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# scipy.linalg.ordqz

`scipy.linalg.``ordqz`(A, B, sort='lhp', output='real', overwrite_a=False, overwrite_b=False, check_finite=True)

  QZ decomposition for a pair of matrices with reordering.

  New in version 0.17.0.

  Parameters: | A : (N, N) array_like 2d array to decompose B : (N, N) array_like 2d array to decompose sort : {callable, ‘lhp’, ‘rhp’, ‘iuc’, ‘ouc’}, optional Specifies whether the upper eigenvalues should be sorted. A callable may be passed that, given an ordered pair `(alpha, beta)` representing the eigenvalue `x = (alpha/beta)`, returns a boolean denoting whether the eigenvalue should be sorted to the top-left (True). For the real matrix pairs `beta` is real while `alpha` can be complex, and for complex matrix pairs both `alpha` and `beta` can be complex. The callable must be able to accept a numpy array. Alternatively, string parameters may be used: ‘lhp’ Left-hand plane (x.real < 0.0) ‘rhp’ Right-hand plane (x.real > 0.0) ‘iuc’ Inside the unit circle (x*x.conjugate() < 1.0) ‘ouc’ Outside the unit circle (x*x.conjugate() > 1.0) With the predefined sorting functions, an infinite eigenvalue (i.e. `alpha != 0` and `beta = 0`) is considered to lie in neither the left-hand nor the right-hand plane, but it is considered to lie outside the unit circle. For the eigenvalue `(alpha, beta) = (0, 0)` the predefined sorting functions all return False. output : str {‘real’,’complex’}, optional Construct the real or complex QZ decomposition for real matrices. Default is ‘real’. overwrite_a : bool, optional If True, the contents of A are overwritten. overwrite_b : bool, optional If True, the contents of B are overwritten. check_finite : bool, optional If true checks the elements of A and B are finite numbers. If false does no checking and passes matrix through to underlying algorithm.
  Returns: | AA : (N, N) ndarray Generalized Schur form of A. BB : (N, N) ndarray Generalized Schur form of B. alpha : (N,) ndarray alpha = alphar + alphai * 1j. See notes. beta : (N,) ndarray See notes. Q : (N, N) ndarray The left Schur vectors. Z : (N, N) ndarray The right Schur vectors.

  See also

  `qz`

  Notes

  On exit, `(ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N`, will be the generalized eigenvalues. `ALPHAR(j) + ALPHAI(j)*i` and `BETA(j),j=1,...,N` are the diagonals of the complex Schur form (S,T) that would result if the 2-by-2 diagonal blocks of the real generalized Schur form of (A,B) were further reduced to triangular form using complex unitary transformations. If ALPHAI(j) is zero, then the j-th eigenvalue is real; if positive, then the `j`-th and `(j+1)`-st eigenvalues are a complex conjugate pair, with `ALPHAI(j+1)` negative.