Составьте двумерный гауссовский язык, используя Matplotlib

Question

Код ниже является двумерным гауссовым распределением. Распределение производится путем корректировки COV matrix для учета конкретных переменных. В частности, каждая координата XY применяется с радиусом ([_Rad]). Затем COV matrix корректируется с помощью коэффициента scaling ([_Scaling]), чтобы расширить радиус в x-direction и сузить в y-direction. Направление этого измеряется с помощью rotation angle ([_Rotation]). Выход выражается в виде функции probability.

Вопрос. Радиус должен охватывать только заданную область. Когда я пытаюсь перевести сценарий в группу координат (ссылка внизу), вероятность распространяется на весь кадр. Вы можете видеть мерцающих цветов, что указывает на переменную вероятность. Но радиус координат колеблется в пределах 8-25. Эта область должна быть фиксированной или привязанной. Не следует расширять весь кадр

Я пытался исправить областей как 0.5, но это не проблема. Я надеюсь изменить код так, чтобы на вероятность влиял только предоставленный радиус.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import scipy.stats as sts
from matplotlib.animation import FuncAnimation

#Create data limits used for the animation frame. Bit rough
DATA_LIMITS = [-100, 100]

def datalimits(*data):
    return DATA_LIMITS  # dmin - spad, dmax + spad

#This is the function used for the rotation matrix
def rot(theta):
    theta = np.deg2rad(theta)
    return np.array([
        [np.cos(theta), -np.sin(theta)],
        [np.sin(theta), np.cos(theta)]
    ])

#Used for the covariance matrix
def getcov(radius=1, scale=1, theta=0):
    cov = np.array([
        [radius*(scale + 1), 0],
        [0, radius/(scale + 1)]
    ])

    r = rot(theta)
    return r @ cov @ r.T

#This is the multivariate probability distribution function
def mvpdf(x, y, xlim, ylim, radius=1, velocity=0, scale=0, theta=0):

    X,Y = np.meshgrid(np.linspace(*xlim), np.linspace(*ylim))

    XY = np.stack([X, Y], 2)

    x,y = rot(theta) @ (velocity/2, 0) + (x, y)

    cov = getcov(radius=radius, scale=scale, theta=theta)

    PDF = sts.multivariate_normal([x, y], cov).pdf(XY)

    return X, Y, PDF

#Used for the animation function
def mvpdfs(xs, ys, xlim, ylim, radius=None, velocity=None, scale=None, theta=None):
    PDFs = []
    for i,(x,y) in enumerate(zip(xs,ys)):
        kwargs = {
            'radius': radius[i] if radius is not None else 1,
            'velocity': velocity[i] if velocity is not None else 0,
            'scale': scale[i] if scale is not None else 0,
            'theta': theta[i] if theta is not None else 0,
            'xlim': xlim,
            'ylim': ylim
        }
        X, Y, PDF = mvpdf(x, y,**kwargs)
        PDFs.append(PDF)

    return X, Y, np.sum(PDFs, axis=0)

fig, ax = plt.subplots(figsize = (10,4))
ax.set_xlim(DATA_LIMITS)
ax.set_ylim(DATA_LIMITS)

#animate the scatter points
line_a, = ax.plot([], [], '.', c='red', alpha = 0.5, markersize=5, animated=True)
line_b, = ax.plot([], [], '.', c='blue', alpha = 0.5, markersize=5, animated=True)
cfs = None

def plotmvs(tdf, xlim=None, ylim=None, fig=fig, ax=ax):
    global cfs  
    if cfs:
        for tp in cfs.collections:

            tp.remove()

    df = tdf[1]

    if xlim is None: xlim = datalimits(df['X'])
    if ylim is None: ylim = datalimits(df['Y'])

    PDFs = []

    for (group, gdf), group_line in zip(df.groupby('group'), (line_a, line_b)):

        # Update the scatter line data
        group_line.set_data(*gdf[['X','Y']].values.T)

        kwargs = {
            'radius': gdf['Radius'].values if 'Radius' in gdf else None,
            'velocity': gdf['Velocity'].values if 'Velocity' in gdf else None,
            'scale': gdf['Scaling'].values if 'Scaling' in gdf else None,
            'theta': gdf['Rotation'].values if 'Rotation' in gdf else None,
            'xlim': xlim,
            'ylim': ylim
        }
        X, Y, PDF = mvpdfs(gdf['X'].values, gdf['Y'].values, **kwargs)
        PDFs.append(PDF)

