utils.py 41.8 KB
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# @author lucasmiranda42
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import cv2
import matplotlib.pyplot as plt
import multiprocessing
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import networkx as nx
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import numpy as np
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import os
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import pandas as pd
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import regex as re
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import seaborn as sns
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from copy import deepcopy
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from itertools import combinations, product
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from joblib import Parallel, delayed
from scipy import spatial
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from scipy import stats
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from sklearn import mixture
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from tqdm import tqdm
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from typing import Tuple, Any, List, Union, Dict, NewType

# DEFINE CUSTOM ANNOTATED TYPES #


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Coordinates = NewType("Coordinates", Any)
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# QUALITY CONTROL AND PREPROCESSING #
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def likelihood_qc(dframe: pd.DataFrame, threshold: float = 0.9) -> np.array:
    """Returns a DataFrame filtered dataframe, keeping only the rows entirely above the threshold.

        Parameters:
            - dframe (pandas.DataFrame): DeepLabCut output, with positions over time and associated likelihhod
            - threshold (float): minimum acceptable confidence

        Returns:
            - filt_mask (np.array): mask on the rows of dframe"""

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    Likes = np.array([dframe[i]["likelihood"] for i in list(dframe.columns.levels[0])])
    Likes = np.nan_to_num(Likes, nan=1.0)
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    filt_mask = np.all(Likes > threshold, axis=0)

    return filt_mask
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def bp2polar(tab: pd.DataFrame) -> pd.DataFrame:
    """Returns the DataFrame in polar coordinates.

        Parameters:
            - tab (pandas.DataFrame):Table with cartesian coordinates

        Returns:
            - polar (pandas.DataFrame): Equivalent to input, but with values in polar coordinates"""

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    tab_ = np.array(tab)
    complex_ = tab_[:, 0] + 1j * tab_[:, 1]
    polar = pd.DataFrame(np.array([abs(complex_), np.angle(complex_)]).T)
    polar.rename(columns={0: "rho", 1: "phi"}, inplace=True)
    return polar


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def tab2polar(cartesian_df: pd.DataFrame) -> pd.DataFrame:
    """Returns a pandas.DataFrame in which all the coordinates are polar.

        Parameters:
            - cartesian_df (pandas.DataFrame):DataFrame containing tables with cartesian coordinates

        Returns:
            - result (pandas.DataFrame): Equivalent to input, but with values in polar coordinates"""

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    result = []
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    for df in list(cartesian_df.columns.levels[0]):
        result.append(bp2polar(cartesian_df[df]))
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    result = pd.concat(result, axis=1)
    idx = pd.MultiIndex.from_product(
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        [list(cartesian_df.columns.levels[0]), ["rho", "phi"]],
        names=["bodyparts", "coords"],
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    )
    result.columns = idx
    return result


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def compute_dist(
    pair_array: np.array, arena_abs: int = 1, arena_rel: int = 1
) -> pd.DataFrame:
    """Returns a pandas.DataFrame with the scaled distances between a pair of body parts.

        Parameters:
            - pair_array (numpy.array): np.array of shape N * 4 containing X,y positions
            over time for a given pair of body parts
            - arena_abs (int): diameter of the real arena in cm
            - arena_rel (int): diameter of the captured arena in pixels

        Returns:
            - result (pd.DataFrame): pandas.DataFrame with the
            absolute distances between a pair of body parts"""

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    lim = 2 if pair_array.shape[1] == 4 else 1
    a, b = pair_array[:, :lim], pair_array[:, lim:]
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    ab = a - b
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    dist = np.sqrt(np.einsum("...i,...i", ab, ab))
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    return pd.DataFrame(dist * arena_abs / arena_rel)


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def bpart_distance(
    dataframe: pd.DataFrame, arena_abs: int = 1, arena_rel: int = 1
) -> pd.DataFrame:
    """Returns a pandas.DataFrame with the scaled distances between all pairs of body parts.

        Parameters:
            - dataframe (pandas.DataFrame): pd.DataFrame of shape N*(2*bp) containing X,y positions
        over time for a given set of bp body parts
            - arena_abs (int): diameter of the real arena in cm
            - arena_rel (int): diameter of the captured arena in pixels
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        Returns:
            - result (pd.DataFrame): pandas.DataFrame with the
            absolute distances between all pairs of body parts"""

    indexes = combinations(dataframe.columns.levels[0], 2)
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    dists = []
    for idx in indexes:
        dist = compute_dist(np.array(dataframe.loc[:, list(idx)]), arena_abs, arena_rel)
        dist.columns = [idx]
        dists.append(dist)

    return pd.concat(dists, axis=1)
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def angle(a: np.array, b: np.array, c: np.array) -> np.array:
    """Returns a numpy.array with the angles between the provided instances.

        Parameters:
            - a (2D np.array): positions over time for a bodypart
            - b (2D np.array): positions over time for a bodypart
            - c (2D np.array): positions over time for a bodypart
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        Returns:
            - ang (1D np.array): angles between the three-point-instances"""

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    ba = a - b
    bc = c - b

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    cosine_angle = np.einsum("...i,...i", ba, bc) / (
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        np.linalg.norm(ba, axis=1) * np.linalg.norm(bc, axis=1)
    )
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    ang = np.arccos(cosine_angle)

    return ang


def angle_trio(bpart_array: np.array) -> np.array:
    """Returns a numpy.array with all three possible angles between the provided instances.
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        Parameters:
            - bpart_array (2D numpy.array): positions over time for a bodypart
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        Returns:
            - ang_trio (2D numpy.array): all-three angles between the three-point-instances"""
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    a, b, c = bpart_array
    ang_trio = np.array([angle(a, b, c), angle(a, c, b), angle(b, a, c)])
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    return ang_trio
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def rotate(
    p: np.array, angles: np.array, origin: np.array = np.array([0, 0])
) -> np.array:
    """Returns a numpy.array with the initial values rotated by angles radians
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        Parameters:
            - p (2D numpy.array): array containing positions of bodyparts over time
            - angles (2D numpy.array): set of angles (in radians) to rotate p with
            - origin (2D numpy.array): rotation axis (zero vector by default)

        Returns:
            - rotated (2D numpy.array): rotated positions over time"""
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    R = np.array([[np.cos(angles), -np.sin(angles)], [np.sin(angles), np.cos(angles)]])

    o = np.atleast_2d(origin)
    p = np.atleast_2d(p)

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    rotated = np.squeeze((R @ (p.T - o.T) + o.T).T)

    return rotated

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def align_trajectories(data: np.array, mode: str = "all") -> np.array:
    """Returns a numpy.array with the positions rotated in a way that the center (0 vector)
    and the body part in the first column of data are aligned with the y axis.
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        Parameters:
            - data (3D numpy.array): array containing positions of body parts over time, where
            shape is N (sliding window instances) * m (sliding window size) * l (features)
            - mode (string): specifies if *all* instances of each sliding window get
            aligned, or only the *center*
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        Returns:
            - aligned_trajs (2D np.array): aligned positions over time"""
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    angles = np.zeros(data.shape[0])
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    data = deepcopy(data)
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    dshape = data.shape
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    if mode == "center":
        center_time = (data.shape[1] - 1) // 2
        angles = np.arctan2(data[:, center_time, 0], data[:, center_time, 1])
    elif mode == "all":
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        data = data.reshape(-1, dshape[-1], order="C")
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        angles = np.arctan2(data[:, 0], data[:, 1])
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    elif mode == "none":
        data = data.reshape(-1, dshape[-1], order="C")
        angles = np.zeros(data.shape[0])
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    aligned_trajs = np.zeros(data.shape)

    for frame in range(data.shape[0]):
        aligned_trajs[frame] = rotate(
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            data[frame].reshape([-1, 2], order="C"), angles[frame],
        ).reshape(data.shape[1:], order="C")
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    if mode == "all" or mode == "none":
        aligned_trajs = aligned_trajs.reshape(dshape, order="C")
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    return aligned_trajs


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def smooth_boolean_array(a: np.array) -> np.array:
    """Returns a boolean array in which isolated appearances of a feature are smoothened

        Parameters:
            - a (1D numpy.array): boolean instances

        Returns:
            - a (1D numpy.array): smoothened boolean instances"""

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    for i in range(1, len(a) - 1):
        if a[i - 1] == a[i + 1]:
            a[i] = a[i - 1]
    return a == 1


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def rolling_window(a: np.array, window_size: int, window_step: int) -> np.array:
    """Returns a 3D numpy.array with a sliding-window extra dimension

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        Parameters:
            - a (2D np.array): N (instances) * m (features) shape
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        Returns:
            - rolled_a (3D np.array):
            N (sliding window instances) * l (sliding window size) * m (features)"""
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    shape = (a.shape[0] - window_size + 1, window_size) + a.shape[1:]
    strides = (a.strides[0],) + a.strides
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    rolled_a = np.lib.stride_tricks.as_strided(
        a, shape=shape, strides=strides, writeable=True
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    )[::window_step]
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    return rolled_a
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def smooth_mult_trajectory(series: np.array, alpha: float = 0.15) -> np.array:
    """Returns a smooths a trajectory using exponentially weighted averages

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        Parameters:
            - series (numpy.array): 1D trajectory array with N (instances) - alpha (float): 0 <= alpha <= 1;
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            indicates the inverse weight assigned to previous observations. Higher (alpha~1) indicates less smoothing;
            lower indicates more (alpha~0)
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        Returns:
            - smoothed_series (np.array): smoothed version of the input, with equal shape"""
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    result = [series[0]]
    for n in range(len(series)):
        result.append(alpha * series[n] + (1 - alpha) * result[n - 1])

