scipy.linalg.rsf2csf

scipy.linalg.rsf2csf(T, Z, check_finite=True)

Convert real Schur form to complex Schur form.

Convert a quasi-diagonal real-valued Schur form to the upper triangular complex-valued Schur form.

Parameters

T(M, M) array_like

Real Schur form of the original array

Z(M, M) array_like

Schur transformation matrix

check_finitebool, optional

Whether to check that the input arrays contain only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.

Returns

T(M, M) ndarray

Complex Schur form of the original array

Z(M, M) ndarray

Schur transformation matrix corresponding to the complex form

See also

schur

Schur decomposition of an array

Examples

>>> from scipy.linalg import schur, rsf2csf
>>> A = np.array([[0, 2, 2], [0, 1, 2], [1, 0, 1]])
>>> T, Z = schur(A)
>>> T
array([[ 2.65896708,  1.42440458, -1.92933439],
       [ 0.        , -0.32948354, -0.49063704],
       [ 0.        ,  1.31178921, -0.32948354]])
>>> Z
array([[0.72711591, -0.60156188, 0.33079564],
       [0.52839428, 0.79801892, 0.28976765],
       [0.43829436, 0.03590414, -0.89811411]])
>>> T2 , Z2 = rsf2csf(T, Z)
>>> T2
array([[2.65896708+0.j, -1.64592781+0.743164187j, -1.21516887+1.00660462j],
       [0.+0.j , -0.32948354+8.02254558e-01j, -0.82115218-2.77555756e-17j],
       [0.+0.j , 0.+0.j, -0.32948354-0.802254558j]])
>>> Z2
array([[0.72711591+0.j,  0.28220393-0.31385693j,  0.51319638-0.17258824j],
       [0.52839428+0.j,  0.24720268+0.41635578j, -0.68079517-0.15118243j],
       [0.43829436+0.j, -0.76618703+0.01873251j, -0.03063006+0.46857912j]])