Easier way to plot multiple Relative Frequencies - python

Plotting multiple relative frequencies (sum of bin to be one, not area of bin to be one) was not easier than I thought.
In Method A, We can use weights argument and plotted properly, but it is not intuitive.
import numpy as np
import pandas as pd
df_a = pd.DataFrame(np.random.randn(1000),columns=['a'])
df_b = pd.DataFrame(1+ np.random.randn(100),columns=['b'])
# Method A
ax = df_a.plot(kind='hist', weights= np.ones_like(df_a) / len(df_a),alpha=0.5)
df_b.plot(kind='hist', weights= np.ones_like(df_b) / len(df_b),alpha=0.5 ,ax= ax )
plt.title("Method A")
plt.show()
In Method B, the part for determining relative frequencies count_a/sum(count_a) is easy to understand, but the diagram is not beautiful.
# Method B
count_a,bins_a = np.histogram(df_a.a)
count_b,bins_b = np.histogram(df_b.b)
plt.bar(bins_a[:-1],count_a/sum(count_a),alpha=0.5 )
plt.bar(bins_b[:-1],count_b/sum(count_b),alpha=0.5 )
plt.title("Method B")
Is there another way to get a graph directly from the data without doing the calculations myself?

The problem with your bar plot is that the width is fixed by default to 0.8. This can easily be adjusted to account for the real width of your histogram:
plt.bar(bins_a[:-1], count_a/sum(count_a), width = bins_a[1:] - bins_a[:-1], alpha = 0.5, align = 'edge')
and this is the result:
In this example the bin width is fixed but by providing a sequence you have a more flexible option, which can be used also in the case of variable bin sizes.
A different option is to use seaborn as suggested in the comment:
import seaborn as sns
df_hist = pd.concat([df_a, df_b]).melt()
sns.histplot(data = df_hist, x = 'value', hue = 'variable', stat = 'probability', common_norm = False)

Related

How to add (or annotate) value labels (or frequencies) on a matplotlib "histogram" chart

I want to add frequency labels to the histogram generated using plt.hist.
Here is the data :
np.random.seed(30)
d = np.random.randint(1, 101, size = 25)
print(sorted(d))
I looked up other questions on stackoverflow like :
Adding value labels on a matplotlib bar chart
and their answers, but apparantly, the objects returnded by plt.plot(kind='bar') are different than than those returned by plt.hist, and I got errors while using the 'get_height' or 'get width' functions, as suggested in some of the answers for bar plot.
Similarly, couldn't find the solution by going through the matplotlib documentation on histograms.
got this error
Here is how I managed it. If anyone has some suggestions to improve my answer, (specifically the for loop and using n=0, n=n+1, I think there must be a better way to write the for loop without having to use n in this manner), I'd welcome it.
# import base packages
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
# generate data
np.random.seed(30)
d = np.random.randint(1, 101, size = 25)
print(sorted(d))
# generate histogram
# a histogram returns 3 objects : n (i.e. frequncies), bins, patches
freq, bins, patches = plt.hist(d, edgecolor='white', label='d', bins=range(1,101,10))
# x coordinate for labels
bin_centers = np.diff(bins)*0.5 + bins[:-1]
n = 0
for fr, x, patch in zip(freq, bin_centers, patches):
height = int(freq[n])
plt.annotate("{}".format(height),
xy = (x, height), # top left corner of the histogram bar
xytext = (0,0.2), # offsetting label position above its bar
textcoords = "offset points", # Offset (in points) from the *xy* value
ha = 'center', va = 'bottom'
)
n = n+1
plt.legend()
plt.show;

