ordqz(A, B, sort='lhp', output='real', overwrite_a=False, overwrite_b=False, check_finite=True)
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 jth eigenvalue is real; if positive, then the j``th and ``(j+1)``st eigenvalues are a
complex conjugate pair, with ``ALPHAI(j+1)
negative.
2-D array to decompose
2-D array to decompose
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 :None:None:`False`
.
Construct the real or complex QZ decomposition for real matrices. Default is 'real'.
If True, the contents of A are overwritten.
If True, the contents of B are overwritten.
If true checks the elements of A
and B
are finite numbers. If false does no checking and passes matrix through to underlying algorithm.
Generalized Schur form of A.
Generalized Schur form of B.
alpha = alphar + alphai * 1j. See notes.
See notes.
The left Schur vectors.
The right Schur vectors.
QZ decomposition for a pair of matrices with reordering.
>>> from scipy.linalg import ordqz
... A = np.array([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]])
... B = np.array([[0, 6, 0, 0], [5, 0, 2, 1], [5, 2, 6, 6], [4, 7, 7, 7]])
... AA, BB, alpha, beta, Q, Z = ordqz(A, B, sort='lhp')
Since we have sorted for left half plane eigenvalues, negatives come first
>>> (alpha/beta).real < 0 array([ True, True, False, False], dtype=bool)See :
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.linalg._decomp_qz.ordqz
scipy.linalg._decomp_qz.qz
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