pyFDN.tiny_rotation_matrix

pyFDN.tiny_rotation_matrix(n, delta, spread=0.1)

Dense orthogonal matrix with small eigenvalue angles.

The eigenvalue angles are delta * pi, randomly spread by the factor spread. Small angles make the feedback matrix close to the identity in effect, which controls how quickly the network mixes (e.g. to model coupled rooms). The Givens-rotation core from rotation_matrix_from_angles() is conjugated by a random orthogonal matrix, so the result is dense but keeps the prescribed eigenvalues. For odd n one eigenvalue is at 1.

Translation of tinyRotationMatrix.m from fdnToolbox. Draws from NumPy’s global random state.

Parameters:

• n (int) – Matrix size.

• delta (float) – Mean normalized eigenvalue angle.

• spread (float) – Spreading of the eigenvalue angles (default 0.1).

Return type:

ndarray

Returns:

Orthogonal matrix of shape (n, n).