    #I've played around with these functions a bit. This is 
    #where I think the probability subtraction from both teams results
    #in the uneven or _flickering_ background probability
    PDF = PDFs[0] - PDFs[1]
    normPDF = PDF - PDF.min()
    normPDF = normPDF / normPDF.max()

    #This function attempted to _fix_ the background
    #to 0.5 or neutral but you can still see the areas
    #not covered by scatter points is still a different
    #probability 
    #normPDF = PDF * .5/max(PDF.max(), -PDF.min()) + .5

    #create the contour
    cfs = ax.contourf(X, Y, normPDF, cmap='viridis', alpha = 0.8,
    levels=10)

    return cfs.collections + [line_a, line_b]

#This big data frame houses the XY coordinates, Radius, Scaling factor
#Rotation for each respective frame
n = 10
time = range(n) 
d = ({
     'A1_X' :    [13.3,13.16,12.99,12.9,12.79,12.56,12.32,12.15,11.93,11.72],
     'A1_Y' :    [26.12,26.44,26.81,27.18,27.48,27.82,28.13,28.37,28.63,28.93],
     'A2_X' :    [6.97,6.96,7.03,6.98,6.86,6.76,6.55,6.26,6.09,5.9],
     'A2_Y' :    [10.92,10.83,10.71,10.52,10.22,10.02,9.86,9.7,9.54,9.37],
     'A3_X' :    [-31.72,-31.93,-32.18,-32.43,-32.7,-32.89,-33.15,-33.51,-33.84,-34.17],
     'A3_Y' :    [21.25,21.52,21.7,21.98,22.25,22.47,22.7,22.95,23.2,23.4],
     'A4_X' :    [37.54,37.42,37.3,37.14,36.97,36.77,36.56,36.37,36.13,35.89],
     'A4_Y' :    [7.31,7.35,7.38,7.43,7.5,7.58,7.65,7.68,7.69,7.69],
     'A5_X' :    [-5.37,-5.31,-5.28,-5.34,-5.41,-5.42,-5.68,-5.84,-6.1,-6.31],
     'A5_Y' :    [-5.42,-5.7,-6,-6.15,-6.41,-6.67,-6.88,-7.11,-7.33,-7.49],
     'A6_X' :    [-3.33,-3.15,-2.97,-2.94,-2.88,-2.79,-2.69,-2.66,-2.54,-2.67],
     'A6_Y' :    [13.69,13.86,14.09,14.34,14.73,15.01,15.38,15.83,16.15,16.73],
     'A7_X' :    [-4.4,-4.56,-4.83,-5.02,-5.18,-5.51,-5.81,-6.03,-6.31,-6.7],
     'A7_Y' :    [21.34,21.53,21.69,21.89,22.03,22.35,22.63,22.91,23.14,23.34],
     'A8_X' :    [-14.89,-15.12,-15.26,-15.52,-15.96,-16.37,-16.7,-17.08,-17.55,-17.95],
     'A8_Y' :    [3.7,3.41,3.14,2.84,2.58,2.26,2.07,1.78,1.45,1.23],
     'A9_X' :    [-51.92,-52.04,-52.15,-52.26,-52.36,-52.54,-52.76,-52.98,-53.17,-53.4],
     'A9_Y' :    [16.45,16.44,16.5,16.61,16.59,16.52,16.52,16.43,16.45,16.49],
     'A10_X' :   [-15.18,-15.18,-15.18,-15.18,-15.18,-15.18,-15.18,-15.18,-15.18,-15.18],
     'A10_Y' :   [26.02,26.02,26.02,26.02,26.02,26.02,26.02,26.02,26.02,26.02],
     'A11_X' :   [15.5,15.22,14.9,14.59,14.36,14.08,13.74,13.43,13.13,12.82],
     'A11_Y' :   [7.25,7.36,7.51,7.61,7.72,7.88,8.05,8.18,8.5,8.8],
