scipy.linalg.cdf2rdf¶
-
scipy.linalg.
cdf2rdf
(w, v)[source]¶ Converts complex eigenvalues
w
and eigenvectorsv
to real eigenvalues in a block diagonal formwr
and the associated real eigenvectorsvr
, such that:vr @ wr = X @ vr
continues to hold, where
X
is the original array for whichw
andv
are the eigenvalues and eigenvectors.New in version 1.1.0.
- Parameters
- w(…, M) array_like
Complex or real eigenvalues, an array or stack of arrays
Conjugate pairs must not be interleaved, else the wrong result will be produced. So
[1+1j, 1, 1-1j]
will give a correct result, but[1+1j, 2+1j, 1-1j, 2-1j]
will not.- v(…, M, M) array_like
Complex or real eigenvectors, a square array or stack of square arrays.
- Returns
- wr(…, M, M) ndarray
Real diagonal block form of eigenvalues
- vr(…, M, M) ndarray
Real eigenvectors associated with
wr
See also
Notes
w
,v
must be the eigenstructure for some real matrixX
. For example, obtained byw, v = scipy.linalg.eig(X)
orw, v = numpy.linalg.eig(X)
in which caseX
can also represent stacked arrays.New in version 1.1.0.
Examples
>>> X = np.array([[1, 2, 3], [0, 4, 5], [0, -5, 4]]) >>> X array([[ 1, 2, 3], [ 0, 4, 5], [ 0, -5, 4]])
>>> from scipy import linalg >>> w, v = linalg.eig(X) >>> w array([ 1.+0.j, 4.+5.j, 4.-5.j]) >>> v array([[ 1.00000+0.j , -0.01906-0.40016j, -0.01906+0.40016j], [ 0.00000+0.j , 0.00000-0.64788j, 0.00000+0.64788j], [ 0.00000+0.j , 0.64788+0.j , 0.64788-0.j ]])
>>> wr, vr = linalg.cdf2rdf(w, v) >>> wr array([[ 1., 0., 0.], [ 0., 4., 5.], [ 0., -5., 4.]]) >>> vr array([[ 1. , 0.40016, -0.01906], [ 0. , 0.64788, 0. ], [ 0. , 0. , 0.64788]])
>>> vr @ wr array([[ 1. , 1.69593, 1.9246 ], [ 0. , 2.59153, 3.23942], [ 0. , -3.23942, 2.59153]]) >>> X @ vr array([[ 1. , 1.69593, 1.9246 ], [ 0. , 2.59153, 3.23942], [ 0. , -3.23942, 2.59153]])