Moving the checkerboard matrix over the main diagonal of the similarity matrix one sample at a time.

    :param kernel_type:
    :param thresh:
    :param similarity_matrix:
    :param kernel_width: the size of one quarter of the checkerboard matrix
    :return: peaks and convolution values

def checkerboard_matrix_filtering(similarity_matrix, kernel_width, kernel_type="default", thresh=0.25):

    """
    Moving the checkerboard matrix over the main diagonal of the similarity matrix one sample at a time.

    :param kernel_type:
    :param thresh:
    :param similarity_matrix:
    :param kernel_width: the size of one quarter of the checkerboard matrix
    :return: peaks and convolution values
    """

    checkerboard_matrix = get_checkerboard_matrix(kernel_width, kernel_type)

    # The values calculated in this step are starting from the 'kernel_width' position and ending
    # at length - kernel_width
    d = []
    for i in range(0, similarity_matrix.shape[0] - 2 * kernel_width):
        base = similarity_matrix[i:i + kernel_width * 2, i:i + kernel_width * 2]
        d.append(np.sum(np.multiply(base, checkerboard_matrix)))

    # The missing values from 0 to kernel_width are calculated here
    top_left_d = []
    for i in range(0, kernel_width):
        base = similarity_matrix[0:i + kernel_width, 0:i + kernel_width]
        top_left_d.append(np.sum(np.multiply(base, checkerboard_matrix[kernel_width - i:, kernel_width - i:])))

    # The missing kernel_width values at the bottom right are set to 0
    convolution_values = top_left_d + d + [0 for i in range(0, kernel_width)]

    # peaks = find_peaks_cwt(convolution_values, np.arange(1, peak_range))
    peaks = peakutils.indexes(convolution_values, thres=thresh)

    peaks = [0] + list(peaks) + [len(convolution_values)-1]
    return peaks, convolution_values