I've animated a bivariate gaussian distribution using matplotlib. I've calculated this distribution by adjusting the COV matrix to account for specific variables. I can provide greater detail on this process but essentially each scatter point covers a specific displacement that is easily identifiable. My question or problem I'm having is trying to set/fix/peg areas that isn't covered by the distribution. You can see the values oscillating around by the variation in colour.
Question: Is it possible to set or peg these neutral areas to a specific value and therefore colour. Specifically, the coordinates that aren't covered by xy values should not change contour values. They should be fixed as 0.5.
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import scipy.stats as sts
from matplotlib.animation import FuncAnimation
DATA_LIMITS = [-100, 100]
def datalimits(*data):
return DATA_LIMITS # dmin - spad, dmax + spad
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):
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
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 = {
'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)
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 = {
'xlim': xlim,
'ylim': ylim
}
X, Y, PDF = mvpdfs(gdf['X'].values, gdf['Y'].values, **kwargs)
PDFs.append(PDF)
PDF = PDFs[0] - PDFs[1]
normPDF = PDF - PDF.min()
normPDF = normPDF / normPDF.max()
cfs = ax.contourf(X, Y, normPDF, levels=10, cmap='viridis', alpha = 0.8)
return cfs.collections + [line_a, line_b]
n = 10
time = range(n)
d = ({
'A1_Y' : [10,20,15,20,25,40,50,60,61,65],
'A1_X' : [15,10,15,20,25,25,30,40,60,61],
'A2_Y' : [10,13,17,10,20,24,29,30,33,40],
'A2_X' : [10,13,15,17,18,19,20,21,26,30],
'A3_Y' : [11,12,15,17,19,20,22,25,27,30],
'A3_X' : [15,18,20,21,22,28,30,32,35,40],
'A4_Y' : [15,20,15,20,25,40,50,60,61,65],
'A4_X' : [16,20,15,30,45,30,40,10,11,15],
'B1_Y' : [18,10,11,13,18,10,30,40,31,45],
'B1_X' : [17,20,15,10,25,20,10,12,14,25],
'B2_Y' : [13,10,14,20,21,12,30,20,11,35],
'B2_X' : [12,20,16,22,15,20,10,20,16,15],
'B3_Y' : [15,20,15,20,25,10,20,10,15,25],
'B3_X' : [18,15,13,20,21,10,20,10,11,15],
'B4_Y' : [19,12,15,18,14,19,13,12,11,18],
'B4_X' : [20,10,12,18,17,15,13,14,19,13],
})
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()
from set or peg bivariate distribution values using matplotlib
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