     'A12_X' :   [-5.36,-5.35,-5.33,-5.28,-5.18,-5.12,-4.99,-4.83,-4.8,-4.71],
     'A12_Y' :   [19.02,18.77,18.56,18.41,18.22,18.03,17.9,17.72,17.69,17.58],
     'A13_X' :   [-45.76,-45.91,-46.13,-46.41,-46.62,-46.82,-47.07,-47.35,-47.61,-47.87],
     'A13_Y' :   [18.9,18.96,19.03,19.12,19.12,19.18,19.31,19.42,19.45,19.53],
     'A14_X' :   [-10.28,-10.3,-10.23,-10.36,-10.53,-10.69,-10.84,-10.95,-11.17,-11.37],
     'A14_Y' :   [18.25,18.42,18.56,18.73,18.86,18.98,19.02,19.19,19.3,19.46],
     'A15_X' :   [29.77,29.6,29.45,29.24,28.9,28.68,28.42,28.06,27.75,27.49],
     'A15_Y' :   [11.59,11.38,11.19,11.02,10.85,10.71,10.58,10.39,10.18,9.98],
     'B1_X' :    [38.35,38.1,37.78,37.55,37.36,37.02,36.78,36.46,36.21,35.79],
     'B1_Y' :    [12.55,12.58,12.58,12.55,12.5,12.47,12.43,12.48,12.44,12.44],
     'B2_X' :    [14.6,14.38,14.16,13.8,13.45,13.11,12.71,12.3,12.06,11.61],
     'B2_Y' :    [4.66,4.44,4.24,4.1,4.01,3.84,3.67,3.56,3.44,3.47],
     'B3_X' :    [-12.16,-12.35,-12.53,-12.73,-12.91,-13.01,-13.24,-13.44,-13.68,-13.93],
     'B3_Y' :    [20.07,20.26,20.34,20.5,20.62,20.69,20.72,20.73,20.63,20.58],
     'B4_X' :    [-3.27,-3.1,-2.83,-2.49,-2.34,-2.13,-1.97,-1.8,-1.67,-1.59],
     'B4_Y' :    [-6.25,-6.37,-6.52,-6.61,-6.76,-6.89,-7.01,-7.1,-7.13,-7.33],
     'B5_X' :    [-21.47,-21.63,-21.84,-22.03,-22.28,-22.53,-22.77,-22.99,-23.27,-23.52],
     'B5_Y' :    [8.94,8.87,8.79,8.68,8.61,8.56,8.48,8.35,8.22,8.12],
     'B6_X' :    [-13.81,-13.83,-13.91,-14.02,-14.15,-14.31,-14.54,-14.77,-14.96,-15.24],
     'B6_Y' :    [25.45,25.81,25.94,26.26,26.56,26.75,26.92,27.07,27.22,27.25],
     'B7_X' :    [-6.28,-6.33,-6.43,-6.44,-6.61,-6.8,-7.02,-7.22,-7.46,-7.7],
     'B7_Y' :    [13.82,13.6,13.43,13.26,13.12,13.09,13.07,13.14,13.19,13.32],
     'B8_X' :    [28.39,28.09,27.91,27.76,27.4,27.14,26.91,26.69,26.34,26.1],
     'B8_Y' :    [8.36,8.2,8.13,8.1,8.01,7.94,7.84,7.76,7.8,7.84],
     'B9_X' :    [-7.55,-7.54,-7.57,-7.65,-7.77,-7.87,-8.01,-8.06,-8.06,-8.06],
     'B9_Y' :    [17.98,17.94,17.97,18.02,18.05,18.09,18.07,18.02,17.97,17.92],
     'B10_X' :   [-32.36,-32.63,-32.92,-33.25,-33.54,-33.78,-34.13,-34.37,-34.69,-35.01],
     'B10_Y' :   [13.27,13.48,13.67,13.9,14.14,14.48,14.76,15.05,15.31,15.62],
     'B11_X' :   [-44.08,-44.19,-44.33,-44.47,-44.64,-44.78,-44.92,-45.16,-45.36,-45.56],
     'B11_Y' :   [15.9,16.09,16.22,16.38,16.49,16.63,16.7,16.79,16.85,16.94],
     'B12_X' :   [-16.47,-16.67,-16.76,-16.86,-16.99,-17.24,-17.48,-17.76,-17.98,-18.29],
