"""
This example demonstrates how to visualize 2D vector fields and their uncertainty using squid glyphs with the ``uvisbox`` library.
The example generates a 2D grid of vectors representing the double gyre flow, creates an ensemble by adding Gaussian noise, and then visualizes the ensemble using squid glyphs to represent uncertainty.
Import necessary libraries
.. code-block:: python
from uvisbox.Modules.UncertaintyLobes import uncertainty_lobes
import numpy as np
import matplotlib.pyplot as plt
generate a 2D grid over [0,2] x [0,1] and use double gyre flow to generate vector field
with some noise to create an ensemble of vector fields
.. code-block:: python
# Define the double gyre flow function
A = 0.1
omega = np.pi
epsilon = 0.25
def double_gyre(x, y, t=0):
a = epsilon * np.sin(omega * t)
b = 1 - 2 * a
f = a * x**2 + b * x
df_dx = 2 * a * x + b
u = -np.pi * A * np.sin(np.pi * f) * np.cos(np.pi * y)
v = np.pi * A * np.cos(np.pi * f) * np.sin(np.pi * y) * df_dx
return u, v
# Change domain to [0,2] x [0,1]
X, Y = np.meshgrid(np.linspace(0, 2, 10), np.linspace(0, 1, 5))
U, V = double_gyre(X, Y)
# Create ensemble data by perturbing vector magnitude and direction with Gaussian noise
n_ensemble = 20 # number of ensemble members
rng = np.random.default_rng(seed=42)
# Flatten the grid for easier perturbation
X_flat = X.flatten()
Y_flat = Y.flatten()
U_flat = U.flatten()
V_flat = V.flatten()
n_points = X_flat.size
# Compute magnitude and angle
mag = np.sqrt(U_flat**2 + V_flat**2)
angle = np.arctan2(V_flat, U_flat)
# Standard deviations for noise (tune as needed)
mag_noise_std = 0.20 * mag.max()
angle_noise_std = np.deg2rad(10) # 5 degree std
n_ensemble = 20
ensemble_vectors = np.zeros((n_points, n_ensemble, 2))
for i in range(n_points):
for j in range(n_ensemble):
# Perturb magnitude and anglels
mag_perturbed = mag[i] + rng.normal(0, mag_noise_std)
angle_perturbed = angle[i] + rng.normal(0, angle_noise_std)
# Convert back to Cartesian coordinates
ensemble_vectors[i, j] = [
mag_perturbed * np.cos(angle_perturbed),
mag_perturbed * np.sin(angle_perturbed)
]
positions = np.vstack((X_flat, Y_flat)).T
Set up the plot for both original vector field and uncertainty squid glyphs
.. code-block:: python
fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(20, 20))
# Plot original vector field with arrows
for i in range(n_points):
for j in range(n_ensemble):
u, v = ensemble_vectors[i, j]
x, y = positions[i]
ax1.arrow(x, y, u, v, head_width=0.03, head_length=0.06, fc='blue', ec='blue', alpha=0.1, length_includes_head=True)
ax1.set_title("Original Vector Field with Ensemble Members")
ax1.set_xlim(-0.25, 2.25)
ax1.set_ylim(-0.25, 1.25)
ax1.set_xlabel("X")
ax1.set_ylabel("Y")
ax1.grid()
# Plot uncertainty lobes
# positions is the first parameter, ensemble_vectors is the second
# percentile1 defaults to 90, percentile2 defaults to 50
ax2 = uncertainty_lobes(positions, ensemble_vectors,
percentile1=50, percentile2=75, scale=0.4, ax=ax2)
ax2.set_title("Uncertainty Lobes for Double Gyre Flow")
ax2.set_xlim(-0.25, 2.25)
ax2.set_ylim(-0.25, 1.25)
ax2.set_xlabel("X")
ax2.set_ylabel("Y")
ax2.grid()
plt.tight_layout()
plt.show()
.. image:: _static/uncertainty_lobes_2D_example.png
:alt: Uncertainty Lobes 2D Example
:align: center
"""
# Import necessary libraries
from uvisbox.Modules.UncertaintyLobes import uncertainty_lobes
import numpy as np
import matplotlib.pyplot as plt
# generate a 2D grid over [0,2] x [0,1] and use double gyre flow to generate vector field
# with some noise to create an ensemble of vector fields
# Define the double gyre flow function
A = 0.1
omega = np.pi
epsilon = 0.25
[docs]
def double_gyre(x, y, t=0):
a = epsilon * np.sin(omega * t)
b = 1 - 2 * a
f = a * x**2 + b * x
df_dx = 2 * a * x + b
u = -np.pi * A * np.sin(np.pi * f) * np.cos(np.pi * y)
v = np.pi * A * np.cos(np.pi * f) * np.sin(np.pi * y) * df_dx
return u, v
# Change domain to [0,2] x [0,1]
X, Y = np.meshgrid(np.linspace(0, 2, 10), np.linspace(0, 1, 5))
U, V = double_gyre(X, Y)
# Create ensemble data by perturbing vector magnitude and direction with Gaussian noise
n_ensemble = 20 # number of ensemble members
rng = np.random.default_rng(seed=42)
# Flatten the grid for easier perturbation
X_flat = X.flatten()
Y_flat = Y.flatten()
U_flat = U.flatten()
V_flat = V.flatten()
n_points = X_flat.size
# Compute magnitude and angle
mag = np.sqrt(U_flat**2 + V_flat**2)
angle = np.arctan2(V_flat, U_flat)
# Standard deviations for noise (tune as needed)
mag_noise_std = 0.20 * mag.max()
angle_noise_std = np.deg2rad(10) # 5 degree std
n_ensemble = 20
ensemble_vectors = np.zeros((n_points, n_ensemble, 2))
for i in range(n_points):
for j in range(n_ensemble):
# Perturb magnitude and anglels
mag_perturbed = mag[i] + rng.normal(0, mag_noise_std)
angle_perturbed = angle[i] + rng.normal(0, angle_noise_std)
# Convert back to Cartesian coordinates
ensemble_vectors[i, j] = [
mag_perturbed * np.cos(angle_perturbed),
mag_perturbed * np.sin(angle_perturbed)
]
positions = np.vstack((X_flat, Y_flat)).T
# Set up the plot for both original vector field and uncertainty squid glyphs
fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(10, 10), sharex=True, sharey=True)
# Plot original vector field with arrows
for i in range(n_points):
for j in range(n_ensemble):
u, v = ensemble_vectors[i, j]
x, y = positions[i]
ax1.arrow(x, y, u, v, head_width=0.03, head_length=0.06, fc='blue', ec='blue', alpha=0.1, length_includes_head=True)
ax1.set_title("Original Vector Field with Ensemble Members")
ax1.set_xlim(-0.25, 2.25)
ax1.set_ylim(-0.25, 1.25)
ax1.set_xlabel("X")
ax1.set_ylabel("Y")
ax1.grid()
# Plot uncertainty lobes
# positions is the first parameter, ensemble_vectors is the second
# percentile1 defaults to 90, percentile2 defaults to 50
ax2 = uncertainty_lobes(positions, ensemble_vectors,
percentile1=90, percentile2=50, scale=0.4, ax=ax2)
ax2.set_title("Uncertainty Lobes for Double Gyre Flow")
ax2.set_xlim(-0.25, 2.25)
ax2.set_ylim(-0.25, 1.25)
ax2.set_xlabel("X")
ax2.set_ylabel("Y")
ax2.grid()
plt.tight_layout()
# plt.savefig("uncertainty_lobes_2D_example.png", dpi=300)
plt.show()