Question

我有工作代码来绘制双变量高斯分布。通过调整COV matrix以考虑特定变量来产生分布。具体来说，每个XY坐标都应用radius。然后通过COV因子调整matrix scaling，以展开radius中的x-direction和y-direction中的收缩。其方向由theta测量。输出表示为probability密度函数(PDF)。

我已经对PDF进行了归一化，因此值落在-1和1之内。但是，我要为每个帧分别调用PDF。这样，最大值改变，因此概率对于每个帧将被不同地变换。

问题：使用@Prasanth的建议。可以在绘制之前为每帧创建归一化的数组，然后再绘制这些数组吗？

以下是我当前用于对单个帧的PDF进行标准化的功能。

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

可以使用问题下方的附加动画显示问题。在各帧之间可以看到变化的colorbar。

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import scipy.stats as sts
import matplotlib.animation as animation
from mpl_toolkits.axes_grid1 import make_axes_locatable

DATA_LIMITS = [-30, 30]

def datalimits(*data):
    return DATA_LIMITS  

def rot(theta):
    theta = np.deg2rad(theta)
    return np.array([
        [np.cos(theta), -np.sin(theta)],
        [np.sin(theta), np.cos(theta)]
    ])

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

def mvpdf(x, y, xlim, ylim, radius=1, velocity=0, scale=0, theta=0):
    """Creates a grid of data that represents the PDF of a multivariate gaussian.

    x, y: The center of the returned PDF
    (xy)lim: The extent of the returned PDF
    radius: The PDF will be dilated by this factor
    scale: The PDF be stretched by a factor of (scale + 1) in the x direction, and squashed by a factor of 1/(scale + 1) in the y direction
    theta: The PDF will be rotated by this many degrees

    returns: X, Y, PDF. X and Y hold the coordinates of the PDF.
    """
    # create the coordinate grids
    X,Y = np.meshgrid(np.linspace(*xlim), np.linspace(*ylim))

    # stack them into the format expected by the multivariate pdf
    XY = np.stack([X, Y], 2)

    # displace xy by half the velocity
    x,y = rot(theta) @ (velocity/2, 0) + (x, y)

    # get the covariance matrix with the appropriate transforms
    cov = getcov(radius=radius, scale=scale, theta=theta)

    # generate the data grid that represents the PDF
    PDF = sts.multivariate_normal([x, y], cov).pdf(XY)

    return X, Y, PDF

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 0.5,
            '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)

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)
lines=[line_a,line_b] 

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'), lines):
        if group in ['A','B']:
            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)

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

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

    divider = make_axes_locatable(ax)
    cax = divider.append_axes("right", size="5%", pad=0.1)
    cbar = fig.colorbar(cfs, ax=ax, cax=cax)
    cbar.set_ticks([-1,-0.8,-0.6,-0.4,-0.2,0,0.2,0.4,0.6,0.8,1])

    return  cfs.collections + [line_a,line_b] 

n = 9
time = range(n)  

d = ({
     'A1_X' :    [13,14,12,13,11,12,13,12,11,10],
     'A1_Y' :    [6,6,7,7,7,8,8,8,9,10],
     'A2_X' :    [7,6,5,7,6,3,4,5,6,6],
     'A2_Y' :    [11,12,11,10,11,12,10,11,10,9],
     'B1_X' :    [8,9,8,7,6,7,5,6,7,6],
     'B1_Y' :    [3,4,3,2,3,4,2,1,2,3],
     'B2_X' :    [13,14,14,14,13,13,13,12,12,12],
     'B2_Y' :    [5,4,3,2,4,5,4,6,3,3],               
    })

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 = 1000
delay_ms = 2000
ani = animation.FuncAnimation(fig, plotmvs, frames=df.groupby('time'), interval=interval_ms, repeat_delay=delay_ms,)

plt.show()

Animation

Answer 1

是否可以在绘制之前为每个帧创建归一化的数组，然后绘制这些数组？

确实可以。在您的情况下，您可能需要在绘制之前在两个值（例如-1和1）之间缩放数组。这样最小值将变为-1，最大值1和中间值将按比例缩放。
您也可以选择0和1或最小值和最大值，但是我们选择-1和1，以使中间值为0。

为此，请在您的代码中替换：

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

具有：

renormPDF = PDFs[0]-PDFs[1]
renormPDF -= renormPDF.min()
normPDF = (renormPDF * 2 / renormPDF.max()) -1

这三行确保normPDF.min() == -1和normPDF.max() == 1。

现在，当绘制动画时，图像右侧的轴不会改变。

Answer 2

您的问题是找到所有帧的SELECT DISTINCT和GROUP BY的最大值。

为什么不对所有计划的帧运行PDFs[0].max()，以便找到PDFs[1].max()和plotmvs的绝对最大值，然后用这些绝对值运行PDFs[0]最大化您的地块？这样，PDFs[1]对于所有帧都是相同的。

归一化所有帧的概率函数的最大值

2 个答案: