pyFDN.rotation_matrix_from_angles#

pyFDN.rotation_matrix_from_angles(angles, n=None)[source]#

Generate orthogonal matrix with prescribed eigenvalue angles.

Builds a block-diagonal matrix of 2x2 Givens rotations, one block per angle, so the eigenvalues are exp(+-1j * angles). For odd matrix sizes, a single eigenvalue at 1 is appended.

Parameters:

angles (Tensor) – Eigenvalue angles in radians, one per conjugate pair
n (int | None) – Matrix size; either 2 * len(angles) or 2 * len(angles) + 1 (default 2 * len(angles))

Returns:

Orthogonal matrix of shape (n, n)

Return type:

rotation_matrix

Example

>>> angles = torch.tensor([0.1, 0.2], dtype=torch.float64)
>>> R = rotation_matrix_from_angles(angles, n=5)
>>> R.shape
torch.Size([5, 5])
>>> torch.allclose(R @ R.T, torch.eye(5, dtype=R.dtype), atol=1e-12)
True