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    smoothed_series = np.array(result)

    return smoothed_series
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# BEHAVIOUR RECOGNITION FUNCTIONS #
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def close_single_contact(
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    pos_dframe: pd.DataFrame,
    left: str,
    right: str,
    tol: float,
    arena_abs: int,
    arena_rel: int,
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) -> np.array:
    """Returns a boolean array that's True if the specified body parts are closer than tol.
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        Parameters:
            - pos_dframe (pandas.DataFrame): DLC output as pandas.DataFrame; only applicable
            to two-animal experiments.
            - left (string): First member of the potential contact
            - right (string): Second member of the potential contact
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            - tol (float): maximum distance for which a contact is reported
            - arena_abs (int): length in mm of the diameter of the real arena
            - arena_rel (int): length in pixels of the diameter of the arena in the video
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        Returns:
            - contact_array (np.array): True if the distance between the two specified points
            is less than tol, False otherwise"""
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    close_contact = (
        np.linalg.norm(pos_dframe[left] - pos_dframe[right], axis=1) * arena_abs
    ) / arena_rel < tol
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    return close_contact
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def close_double_contact(
    pos_dframe: pd.DataFrame,
    left1: str,
    left2: str,
    right1: str,
    right2: str,
    tol: float,
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    arena_abs: int,
    arena_rel: int,
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    rev: bool = False,
) -> np.array:
    """Returns a boolean array that's True if the specified body parts are closer than tol.

        Parameters:
            - pos_dframe (pandas.DataFrame): DLC output as pandas.DataFrame; only applicable
            to two-animal experiments.
            - left1 (string): First contact point of animal 1
            - left2 (string): Second contact point of animal 1
            - right1 (string): First contact point of animal 2
            - right2 (string): Second contact point of animal 2
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            - tol (float): maximum distance for which a contact is reported
            - arena_abs (int): length in mm of the diameter of the real arena
            - arena_rel (int): length in pixels of the diameter of the arena in the video
            - rev (bool): reverses the default behaviour (nose2tail contact for both mice)
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        Returns:
            - double_contact (np.array): True if the distance between the two specified points
            is less than tol, False otherwise"""

    if rev:
        double_contact = (
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            (np.linalg.norm(pos_dframe[right1] - pos_dframe[left2], axis=1) * arena_abs)
            / arena_rel
            < tol
        ) & (
            (np.linalg.norm(pos_dframe[right2] - pos_dframe[left1], axis=1) * arena_abs)
            / arena_rel
            < tol
        )
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    else:
        double_contact = (
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            (np.linalg.norm(pos_dframe[right1] - pos_dframe[left1], axis=1) * arena_abs)
            / arena_rel
            < tol
        ) & (
            (np.linalg.norm(pos_dframe[right2] - pos_dframe[left2], axis=1) * arena_abs)
            / arena_rel
            < tol
        )
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    return double_contact
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def recognize_arena(
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    videos: list,
    vid_index: int,
    path: str = ".",
    recoglimit: int = 1,
    arena_type: str = "circular",
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) -> Tuple[np.array, int, int]:
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    """Returns numpy.array with information about the arena recognised from the first frames
    of the video. WARNING: estimates won't be reliable if the camera moves along the video.

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        Parameters:
            - videos (list): relative paths of the videos to analise
            - vid_index (int): element of videos to use
            - path (string): full path of the directory where the videos are
            - recoglimit (int): number of frames to use for position estimates
            - arena_type (string): arena type; must be one of ['circular']
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        Returns:
            - arena (np.array): 1D-array containing information about the arena.
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            "circular" (3-element-array) -> x-y position of the center and the radius
            - h (int): height of the video in pixels
            - w (int): width of the video in pixels"""
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    cap = cv2.VideoCapture(os.path.join(path, videos[vid_index]))
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    # Loop over the first frames in the video to get resolution and center of the arena
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    arena, fnum, h, w = False, 0, None, None
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    while cap.isOpened() and fnum < recoglimit:
        ret, frame = cap.read()
        # if frame is read correctly ret is True
        if not ret:
            print("Can't receive frame (stream end?). Exiting ...")
            break

        if arena_type == "circular":

            # Detect arena and extract positions
            arena = circular_arena_recognition(frame)[0]
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            if h is None and w is None:
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                h, w = frame.shape[0], frame.shape[1]

        fnum += 1

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    cap.release()
    cv2.destroyAllWindows()

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    return arena, h, w
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def circular_arena_recognition(frame: np.array) -> np.array:
    """Returns x,y position of the center and the radius of the recognised arena
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        Parameters:
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            - frame (np.array): numpy.array representing an individual frame of a video
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        Returns:
            - circles (np.array): 3-element-array containing x,y positions of the center
            of the arena, and a third value indicating the radius"""
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    # Convert image to greyscale, threshold it, blur it and detect the biggest best fitting circle
    # using the Hough algorithm
    gray_image = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
    ret, thresh = cv2.threshold(gray_image, 50, 255, 0)
    frame = cv2.medianBlur(thresh, 9)
    circle = cv2.HoughCircles(
        frame,
        cv2.HOUGH_GRADIENT,
        1,
        300,
        param1=50,
        param2=10,
        minRadius=0,
        maxRadius=0,
    )

    circles = []

    if circle is not None:
        circle = np.uint16(np.around(circle[0]))
        circles.append(circle)

    return circles[0]


