How to draw the Probability Density Function (PDF) plot in Python? - python

I'd like to ask how to draw the Probability Density Function (PDF) plot in Python.
This is my codes.
import numpy as np
import pandas as pd
from pandas import DataFrame
import matplotlib.pyplot as plt
import scipy.stats as stats
.
x = np.random.normal(50, 3, 1000)
source = {"Genotype": ["CV1"]*1000, "AGW": x}
df=pd.DataFrame(source)
df
I generated a data frame. Then, I tried to draw a PDF graph.
df["AGW"].sort_values()
df_mean = np.mean(df["AGW"])
df_std = np.std(df["AGW"])
pdf = stats.norm.pdf(df["AGW"], df_mean, df_std)
plt.plot(df["AGW"], pdf)
I obtained above graph. What I did wrong? Could you let me how to draw the Probability Density Function (PDF) Plot which is also known as normal distribution graph.
Could you let me know which codes (or library) I need to use to draw the PDF graph?
Always many thanks!!

You just need to sort the values (not really check what's after edit)
pdf = stats.norm.pdf(df["AGW"].sort_values(), df_mean, df_std)
plt.plot(df["AGW"].sort_values(), pdf)
And it will work.
The line df["AGW"].sort_values() doesn't change df. Maybe you meant df.sort_values(by=['AGW'], inplace=True).
In that case the full code will be :
import numpy as np
import pandas as pd
from pandas import DataFrame
import matplotlib.pyplot as plt
import scipy.stats as stats
x = np.random.normal(50, 3, 1000)
source = {"Genotype": ["CV1"]*1000, "AGW": x}
df=pd.DataFrame(source)
df.sort_values(by=['AGW'], inplace=True)
df_mean = np.mean(df["AGW"])
df_std = np.std(df["AGW"])
pdf = stats.norm.pdf(df["AGW"], df_mean, df_std)
plt.plot(df["AGW"], pdf)
Which gives :
Edit :
I think here we already have the distribution (x is normally distributed) so we dont need to generate the pdf of x. As the use of the pdf is for something like this :
mu = 50
variance = 3
sigma = math.sqrt(variance)
x = np.linspace(mu - 5*sigma, mu + 5*sigma, 1000)
plt.plot(x, stats.norm.pdf(x, mu, sigma))
plt.show()
Here we dont need to generate the distribution from x points, we only need to plot the density of the distribution we already have .
So you might use this :
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
x = np.random.normal(50, 3, 1000) #Generating Data
source = {"Genotype": ["CV1"]*1000, "AGW": x}
df=pd.DataFrame(source) #Converting to pandas DataFrame
df.plot(kind = 'density'); # or df["AGW"].plot(kind = 'density');
Which gives :
You might use other packages if you want, like seaborn :
import seaborn as sns
plt.figure(figsize = (5,5))
sns.kdeplot(df["AGW"] , bw = 0.5 , fill = True)
plt.show()
Or this :
import seaborn as sns
sns.set_style("whitegrid") # Setting style(Optional)
plt.figure(figsize = (10,5)) #Specify the size of figure
sns.distplot(x = df["AGW"] , bins = 10 , kde = True , color = 'teal'
, kde_kws=dict(linewidth = 4 , color = 'black')) #kde for normal distribution
plt.show()
Check this article for more.

Related

How to plot Multiline Graphs Via Seaborn library in Python?

I have written a code that looks like this:
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
T = np.array([10.03,100.348,1023.385])
power1 = np.array([100000,86000,73000])
power2 = np.array([1008000,95000,1009000])
df1 = pd.DataFrame(data = {'Size': T, 'Encrypt_Time': power1, 'Decrypt_Time': power2})
exp1= sns.lineplot(data=df1)
plt.savefig('exp1.png')
exp1_smooth= sns.lmplot(x='Size', y='Time', data=df, ci=None, order=4, truncate=False)
plt.savefig('exp1_smooth.png')
That gives me Graph_1:
The Size = x- axis is a constant line but as you can see in my code it varies from (10,100,1000).
How does this produces a constant line? I want to produce a multiline graph with x-axis = Size(T),y- axis= Encrypt_Time and Decrypt_Time (power1 & power2).
Also I wanted to plot a smooth graph of the same graph I am getting right now but it gives me error. What needs to be done to achieve a smooth multi-line graph with x-axis = Size(T),y- axis= Encrypt_Time and Decrypt_Time (power1 & power2)?
I think it not the issue, the line represents for size looks like constant but it NOT.
Can see that values of size in range 10-1000 while the minimum division of y-axis is 20,000 (20 times bigger), make it look like a horizontal line on your graph.
You can try with a bigger values to see the slope clearly.
If you want 'size` as x-axis, you can try below example:
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
T = np.array([10.03,100.348,1023.385])
power1 = np.array([100000,86000,73000])
power2 = np.array([1008000,95000,1009000])
df1 = pd.DataFrame(data = {'Size': T, 'Encrypt_Time': power1, 'Decrypt_Time': power2})
fig = plt.figure()
fig = sns.lineplot(data=df1, x='Size',y='Encrypt_Time' )
fig = sns.lineplot(data=df1, x='Size',y='Decrypt_Time' )

