sf.decompositions.williamson¶
-
williamson
(V, tol=1e-11)[source]¶ Williamson decomposition of positive-definite (real) symmetric matrix.
Note that it is assumed that the symplectic form is
\[\begin{split}\Omega = \begin{bmatrix}0&I\\-I&0\end{bmatrix}\end{split}\]where \(I\) is the identity matrix and \(0\) is the zero matrix.
- Parameters
V (array[float]) – positive definite symmetric (real) matrix
tol (float) – the tolerance used when checking if the matrix is symmetric: \(|V-V^T| \leq\) tol
- Returns
(Db, S)
whereDb
is a diagonal matrixand
S
is a symplectic matrix such that \(V = S^T Db S\)
- Return type
tuple[array,array]
code/api/strawberryfields.decompositions.williamson
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