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def climb_wall(
    arena_type: str, arena: np.array, pos_dict: pd.DataFrame, tol: float, nose: str
) -> np.array:
    """Returns True if the specified mouse is climbing the wall
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        Parameters:
            - arena_type (str): arena type; must be one of ['circular']
            - arena (np.array): contains arena location and shape details
            - pos_dict (table_dict): position over time for all videos in a project
            - tol (float): minimum tolerance to report a hit
            - nose (str): indicates the name of the body part representing the nose of
            the selected animal

        Returns:
            - climbing (np.array): boolean array. True if selected animal
            is climbing the walls of the arena"""

    nose = pos_dict[nose]
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    if arena_type == "circular":
        center = np.array(arena[:2])
        climbing = np.linalg.norm(nose - center, axis=1) > (arena[2] + tol)

    else:
        raise NotImplementedError("Supported values for arena_type are ['circular']")
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    return climbing
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def rolling_speed(
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    dframe: pd.DatetimeIndex, window: int = 5, rounds: int = 10, deriv: int = 1
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) -> pd.DataFrame:
    """Returns the average speed over n frames in pixels per frame
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        Parameters:
            - dframe (pandas.DataFrame): position over time dataframe
            - pause (int):  frame-length of the averaging window
            - rounds (int): float rounding decimals
            - deriv (int): position derivative order; 1 for speed,
            2 for acceleration, 3 for jerk, etc
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        Returns:
            - speeds (pd.DataFrame): containing 2D speeds for each body part
            in the original data or their consequent derivatives"""

    original_shape = dframe.shape
    body_parts = dframe.columns.levels[0]
    speeds = pd.DataFrame

    for der in range(deriv):
        distances = np.concatenate(
            [
                np.array(dframe).reshape([-1, (2 if der == 0 else 1)], order="F"),
                np.array(dframe.shift()).reshape(
                    [-1, (2 if der == 0 else 1)], order="F"
                ),
            ],
            axis=1,
        )
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        distances = np.array(compute_dist(distances))
        distances = distances.reshape(
            [original_shape[0], original_shape[1] // 2], order="F"
        )
        distances = pd.DataFrame(distances, index=dframe.index)
        speeds = np.round(distances.rolling(window).mean(), rounds)
        speeds[np.isnan(speeds)] = 0.0
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        dframe = speeds
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    speeds.columns = body_parts
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    return speeds


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def huddle(
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    pos_dframe: pd.DataFrame,
    speed_dframe: pd.DataFrame,
    tol_forward: float,
    tol_spine: float,
    tol_speed: float,
    animal_id: str = "",
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) -> np.array:
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    """Returns true when the mouse is huddling using simple rules. (!!!) Designed to
    work with deepof's default DLC mice models; not guaranteed to work otherwise.
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        Parameters:
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            - pos_dframe (pandas.DataFrame): position of body parts over time
            - speed_dframe (pandas.DataFrame): speed of body parts over time
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            - tol_forward (float): Maximum tolerated distance between ears and
            forward limbs
            - tol_rear (float): Maximum tolerated average distance between spine
            body parts
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            - tol_speed (float): Maximum tolerated speed for the center of the mouse
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        Returns:
            hudd (np.array): True if the animal is huddling, False otherwise
        """

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    if animal_id != "":
        animal_id += "_"

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    forward = (
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        np.linalg.norm(
            pos_dframe[animal_id + "Left_ear"] - pos_dframe[animal_id + "Left_fhip"],
            axis=1,
        )
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        < tol_forward
    ) & (
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        np.linalg.norm(
            pos_dframe[animal_id + "Right_ear"] - pos_dframe[animal_id + "Right_fhip"],
            axis=1,
        )
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        < tol_forward
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    )

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    spine = [
        animal_id + "Spine_1",
        animal_id + "Center",
        animal_id + "Spine_2",
        animal_id + "Tail_base",
    ]
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    spine_dists = []
    for comb in range(2):
        spine_dists.append(
            np.linalg.norm(
                pos_dframe[spine[comb]] - pos_dframe[spine[comb + 1]], axis=1
            )
        )
    spine = np.mean(spine_dists) < tol_spine
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    speed = speed_dframe[animal_id + "Center"] < tol_speed
    hudd = forward & spine & speed
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    return hudd

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def following_path(
    distance_dframe: pd.DataFrame,
    position_dframe: pd.DataFrame,
    follower: str,
    followed: str,
    frames: int = 20,
    tol: float = 0,
) -> np.array:
    """For multi animal videos only. Returns True if 'follower' is closer than tol to the path that
    followed has walked over the last specified number of frames

        Parameters:
            - distance_dframe (pandas.DataFrame): distances between bodyparts; generated by the preprocess module
            - position_dframe (pandas.DataFrame): position of bodyparts; generated by the preprocess module
            - follower (str) identifier for the animal who's following
            - followed (str) identifier for the animal who's followed
            - frames (int) frames in which to track whether the process consistently occurs,
            - tol (float) Maximum distance for which True is returned

