Software

My research activity includes developing software for the smooth decomposition of matrix-valued functions of one real parameter. Together with Alessandra Papini (Università degli Studi di Firenze), and based on joint work with Alessandra Papini and Luca Dieci (Georgia Institute of Technology), I have developed MATLAB software, available on MATLAB File Exchange, for the numerical computation of:

• Smooth Schur decomposition of real symmetric and complex Hermitian matrix-valued functions

• Smooth singular value decomposition (SVD) of real and complex matrix-valued functions

• Smooth Takagi decomposition of complex symmetric matrix-valued functions

• Smooth generalized eigendecomposition of real symmetric positive definite pencil-valued functions

In collaboration with Giuseppe Patera (Université de Lille) I have developed MATLAB and Python software for the smooth Bloch–Messiah decomposition of conjugate symplectic matrix-valued functions of one parameter. It is available on MATLAB File Exchange and GitHub.

This software has been used to compute geometric (Berry) phases and to detect spectral degeneracies - such as conical intersections, diabolical points, and loss of rank - in matrix-valued functions depending on one or several parameters. For more details, see my Research page.