r"""
Symmetrize
==========

This example shows how to use the :py:class:`pylops.Symmetrize`
operator which takes an input signal and returns a symmetric signal
by pre-pending the input signal in reversed order. Such an operation can be
inverted as we will see in this example.

Moreover the :py:class:`pylops.Symmetrize` can be used as *preconditioning*
to any inverse problem where we are after inverting for a signal that we
want to ensure is symmetric. Refer to :ref:`sphx_glr_gallery_plot_wavest.py`
for an example of such a type.
"""
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.
Sop = pylops.Symmetrize(nt)
y = Sop * x
xadj = Sop.H * y
xinv = Sop / y

plt.figure(figsize=(7, 3))
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.plot(xinv, "--m", lw=3, label=r"$x_{inv} = F^{-1} y$")
plt.title("Symmetrize in 1st direction", fontsize=14, fontweight="bold")
plt.legend()
plt.tight_layout()

###############################################################################
# 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, 6
x = np.outer(np.arange(nt), np.ones(nx))

Sop = pylops.Symmetrize((nt, nx), axis=0)
y = Sop * x
xadj = Sop.H * y
xinv = Sop / y.ravel()
xinv = xinv.reshape(Sop.dims)

fig, axs = plt.subplots(1, 3, figsize=(7, 3))
fig.suptitle(
    "Symmetrize in 2nd direction for 2d data", fontsize=14, fontweight="bold", y=0.95
)
axs[0].imshow(x, cmap="rainbow", vmin=0, vmax=9)
axs[0].set_title(r"$x$")
axs[0].axis("tight")
axs[1].imshow(y, cmap="rainbow", vmin=0, vmax=9)
axs[1].set_title(r"$y=Fx$")
axs[1].axis("tight")
axs[2].imshow(xinv, cmap="rainbow", vmin=0, vmax=9)
axs[2].set_title(r"$x_{adj}=F^{-1}y$")
axs[2].axis("tight")
plt.tight_layout()
plt.subplots_adjust(top=0.8)


x = np.outer(np.ones(nt), np.arange(nx))
Sop = pylops.Symmetrize((nt, nx), axis=1)

y = Sop * x
xadj = Sop.H * y
xinv = Sop / y.ravel()
xinv = xinv.reshape(Sop.dims)

# sphinx_gallery_thumbnail_number = 3
fig, axs = plt.subplots(1, 3, figsize=(7, 3))
fig.suptitle(
    "Symmetrize in 2nd direction for 2d data", fontsize=14, fontweight="bold", y=0.95
)
axs[0].imshow(x, cmap="rainbow", vmin=0, vmax=9)
axs[0].set_title(r"$x$")
axs[0].axis("tight")
axs[1].imshow(y, cmap="rainbow", vmin=0, vmax=9)
axs[1].set_title(r"$y=Fx$")
axs[1].axis("tight")
axs[2].imshow(xinv, cmap="rainbow", vmin=0, vmax=9)
axs[2].set_title(r"$x_{adj}=F^{-1}y$")
axs[2].axis("tight")
plt.tight_layout()
plt.subplots_adjust(top=0.8)