Line-based heatmap or 2D line histogram

I have a synthetic dataset with 1000 noisy polygons of various orders and sin/cos curves that I can plot as lines using python seaborn.
Since I have quite a few lines that are overlapping, I'd like to plot some sort of heatmap or histogram of my line graphs.
I've tried iterating over the columns and aggregating the counts to use seaborn's heatmap graph, but with many lines this takes quite a while.
The next best thing that results in what I want was a hexbin graph (with seaborn jointgraph).
But it's a compromise between runtime and granularity (the shown graph has gridsize 750). I couldn't find any other graph-type for my problem. But I also don't know exactly what it might be called.
I've also tried with line alpha set to 0.2. This results in a similar graph to what I want. But it's less precise (if more than 5 lines overlap at the same point I already have zero transparency left). Also, it misses the typical coloration of heatmaps.
(Moot search terms were: heatmap, 2D line histogram, line histogram, density plots...)
Does anybody know packages to plot this more efficiently and high(er) quality or knows how to do it with the popular python plotters (i.e. the matplotlib family: matplotlib, seaborn, bokeh). I'm really fine with any package though.
It took me awhile, but I finally solved this using Datashader. If using a notebook, the plots can be embedded into interactive Bokeh plots, which looks really nice.
Anyhow, here is the code for static images, in case someone else is in need of something similar:
# coding: utf-8
import time
import numpy as np
from numpy.polynomial import polynomial
import pandas as pd
import matplotlib.pyplot as plt
import datashader as ds
import datashader.transfer_functions as tf
plt.style.use("seaborn-whitegrid")
def create_data():
# ...
# Each column is one data sample
df = create_data()
# Following will append a nan-row and reshape the dataframe into two columns, with each sample stacked on top of each other
# THIS IS CRUCIAL TO OPTIMIZE SPEED: https://github.com/bokeh/datashader/issues/286
# Append row with nan-values
df = df.append(pd.DataFrame([np.array([np.nan] * len(df.columns))], columns=df.columns, index=[np.nan]))
# Reshape
x, y = df.shape
arr = df.as_matrix().reshape((x * y, 1), order='F')
df_reshaped = pd.DataFrame(arr, columns=list('y'), index=np.tile(df.index.values, y))
df_reshaped = df_reshaped.reset_index()
df_reshaped.columns.values[0] = 'x'
# Plotting parameters
x_range = (min(df.index.values), max(df.index.values))
y_range = (df.min().min(), df.max().max())
w = 1000
h = 750
dpi = 150
cvs = ds.Canvas(x_range=x_range, y_range=y_range, plot_height=h, plot_width=w)
# Aggregate data
t0 = time.time()
aggs = cvs.line(df_reshaped, 'x', 'y', ds.count())
print("Time to aggregate line data: {}".format(time.time()-t0))
# One colored plot
t1 = time.time()
stacked_img = tf.Image(tf.shade(aggs, cmap=["darkblue", "darkblue"]))
print("Time to create stacked image: {}".format(time.time() - t1))
# Save
f0 = plt.figure(figsize=(w / dpi, h / dpi), dpi=dpi)
ax0 = f0.add_subplot(111)
ax0.imshow(stacked_img.to_pil())
ax0.grid(False)
f0.savefig("stacked.png", bbox_inches="tight", dpi=dpi)
# Heat map - This uses a equalized histogram (built-in default), there are other options, though.
t2 = time.time()
heatmap_img = tf.Image(tf.shade(aggs, cmap=plt.cm.Spectral_r))
print("Time to create stacked image: {}".format(time.time() - t2))