        Returns:
            - follow (np.array): boolean sequence, True if conditions are fulfilled, False otherwise"""
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    # Check that follower is close enough to the path that followed has passed though in the last frames
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    shift_dict = {
        i: position_dframe[followed + "_Tail_base"].shift(i) for i in range(frames)
    }
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    dist_df = pd.DataFrame(
        {
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            i: np.linalg.norm(
                position_dframe[follower + "_Nose"] - shift_dict[i], axis=1
            )
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            for i in range(frames)
        }
    )

    # Check that the animals are oriented follower's nose -> followed's tail
    right_orient1 = (
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        distance_dframe[tuple(sorted([follower + "_Nose", followed + "_Tail_base"]))]
        < distance_dframe[
            tuple(sorted([follower + "_Tail_base", followed + "_Tail_base"]))
        ]
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    )

    right_orient2 = (
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        distance_dframe[tuple(sorted([follower + "_Nose", followed + "_Tail_base"]))]
        < distance_dframe[tuple(sorted([follower + "_Nose", followed + "_Nose"]))]
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    )

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    follow = np.all(
        np.array([(dist_df.min(axis=1) < tol), right_orient1, right_orient2]), axis=0,
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    )

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    return follow

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def single_behaviour_analysis(
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    behaviour_name: str,
    treatment_dict: dict,
    behavioural_dict: dict,
    plot: int = 0,
    stat_tests: bool = True,
    save: str = None,
    ylim: float = None,
) -> list:
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    """Given the name of the behaviour, a dictionary with the names of the groups to compare, and a dictionary
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       with the actual tags, outputs a box plot and a series of significance tests amongst the groups

        Parameters:
            - behaviour_name (str): name of the behavioural trait to analize
            - treatment_dict (dict): dictionary containing video names as keys and experimental conditions as values
            - behavioural_dict (dict): tagged dictionary containing video names as keys and annotations as values
            - plot (int): Silent if 0; otherwise, indicates the dpi of the figure to plot
            - stat_tests (bool): performs FDR corrected Mann-U non-parametric tests among all groups if True
            - save (str): Saves the produced figure to the specified file
            - ylim (float): y-limit for the boxplot. Ignored if plot == False

        Returns:
            - beh_dict (dict): dictionary containing experimental conditions as keys and video names as values
            - stat_dict (dict): dictionary containing condition pairs as keys and stat results as values"""
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    beh_dict = {condition: [] for condition in treatment_dict.keys()}

    for condition in beh_dict.keys():
        for ind in treatment_dict[condition]:
            beh_dict[condition].append(
                np.sum(behavioural_dict[ind][behaviour_name])
                / len(behavioural_dict[ind][behaviour_name])
            )

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    return_list = [beh_dict]
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    if plot > 0:
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        fig, ax = plt.subplots(dpi=plot)
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        sns.boxplot(
            list(beh_dict.keys()), list(beh_dict.values()), orient="vertical", ax=ax
        )

        ax.set_title("{} across groups".format(behaviour_name))
        ax.set_ylabel("Proportion of frames")

        if ylim is not None:
            ax.set_ylim(ylim)
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        if save is not None:
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            plt.savefig(save)

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        return_list.append(ax)
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    if stat_tests:
        stat_dict = {}
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        for i in combinations(treatment_dict.keys(), 2):
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            # Solves issue with automatically generated examples
            if (
                beh_dict[i[0]] == beh_dict[i[1]]
                or np.var(beh_dict[i[0]]) == 0
                or np.var(beh_dict[i[1]]) == 0
            ):
                stat_dict[i] = "Identical sources. Couldn't run"
            else:
                stat_dict[i] = stats.mannwhitneyu(
                    beh_dict[i[0]], beh_dict[i[1]], alternative="two-sided"
                )
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        return_list.append(stat_dict)
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    return return_list
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def max_behaviour(
    behaviour_dframe: pd.DataFrame, window_size: int = 10, stepped: bool = False
) -> np.array:
    """Returns the most frequent behaviour in a window of window_size frames

        Parameters:
                - behaviour_dframe (pd.DataFrame): boolean matrix containing occurrence
                of tagged behaviours per frame in the video
                - window_size (int): size of the window to use when computing
                the maximum behaviour per time slot
                - stepped (bool): sliding windows don't overlap if True. False by default

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        Returns:
            - max_array (np.array): string array with the most common behaviour per instance
            of the sliding window"""
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    speeds = [col for col in behaviour_dframe.columns if "speed" in col.lower()]

    behaviour_dframe = behaviour_dframe.drop(speeds, axis=1).astype("float")
    win_array = behaviour_dframe.rolling(window_size, center=True).sum()
    if stepped:
        win_array = win_array[::window_size]
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    max_array = win_array[1:].idxmax(axis=1)

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    return np.array(max_array)


# MACHINE LEARNING FUNCTIONS #
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def gmm_compute(x: np.array, n_components: int, cv_type: str) -> list:
    """Fits a Gaussian Mixture Model to the provided data and returns evaluation metrics.

