Tasks 1-6 of the summer practice 2025

B_mean.py

@@ -0,0 +1,95 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.linalg import norm
+from scipy.ndimage import map_coordinates
+from typing import Tuple
+
+
+def linear_extrapolate(data_, points):
+    return map_coordinates(data_, points.T, order=1, mode='nearest')
+
+
+data = np.load("C:/Users/user/Downloads/vtk_field/npy_field/Bnlfffe_NORH_NLFFFE_170904_055842.npy")
+
+nx, ny, nz = data.shape[:3]
+x, y, z = np.arange(nx), np.arange(ny), np.arange(nz)
+X, Y, Z = np.meshgrid(x, y, z, indexing='ij')
+coordinates = np.stack((X, Y, Z), axis=-1)
+
+
+def calculate_b_mean(data_, coordinates_, center_, radius_):
+    squared_dist = np.sum((coordinates_ - np.array(center_)) ** 2, axis=-1)
+    mask = np.array(squared_dist <= radius_**2)
+    return np.mean(data_[mask], axis=0), np.where(mask.ravel())[0]
+
+
+# noinspection PyUnreachableCode
+def create_local_frame(b_mean_: np.ndarray) -> Tuple[np.ndarray, np.ndarray]:
+    b_n_ = b_mean_ / norm(b_mean_)
+    basis = np.eye(3)
+    x_prime = np.cross(basis[np.argmin(np.abs(basis @ b_n_))], b_n_)
+    x_prime /= norm(x_prime)
+    y_prime = np.cross(b_n_, x_prime)
+    y_prime /= norm(y_prime)
+    return np.vstack([x_prime, y_prime, b_n_]), b_n_
+
+
+def transform_field(b_, rotation_matrix_):
+    return np.dot(b_, rotation_matrix_.T)
+
+
+def plot_all_2d_components(b_local_, center_, radius_, rotation_matrix_, title_prefix=""):
+    fig, axes = plt.subplots(1, 3, figsize=(18, 6))
+    x_prime, y_prime = rotation_matrix_[0], rotation_matrix_[1]
+
+    u = v = np.linspace(-radius_, radius_, int(2 * radius_))
+    u_grid, v_grid = np.meshgrid(u, v)
+    x_plane = center_[0] + u_grid * x_prime[0] + v_grid * y_prime[0]
+    y_plane = center_[1] + u_grid * x_prime[1] + v_grid * y_prime[1]
+    z_plane = center_[2] + u_grid * x_prime[2] + v_grid * y_prime[2]
+    sample_points = np.stack((x_plane, y_plane, z_plane), axis=-1)
+
+    b_x = linear_extrapolate(b_local_[..., 0], sample_points)
+    b_y = linear_extrapolate(b_local_[..., 1], sample_points)
+    b_z = linear_extrapolate(b_local_[..., 2], sample_points)
+
+    phi = np.arctan2(v_grid, u_grid)
+    b_r = b_x * np.cos(phi) + b_y * np.sin(phi)
+    b_phi = -b_x * np.sin(phi) + b_y * np.cos(phi)
+
+    vmax = max(np.max(np.abs(b_r)), np.max(np.abs(b_phi)), np.max(np.abs(b_z)), 1e-6)
+    for ax, component in zip(axes, [b_r, b_phi, b_z]):
+        im = ax.imshow(component, cmap='bwr', vmin=-vmax, vmax=vmax,
+                       extent=[u[0], u[-1], v[-1], v[0]], origin='lower')
+        plt.colorbar(im, ax=ax)
+        ax.add_patch(plt.Circle((0, 0), radius, color='k', fill=False, linestyle='--'))
+        ax.scatter(0, 0, c='k', s=100, marker='*')
+        ax.grid(True, linestyle=':', alpha=0.5)
+
+    axes[0].set_title(fr"{title_prefix}$B_r$")
+    axes[1].set_title(fr"{title_prefix}$B_\phi$")
+    axes[2].set_title(fr"{title_prefix}$B_n$")
+    plt.tight_layout()
+    plt.show()
+
+
+def calculate_curl(b_):
+    gradients = np.stack(np.gradient(b_, axis=(0, 1, 2)), axis=-1)
+    curl = np.stack([gradients[..., 2, 1] - gradients[..., 1, 2],
+                     gradients[..., 0, 2] - gradients[..., 2, 0],
+                     gradients[..., 1, 0] - gradients[..., 0, 1]], axis=-1)
+    return curl
+
+
+center = (203, 10, 1)
+radius = 15
+
+b_mean, indices = calculate_b_mean(data, coordinates, center, radius)
+rotation_matrix, B_n = create_local_frame(b_mean)
+b_local = np.apply_along_axis(transform_field, 3, data, rotation_matrix)
+
+plot_all_2d_components(b_local, center, radius, rotation_matrix, "Local components: ")
+
+curl_global = calculate_curl(data)
+curl_local = np.apply_along_axis(transform_field, 3, curl_global, rotation_matrix)
+plot_all_2d_components(curl_local, center, radius, rotation_matrix, "Curl ")

requirements.txt

@@ -16,6 +16,7 @@ idna==3.10
 isodate==0.7.2
 joblib==1.5.0
 lxml==5.4.0
+matplotlib==3.10.3
 multidict==6.4.3
 numpy==2.2.5
 packaging==25.0