Padding

This example shows how to use the pylops.Pad operator to zero-pad a model

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.gridspec as pltgs

import pylops

plt.close('all')

Let’s define a pad operator Pop for one dimensional data

dims = 10
pad = (2, 3)

Pop = pylops.Pad(dims, pad)

x = np.arange(dims)+1.
y = Pop*x
xadj = Pop.H*y

print('x = %s ' % x)
print('P*x = %s ' % y)
print('P\'*y = %s ' % xadj)

Out:

x = [ 1.  2.  3.  4.  5.  6.  7.  8.  9. 10.]
P*x = [ 0.  0.  1.  2.  3.  4.  5.  6.  7.  8.  9. 10.  0.  0.  0.]
P'*y = [ 1.  2.  3.  4.  5.  6.  7.  8.  9. 10.]

We move now to a multi-dimensional case. We pad the input model with different extents along both dimensions

dims = (5, 4)
pad = ((1, 0), (3, 4))

Pop = pylops.Pad(dims, pad)

x = (np.arange(np.prod(np.array(dims)))+1.).reshape(dims)
y = Pop*x.ravel()
xadj = Pop.H*y

y = y.reshape(Pop.dimsd)
xadj = xadj.reshape(dims)

fig, axs = plt.subplots(1, 3, figsize=(10, 2))
fig.suptitle('Pad for 2d data', fontsize=14, fontweight='bold', y=1.15)
axs[0].imshow(x, cmap='rainbow', vmin=0, vmax=np.prod(np.array(dims))+1)
axs[0].set_title(r'$x$')
axs[0].axis('tight')
axs[1].imshow(y, cmap='rainbow', vmin=0, vmax=np.prod(np.array(dims))+1)
axs[1].set_title(r'$y = P x$')
axs[1].axis('tight')
axs[2].imshow(xadj, cmap='rainbow', vmin=0, vmax=np.prod(np.array(dims))+1)
axs[2].set_title(r'$x_{adj} = P^{H} y$')
axs[2].axis('tight')

Out:

(-0.5, 3.5, 4.5, -0.5)