# Save
f1 = plt.figure(figsize=(w / dpi, h / dpi), dpi=dpi)
ax1 = f1.add_subplot(111)
ax1.imshow(heatmap_img.to_pil())
ax1.grid(False)
f1.savefig("heatmap.png", bbox_inches="tight", dpi=dpi)
With following run times (in seconds):
Time to aggregate line data: 0.7710442543029785
Time to create stacked image: 0.06000351905822754
Time to create stacked image: 0.05600309371948242
The resulting plots:
Although it seems you have tried this, plotting the counts seems to give a good representation of the data. However, it really depends what you're trying to find in your data, what is it supposed to tell you?
The reason for the long run time is due to plotting so many lines, a heatmap based on the counts however will plot fairly quickly.
I created some dummy data for sinus waves, based on noise, no. of lines, amplitude and shift. Added both a boxplot and heatmap.
import matplotlib.pyplot as plt
import numpy as np
import matplotlib as mpl
import random
import pandas as pd
np.random.seed(0)
#create dummy data
N = 200
sinuses = []
no_lines = 200
for i in range(no_lines):
a = np.random.randint(5, 40)/5 #amplitude
x = random.choice([int(N/5), int(N/(2/5))]) #random shift
sinuses.append(np.roll(a * np.sin(np.linspace(0, 2 * np.pi, N)) + np.random.randn(N), x))
fig = plt.figure(figsize=(20 / 2.54, 20 / 2.54))
sins = pd.DataFrame(sinuses, )
ax1 = plt.subplot2grid((3,10), (0,0), colspan=10)
ax2 = plt.subplot2grid((3,10), (1,0), colspan=10)
ax3 = plt.subplot2grid((3,10), (2,0), colspan=9)
ax4 = plt.subplot2grid((3,10), (2,9))
# plot line data
sins.T.plot(ax=ax1, color='lightblue',linewidth=.3)
ax1.legend_.remove()
ax1.set_xlim(0, N)
# try boxplot
sins.plot.box(ax=ax2, showfliers=False)
xticks = ax2.xaxis.get_major_ticks()
for index, label in enumerate(ax2.get_xaxis().get_ticklabels()):
xticks[index].set_visible(False) # hide ticks where labels are hidden
#make a list of bins
no_bins = 20
bins = list(np.arange(sins.min().min(), sins.max().max(), int(abs(sins.min().min())+sins.max().max())/no_bins))
bins.append(sins.max().max())
# calculate histogram
hists = []
for col in sins.columns:
count, division = np.histogram(sins.iloc[:,col], bins=bins)
hists.append(count)
hists = pd.DataFrame(hists, columns=[str(i) for i in bins[1:]])
print(hists.shape, '\n', hists.head())
cmap = mpl.colors.ListedColormap(['white', '#FFFFBB', '#C3FDB8', '#B5EAAA', '#64E986', '#54C571',
'#4AA02C', '#347C17', '#347235', '#25383C', '#254117'])
#heatmap
im = ax3.pcolor(hists.T, cmap=cmap)
cbar = plt.colorbar(im, cax=ax4)
yticks = np.arange(0, len(bins))
yticklabels = hists.columns.tolist()
ax3.set_yticks(yticks)
ax3.set_yticklabels([round(i,1) for i in bins])
ax3.set_title('Count')
yticks = ax3.yaxis.get_major_ticks()
for index, label in enumerate(ax3.get_yaxis().get_ticklabels()):
if index % 3 != 0: #make some labels invisible
yticks[index].set_visible(False) # hide ticks where labels are hidden
plt.show()
Although the boxplot is easy to interpret, it doesn't show the actual distribution of the data very well, but knowing where the median and quantiles lie may be helpful.
Increasing the number of lines and amount of values per line will increase plotting time considerably for the line plots, the heatmap is still fairly quick though to generate. The boxplot becomes indiscernible however.
I couldn't exactly replicate your data (or know the actual size of it), but perhaps the heatmap may be helpful.

