quatica.visualization

`quatica.visualization`

`Visualizer`

`plot_convergence_comparison(data_dict, title='Convergence Comparison', xlabel='Iteration', ylabel='Residual', logscale=True, save_path=None)` `staticmethod`

Plot convergence comparison for multiple algorithms/variants.

`plot_covariances(covariances, title='Covariance Deviation', subtitle='')` `staticmethod`

Plot covariance deviation ||AX - I|| or ||XA - I|| over iterations.

Visualizes how well the computed pseudoinverse satisfies the covariance conditions during Newton-Schulz iterations.

Parameters:

covariances : list[float] List of covariance deviation values over iterations title : str, optional Main plot title (default: "Covariance Deviation") subtitle : str, optional Additional subtitle text (default: "")

Notes:

Uses logarithmic scale to track convergence. The covariance deviation measures how close XA (or AX) is to the identity matrix.

`plot_residuals(residuals, title='Residual Norms', subtitle='')` `staticmethod`

Plot Moore-Penrose residual norms over iterations.

Creates a logarithmic plot showing the convergence behavior of different residual types during pseudoinverse computation.

Parameters:

residuals : dict[str, list[float]] Dictionary mapping residual names to their values over iterations title : str, optional Main plot title (default: "Residual Norms") subtitle : str, optional Additional subtitle text (default: "")

Notes:

Uses semilogy scale to better visualize exponential convergence patterns typical in iterative pseudoinverse algorithms.

`visualize_matrix(A, component=0, cmap='viridis', title='Matrix Component Heatmap', subtitle='')` `staticmethod`

Heatmap of a chosen quaternion component (0=w, 1=x, 2=y, 3=z).

Displays a specific quaternion component as a 2D heatmap to visualize the structure and patterns within the matrix.

Parameters:

A : np.ndarray or SparseQuaternionMatrix Input quaternion matrix component : int, optional Quaternion component to visualize: 0=w, 1=x, 2=y, 3=z (default: 0) cmap : str, optional Matplotlib colormap name (default: 'viridis') title : str, optional Main plot title (default: "Matrix Component Heatmap") subtitle : str, optional Additional subtitle text (default: "")

Notes:

Automatically handles both dense and sparse quaternion matrices by converting sparse matrices to dense format for visualization.

`visualize_matrix_abs(A, cmap='viridis', title='Matrix Absolute Value', subtitle='')` `staticmethod`

Heatmap of quaternion matrix absolute values |q| = sqrt(w² + x² + y² + z²).

Displays the magnitude of each quaternion entry as a 2D heatmap, providing insight into the overall structure and numerical behavior.

Parameters:

A : np.ndarray or SparseQuaternionMatrix Input quaternion matrix cmap : str, optional Matplotlib colormap name (default: 'viridis') title : str, optional Main plot title (default: "Matrix Absolute Value") subtitle : str, optional Additional subtitle text (default: "")

Notes:

The absolute value (magnitude) is computed as the quaternion norm, which is invariant under quaternion rotations and provides a scalar measure of quaternion "size".

`visualize_schur_structure(T, title='Schur Form Structure', subtitle='', threshold=1e-12)` `staticmethod`

Visualize the structure of a Schur form matrix T and compute structure metrics.

Returns:

Type	Description
`Tuple[float, float]`	Tuple of (below_diagonal_max, subdiagonal_max) for quantitative analysis

`visualize_tensor_slice(T, mode=0, slice_idx=0, cmap='viridis', title='Tensor Slice', show_abs=True)` `staticmethod`

Visualize a 2D slice of a quaternion tensor T(I×J×K).

quatica.visualization