     'B12_Y' :   [29.76,29.96,30.07,30.3,30.45,30.59,30.61,30.67,30.62,30.66],
     'B13_X' :   [-50.27,-50.38,-50.55,-50.74,-50.92,-51.02,-51.13,-51.3,-51.46,-51.65],
     'B13_Y' :   [16.31,16.3,16.31,16.33,16.36,16.28,16.25,16.22,16.21,16.27],
     'B14_X' :   [-15.55,-15.81,-16.05,-16.35,-16.67,-16.96,-17.35,-17.76,-18.09,-18.6],
     'B14_Y' :   [8.56,8.53,8.54,8.57,8.62,8.6,8.58,8.49,8.44,8.55],
     'B15_X' :   [9.79,9.47,9.2,8.77,8.41,8.07,7.65,7.19,6.76,6.42],
     'B15_Y' :   [27.61,27.79,27.99,28.16,28.37,28.53,28.68,28.82,28.9,29.06],
     'A1_Radius' :  [10.33,10.34,10.34,10.37,10.38,10.37,10.36,10.36,10.35,10.35],
     'A2_Radius' :  [9.05,9.06,9.07,9.08,9.09,9.09,9.08,9.06,9.05,9.04],
     'A3_Radius' :  [13.04,13.15,13.29,13.44,13.6,13.72,13.88,14.1,14.31,14.52],
     'A4_Radius' :  [25,25,25,25,25,25,25,25,25,24.81],
     'A5_Radius' :  [11.24,11.33,11.44,11.49,11.59,11.68,11.77,11.86,11.95,12.02],
     'A6_Radius' :  [8.19,8.19,8.18,8.17,8.15,8.14,8.13,8.11,8.11,8.09],
     'A7_Radius' :  [8.18,8.19,8.2,8.21,8.22,8.25,8.27,8.29,8.31,8.33],
     'A8_Radius' :  [9.71,9.79,9.85,9.94,10.05,10.17,10.26,10.38,10.53,10.65],
     'A9_Radius' :  [25,25,25,25,25,25,25,25,25,25],
     'A10_Radius' : [9.08,9.08,9.08,9.08,9.08,9.08,9.08,9.08,9.08,9.08],
     'A11_Radius' : [11.12,11.03,10.91,10.81,10.74,10.64,10.54,10.45,10.34,10.23],
     'A12_Radius' : [8.07,8.06,8.05,8.05,8.04,8.03,8.02,8.01,8.01,8.01],
     'A13_Radius' : [24.16,24.36,24.62,24.98,25,25,25,25,25,25],
     'A14_Radius' : [8.3,8.3,8.3,8.31,8.32,8.33,8.34,8.35,8.37,8.39],
     'A15_Radius' : [17.86,17.75,17.66,17.52,17.28,17.14,16.96,16.73,16.53,16.38],
     'B1_Radius' :  [25,25,25,25,25,25,24.84,24.45,24.15,23.65],
     'B2_Radius' :  [11.3,11.28,11.26,11.19,11.11,11.06,10.99,10.91,10.88,10.77],
     'B3_Radius' :  [8.46,8.48,8.5,8.52,8.54,8.55,8.57,8.59,8.61,8.63],
     'B4_Radius' :  [11.54,11.59,11.65,11.69,11.75,11.81,11.86,11.9,11.92,12],
     'B5_Radius' :  [10.08,10.13,10.18,10.24,10.3,10.37,10.43,10.5,10.59,10.66],
     'B6_Radius' :  [8.89,8.92,8.94,8.98,9.02,9.06,9.1,9.14,9.18,9.21],
     'B7_Radius' :  [8.19,8.2,8.22,8.23,8.24,8.24,8.25,8.25,8.26,8.26],
     'B8_Radius' :  [17.34,17.15,17.03,16.93,16.69,16.52,16.38,16.25,16.01,15.84],
     'B9_Radius' :  [8.13,8.13,8.14,8.14,8.15,8.15,8.16,8.16,8.16,8.16],
     'B10_Radius' : [13.38,13.5,13.64,13.8,13.94,14.05,14.23,14.35,14.53,14.7],
     'B11_Radius' : [22.24,22.35,22.5,22.65,22.84,23,23.16,23.44,23.67,23.9],
     'B12_Radius' : [9.68,9.74,9.77,9.82,9.86,9.92,9.96,10.02,10.05,10.1],
