SciPy

scipy.linalg.rsf2csf

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

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_finite : bool, 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]])

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