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. - The documentation is written assuming array arguments are of specified “core” shapes. However, array argument(s) of this function may have additional “batch” dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see Batched Linear Operations for details. - 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 - >>> import numpy as np >>> 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]])