how to generate a random convex piecewise-linear function-CodePudding

I want to generate a toy example to illustrate a convex piecewise linear function in python, but I couldn't figure out the best way to do this. What I want to do is to indicate the number of lines and generate the function randomly.

A convex piecewise-linear function is defined as:

To print this figure:

import matplotlib.pyplot as plt
fig, ax = plt.subplots()
ax.plot(x_points,y_points, '-o', label="convex piecewise-linear function")
ax.legend()
fig.patch.set_facecolor('white')
plt.show()

CodePudding user response：

make sure the gradient (=dx/dy) is increasing. Pseudocode:

s = 1;
x = 0;
y = 0;
n = 4;
while(--n>0)
{
  //increase x randomly
  dx = rand(3);
  dy = dx * s;
  x  = dx;
  y  = dy; 
  //increase gradient randomly
  s  = rand(3);
  print x   "/"  y;
}