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how to plot some lists with different shape?

I have some lists that each of which has a different shape and I would like to plot all of them together in one polar scatter plot. I also tried to use iter tools but I could not find the solution.
import numpy as np
import matplotlib.pyplot as plt
a1=[1,2,3,4,5,6]
a2=[2,3,5,6]
a3=[1,2,3]
a4=[1,2,3,4,4,56,7,8]
ax1 = plt.subplot(111,polar= True)
for i in range (0,3):
theta = 4 * np.pi * np.random.rand(len(a[i]))
ax1.set_ylim(0,0.1)
ax1.set_rlabel_position(180)
for i in range (0,3):
ax1.scatter(theta,a[i], cmap='hsv', alpha=0.5)

Be carefull i modified your lists for a better visual exmaple!
I hope I understood your question correctly...
import numpy as np
import matplotlib.pyplot as plt
a1=[1,2,3,4,5,6]
a2=[2,3,5,6]
a3=[1,2,3]
a4=[1,2,3,4,4,7,7,8]
ax1 = plt.subplot(111,polar= True)
for onelist in [a1,a2,a3,a4]:
theta_list = np.linspace(0,2*np.pi,len(onelist))
ax1.plot(theta_list,onelist,marker="x")
plt.show()

Matplotlib does not show some graphs

Trying to plot a simple graph in Jupyter Notebook with the package matplotlib, I came accross a strange problem that I had never had before.
I've seen that it has hapenned before to other people, and the answers talk about backends and other complicated stuff that I can't understand, me having only a rather basic knowledge of Python.
Here comes the code:
import numpy as np
import matplotlib.pyplot as plt
time_samples = np.arange(17000)
force_samples = np.arange(17000)
plt.plot(time_samples,force_samples)
plt.show()
time_samples2 = np.random.rand(1,1000)
force_samples2 = np.random.rand(1,1000)
plt.plot(time_samples2,force_samples2)
plt.show()
And this is what I get:
I have no clue why this is happenning.

I think the array dimension is the issue. x and y should be a 1D array.
import numpy as np
import matplotlib.pyplot as plt
time_samples = np.arange(17000)
force_samples = np.arange(17000)
plt.plot(time_samples,force_samples)
plt.show()
time_samples2 = np.random.rand(1000)
force_samples2 = np.random.rand(1000)
plt.plot(time_samples2,force_samples2)
plt.show()

Using a colormap for a pandas Series

I have pandas series of complex numbers, which I would like to plot. Currently, I am looping through each point and assigning it a color. I would prefer to generate the plot without the need to loop over each point... Using Series.plot() would be preferable. Converting series to numpy is ok though.
Here is an example of what I currently have:
import pandas as pd
import numpy as np
from matplotlib import pyplot
s = pd.Series((1+np.random.randn(500)*0.05)*np.exp(1j*np.linspace(-np.pi, np.pi, 500)))
cmap = pyplot.cm.viridis
for i, val in enumerate(s):
pyplot.plot(np.real(val), np.imag(val), 'o', ms=10, color=cmap(i/(len(s)-1)))
pyplot.show()

You can use pyplot.scatter, which allows coloring of points based on a value.
pyplot.scatter(np.real(s), np.imag(s), s=50, c=np.arange(len(s)), cmap='viridis')
Here, we set c to an increasing sequence to get the same result as in the question.

You can simply plot the real and imaginary part of the series without a loop.
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
s = pd.Series((1+np.random.randn(500)*0.05)*np.exp(1j*np.linspace(-np.pi, np.pi, 500)))
plt.plot(s.values.real,s.values.imag, marker="o", ls="")
plt.show()
However, you need to use a scatter plot if you want to have different colors:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
s = pd.Series((1+np.random.randn(500)*0.05)*np.exp(1j*np.linspace(-np.pi, np.pi, 500)))
plt.scatter(s.values.real,s.values.imag, c = range(len(s)), cmap=plt.cm.viridis)
plt.show()

Smoothing curve for matplotlib.pyplot using pandas or numpy/scipy

I have a series of data which consists of values from several experiments (1-40, in the MWE it is 1-5). The overall amount of entries in my original data is ~4.000.000, which I try to smooth in order to display it:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import spline
from statsmodels.nonparametric.smoothers_lowess import lowess
df = pd.DataFrame()
df["values"] = np.random.randint(100000, 200000, 1000)
df["id"] = [1,2,3,4,5] * 200
plt.figure(1, figsize=(11.69,8.27))
# Both fail for my amount of data:
plt.plot(spline(df["values"], df["id"], range(100)), "r-")
plt.plot(lowess(df["values"], df["id"]), "r-")
Both, scipy.interplate and statsmodels.nonparametric.smoothers_lowess.lowess, throw out of memory exceptions for my data. Is there any efficient way to solve this like in, e.g., GNU R using ggplot2 and geom_smooth()?

I can't quite tell what you're getting at with all the dimensions to your data, but one very simple thing you can try is to just use the 'markevery' kwarg like so:
import numpy as np
import matplotlib.pyplot as plt
x=np.linspace(1,100,1E7)
y=x**2
plt.figure(1, figsize=(11.69,8.27))
plt.plot(x,y,markevery=100)
plt.show()
This will only plot every nth point (n=100 here).
If that doesn't help then you may want to try just a simple numpy interpolation with fewer samples like so:
x_large=np.linspace(1,100,1E7)
y_large=x**2
x_small=np.linspace(1,100,1E3)
y_small=np.interp(x_small,x_large,y_large)
plt.plot(x_small,y_small)

pyplot: loglog() with base e

Python (and matplotlib) newbie here coming over from R, so I hope this question is not too idiotic. I'm trying to make a loglog plot on a natural log scale. But after some googling I cannot somehow figure out how to force pyplot to use a base e scale on the axes. The code I have currently:
import matplotlib.pyplot as pyplot
import math
e = math.exp(1)
pyplot.loglog(range(1,len(degrees)+1),degrees,'o',basex=e,basey=e)
Where degrees is a vector of counts at each value of range(1,len(degrees)+1). For some reason when I run this code, pyplot keeps giving me a plot with powers of 2 on the axes. I feel like this ought to be easy, but I'm stumped...
Any advice is greatly appreciated!

When plotting using plt.loglog you can pass the keyword arguments basex and basey as shown below.
From numpy you can get the e constant with numpy.e (or np.e if you import numpy as np)
import numpy as np
import matplotlib.pyplot as plt
# Generate some data.
x = np.linspace(0, 2, 1000)
y = x**np.e
plt.loglog(x,y, basex=np.e, basey=np.e)
plt.show()
Edit
Additionally if you want pretty looking ticks you can use matplotlib.ticker to choose the format of your ticks, an example of which is given below.
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.ticker as mtick
x = np.linspace(1, 4, 1000)
y = x**3
fig, ax = plt.subplots()
ax.loglog(x,y, basex=np.e, basey=np.e)
def ticks(y, pos):
return r'$e^{:.0f}$'.format(np.log(y))
ax.xaxis.set_major_formatter(mtick.FuncFormatter(ticks))
ax.yaxis.set_major_formatter(mtick.FuncFormatter(ticks))
plt.show()

It can also works for semilogx and semilogy to show them in e and also change their name.
import matplotlib.ticker as mtick
fig, ax = plt.subplots()
def ticks(y, pos):
return r'$e^{:.0f}$'.format(np.log(y))
plt.semilogy(Time_Series, California_Pervalence ,'gray', basey=np.e )
ax.yaxis.set_major_formatter(mtick.FuncFormatter(ticks))
plt.show()
Take a look at the image.