        Parameters:
            - x (numpy.array): data matrix to train the model
            - n_components (int): number of Gaussian components to use
            - cv_type (str): covariance matrix type to use.
            Must be one of "spherical", "tied", "diag", "full"

        Returns:
            - gmm_eval (list): model and associated BIC for downstream selection
    """

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    gmm = mixture.GaussianMixture(
        n_components=n_components,
        covariance_type=cv_type,
        max_iter=100000,
        init_params="kmeans",
    )
    gmm.fit(x)
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    gmm_eval = [gmm, gmm.bic(x)]
    return gmm_eval


def gmm_model_selection(
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    x: pd.DataFrame,
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    n_components_range: range,
    part_size: int,
    n_runs: int = 100,
    n_cores: int = False,
    cv_types: Tuple = ("spherical", "tied", "diag", "full"),
) -> Tuple[List[list], List[np.ndarray], Union[int, Any]]:
    """Runs GMM clustering model selection on the specified X dataframe, outputs the bic distribution per model,
       a vector with the median BICs and an object with the overall best model
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        Parameters:
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            - x (pandas.DataFrame): data matrix to train the models
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            - n_components_range (range): generator with numbers of components to evaluate
            - n_runs (int): number of bootstraps for each model
            - part_size (int): size of bootstrap samples for each model
            - n_cores (int): number of cores to use for computation
            - cv_types (tuple): Covariance Matrices to try. All four available by default
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        Returns:
            - bic (list): All recorded BIC values for all attempted parameter combinations
            (useful for plotting)
            - m_bic(list): All minimum BIC values recorded throughout the process
            (useful for plottinh)
            - best_bic_gmm (sklearn.GMM): unfitted version of the best found model
    """
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    # Set the default of n_cores to the most efficient value
    if not n_cores:
        n_cores = min(multiprocessing.cpu_count(), n_runs)

    bic = []
    m_bic = []
    lowest_bic = np.inf
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    best_bic_gmm = 0
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    pbar = tqdm(total=len(cv_types) * len(n_components_range))

    for cv_type in cv_types:

        for n_components in n_components_range:

            res = Parallel(n_jobs=n_cores, prefer="threads")(
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                delayed(gmm_compute)(
                    x.sample(part_size, replace=True), n_components, cv_type
                )
                for _ in range(n_runs)
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            )
            bic.append([i[1] for i in res])

            pbar.update(1)
            m_bic.append(np.median([i[1] for i in res]))
            if m_bic[-1] < lowest_bic:
                lowest_bic = m_bic[-1]
                best_bic_gmm = res[0][0]

    return bic, m_bic, best_bic_gmm

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# RESULT ANALYSIS FUNCTIONS #
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def cluster_transition_matrix(
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    cluster_sequence: np.array,
    nclusts: int,
    autocorrelation: bool = True,
    return_graph: bool = False,
) -> Tuple[Union[nx.Graph, Any], np.ndarray]:
    """Computes the transition matrix between clusters and the autocorrelation in the sequence.

        Parameters:
            - cluster_sequence (numpy.array):
            - nclusts (int):
            - autocorrelation (bool):
            - return_graph (bool):

        Returns:
            - trans_normed (numpy.array / networkx.Graph:
            - autocorr (numpy.array):
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    """

    # Stores all possible transitions between clusters
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    clusters = [str(i) for i in range(nclusts)]
    cluster_sequence = cluster_sequence.astype(str)

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    trans = {t: 0 for t in product(clusters, clusters)}
    k = len(clusters)

    # Stores the cluster sequence as a string
    transtr = "".join(list(cluster_sequence))

    # Assigns to each transition the number of times it occurs in the sequence
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    for t in trans.keys():
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        trans[t] = len(re.findall("".join(t), transtr, overlapped=True))

    # Normalizes the counts to add up to 1 for each departing cluster
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    trans_normed = np.zeros([k, k]) + 1e-5
    for t in trans.keys():
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        trans_normed[int(t[0]), int(t[1])] = np.round(
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            trans[t]
            / (sum({i: j for i, j in trans.items() if i[0] == t[0]}.values()) + 1e-5),
            3,
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        )

    # If specified, returns the transition matrix as an nx.Graph object
    if return_graph:
        trans_normed = nx.Graph(trans_normed)

    if autocorrelation:
        cluster_sequence = list(map(int, cluster_sequence))
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        autocorr = np.corrcoef(cluster_sequence[:-1], cluster_sequence[1:])
        return trans_normed, autocorr
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    return trans_normed

