Possible zero-generator issue in conSet/@zonotope/enclosePoints.m

[lili1039]

Description

The generator length in function aux_cloud2zonotope (in conSet/@zonotope/enclosePoints.m) is currently computed as

g = ratio * abs(dot(u,r)) * u;

where u is the dominant left singular vector of the residual point cloud and r is the radius vector of its axis-aligned interval enclosure.

The quantity abs(dot(u,r)) is the projection of the specific interval vertex r onto u. Since the entries of u may have different signs, positive and negative terms can cancel even when both u and r are nonzero. This may produce g = 0, followed by a 0/0 operation in function aux_compress:

u = g / norm(g);

For an axis-aligned interval with radius vector r, its support radius in direction u is supposed to be

dot(abs(u),r)

Therefore, the generator construction may be more appropriately written as

g = ratio * dot(abs(u),r) * u;

A numerical safeguard in aux_compress can also prevent division by zero as

function X = aux_compress(X,g)

    ng = norm(g);
    tol = 1e-12;

    if ng <= tol
        return;
    end

    u = g/ng;

    for i = 1:size(X,2)
        d = dot(X(:,i),u);
        d = min(ng,max(-ng,d));
        X(:,i) = X(:,i) - d*u;
    end
end

Steps to Reproduce the Issue

I have attached the point data file that triggered the issue, along with a minimal reproduction script.
Point data file: https://drive.google.com/file/d/1OLIA6q_IVsjmZsQsqB31v0_vyR-7tgVI/view?usp=drive_link

load('data.mat');
Zono_omega = zonotope.enclosePoints(omega);

In my case, the issue occurred at the last iteration in aux_cloud2zonotope. At that iteration,

norm(u) > 0
norm(r) > 0
dot(u,r) == 0
dot(abs(u),r) > 0

The above modification resolves the issue for this dataset.

Current Behavior

Sign cancellation in dot(u,r) may produce a zero generator even though the residual point cloud has nonzero extent. The subsequent normalization of g introduces NaN values into X and the resulting zonotope.

Expected Behavior

cloud2zonotope should return a valid zonotope without introducing NaN values.

Versions

• Matlab version: R2024a
• OS: Windows