From 984d56b4d94bf298a197f1567834451acf49cab9 Mon Sep 17 00:00:00 2001
From: "Eugeniy E. Mikhailov" <evgmik@gmail.com>
Date: Tue, 19 Nov 2024 13:40:38 -0500
Subject: dir rename

---
 python_src/williamson.py | 70 ------------------------------------------------
 1 file changed, 70 deletions(-)
 delete mode 100644 python_src/williamson.py

(limited to 'python_src/williamson.py')

diff --git a/python_src/williamson.py b/python_src/williamson.py
deleted file mode 100644
index 19a2f5f..0000000
--- a/python_src/williamson.py
+++ /dev/null
@@ -1,70 +0,0 @@
-def williamson(V, tol=1e-11):
-    r"""Williamson decomposition of positive-definite (real) symmetric matrix.
-
-    See :ref:`williamson`.
-
-    Note that it is assumed that the symplectic form is
-
-    .. math:: \Omega = \begin{bmatrix}0&I\\-I&0\end{bmatrix}
-
-    where :math:`I` is the identity matrix and :math:`0` is the zero matrix.
-
-    See https://math.stackexchange.com/questions/1171842/finding-the-symplectic-matrix-in-williamsons-theorem/2682630#2682630
-
-    Args:
-        V (array[float]): positive definite symmetric (real) matrix
-        tol (float): the tolerance used when checking if the matrix is symmetric: :math:`|V-V^T| \leq` tol
-
-    Returns:
-        tuple[array,array]: ``(Db, S)`` where ``Db`` is a diagonal matrix
-            and ``S`` is a symplectic matrix such that :math:`V = S^T Db S`
-    """
-    (n, m) = V.shape
-
-    if n != m:
-        raise ValueError("The input matrix is not square")
-
-    diffn = np.linalg.norm(V - np.transpose(V))
-
-    if diffn >= tol:
-        raise ValueError("The input matrix is not symmetric")
-
-    if n % 2 != 0:
-        raise ValueError("The input matrix must have an even number of rows/columns")
-
-    n = n // 2
-    omega = sympmat(n)
-    vals = np.linalg.eigvalsh(V)
-
-    for val in vals:
-        if val <= 0:
-            raise ValueError("Input matrix is not positive definite")
-
-    Mm12 = sqrtm(np.linalg.inv(V)).real
-    r1 = Mm12 @ omega @ Mm12
-    s1, K = schur(r1)
-    X = np.array([[0, 1], [1, 0]])
-    I = np.identity(2)
-    seq = []
-
-    # In what follows I construct a permutation matrix p  so that the Schur matrix has
-    # only positive elements above the diagonal
-    # Also the Schur matrix uses the x_1,p_1, ..., x_n,p_n  ordering thus I use rotmat to
-    # go to the ordering x_1, ..., x_n, p_1, ... , p_n
-
-    for i in range(n):
-        if s1[2 * i, 2 * i + 1] > 0:
-            seq.append(I)
-        else:
-            seq.append(X)
-
-    p = block_diag(*seq)
-    Kt = K @ p
-    s1t = p @ s1 @ p
-    dd = xpxp_to_xxpp(s1t)
-    perm_indices = xpxp_to_xxpp(np.arange(2 * n))
-    Ktt = Kt[:, perm_indices]
-    Db = np.diag([1 / dd[i, i + n] for i in range(n)] + [1 / dd[i, i + n] for i in range(n)])
-    S = Mm12 @ Ktt @ sqrtm(Db)
-    return Db, np.linalg.inv(S).T
-
-- 
cgit v1.2.3