在概率单纯形上绘制曲线 [英] Plotting a curve on probability simplex

问题描述

我想绘制由给出的概率向量的参数曲线(p_1，p_2，p_3)

I would like plot the parametric curve (p_1,p_2,p_3) of probability vectors given by

p_1 = 1/3 +(10/3)t，p_2 = 1/3-(2/3)t，p_3 = 1/3-(8/3)t

p_1 = 1/3 + (10/3)t, p_2 = 1/3 - (2/3)t, and p_3 = 1/3 - (8/3)t

使得p_1，p_2，p_3> = 0(注意方程已经满足p_1 + p_2 + p_3 = 1)的概率为单纯形{{p_1，p_2，p_3):p_1，p_2，p_3> = 0并且p_1 + p_2 + p_3 = 1}.

such that p_1, p_2, p_3 >= 0 (note that the equations already satisfy p_1 + p_2 + p_3 = 1) on the probability simplex {(p_1,p_2,p_3) : p_1, p_2, p_3 >= 0 and p_1 + p_2 + p_3 = 1}.

我希望将其视为2D图，即单纯形平面中的曲线.有没有办法在Matlab中做到这一点?有人可以帮忙吗?

I would like to see this as a 2D plot, i.e., a curve in the simplex plane. Is there a way to do this in matlab? Can someone help?

我使用了3D图

ezplot3('1/3 + 10/3 * t'，'1/3-2/3 * t'，'1/3-8/3 * t'，[-5,1/8])

ezplot3('1/3+10/3*t','1/3-2/3*t','1/3-8/3*t',[-5,1/8])

但这并不能给我关于曲线的好主意.

But this doesn't give me a good idea about the curve.

推荐答案

如果这是一条曲线，这就是我在MATLAB中的绘制方式:

This is how I would plot it in MATLAB, if it were a curve :

clf, clc, clear all

%% First lets draw a 2-simplex (three vertices). 
line_width = 2; 
k=2; %2-simplex
simplex_vertices = eye(k+1);

%% for plotting
figure(1), clf,
simp_vert = [simplex_vertices, simplex_vertices(:,1)];
plot3(simp_vert(1,:),simp_vert(2,:),simp_vert(3,:));
hold on

%% Now let s generate t within some range
t = -0.1:0.001:0.1;
x1 = (1/3) + (10/3).*t;
x2 = (1/3) - (2/3)*t;
x3 = (1/3) - (8/3)*t;

%check: sum(x) is equal to 1


%% Plotting
plot3(x1, x2, x3, 'go', 'LineWidth',line_width);

据我了解，虽然您有一行..constant(1/3)+ vector(v)* scalar(t)定义了一行.

As I understand it, you have a line though.. constant(1/3) + vector(v)*scalar(t) defines a line.

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