Plot power profiles for various parameters

This example shows how one can plot the received power profiles, i.e., the power received along a line as the sum of the power from each transmitter, for a variety of approximation parameters.

The receiver shown on the plot is just indicative, but are not actually used in the process of computing the power profiles.

Various lines shows how the alpha parameter in activation impacts the power computation.

As shown, the higher alpha, the closer it gets to the Without approx. case.

Imports

First, we need to import the necessary modules.

import jax.numpy as jnp
import matplotlib.pyplot as plt
from jaxtyping import Array, Float

from differt2d.scene import Scene
from differt2d.utils import P0, received_power

Scene

The following code will work with any scene, but be aware that large scenes may introduces a long computation time.

You can easily change the scene by modifying the following line:

scene = Scene.square_scene_with_wall()

Plot setup

Below, we setup the plot with two axes.

fig, axes = plt.subplots(2, 1, sharex=True, tight_layout=True)

annotate_kwargs = {"color": "red", "fontsize": 12, "fontweight": "bold"}

# sphinx_gallery_defer_figures

First axis

On the first axis, we plot a top-down view of the scene, as well as the power map for a fixed transmitter location, and a received location given by the coordinates. This is performed without approximation.

scene.plot(
    axes[0],
    transmitters_kwargs={"annotate_kwargs": annotate_kwargs},
    receivers_kwargs={"annotate_kwargs": annotate_kwargs},
)

X, Y = scene.grid(300)
P: Float[Array, "300 300"] = scene.accumulate_on_receivers_grid_over_paths(
    X,
    Y,
    fun=received_power,
    reduce_all=True,
    approx=False,
    min_order=0,
    max_order=0,
)  # type: ignore

PdB = 10.0 * jnp.log10(P / P0)

axes[0].pcolormesh(X, Y, PdB, vmin=-50, vmax=5, zorder=-1)
axes[0].set_ylabel("y coordinate")
_ = axes[1].set_title("Without approx.")  # dummy assign only needed for docs

# sphinx_gallery_defer_figures

Second axis

We plot various power profiles, along a line that joins the transmitter and receiver shown on the first axis.

The first profile is the no-approximation case. Subsequent profiles are using approximation and have different alpha values.

x = jnp.linspace(0.2, 0.8, 200)
y = jnp.array([0.5])

X, Y = jnp.meshgrid(x, y)

P: Float[Array, "200 1"] = scene.accumulate_on_receivers_grid_over_paths(
    X,
    Y,
    fun=received_power,
    reduce_all=True,
    approx=False,
    min_order=0,
    max_order=0,
)  # type: ignore

PdB = 10.0 * jnp.log10(P.reshape(-1) / P0)

axes[1].plot(x, PdB, label="Without")

for alpha in [1.0, 10.0, 100.0, 1000.0]:
    P: Float[Array, "200 1"] = scene.accumulate_on_receivers_grid_over_paths(
        X,
        Y,
        fun=received_power,
        reduce_all=True,
        approx=True,
        alpha=alpha,
        min_order=0,
        max_order=0,
    )  # type: ignore

    PdB = 10.0 * jnp.log10(P.reshape(-1) / P0)

    axes[1].plot(x, PdB, label=f"With + $\\alpha = {alpha:.0e}$")

axes[1].set_ylabel("Power (dB)")
axes[1].set_title("With approx.")
axes[1].set_ylim([-20, 0])

axes[-1].set_xlabel("x coordinate")
plt.legend()
plt.show()  # doctest: +SKIP