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import numpy as np
import math
def layer_wise_dot_product(*matrices: np.ndarray) -> np.ndarray:
"""
Performs the sequential layer-wise dot product of multiple 3D matrices along the last dimension.
Args:
*matrices: A variable number of 3D numpy arrays.
Returns:
A 3D numpy array containing the sequential dot product results for each layer in the last dimension.
"""
if not all(matrix.shape == matrices[0].shape for matrix in matrices):
raise ValueError("All matrices must have the same dimensions.")
result = np.zeros_like(matrices[0], dtype="complex")
_, _, num_layers = matrices[0].shape
for layer_i in range(num_layers):
# Start the product with the identity matrix for the first multiplication
dot_product = np.eye(result.shape[0])
for matrix in matrices:
dot_product = np.dot(dot_product, matrix[:, :, layer_i])
result[:, :, layer_i] = dot_product
return result
def bessel(z):
"""
Bessel function aproximation for air radiation impedance
"""
bessel_sum = 0
for k in range(25):
bessel_i = ((-1) ** k * (z / 2) ** (2 * k + 1)) / (
math.factorial(k) * math.factorial(k + 1)
)
bessel_sum = bessel_sum + bessel_i
return bessel_sum
def struve(z):
"""
Srtuve function aproximation for air radiation impedance
"""
struve_sum = 0
for k in range(25):
struve_i = (((-1) ** k * (z / 2) ** (2 * k + 2))) / (
math.factorial(int(k + 1 / 2)) * math.factorial(int(k + 3 / 2))
)
struve_sum = struve_sum + struve_i
return struve_sum
def to_db(x):
"""
decibel calculus
"""
db = 20 * np.log10(np.abs(x))
return db
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