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# MAIN BEHAVIOUR TAGGING FUNCTION #


def rule_based_tagging(
    tracks: List,
    videos: List,
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    coordinates: Coordinates,
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    vid_index: int,
    animal_ids: List = None,
    show: bool = False,
    save: bool = False,
    fps: float = 25.0,
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    speed_pause: int = 10,
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    frame_limit: float = np.inf,
    recog_limit: int = 1,
    path: str = os.path.join("./"),
    arena_type: str = "circular",
    classifiers: Dict = None,
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    close_contact_tol: int = 15,
    side_contact_tol: int = 15,
    follow_frames: int = 20,
    follow_tol: int = 20,
    huddle_forward: int = 15,
    huddle_spine: int = 10,
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    huddle_speed: int = 1,
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) -> pd.DataFrame:
    """Outputs a dataframe with the motives registered per frame."""
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    vid_name = re.findall("(.*?)_", tracks[vid_index])[0]

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    coords = coordinates.get_coords()[vid_name]
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    speeds = coordinates.get_coords(speed=1)[vid_name]
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    arena_abs = coordinates.get_arenas[1][0]
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    arena, h, w = recognize_arena(videos, vid_index, path, recog_limit, arena_type)

    # Dictionary with motives per frame
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    tag_dict = {}
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    if animal_ids:
        # Define behaviours that can be computed on the fly from the distance matrix
        tag_dict["nose2nose"] = smooth_boolean_array(
            close_single_contact(
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                coords,
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                animal_ids[0] + "_Nose",
                animal_ids[1] + "_Nose",
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                close_contact_tol,
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                arena_abs,
                arena[2],
            )
        )
        tag_dict[animal_ids[0] + "_nose2tail"] = smooth_boolean_array(
            close_single_contact(
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                animal_ids[0] + "_Nose",
                animal_ids[1] + "_Tail_base",
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                arena_abs,
                arena[2],
            )
        )
        tag_dict[animal_ids[1] + "_nose2tail"] = smooth_boolean_array(
            close_single_contact(
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                coords,
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                animal_ids[1] + "_Nose",
                animal_ids[0] + "_Tail_base",
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                close_contact_tol,
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                arena_abs,
                arena[2],
            )
        )
        tag_dict["sidebyside"] = smooth_boolean_array(
            close_double_contact(
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                animal_ids[0] + "_Nose",
                animal_ids[0] + "_Tail_base",
                animal_ids[1] + "_Nose",
                animal_ids[1] + "_Tail_base",
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                side_contact_tol,
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                rev=False,
                arena_abs=arena_abs,
                arena_rel=arena[2],
            )
        )
        tag_dict["sidereside"] = smooth_boolean_array(
            close_double_contact(
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                animal_ids[0] + "_Nose",
                animal_ids[0] + "_Tail_base",
                animal_ids[1] + "_Nose",
                animal_ids[1] + "_Tail_base",
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                rev=True,
                arena_abs=arena_abs,
                arena_rel=arena[2],
            )
        )
        for _id in animal_ids:
            tag_dict[_id + "_following"] = smooth_boolean_array(
                following_path(
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                    coords[vid_name],
                    coords,
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                    follower=_id,
                    followed=[i for i in animal_ids if i != _id][0],
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                    frames=follow_frames,
                    tol=follow_tol,
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                )
            )
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            tag_dict[_id + "_climbing"] = smooth_boolean_array(
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                pd.Series(
                    (
                        spatial.distance.cdist(
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                        )
                        > (w / 200 + arena[2])
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                    ).reshape(coords.shape[0]),
                    index=coords.index,
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                ).astype(bool)
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            tag_dict[_id + "_speed"] = speeds[_id + "_speed"]
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            tag_dict[_id + "_huddle"] = smooth_boolean_array(
                huddle(coords, speeds, huddle_forward, huddle_spine, huddle_speed)
            )
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    else:
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        tag_dict["climbing"] = smooth_boolean_array(
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                (
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                ).reshape(coords.shape[0]),
                index=coords.index,
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        )
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        tag_dict["speed"] = speeds["Center"]
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        tag_dict["huddle"] = smooth_boolean_array(
            huddle(coords, speeds, huddle_forward, huddle_spine, huddle_speed)
        )
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    if any([show, save]):

        cap = cv2.VideoCapture(os.path.join(path, videos[vid_index]))
        # Keep track of the frame number, to align with the tracking data
        fnum = 0
        writer = None
        frame_speeds = {_id: -np.inf for _id in animal_ids} if animal_ids else -np.inf

        # Loop over the frames in the video
        pbar = tqdm(total=min(coords.shape[0] - recog_limit, frame_limit))
        while cap.isOpened() and fnum < frame_limit:

            ret, frame = cap.read()
            # if frame is read correctly ret is True
            if not ret:
                print("Can't receive frame (stream end?). Exiting ...")
                break

            font = cv2.FONT_HERSHEY_COMPLEX_SMALL

            # Label positions
            downleft = (int(w * 0.3 / 10), int(h / 1.05))
            downright = (int(w * 6.5 / 10), int(h / 1.05))
            upleft = (int(w * 0.3 / 10), int(h / 20))
            upright = (int(w * 6.3 / 10), int(h / 20))

            # Capture speeds
            try:
                if list(frame_speeds.values())[0] == -np.inf or fnum % speed_pause == 0:
                    for _id in animal_ids:
                        frame_speeds[_id] = speeds[_id + "_Center"][fnum]
            except AttributeError:
                if frame_speeds == -np.inf or fnum % speed_pause == 0:
                    frame_speeds = speeds["Center"][fnum]

