# Example: Basex Gaussian¶

```# -*- coding: utf-8 -*-
import numpy as np
import matplotlib.pyplot as plt
import abel

# This example performs a BASEX transform of a simple 1D Gaussian function and
# compares this to the analytical inverse Abel transform

fig, ax = plt.subplots(1, 1)
plt.title('Abel tranforms of a gaussian function')

# Analytical inverse Abel:
n = 101
r_max = 20
sigma = 10

ref = abel.tools.analytical.GaussianAnalytical(n, r_max, sigma, symmetric=False)

ax.plot(ref.r, ref.func, 'b', label='Original signal')
ax.plot(ref.r, ref.abel, 'r', label='Direct Abel transform ×0.05 [analytical]')

center = n // 2

# BASEX Transform:
# Calculate the inverse abel transform for the centered data
recon = abel.basex.basex_transform(ref.abel, verbose=True, basis_dir=None,
dr=ref.dr, direction='inverse')

ax.plot(ref.r, recon, 'o', color='red', label='Inverse transform [BASEX]',
ms=5, mec='none', alpha=0.5)

ax.legend()

ax.set_xlim(0, 20)
ax.set_xlabel('\$x\$')
ax.set_ylabel('\$f(x)\$')

plt.legend()
plt.show()
```