Plotting probability density function in Python

I want to plot two probability density functions (pdf) based on values of a certain column in a dataframe. The first one for all the values that correspond to rows with target label = 0 and second one where target label = 1.
My attempt is below, but as you can see the curves do not look like a pdf (the max value is 0 and they are not confined to X axis in range 0-1 and 5-6. I assume I can get something close by playing around with bw factor, but I am looking for a one-liner that just figures out right params and plots a pdf(including figuiring out the right X-axis start/end to use). Is there any such built in function that does this. If not, would appreciate some pointers on how to build something like this.
#matplotloib inline
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from sklearn.neighbors import KernelDensity
values = np.random.rand(10)
values_shift5 = np.random.rand(10) + 5
df = pd.DataFrame({'values' : values, 'label' : np.zeros(10)})
df = pd.concat([df, pd.DataFrame({'values' : values_shift5, 'label' : np.ones(10)})])
kde_label_0 = KernelDensity(kernel='gaussian', bandwidth=0.5).fit(df[df.label == 0]['values'].values.reshape(-1, 1))
kde_label_1 = KernelDensity(kernel='gaussian', bandwidth=0.5).fit(df[df.label == 1]['values'].values.reshape(-1, 1))
X_plot = np.linspace(0, 10, 50).reshape(-1, 1)
log_density_0 = kde_label_0.score_samples(X_plot)
log_density_1 = kde_label_1.score_samples(X_plot)
plt.plot(X_plot, log_density_0, label='Label 0')
plt.plot(X_plot, log_density_1, label='Label 1')
plt.legend()
plt.show()

Python Plotly CDF with Frequency DIstribution Data

How do you make a CDF plot with frequency distribution data in a Pandas DataFrame using Plotly? Suppose the following toy data
value freq
1 3
2 2
3 1
All of the examples show how to do it with raw data that looks like:
value
1
1
1
2
2
3
I am able to do it with Pandas .plot like so (but I would prefer to do the same with Plotly):
stats_df = df
stats_df['pdf'] = stats_df['count'] / sum(stats_df['count'])
# calculate CDF
stats_df['cdf'] = stats_df['pdf'].cumsum()
stats_df = stats_df.reset_index()
# plot
stats_df.plot(x = 'n_calls',
y = ['pdf', 'cdf'],
logx = True,
kind = 'line',
grid = True)
If you would like to demonstrate with a toy dataset, here's one: https://raw.githubusercontent.com/plotly/datasets/master/2010_alcohol_consumption_by_country.csv
References:
https://plotly.com/python/v3/discrete-frequency/
https://plotly.com/python/distplot/
It is not possible to build a CDF in the Plotly.
On Plotly, only PDF and a histogram can be plotted (see below for alcohol sample).
The code for the graph above looks like this:
import plotly.figure_factory as ff
import pandas as pd
data = pd.read_csv(
'https://raw.githubusercontent.com/plotly/datasets/master/2010_alcohol_consumption_by_country.csv')
x = data['alcohol'].values.tolist()
group_labels = ['']
fig = ff.create_distplot([x], group_labels,
bin_size=.25, show_rug=False)
fig.show()
If you need exactly the CDF, then use third-party libraries for data preparation.
In the example below, I am using Numpy.
The code for the graph above looks like this:
import plotly.graph_objs as go
import numpy as np
import pandas as pd
data = pd.read_csv(
'https://raw.githubusercontent.com/plotly/datasets/master/2010_alcohol_consumption_by_country.csv')
x = data['alcohol'].values.tolist()
hist, bin_edges = np.histogram(x, bins=100, density=True)
cdf = np.cumsum(hist * np.diff(bin_edges))
fig = go.Figure(data=[
go.Bar(x=bin_edges, y=hist, name='Histogram'),
go.Scatter(x=bin_edges, y=cdf, name='CDF')
])
fig.show()
Note that the CDF is a broken line. This is due to the fact that this is not an approximate function for the unknown distribution.
To get a smooth function, you need to know the distribution law.

