Resona

Resona is a Python library for comprehensive spectral analysis of operators without ever constructing or storing the full matrix — “the FFT of operators.”

Everything runs on a single primitive: the matrix–vector product v ↦ A·v. From that alone, Resona extracts eigenvalues, densities of states, effective rank, pseudospectra and condition numbers; composes operators algebraically via free probability (Pastur subordination, Brown measure for non-Hermitian operators); and even synthesizes new operators matching target spectral properties.

Under the hood: stochastic Lanczos quadrature, Krylov methods, Carleman linearization. Dependencies: NumPy and SciPy — nothing else.

Applications span Gaussian processes, neural-network Hessians, PDEs, quantum systems, and Anderson localization.

Source: github.com/dimaq12/resona