bundles / scipy 1.17.1 / scipy / linalg / _decomp / cdf2rdf
function
scipy.linalg._decomp:cdf2rdf
source: /scipy/linalg/_decomp.py :1498
Signature
def cdf2rdf ( w , v ) Summary
Complex diagonal form to real diagonal block form.
Extended Summary
Converts complex eigenvalues w and eigenvectors v to real eigenvalues in a block diagonal form wr and the associated real eigenvectors vr, such that
vr @ wr = X @ vrcontinues to hold, where X is the original array for which w and v are the eigenvalues and eigenvectors.
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 linalg_batch for details.
Parameters
w: (..., M) array_likeComplex 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_likeComplex or real eigenvectors, a square array or stack of square arrays.
Returns
wr: (..., M, M) ndarrayReal diagonal block form of eigenvalues
vr: (..., M, M) ndarrayReal eigenvectors associated with
wr
Notes
w, v must be the eigenstructure for some real matrix X. For example, obtained by w, v = scipy.linalg.eig(X) or w, v = numpy.linalg.eig(X) in which case X can also represent stacked arrays.
Examples
import numpy as np X = np.array([[1, 2, 3], [0, 4, 5], [0, -5, 4]]) X✓
from scipy import linalg w, v = linalg.eig(X)✓
w v✗
wr, vr = linalg.cdf2rdf(w, v) wr✓
vr
✗vr @ wr X @ vr✗
See also
Aliases
-
scipy.linalg.cdf2rdf