            # Display all annotations in the output video
            if animal_ids:
                if tag_dict["nose2nose"][fnum] and not tag_dict["sidebyside"][fnum]:
                    cv2.putText(
                        frame,
                        "Nose-Nose",
                        (
                            downleft
                            if frame_speeds[animal_ids[0]] > frame_speeds[animal_ids[1]]
                            else downright
                        ),
                        font,
                        1,
                        (255, 255, 255),
                        2,
                    )
                if (
                    tag_dict[animal_ids[0] + "_nose2tail"][fnum]
                    and not tag_dict["sidereside"][fnum]
                ):
                    cv2.putText(
                        frame, "Nose-Tail", downleft, font, 1, (255, 255, 255), 2
                    )
                if (
                    tag_dict[animal_ids[1] + "_nose2tail"][fnum]
                    and not tag_dict["sidereside"][fnum]
                ):
                    cv2.putText(
                        frame, "Nose-Tail", downright, font, 1, (255, 255, 255), 2
                    )
                if tag_dict["sidebyside"][fnum]:
                    cv2.putText(
                        frame,
                        "Side-side",
                        (
                            downleft
                            if frame_speeds[animal_ids[0]] > frame_speeds[animal_ids[1]]
                            else downright
                        ),
                        font,
                        1,
                        (255, 255, 255),
                        2,
                    )
                if tag_dict["sidereside"][fnum]:
                    cv2.putText(
                        frame,
                        "Side-Rside",
                        (
                            downleft
                            if frame_speeds[animal_ids[0]] > frame_speeds[animal_ids[1]]
                            else downright
                        ),
                        font,
                        1,
                        (255, 255, 255),
                        2,
                    )
                for _id, down_pos, up_pos in zip(
                    animal_ids, [downleft, downright], [upleft, upright]
                ):
                    if tag_dict[_id + "_climbing"][fnum]:
                        cv2.putText(
                            frame, "Climbing", down_pos, font, 1, (255, 255, 255), 2
                        )
                    if (
                        tag_dict[_id + "_huddle"][fnum]
                        and not tag_dict[_id + "_climbing"][fnum]
                    ):
                        cv2.putText(
                            frame, "Huddling", down_pos, font, 1, (255, 255, 255), 2
                        )
                    if (
                        tag_dict[_id + "_following"][fnum]
                        and not tag_dict[_id + "_climbing"][fnum]
                    ):
                        cv2.putText(
                            frame,
                            "*f",
                            (int(w * 0.3 / 10), int(h / 10)),
                            font,
                            1,
                            (
                                (150, 150, 255)
                                if frame_speeds[animal_ids[0]]
                                > frame_speeds[animal_ids[1]]
                                else (150, 255, 150)
                            ),
                            2,
                        )
                    cv2.putText(
                        frame,
                        _id + ": " + str(np.round(frame_speeds[_id], 2)) + " mmpf",
                        (up_pos[0] - 20, up_pos[1]),
                        font,
                        1,
                        (
                            (150, 150, 255)
                            if frame_speeds[_id] == max(list(frame_speeds.values()))
                            else (150, 255, 150)
                        ),
                        2,
                    )

            else:
                if tag_dict["climbing"][fnum]:
                    cv2.putText(
                        frame, "Climbing", downleft, font, 1, (255, 255, 255), 2
                    )
                if tag_dict["huddle"][fnum] and not tag_dict["climbing"][fnum]:
                    cv2.putText(frame, "huddle", downleft, font, 1, (255, 255, 255), 2)
                cv2.putText(
                    frame,
                    str(np.round(frame_speeds, 2)) + " mmpf",
                    upleft,
                    font,
                    1,
                    (
                        (150, 150, 255)
                        if huddle_speed > frame_speeds
                        else (150, 255, 150)
                    ),
                    2,
1188
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                )

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            if show:
                cv2.imshow("frame", frame)

                if cv2.waitKey(1) == ord("q"):
                    break

            if save:

                if writer is None:
                    # Define the codec and create VideoWriter object.The output is stored in 'outpy.avi' file.
                    # Define the FPS. Also frame size is passed.
                    writer = cv2.VideoWriter()
                    writer.open(
                        re.findall("(.*?)_", tracks[vid_index])[0] + "_tagged.avi",
                        cv2.VideoWriter_fourcc(*"MJPG"),
                        fps,
                        (frame.shape[1], frame.shape[0]),
                        True,
                    )

                writer.write(frame)

            pbar.update(1)
            fnum += 1

        cap.release()
        cv2.destroyAllWindows()
1217

1218
    tag_df = pd.DataFrame(tag_dict)
1219

1220
    return tag_df
1221
1222


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# TODO:
#    - Add sequence plot to single_behaviour_analysis (show how the condition varies across a specified time window)
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#    - Add digging to rule_based_tagging
#    - Add center to rule_based_tagging
#    - Check for features requested by Joeri