errorMeasures.py

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#                                         errorMeasures.py                                         #
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# Authors: J. M.                                                                                   #
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# Created: 27/04/21                                                                                #
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# Purpose: Definitions of custom error measures used to evaluate DoA estimation algorithms.        #
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#*************#
#   imports   #
#*************#
import numpy as np

from utils import permutations


#***********************************************#
#   eliminate randomness to reproduce results   #
#***********************************************#
np.random.seed(42)


#**********************#
#   simple mean rmse   #
#**********************#
def mean_naive_rmse(predDoA, trueDoA):
    """
            Calculates the mean of all the samples of a naive rmse, i.e. an rmse that
            takes the squared error by padding/truncating and then sorting the DoA.

            @param predDoA -- The estimated DoA angles in radians (same length as true DoA).
            @param trueDoA -- The ground truth DoA angles in radians.

            @returns -- The mean of the naive rmse.
    """
    num_samples = trueDoA.shape[0]

    allMSE = np.zeros(num_samples)
    for i in range(num_samples):

        # angular difference
        diff = ((np.sort(predDoA[i]) - np.sort(trueDoA[i])) + np.pi / 2) % np.pi - np.pi / 2

        # rmse
        allMSE[i] = np.mean(diff ** 2) ** (1 / 2)

    return np.mean(allMSE)


#***********************************#
#   mean minimal permutation rmse   #
#***********************************#
def mean_min_perm_rmse(predDoA, trueDoA):
    """
            Calculates the mean of all the samples of the minimal rmse of
            (all permutations of) the predicted DoA and the true DoA.

            @param predDoA -- The estimated DoA angles in radians (same length as true DoA).
            @param trueDoA -- The ground truth DoA angles in radians.

            @returns -- The mean of minimal rmse.
    """
    num_samples = trueDoA.shape[0]

    allMSE = np.zeros(num_samples)
    for i in range(num_samples):

        # get permutations of estimated DoA
        diffs = np.zeros(np.math.factorial(trueDoA.shape[1]))
        for j, perm in enumerate(permutations(list(predDoA[i]))):

            # angular difference
            diff = ((perm - trueDoA[i]) + np.pi / 2) % np.pi - np.pi / 2

            # rmse
            diffs[j] = np.mean(diff ** 2) ** (1 / 2)

        # choose minimal rmse as error
        allMSE[i] = np.amin(diffs)

    return np.mean(allMSE)