Plotting large datasets with pandas

I convert an oscilloscope dataset with millions of values into a pandas DataFrame. Next step is to plot it. But Matplotlib needs on my fairly powerful machine ~50 seconds to plot the DataFrame.
import pandas as pd
import matplotlib.pyplot as plt
import readTrc
datX, datY, m = readTrc.readTrc('C220180104_ch2_UHF00000.trc')
srx, sry = pd.Series(datX), pd.Series(datY)
df = pd.concat([srx, sry], axis = 1)
df.set_index(0, inplace = True)
df.plot(grid = 1)
plt.show()
Now I found out that there is a way to make matplotlib faster with large datasets by using 'Agg'.
import matplotlib
matplotlib.use('Agg')
import pandas as pd
import matplotlib.pyplot as plt
import readTrc
datX, datY, m = readTrc.readTrc('C220180104_ch2_UHF00000.trc')
srx, sry = pd.Series(datX), pd.Series(datY)
df = pd.concat([srx, sry], axis = 1)
df.set_index(0, inplace = True)
df.plot(grid = 1)
plt.show()
Unfortunately no plot is shown. The process of processing the plot takes ~5 seconds (a big improvement) but no plot is shown. Is this method not compatible with pandas?
You can use Ploty and Lenspy (was built to solve this exact problem). Here is an example of how you can plot 10m points on scatter plot. This plot runs super fast on my 2016 MacBook.
import numpy as np
import plotly.graph_objects as go
from lenspy import DynamicPlot
# First, let's create a very large figure
x = np.arange(1, 11, 1e-6)
y = 1e-2*np.sin(1e3*x) + np.sin(x) + 1e-3*np.sin(1e10*x)
fig = go.Figure(data=[go.Scattergl(x=x, y=y)])
fig.update_layout(title=f"{len(x):,} Data Points.")
# Use DynamicPlot.show to view the plot
plot = DynamicPlot(fig)
plot.show()
# Plot will be available in the browser at http://127.0.0.1:8050/
For your use case (again, I cannot test this since I don’t have access to your dataset):
import pandas as pd
import matplotlib.pyplot as plt
import readTrc
from lenspy import DynamicPlot
import plotly.graph_objects as go
datX, datY, m = readTrc.readTrc('C220180104_ch2_UHF00000.trc')
srx, sry = pd.Series(datX), pd.Series(datY)
fig = go.Figure(data=[go.Scattergl(x=srx, y=sry)])
fig.update_layout(title=f"{len(x):,} Data Points.")
# Use DynamicPlot.show to view the plot
plot = DynamicPlot(fig)
plot.show()
Disclaimer: I am the creator of Lenspy

Dendrogram using pandas and scipy

I wish to generate a dendrogram based on correlation using pandas and scipy. I use a dataset (as a DataFrame) consisting of returns, which is of size n x m, where n is the number of dates and m the number of companies. Then I simply run the script
import pandas as pd
import matplotlib.pyplot as plt
from scipy.cluster import hierarchy as hc
import numpy as np
m = 5
dates = pd.date_range('2013-01-01', periods=365)
random_matrix = np.random.normal(0, 0.01, size=(len(dates), m))
dataframe = pd.DataFrame(data=random_matrix, index=dates)
z = hc.linkage(dataframe.values.T, method='average', metric='correlation')
dendrogram = hc.dendrogram(z, labels=dataframe.columns)
plt.show()
and I get a nice dendrogram. Now, the thing is that I'd also like to use other correlation measures apart from just ordinary Pearson correlation, which is a feature that's incorporated in pandas by simply invoking DataFrame.corr(method='<method>'). So, I thought at first that it was to simply run the following code
import pandas as pd
import matplotlib.pyplot as plt
from scipy.cluster import hierarchy as hc
import numpy as np
m = 5
dates = pd.date_range('2013-01-01', periods=365)
random_returns = np.random.normal(0, 0.01, size=(len(dates), m))
dataframe = pd.DataFrame(data=random_returns, index=dates)
corr = dataframe.corr()
z = hc.linkage(corr.values, method='average')
dendrogram = hc.dendrogram(z, labels=corr.columns)
plt.show()
However, if I do this I get strange values on the y-axis as the maximum value > 1.4. Whereas if I run the first script it's about 1. What am I doing wrong? Am I using the wrong metric in hc.linkage?
EDIT I might add that the shape of the dendrogram is exactly the same. Do I have to normalize the third column of the resulting z with the maximum value?
Found the solution. If you have already calculated a distance matrix (be it correlation or whatever), you simply have to condense the matrix using distance.squareform. That is,
dataframe = pd.DataFrame(data=random_returns, index=dates)
corr = 1 - dataframe.corr()
corr_condensed = hc.distance.squareform(corr) # convert to condensed
z = hc.linkage(corr_condensed, method='average')
dendrogram = hc.dendrogram(z, labels=corr.columns)
plt.show()

Categories