.pyplot as plt
import sympy as sy
x, y = sy.symbols("x y")
psi_expression = x**3 - y**3
psi_function = sy.lambdify((x, y), psi_expression)
Y, X = np.mgrid[-10:10:0.01, -10:10:0.01]
psi_evaluated = psi_function(X, Y)
U, V = Y**2, X**2
contour_levels = np.linspace(np.amin(psi_evaluated), np.amax(psi_evaluated), 30)
# Draw a temporary contour plot.
temp_figure = plt.figure()
contour_plot = plt.contour(X, Y, psi_evaluated, contour_levels)
plt.close(temp_figure)
points_list = []
# Iterate over each contour.
for collection in contour_plot.collections:
# Iterate over each segment in this contour.
for path in collection.get_paths():
middle_point = path.vertices[len(path.vertices) // 2]
points_list.append(middle_point)
# Reshape python list into numpy array of coords.
stream_points = np.reshape(np.array(points_list), (-1, 2))
plt.streamplot(X, Y, U, V, density=1, start_points=stream_points, broken_streamlines=False)
plt.show(False)
I’ve a scatter plot which almost looks like a circle. I would like to join the outer points with a line to show that almost circle like shape. Is there a way to do that in matplotlib?
You can use ConvexHull from scipy.spatial to find the outer points of your scatter plot and then connect these points using a PolyCollection from matplotlib.collections:
from matplotlib import pyplot as plt
import numpy as np
from scipy.spatial import ConvexHull
from matplotlib.collections import PolyCollection
fig, ax = plt.subplots()
length = 1000
#using some normally distributed data as example:
x = np.random.normal(0, 1, length)
y = np.random.normal(0, 1, length)
points = np.concatenate([x,y]).reshape((2,length)).T
hull = ConvexHull(points)
ax.scatter(x,y)
ax.add_collection(PolyCollection(
[points[hull.vertices,:]],
edgecolors='r',
facecolors='w',
linewidths=2,
zorder=-1,
))
plt.show()
The result looks like this:
EDIT
Actually, you can skip the PolyCollection and just do a simple line plot using the hull vertices. You only have to make the line circular by appending the first vertex to the list of vertices (making that list one element longer):
circular_hull_verts = np.append(hull.vertices,hull.vertices[0])
ax.plot(
x[circular_hull_verts], y[circular_hull_verts], 'r-', lw=2, zorder=-1,
)
EDIT 2:
I noticed that there is an example in the scipy documentation that looks quite similar to mine.
I am trying to make a filled contour for a dataset. It should be fairly straightforward:
plt.contourf(x, y, z, label = 'blah', cm = matplotlib.cm.RdBu)
However, what do I do if my dataset is not symmetric about 0? Let's say I want to go from blue (negative values) to 0 (white), to red (positive values). If my dataset goes from -8 to 3, then the white part of the color bar, which should be at 0, is in fact slightly negative. Is there some way to shift the color bar?
First off, there's more than one way to do this.
Pass an instance of DivergingNorm as the norm kwarg.
Use the colors kwarg to contourf and manually specify the colors
Use a discrete colormap constructed with matplotlib.colors.from_levels_and_colors.
The simplest way is the first option. It is also the only option that allows you to use a continuous colormap.
The reason to use the first or third options is that they will work for any type of matplotlib plot that uses a colormap (e.g. imshow, scatter, etc).
The third option constructs a discrete colormap and normalization object from specific colors. It's basically identical to the second option, but it will a) work with other types of plots than contour plots, and b) avoids having to manually specify the number of contours.
As an example of the first option (I'll use imshow here because it makes more sense than contourf for random data, but contourf would have identical usage other than the interpolation option.):
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import DivergingNorm
data = np.random.random((10,10))
data = 10 * (data - 0.8)
fig, ax = plt.subplots()
im = ax.imshow(data, norm=DivergingNorm(0), cmap=plt.cm.seismic, interpolation='none')
fig.colorbar(im)
plt.show()
As an example of the third option (notice that this gives a discrete colormap instead of a continuous colormap):
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import from_levels_and_colors
data = np.random.random((10,10))
data = 10 * (data - 0.8)
num_levels = 20
vmin, vmax = data.min(), data.max()
midpoint = 0
levels = np.linspace(vmin, vmax, num_levels)
midp = np.mean(np.c_[levels[:-1], levels[1:]], axis=1)
vals = np.interp(midp, [vmin, midpoint, vmax], [0, 0.5, 1])
colors = plt.cm.seismic(vals)
cmap, norm = from_levels_and_colors(levels, colors)
fig, ax = plt.subplots()
im = ax.imshow(data, cmap=cmap, norm=norm, interpolation='none')
fig.colorbar(im)
plt.show()
I would like to plot a curve in the (x,y) plane, where the color of the curve depends on a value of another variable T. x is a 1D numpy array, y is a 1D numpy array.
T=np.linspace(0,1,np.size(x))**2
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(x,y)
I want the line to change from blue to red (using RdBu colormap) depending on the value of T (one value of T exists for every (x,y) pair).
I found this, but I don't know how to warp it to my simple example. How would I use the linecollection for my example? http://matplotlib.org/examples/pylab_examples/multicolored_line.html
Thanks.
One idea could be to set the color using color=(R,G,B) then split your plot into n segments and continuously vary either one of the R, G or B (or a combinations)
import pylab as plt
import numpy as np
# Make some data
n=1000
x=np.linspace(0,100,n)
y=np.sin(x)
# Your coloring array
T=np.linspace(0,1,np.size(x))**2
fig = plt.figure()
ax = fig.add_subplot(111)
# Segment plot and color depending on T
s = 10 # Segment length
for i in range(0,n-s,s):
ax.plot(x[i:i+s+1],y[i:i+s+1],color=(0.0,0.5,T[i]))
Hope this is helpful