Validate Gaussian mixture parameter shapes

[FlorianPfaff]

Bug

GaussianMixture.mixture_parameters_to_gaussian_parameters() accepted means and covariance tensors without verifying that both described the same component set.

For example, two scalar component means and two weights could be combined with only one covariance matrix. NumPy-style broadcasting duplicated that single covariance across the component axis and returned a plausible Gaussian instead of reporting incomplete mixture data. A covariance matrix with no component axis could be broadcast similarly.

Fix

• normalize the public means and covariance inputs to backend arrays before structural validation;
• accept scalar-component means shaped (n_components,) and vector-component means shaped (n_components, state_dim);
• require at least one nonempty component mean;
• require covariance tensors to have the exact shape (state_dim, state_dim, n_components) before weighting;
• preserve the existing weight normalization and moment-matching calculation for valid inputs.

Regression coverage

• reject two means supplied with only one scalar covariance;
• reject a multidimensional covariance matrix that omits the component axis;
• verify matching scalar-component inputs still produce mean 1.5 and covariance 3.25.

Validation

• branch is 2 commits ahead and 0 behind current main;
• final diff is limited to the Gaussian-mixture implementation and one focused regression module;
• full backend, test, lint, documentation, packaging, and security validation is delegated to GitHub Actions.

[github-actions]

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[FlorianPfaff]

Closing as superseded by #5238. Both change GaussianMixture.mixture_parameters_to_gaussian_parameters, but #5238 fixes the same component/covariance shape bug while preserving valid scalar, 1-D, and single-component (dim, dim) covariance shorthands. Keeping both would create overlapping, incompatible implementations and duplicate regression coverage.