[FIXED] Is there a way to add hatch marks on a seaborn displot using a kernal density estimation plot?

Issue

I am trying my best to combine the following four figures to three plots and show how (a) & (b) differ from (c) & (d) using colors and hatch marks. All four green plots are the same parameter, just grouped accordingly. Same with orange and blue.

Here is how I created each individual plot using the melt function:

df_CohDmg
Out[13]: 
        Region          Age60 CohDmg          value
0    Posterior  Age $\leq$ 60     tn    1844.377999
1    Posterior  Age $\leq$ 60     tn     654.815766
2      Equator  Age $\leq$ 60     tn  287073.028315
3      Equator  Age $\leq$ 60     tn  301519.815540
4    Posterior  Age $\leq$ 60     tn     838.798937
..         ...            ...    ...            ...
112  Posterior  Age $\leq$ 60     tt   11185.849816
113    Equator     Age $>$ 60     tt   15345.033316
114  Posterior     Age $>$ 60     tt      62.232998
115    Equator     Age $>$ 60     tt     490.447922
116    Equator     Age $>$ 60     tt   11468.986366

[117 rows x 4 columns]

df_CohDmg = pd.melt(md, id_vars=[R, A60], 
                    value_vars=['tn', 'ts', 'tt'], 
                    var_name='CohDmg')

def CohDmgDistPlot(dataSubset=None, figName=None, hue=None, hue_order=None, 
                   labels=None):
    f, ax = plt.subplots()
    
    sns.set_context("paper", rc={"font.size":12, "axes.titlesize":8, 
                                 "axes.labelsize":12})
    
    ax = sns.displot(data=dataSubset, hue=hue, hue_order=hue_order, 
                     x='value', kind="kde", fill=True, legend=False, height=5, 
                     aspect=1.6, bw_adjust=1, log_scale=True)
    ax.set(xlabel='Cohesive Damage Initiation Parameters [Pa]', 
           ylabel='Kernel Density Estimation')
    
    if labels != None:
        # Legend
        plt.legend(labels=labels, loc='best').set_title("Parameter")
    
    # Set limits so all plots are the same scale
    ax.set(ylim=(0, 0.3))
    ax.set(xlim=(8*10**-1, 4*10**7))
    
    ax.savefig(os.path.join(SF, 'Cohesive_Damage_Initiation_Distribution' + 
                            '{}.pdf'.format(figName)), 
               bbox_inches='tight')
    
    plt.close(f)

From this function that I defined here is how I am calling each subset of the data:

# Simplify plots
labels = [r'$t_{n}$', r'$t_{s}$', r'$t_{t}$']
hue = 'CohDmg'
hue_order = [Eq, Po]

CohDmgDistPlot(df_CohDmg, figName='', labels=labels, hue=hue)

CohDmgDistPlot(df_CohDmg[(df_CohDmg[R] == Po)], figName='_Posterior', 
               hue=hue, labels=labels)

CohDmgDistPlot(df_CohDmg[(df_CohDmg[R] == Eq)], figName='_Equator', 
               hue=hue, labels=labels)

CohDmgDistPlot(df_CohDmg[(df_CohDmg[A60] == Aleq60)], figName='_AgeLeq60', 
               hue=hue, labels=labels)

CohDmgDistPlot(df_CohDmg[(df_CohDmg[A60] == Ag60)], figName='_Ageg60', 
               hue=hue, labels=labels)

CohDmgDistPlot(df_CohDmg[(df_CohDmg[R]   == Po) & (df_CohDmg[A60] == Aleq60)], 
            figName='_Posterior_Leq60', hue=hue, labels=labels)

CohDmgDistPlot(df_CohDmg[(df_CohDmg[R]   == Po) & (df_CohDmg[A60] == Ag60)], 
            figName='_Posterior_g60', hue=hue, labels=labels)

CohDmgDistPlot(df_CohDmg[(df_CohDmg[R]   == Eq) & (df_CohDmg[A60] == Aleq60)], 
            figName='_Equator_Leq60', hue=hue, labels=labels)

CohDmgDistPlot(df_CohDmg[(df_CohDmg[R]   == Eq) & (df_CohDmg[A60] == Ag60)], 
            figName='_Equator_g60', hue=hue, labels=labels)

Ideally, I would use the paired colors to represent (a) & (b) and hatch marks for (b) & (d).

Thank you so much as I have been able to figure this out.

Solution

Here is an example with 3 subplots. Each subplot first gets a kdeplot for one region, and then a kdeplot for the other with different colors. Each individual kdeplot uses hue to differentiate between the ages. Also, these age groups are stacked instead of being drawn on top of each other. Further, one age group gets a hatching.

Some manipulations are needed to get a proper legend. set_hach is called both on the legend handles as on the polygon forming the kdeplot. The stacking first creates the last age group, so the hatching needs to reverse the list.

Many variations are possible, also depending on what you want to show and how much the graphs overlap. For example, a new column could be created combining two columns for the hue, and they all could be stacked instead of drawn on top of each other.

Also note that kdeplot has a parameter common_norm that default to True and reduces the graph for each hue-group depending on the group's size.

from matplotlib import pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns

regions = ['Posterior', 'Equator']
ages = ['Age $\leq$ 60 ', 'Age $>$ 60 ']
coh_dmgs = ['tn', 'ts', 'tt']

df_CohDmg = pd.DataFrame({'Region': np.random.choice(regions, 200),
                          'Age60': np.random.choice(ages, 200),
                          'CohDmg': np.random.choice(coh_dmgs, 200),
                          'value': np.random.randn(20, 10).cumsum(axis=0).ravel() * 20 + 100})
df_CohDmg.loc[df_CohDmg['Region'] == regions[1], 'value'] += 100
df_CohDmg.loc[df_CohDmg['Age60'] == ages[1], 'value'] += 50
'''
df_CohDmg['Region'] = pd.Categorical(df_CohDmg['Region'], categories=regions)
df_CohDmg['Age60'] = pd.Categorical(df_CohDmg['Age60'], categories=ages)
df_CohDmg['CohDmg'] = pd.Categorical(df_CohDmg['CohDmg'], categories=coh_dmgs)
'''
fig, axs = plt.subplots(ncols=3, figsize=(15, 3), sharex=True, sharey=True)
colors = [plt.cm.tab20.colors[i:i + 2] for i in range(0, len(regions) * 2, 2)]
hatches = ['', '//']
for ax, coh_dmg in zip(axs, coh_dmgs):
    handles = []
    for region, palette in zip(regions, colors):
        sns.kdeplot(data=df_CohDmg[(df_CohDmg['CohDmg'] == coh_dmg) & (df_CohDmg['Region'] == region)],
                    x='value', hue='Age60', hue_order=ages, multiple='stack', palette=palette, ax=ax)
        for h, age, hatch in zip(ax.legend_.legendHandles, ages, hatches):
            h.set_label(f'{region}, {age}')
            h.set_hatch(hatch)
            handles.append(h)
    ax.legend_.remove() # remove the automatic legends
    ax.set_title(f'CohDmg={coh_dmg}')
    for collection, hatch in zip(ax.collections[::-1], hatches * len(regions)):
        collection.set_hatch(hatch)

axs[-1].legend(handles=handles, loc='upper left', bbox_to_anchor=[1.01, 1.01])
plt.tight_layout()
plt.show()

Answered By - JohanC