Flip along an axis

This example shows how to use the pylops.Flip operator to simply flip an input signal along an axis.

import matplotlib.pyplot as plt
import numpy as np

import pylops

plt.close("all")

Let’s start with a 1D example. Define an input signal composed of nt samples

nt = 10
x = np.arange(nt)

We can now create our flip operator and apply it to the input signal. We can also apply the adjoint to the flipped signal and we can see how for this operator the adjoint is effectively equivalent to the inverse.

Fop = pylops.Flip(nt)
y = Fop * x
xadj = Fop.H * y

plt.figure(figsize=(3, 5))
plt.plot(x, "k", lw=3, label=r"$x$")
plt.plot(y, "r", lw=3, label=r"$y=Fx$")
plt.plot(xadj, "--g", lw=3, label=r"$x_{adj} = F^H y$")
plt.title("Flip in 1st direction", fontsize=14, fontweight="bold")
plt.legend()

Out:

<matplotlib.legend.Legend object at 0x7f90d0c6d780>

Let’s now repeat the same exercise on a two dimensional signal. We will first flip the model along the first axis and then along the second axis

nt, nx = 10, 5
x = np.outer(np.arange(nt), np.ones(nx))
Fop = pylops.Flip(nt * nx, dims=(nt, nx), dir=0)
y = Fop * x.ravel()
xadj = Fop.H * y.ravel()
y = y.reshape(nt, nx)
xadj = xadj.reshape(nt, nx)

fig, axs = plt.subplots(1, 3, figsize=(7, 3))
fig.suptitle(
    "Flip in 1st direction for 2d data", fontsize=14, fontweight="bold", y=0.95
)
axs[0].imshow(x, cmap="rainbow")
axs[0].set_title(r"$x$")
axs[0].axis("tight")
axs[1].imshow(y, cmap="rainbow")
axs[1].set_title(r"$y = F x$")
axs[1].axis("tight")
axs[2].imshow(xadj, cmap="rainbow")
axs[2].set_title(r"$x_{adj} = F^H y$")
axs[2].axis("tight")
plt.tight_layout()
plt.subplots_adjust(top=0.8)


x = np.outer(np.ones(nt), np.arange(nx))
Fop = pylops.Flip(nt * nx, dims=(nt, nx), dir=1)
y = Fop * x.ravel()
xadj = Fop.H * y.ravel()
y = y.reshape(nt, nx)
xadj = xadj.reshape(nt, nx)

# sphinx_gallery_thumbnail_number = 3
fig, axs = plt.subplots(1, 3, figsize=(7, 3))
fig.suptitle(
    "Flip in 2nd direction for 2d data", fontsize=14, fontweight="bold", y=0.95
)
axs[0].imshow(x, cmap="rainbow")
axs[0].set_title(r"$x$")
axs[0].axis("tight")
axs[1].imshow(y, cmap="rainbow")
axs[1].set_title(r"$y = F x$")
axs[1].axis("tight")
axs[2].imshow(xadj, cmap="rainbow")
axs[2].set_title(r"$x_{adj} = F^H y$")
axs[2].axis("tight")
plt.tight_layout()
plt.subplots_adjust(top=0.8)

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