Sanity check for convex optimization set
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May 17, 2023 09:47
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| import numpy as np | |
| import matplotlib.pyplot as plt | |
| import cvxpy as cp | |
| import scipy | |
| np.random.seed(1) | |
| b = np.array([[.5, 1.]]).T | |
| α = 0.3 | |
| A = np.array([[1., α], [α, 1.5]]) | |
| A_inv = np.linalg.inv(A) | |
| A_sqrt = scipy.linalg.sqrtm(A) | |
| n_pts = 10000 | |
| pts_base = (np.random.rand(2, n_pts)-.5)*5 | |
| pts = pts_base+b | |
| ε_1 = pts[:, [(pts-b)[:,i].T@A_inv@(pts-b)[:,i]<=1 for i in range(n_pts)]] | |
| plt.scatter(*ε_1, c="C1", alpha=.5, label=r"$\mathcal{E} = \left \{ x | (x-x_c)^\mathsf{T}P^{-1}(x-x_c) \leq 1 \right \}$") | |
| pts = pts_base[:, np.linalg.norm(pts_base, axis=0) <= 1] | |
| ε_2 = b+A_sqrt@pts | |
| plt.scatter(*ε_2, c="C2", alpha=.5, label=r"$\mathcal{E} = \left \{ x_c+Au \,|\, \| u \| \leq 1 \right \}$") | |
| plt.legend() | |
| plt.show() |
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