MatPlotlib Seaborn Multiple Plots formatting

I am translating a set of R visualizations to Python. I have the following target R multiple plot histograms:
Using Matplotlib and Seaborn combination and with the help of a kind StackOverflow member (see the link: Python Seaborn Distplot Y value corresponding to a given X value), I was able to create the following Python plot:
I am satisfied with its appearance, except, I don't know how to put the Header information in the plots. Here is my Python code that creates the Python Charts
""" Program to draw the sampling histogram distributions """
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.backends.backend_pdf import PdfPages
import seaborn as sns
def main():
""" Main routine for the sampling histogram program """
sns.set_style('whitegrid')
markers_list = ["s", "o", "*", "^", "+"]
# create the data dataframe as df_orig
df_orig = pd.read_csv('lab_samples.csv')
df_orig = df_orig.loc[df_orig.hra != -9999]
hra_list_unique = df_orig.hra.unique().tolist()
# create and subset df_hra_colors to match the actual hra colors in df_orig
df_hra_colors = pd.read_csv('hra_lookup.csv')
df_hra_colors['hex'] = np.vectorize(rgb_to_hex)(df_hra_colors['red'], df_hra_colors['green'], df_hra_colors['blue'])
df_hra_colors.drop(labels=['red', 'green', 'blue'], axis=1, inplace=True)
df_hra_colors = df_hra_colors.loc[df_hra_colors['hra'].isin(hra_list_unique)]
# hard coding the current_component to pc1 here, we will extend it by looping
# through the list of components
current_component = 'pc1'
num_tests = 5
df_columns = df_orig.columns.tolist()
start_index = 5
for test in range(num_tests):
current_tests_list = df_columns[start_index:(start_index + num_tests)]
# now create the sns distplots for each HRA color and overlay the tests
i = 1
for _, row in df_hra_colors.iterrows():
plt.subplot(3, 3, i)
select_columns = ['hra', current_component] + current_tests_list
df_current_color = df_orig.loc[df_orig['hra'] == row['hra'], select_columns]
y_data = df_current_color.loc[df_current_color[current_component] != -9999, current_component]
axs = sns.distplot(y_data, color=row['hex'],
hist_kws={"ec":"k"},
kde_kws={"color": "k", "lw": 0.5})
data_x, data_y = axs.lines[0].get_data()
axs.text(0.0, 1.0, row['hra'], horizontalalignment="left", fontsize='x-small',
verticalalignment="top", transform=axs.transAxes)
for current_test_index, current_test in enumerate(current_tests_list):
# this_x defines the series of current_component(pc1,pc2,rhob) for this test
# indicated by 1, corresponding R program calls this test_vector
x_series = df_current_color.loc[df_current_color[current_test] == 1, current_component].tolist()
for this_x in x_series:
this_y = np.interp(this_x, data_x, data_y)
axs.plot([this_x], [this_y - current_test_index * 0.05],
markers_list[current_test_index], markersize = 3, color='black')
axs.xaxis.label.set_visible(False)
axs.xaxis.set_tick_params(labelsize=4)
axs.yaxis.set_tick_params(labelsize=4)
i = i + 1
start_index = start_index + num_tests
# plt.show()
pp = PdfPages('plots.pdf')
pp.savefig()
pp.close()
def rgb_to_hex(red, green, blue):
"""Return color as #rrggbb for the given color values."""
return '#%02x%02x%02x' % (red, green, blue)
if __name__ == "__main__":
main()
The Pandas code works fine and it is doing what it is supposed to. It is my lack of knowledge and experience of using 'PdfPages' in Matplotlib that is the bottleneck. How can I show the header information in Python/Matplotlib/Seaborn that I can show in the corresponding R visalization. By the Header information, I mean What The R visualization has at the top before the histograms, i.e., 'pc1', MRP, XRD,....
I can get their values easily from my program, e.g., current_component is 'pc1', etc. But I don't know how to format the plots with the Header. Can someone provide some guidance?
You may be looking for a figure title or super title, fig.suptitle:
fig.suptitle('this is the figure title', fontsize=12)
In your case you can easily get the figure with plt.gcf(), so try
plt.gcf().suptitle("pc1")
The rest of the information in the header would be called a legend.
For the following let's suppose all subplots have the same markers. It would then suffice to create a legend for one of the subplots.
To create legend labels, you can put the labelargument to the plot, i.e.
axs.plot( ... , label="MRP")
When later calling axs.legend() a legend will automatically be generated with the respective labels. Ways to position the legend are detailed e.g. in this answer.
Here, you may want to place the legend in terms of figure coordinates, i.e.
ax.legend(loc="lower center",bbox_to_anchor=(0.5,0.8),bbox_transform=plt.gcf().transFigure)

