cdf2rdf#
- scipy.linalg.cdf2rdf(w, v)[source]#
- Converts complex eigenvalues - wand eigenvectors- vto real eigenvalues in a block diagonal form- wrand the associated real eigenvectors- vr, such that:- vr @ wr = X @ vr - continues to hold, where - Xis the original array for which- wand- vare the eigenvalues and eigenvectors.- Added 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,- vmust 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- Xcan also represent stacked arrays.- Added in version 1.1.0. - Examples - >>> import numpy as np >>> 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]])