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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.

  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_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

      >>> 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]])