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