diff --git a/control/modelsimp.py b/control/modelsimp.py
index d2eadc4c3..b3423e4ae 100644
--- a/control/modelsimp.py
+++ b/control/modelsimp.py
@@ -377,14 +377,14 @@ def minimal_realization(sys, tol=None, verbose=True):
def _block_hankel(Y, m, n):
"""Create a block Hankel matrix from impulse response."""
q, p, _ = Y.shape
- YY = Y.transpose(0,2,1) # transpose for reshape
+ YY = Y.transpose(0, 2, 1) # transpose for reshape
- H = np.zeros((q*m,p*n))
+ H = np.zeros((q*m, p*n))
for r in range(m):
# shift and add row to Hankel matrix
- new_row = YY[:,r:r+n,:]
- H[q*r:q*(r+1),:] = new_row.reshape((q,p*n))
+ new_row = YY[:, r:r+n, :]
+ H[q*r:q*(r+1), :] = new_row.reshape((q, p*n))
return H
@@ -480,22 +480,22 @@ def eigensys_realization(arg, r, m=None, n=None, dt=True, transpose=False):
if (l-1) < m+n:
raise ValueError("not enough data for requested number of parameters")
- H = _block_hankel(YY[:,:,1:], m, n+1) # Hankel matrix (q*m, p*(n+1))
- Hf = H[:,:-p] # first p*n columns of H
- Hl = H[:,p:] # last p*n columns of H
+ H = _block_hankel(YY[:, :, 1:], m, n+1) # Hankel matrix (q*m, p*(n+1))
+ Hf = H[:, :-p] # first p*n columns of H
+ Hl = H[:, p:] # last p*n columns of H
U,S,Vh = np.linalg.svd(Hf, True)
- Ur =U[:,0:r]
- Vhr =Vh[0:r,:]
+ Ur =U[:, 0:r]
+ Vhr =Vh[0:r, :]
# balanced realizations
Sigma_inv = np.diag(1./np.sqrt(S[0:r]))
Ar = Sigma_inv @ Ur.T @ Hl @ Vhr.T @ Sigma_inv
- Br = Sigma_inv @ Ur.T @ Hf[:,0:p]*dt # dt scaling for unit-area impulse
- Cr = Hf[0:q,:] @ Vhr.T @ Sigma_inv
- Dr = YY[:,:,0]
+ Br = Sigma_inv @ Ur.T @ Hf[:, 0:p]*dt # dt scaling for unit-area impulse
+ Cr = Hf[0:q, :] @ Vhr.T @ Sigma_inv
+ Dr = YY[:, :, 0]
- return StateSpace(Ar,Br,Cr,Dr,dt), S
+ return StateSpace(Ar, Br, Cr, Dr, dt), S
def markov(*args, m=None, transpose=False, dt=None, truncate=False):
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