     'B13_Radius' : [25,25,25,25,25,25,25,25,25,25],
     'B14_Radius' : [9.17,9.2,9.23,9.26,9.3,9.34,9.4,9.47,9.52,9.59],
     'B15_Radius' : [9.8,9.76,9.74,9.7,9.67,9.63,9.59,9.55,9.5,9.48],
     'A1_Scaling' : [0,0.07,0.1,0.09,0.06,0.1,0.09,0.05,0.07,0.08],
     'A2_Scaling' : [0,0.01,0.01,0.02,0.06,0.03,0.04,0.07,0.03,0.04],
     'A3_Scaling' : [0,0.07,0.06,0.08,0.09,0.05,0.07,0.11,0.1,0.09],
     'A4_Scaling' : [0,0.01,0.01,0.02,0.02,0.03,0.03,0.02,0.03,0.04],
     'A5_Scaling' : [0,0.05,0.05,0.02,0.04,0.04,0.07,0.05,0.07,0.04],
     'A6_Scaling' : [0,0.04,0.05,0.04,0.09,0.05,0.09,0.12,0.07,0.21],
     'A7_Scaling' : [0,0.04,0.06,0.05,0.03,0.13,0.1,0.07,0.08,0.11],
     'A8_Scaling' : [0,0.08,0.06,0.09,0.16,0.16,0.08,0.14,0.19,0.12],
     'A9_Scaling' : [0,0.01,0.01,0.02,0.01,0.02,0.03,0.03,0.02,0.03],
     'A10_Scaling' :    [0,0,0,0,0,0,0,0,0,0],
     'A11_Scaling' :    [0,0.05,0.07,0.06,0.04,0.06,0.09,0.06,0.11,0.11],
     'A12_Scaling' :    [0,0.04,0.03,0.02,0.02,0.02,0.02,0.03,0,0.01],
     'A13_Scaling' :    [0,0.02,0.03,0.05,0.03,0.03,0.05,0.05,0.04,0.04],
     'A14_Scaling' :    [0,0.02,0.02,0.03,0.03,0.02,0.01,0.03,0.03,0.04],
     'A15_Scaling' :    [0,0.04,0.03,0.04,0.08,0.04,0.05,0.1,0.08,0.06],
     'B1_Scaling' : [0,0.04,0.06,0.03,0.02,0.07,0.04,0.06,0.04,0.11],
     'B2_Scaling' : [0,0.06,0.05,0.09,0.08,0.08,0.11,0.1,0.04,0.12],
     'B3_Scaling' : [0,0.04,0.02,0.04,0.03,0.01,0.03,0.02,0.04,0.04],
     'B4_Scaling' : [0,0.03,0.06,0.07,0.03,0.03,0.02,0.02,0.01,0.03],
     'B5_Scaling' : [0,0.02,0.03,0.03,0.04,0.04,0.04,0.04,0.06,0.04],
     'B6_Scaling' : [0,0.08,0.01,0.07,0.06,0.04,0.05,0.05,0.04,0.05],
     'B7_Scaling' : [0,0.03,0.02,0.02,0.03,0.02,0.03,0.02,0.04,0.04],
     'B8_Scaling' : [0,0.07,0.02,0.01,0.08,0.04,0.04,0.03,0.07,0.04],
     'B9_Scaling' : [0,0,0,0.01,0.01,0.01,0.01,0,0,0],
     'B10_Scaling' :    [0,0.07,0.07,0.09,0.08,0.11,0.12,0.09,0.1,0.11],
     'B11_Scaling' :    [0,0.03,0.02,0.03,0.03,0.02,0.02,0.04,0.03,0.03],
     'B12_Scaling' :    [0,0.05,0.01,0.04,0.02,0.05,0.04,0.05,0.03,0.05],
     'B13_Scaling' :    [0,0.01,0.02,0.02,0.02,0.01,0.01,0.02,0.01,0.02],
     'B14_Scaling' :    [0,0.04,0.04,0.05,0.06,0.05,0.09,0.1,0.07,0.16],
     'B15_Scaling' :    [0,0.08,0.06,0.13,0.1,0.08,0.11,0.14,0.12,0.08],           
     'A1_Rotation' :    [0,112.81,114.01,110.56,110.6,113.37,116.02,116.99,118.62,119.38],
     'A2_Rotation' :    [0,-94.27,-73.02,-87.73,-98.57,-102.94,-111.2,-119.95,-122.41,-124.66],
     'A3_Rotation' :    [0,128.47,135.84,134.06,134.75,133.94,134.69,136.59,137.5,138.85],
