python : using a subplot as legend for the others subplots

Question

I have the script below that generates a plot consisted of 5 histograms (5 subplots) :

import matplotlib.pyplot as plt
import numpy as np

from scipy.stats import norm
from scipy.optimize import curve_fit

mean_o = list()
sigma_o = list()
y3 = list()

### generate some data
for i in range( 5 ):
    y3.append( norm.rvs( size=150000 ) )
y3 = np.transpose( y3 )

for i in range(5):
    mean_o.append( np.mean( y3[ :, i ] ) )
    sigma_o.append(  np.std( y3[ :, i ] ) )

## Histograms
# Number of bins
Nbins=100
binwidth = np.zeros(5)

# Fitting curves
def gaussian( x, a , mean, sigma ):
  return a * np.exp( -( ( x - mean )**2 / (2 * sigma**2 ) ) )

fig = plt.figure()
ax = { i : fig.add_subplot( 2, 3, i+1) for i in range( 5 ) }


for i in range(5):
    ymin = min(y3[:,i])
    ymax = max(y3[:,i])
    binwidth[i] = ( ymax - ymin) / Nbins
    bins_plot = np.arange( ymin, ymax + binwidth[i], binwidth[i])
    histdata = ax[i].hist(
        y3[:,i],
        bins=bins_plot,
        label='bin '+str(i)
    )

    range_fit = np.linspace( ymin, ymax, 250)
    # Fitting and plot version 1
    popt, pcov = curve_fit(
        gaussian,
        0.5 * ( histdata[1][:-1] + histdata[1][1:] ),
        histdata[0],
        p0=( max(histdata[0]), mean_o[i], sigma_o[i] ) )
    ax[i].plot(range_fit, gaussian( range_fit, *popt ) )
    ax[i].axvline( x=mean_o[i], ls=':', c='r' )

    # Fitting and plot version 2
    params = norm.fit( y3[ ::, i ], loc=mean_o[i], scale=sigma_o[i] )
    nth = gaussian(
        range_fit,
        len( y3[::, i]) * binwidth[i] / np.sqrt( 2 * np.pi ),
        *params
    )
    ax[i].plot(range_fit, nth, ls="--" )
plt.tight_layout()
plt.show()

that generates the following figure :

Now, I would like to use in the 6th subplot on the right bottom as a legend for the 5 other subplots where the best fit values appear with a corresponding box and value to each subplot (like a color code) :

I don't know at all how to use a subplot as a legend, Does anyone get an idea ?

Answer 1

You can create an extra subplot and put a custom legend in it. The custom legend could use dummy handles and a list of labels. To customize how the legend looks , many parameters can be used. ax.axes('off') will switch off the unneeded surrounding axes of the last subplot.

Here is some example code. To simplify the calculations, y3 is represented by a 2D numpy array.

import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import norm
from scipy.optimize import curve_fit

### generate some data
y3 = norm.rvs(size=(5, 5000))
mean_o = np.mean(y3, axis=1)
sigma_o = np.std(y3, axis=1)

## Histograms
# Number of bins
Nbins = 100

# Fitting curves
def gaussian(x, a, mean, sigma):
     return a * np.exp(-((x - mean) ** 2 / (2 * sigma ** 2)))


fig = plt.figure(figsize=(15, 7))
ax = {i: fig.add_subplot(2, 3, i + 1) for i in range(5)}

ymin = y3.min(axis=1)
ymax = y3.max(axis=1)
legend_labels = []

for i in range(5):
     bins_plot = np.linspace(ymin[i], ymax[i], Nbins + 1)
     values, bins, patches = ax[i].hist(
          y3[i],
          bins=bins_plot,
          label='bin ' + str(i))

     range_fit = np.linspace(ymin[i], ymax[i], 250)
     # Fitting and plot version 1
     popt, pcov = curve_fit(
          gaussian,
          0.5 * (bins[:-1] + bins[1:]),
          values,
          p0=(values.max(), mean_o[i], sigma_o[i]))
     ax[i].plot(range_fit, gaussian(range_fit, *popt))
     ax[i].axvline(x=mean_o[i], ls=':', c='r')

     # Fitting and plot version 2
     params = norm.fit(y3[::, i], loc=mean_o[i], scale=sigma_o[i])
     nth = gaussian(
          range_fit,
          len(y3[::, i]) * binwidth[i] / np.sqrt(2 * np.pi),
          *params
     )
     ax[i].plot(range_fit, nth, ls="--")
     legend_labels.append(f'bin {i + 1}: {mean_o[i]:.5f}')
ax5 = fig.add_subplot(2, 3, 6)
dummy_handle = plt.Rectangle((0, 0), 0, 0, color='none')
ax5.legend(handles=[dummy_handle] * len(legend_labels), labels=legend_labels,
           handlelength=0, handletextpad=0, fontsize=24,
           loc='center', shadow=True, facecolor='lightgrey')
ax5.axis('off')

plt.tight_layout()
plt.show()