rsf2csf — SciPy v1.15.2 Manual (original) (raw)
scipy.linalg.
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_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 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]])