     'A4_Rotation' :    [0,164.64,165.45,163.48,161.42,160.63,161.31,162.54,164.99,167.17],
     'A5_Rotation' :    [0,-78.78,-81.19,-87.73,-92.23,-92.33,-101.96,-105.48,-111.09,-114.38],
     'A6_Rotation' :    [0,43.84,48.03,59.34,66.72,67.83,69.48,72.62,72.2,77.81],
     'A7_Rotation' :    [0,131.01,141.7,138.59,138.53,137.8,137.64,136.12,136.75,139.03],
     'A8_Rotation' :    [0,-127.32,-123.16,-125.78,-133.66,-135.66,-137.83,-138.76,-139.64,-141.01],
     'A9_Rotation' :    [0,-173.6,166.75,154.39,162.16,173.26,175.63,-178.69,-179.76,178.52],
     'A10_Rotation' :   [0,0,0,0,0,0,0,0,0,0],
     'A11_Rotation' :   [0,159.85,156.67,158.48,157.77,156.11,155.54,155.77,152.28,149.97],
    'A12_Rotation' :    [0,-87.73,-86.34,-82.59,-77.52,-76.38,-71.91,-67.87,-66.98,-65.81],
     'A13_Rotation' :   [0,157.86,160.03,161.3,165.63,165.1,162.84,162.02,163.42,163.4],
     'A14_Rotation' :   [0,96.06,80.08,98.93,112.07,119.3,125.62,125.42,130.18,131.8],
     'A15_Rotation' :   [0,-128.97,-128.41,-133.2,-139.65,-141,-143.05,-144.79,-145.08,-144.84],
     'B1_Rotation' :    [0,172.04,176.94,179.74,-177.22,-176.59,-175.81,-178,-177.26,-177.53],
     'B2_Rotation' :    [0,-135.52,-136.05,-144.97,-150.41,-151.25,-152.35,-154.52,-154.34,-158.27],
     'B3_Rotation' :    [0,136.51,144.7,143.29,144.27,144.21,149.19,152.95,159.91,164.19],
     'B4_Rotation' :    [0,-34.26,-30.8,-24.57,-28.69,-29.15,-30.36,-29.83,-28.55,-32.58],
     'B5_Rotation' :    [0,-157.4,-157.25,-155.34,-157.7,-160.03,-160.33,-158.82,-158.14,-158.21],
     'B6_Rotation' :    [0,92.27,101.22,104.5,106.63,110.85,116.25,120.35,122.84,128.35],
     'B7_Rotation' :    [0,-105.22,-111.46,-106.51,-115.8,-125.96,-134.82,-144.07,-152.07,-160.76],
     'B8_Rotation' :    [0,-151.19,-154.33,-157.13,-160.12,-161.43,-160.74,-160.39,-164.53,-167.14],
     'B9_Rotation' :    [0,-73.61,-155.92,158.51,161.67,160.64,169.2,175.38,-178.71,-172.8],                         
     'B10_Rotation' :   [0,142.69,144.41,144.93,143.57,139.61,139.91,138.54,138.86,138.47],
     'B11_Rotation' :   [0,119.54,127.13,128.87,133.1,133.59,136.35,140.45,143.34,144.72],
     'B12_Rotation' :   [0,134.03,132.68,125.29,126.67,132.59,139.67,144.84,150.2,153.44],
     'B13_Rotation' :   [0,-177.72,178.64,176.87,175.25,-177.73,-175.96,-175.29,-175.61,-178.46],
     'B14_Rotation' :   [0,-173.78,-177.74,179.11,176.83,178.31,179.19,-178.19,-177.33,-179.89],
     'B15_Rotation' :   [0,152.39,147.79,151.7,151.38,151.96,153.65,155.22,157.01,156.86],
     })