Timeseries plot with min/max shading using Seaborn

I am trying to create a 3-line time series plot based on the following data , in a Week x Overload graph, where each Cluster is a different line.
I have multiple observations for each (Cluster, Week) pair (5 for each atm, will have 1000). I would like the points on the line to be the average Overload value for that specific (Cluster, Week) pair, and the band be the min/max values of it.
Currently using the following bit of code to plot it, but I'm not getting any lines, as I don't know what unit to specify using the current dataframe:
ax14 = sns.tsplot(data = long_total_cluster_capacity_overload_df, value = "Overload", time = "Week", condition = "Cluster")
GIST Data
I have a feeling I still need to re-shape my dataframe, but I have no idea how. Looking for a final results that looks like this
Based off this incredible answer, I was able to create a monkey patch to beautifully do what you are looking for.
import pandas as pd
import seaborn as sns
import seaborn.timeseries
def _plot_range_band(*args, central_data=None, ci=None, data=None, **kwargs):
upper = data.max(axis=0)
lower = data.min(axis=0)
#import pdb; pdb.set_trace()
ci = np.asarray((lower, upper))
kwargs.update({"central_data": central_data, "ci": ci, "data": data})
seaborn.timeseries._plot_ci_band(*args, **kwargs)
seaborn.timeseries._plot_range_band = _plot_range_band
cluster_overload = pd.read_csv("TSplot.csv", delim_whitespace=True)
cluster_overload['Unit'] = cluster_overload.groupby(['Cluster','Week']).cumcount()
ax = sns.tsplot(time='Week',value="Overload", condition="Cluster", unit="Unit", data=cluster_overload,
err_style="range_band", n_boot=0)
Output Graph:
Notice that the shaded regions line up with the true maximum and minimums in the line graph!
If you figure out why the unit variable is required, please let me know.
If you do not want them all on the same graph then:
import pandas as pd
import seaborn as sns
import seaborn.timeseries
def _plot_range_band(*args, central_data=None, ci=None, data=None, **kwargs):
upper = data.max(axis=0)
lower = data.min(axis=0)
#import pdb; pdb.set_trace()
ci = np.asarray((lower, upper))
kwargs.update({"central_data": central_data, "ci": ci, "data": data})
seaborn.timeseries._plot_ci_band(*args, **kwargs)
seaborn.timeseries._plot_range_band = _plot_range_band
cluster_overload = pd.read_csv("TSplot.csv", delim_whitespace=True)
cluster_overload['subindex'] = cluster_overload.groupby(['Cluster','Week']).cumcount()
def customPlot(*args,**kwargs):
df = kwargs.pop('data')
pivoted = df.pivot(index='subindex', columns='Week', values='Overload')
ax = sns.tsplot(pivoted.values, err_style="range_band", n_boot=0, color=kwargs['color'])
g = sns.FacetGrid(cluster_overload, row="Cluster", sharey=False, hue='Cluster', aspect=3)
g = g.map_dataframe(customPlot, 'Week', 'Overload','subindex')
Which produces the following, (you can obviously play with the aspect ratio if you think the proportions are off)
I finally used the good old plot with a design (subplots) that seems (to me) more readable.
df = pd.read_csv('TSplot.csv', sep='\t', index_col=0)
# Compute the min, mean and max (could also be other values)
grouped = df.groupby(["Cluster", "Week"]).agg({'Overload': ['min', 'mean', 'max']}).unstack("Cluster")
# Plot with sublot since it is more readable
axes = grouped.loc[:,('Overload', 'mean')].plot(subplots=True)
# Getting the color palette used
palette = sns.color_palette()
# Initializing an index to get each cluster and each color
index = 0
for ax in axes:
ax.fill_between(grouped.index, grouped.loc[:,('Overload', 'mean', index + 1)],
grouped.loc[:,('Overload', 'max', index + 1 )], alpha=.2, color=palette[index])
ax.fill_between(grouped.index,
grouped.loc[:,('Overload', 'min', index + 1)] , grouped.loc[:,('Overload', 'mean', index + 1)], alpha=.2, color=palette[index])
index +=1
I really thought I would be able to do it with seaborn.tsplot. But it does not quite look right. Here is the result I get with seaborn:
cluster_overload = pd.read_csv("TSplot.csv", delim_whitespace=True)
cluster_overload['Unit'] = cluster_overload.groupby(['Cluster','Week']).cumcount()
ax = sns.tsplot(time='Week',value="Overload", condition="Cluster", ci=100, unit="Unit", data=cluster_overload)
Outputs:
I am really confused as to why the unit parameter is necessary since my understanding is that all the data is aggregated based on (time, condition) The Seaborn Documentation defines unit as
Field in the data DataFrame identifying the sampling unit (e.g.
subject, neuron, etc.). The error representation will collapse over
units at each time/condition observation. This has no role when data
is an array.
I am not certain of the meaning of 'collapsed over'- especially since my definition wouldn't make it a required variable.
Anyways, here's the output if you want exactly what you discussed, not nearly as pretty. I am not sure how to manually shade in those regions, but please share if you figure it out.
cluster_overload = pd.read_csv("TSplot.csv", delim_whitespace=True)
grouped = cluster_overload.groupby(['Cluster','Week'],as_index=False)
stats = grouped.agg(['min','mean','max']).unstack().T
stats.index = stats.index.droplevel(0)
colors = ['b','g','r']
ax = stats.loc['mean'].plot(color=colors, alpha=0.8, linewidth=3)
stats.loc['max'].plot(ax=ax,color=colors,legend=False, alpha=0.3)
stats.loc['min'].plot(ax=ax,color=colors,legend=False, alpha=0.3)
Outputs:

How to create bar chart with secondary_y from dataframe

I want to create a bar chart of two series (say 'A' and 'B') contained in a Pandas dataframe. If I wanted to just plot them using a different y-axis, I can use secondary_y:
df = pd.DataFrame(np.random.uniform(size=10).reshape(5,2),columns=['A','B'])
df['A'] = df['A'] * 100
df.plot(secondary_y=['A'])
but if I want to create bar graphs, the equivalent command is ignored (it doesn't put different scales on the y-axis), so the bars from 'A' are so big that the bars from 'B' are cannot be distinguished:
df.plot(kind='bar',secondary_y=['A'])
How can I do this in pandas directly? or how would you create such graph?
I'm using pandas 0.10.1 and matplotlib version 1.2.1.
Don't think pandas graphing supports this. Did some manual matplotlib code.. you can tweak it further
import pylab as pl
fig = pl.figure()
ax1 = pl.subplot(111,ylabel='A')
#ax2 = gcf().add_axes(ax1.get_position(), sharex=ax1, frameon=False, ylabel='axes2')
ax2 =ax1.twinx()
ax2.set_ylabel('B')
ax1.bar(df.index,df.A.values, width =0.4, color ='g', align = 'center')
ax2.bar(df.index,df.B.values, width = 0.4, color='r', align = 'edge')
ax1.legend(['A'], loc = 'upper left')
ax2.legend(['B'], loc = 'upper right')
fig.show()
I am sure there are ways to force the one bar further tweak it. move bars further apart, one slightly transparent etc.
Ok, I had the same problem recently and even if it's an old question, I think that I can give an answer for this problem, in case if someone else lost his mind with this. Joop gave the bases of the thing to do, and it's easy when you only have (for exemple) two columns in your dataframe, but it becomes really nasty when you have a different numbers of columns for the two axis, due to the fact that you need to play with the position argument of the pandas plot() function. In my exemple I use seaborn but it's optionnal :
import pandas as pd
import seaborn as sns
import pylab as plt
import numpy as np
df1 = pd.DataFrame(np.array([[i*99 for i in range(11)]]).transpose(), columns = ["100"], index = [i for i in range(11)])
df2 = pd.DataFrame(np.array([[i for i in range(11)], [i*2 for i in range(11)]]).transpose(), columns = ["1", "2"], index = [i for i in range(11)])
fig, ax = plt.subplots()
ax2 = ax.twinx()
# we must define the length of each column.
df1_len = len(df1.columns.values)
df2_len = len(df2.columns.values)
column_width = 0.8 / (df1_len + df2_len)
# we calculate the position of each column in the plot. This value is based on the position definition :
# Specify relative alignments for bar plot layout. From 0 (left/bottom-end) to 1 (right/top-end). Default is 0.5 (center)
# http://pandas.pydata.org/pandas-docs/dev/generated/pandas.DataFrame.plot.html
df1_posi = 0.5 + (df2_len/float(df1_len)) * 0.5
df2_posi = 0.5 - (df1_len/float(df2_len)) * 0.5
# In order to have nice color, I use the default color palette of seaborn
df1.plot(kind='bar', ax=ax, width=column_width*df1_len, color=sns.color_palette()[:df1_len], position=df1_posi)
df2.plot(kind='bar', ax=ax2, width=column_width*df2_len, color=sns.color_palette()[df1_len:df1_len+df2_len], position=df2_posi)
ax.legend(loc="upper left")
# Pandas add line at x = 0 for each dataframe.
ax.lines[0].set_visible(False)
ax2.lines[0].set_visible(False)
# Specific to seaborn, we have to remove the background line
ax2.grid(b=False, axis='both')
# We need to add some space, the xlim don't manage the new positions
column_length = (ax2.get_xlim()[1] - abs(ax2.get_xlim()[0])) / float(len(df1.index))
ax2.set_xlim([ax2.get_xlim()[0] - column_length, ax2.get_xlim()[1] + column_length])
fig.patch.set_facecolor('white')
plt.show()
And the result : http://i.stack.imgur.com/LZjK8.png
I didn't test every possibilities but it looks like it works fine whatever the number of columns in each dataframe you use.

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