pyFDN.tiny_rotation_matrix#

pyFDN.tiny_rotation_matrix(n, delta, spread=0.1, dtype=None)[source]#

Generate orthogonal matrix with small eigenvalue angles.

Creates a rotation matrix suitable for use in FDN feedback structures, where small eigenvalue angles help control the density of the impulse response. The eigenvalue angles are delta * pi, randomly spread by the spread factor. The matrix is constructed from 2x2 Givens rotations with these angles, pre- and post-multiplied by a random orthogonal matrix so that the result is dense but keeps the prescribed eigenvalues. For odd matrix sizes, one eigenvalue is at 1.

Parameters:

  • n (int) – Matrix size

  • delta (float) – Mean normalized eigenvalue angle

  • spread (float) – Spreading of eigenvalue angle (default 0.1)

  • dtype (dtype | None) – Floating point dtype of the result (default torch default)

Returns:

Orthogonal matrix of shape (n, n)

Return type:

rotation_matrix

Example

>>> R = tiny_rotation_matrix(6, 12)
>>> R.shape
torch.Size([6, 6])
>>> torch.allclose(R @ R.T, torch.eye(6), atol=1e-5)
True
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