tuples = [((t, k.split('_')[0][0], int(k.split('_')[0][1:]), k.split('_')[1]), v[i]) 
      for k,v in d.items() for i,t in enumerate(time)]

df = pd.Series(dict(tuples)).unstack(-1)
df.index.names = ['time', 'group', 'id']

interval_ms = 200
delay_ms = 1000
ani = FuncAnimation(fig, plotmvs, frames=df.groupby('time'),
                blit=True, interval=interval_ms, repeat_delay=delay_ms)

plt.show()

Answer 1

Ваша проблема на самом деле не в пространственном экстенте ваших функций распределения вероятностей, а скорее в нормализации, которую вы используете для отображения ваших композиционных функций.В частности, значение «ноль» должно означать нулевую вероятность, и, конечно же, это выгодно, если это значение привязано к одному цвету в каждом кадре.Нормализация, которую вы используете в своем коде, а именно

normPDF = PDF - PDF.min()
normPDF = normPDF / normPDF.max()

, не гарантирует это свойство.В качестве примера рассмотрим минимальное и максимальное значения PDF, равные -0,8 и 0,9 соответственно.После преобразования минимальное и максимальное значения normPDF будут равны 0 и 1, т. Е. Ваше преобразование будет выполнять -0.8 --> 0 и 0.9 --> 1.В то же время первоначальная нулевая вероятность также трансформируется: 0 --> 0.8/(0.9+0.8) = 0.47058823529411764.Поскольку ваши функции распределения меняются в каждом кадре, также меняются их максимальные значения, и, следовательно, ваша нулевая вероятность будет преобразовываться в другое значение в каждом кадре.

Чтобы избежать этого, лучше использовать нормализацию, которая сохраняет вашинулевая вероятность.Самое простое преобразование, которое приходит на ум, - это то, которое нормализует вероятность к интервалу [-1,1] (-1, потому что вы вычитаете распределения вероятностей друг от друга), чего можно достичь, разделив распределение на максимальную вероятность:

normPDF = (PDFs[0]-PDFs[1])/max(PDFs[0].max(),PDFs[1].max())

При такой нормализации никакое значение в normPDF никогда не будет меньше -1 или больше 1.Однако обратите внимание, что normPDF не обязательно охватывает все значения от -1 до 1, но скорее ограничивается этими значениями.Кроме того, нулевая вероятность всегда остается нулевой по определению.Теперь, когда распределение нормализовано, нам все еще нужно позаботиться о том, чтобы нулевой вероятности всегда присваивался один и тот же цвет.Это можно сделать, указав contourf, какими должны быть уровни контурного графика.Это можно сделать, используя уровни keyword, которые могут быть либо целыми числами (тогда фиксированное количество контуров только здесь; этого недостаточно), либо итерацией, которая содержит все требуемые уровни.Самыми простыми были бы уровни с равным интервалом и np.linspace(-1,1,n), при этом n - это количество уровней, которое вы хотите, будет рисовать уровни только между пределами нормализации:

cfs = ax.contourf(X, Y, normPDF, cmap='viridis', alpha = 1, levels=np.linspace(-1,1,10))

Слово предостережения : если вы выполняете нормализацию отдельно для каждого кадра, как это делается в вашем коде сейчас, значения (кроме 0), назначенные определенным цветам, скорее всего, будут меняться от кадра к кадру.Это потому, что минимальные и максимальные значения ваших PDF-файлов меняются.Если вы хотите также показать цветную полосу рядом с графиком, вам придется обновить цветную полосу для каждого кадра.Однако это усложнит анимацию.Вместо этого я бы предложил сначала рассчитать PDF-файлы для всех кадров, вычислить максимальные значения для всех кадров, а затем нормализовать все кадры одновременно с этим «глобальным» максимальным значением.Таким образом, вам нужно нарисовать вашу цветовую панель только один раз.