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Module « scipy.linalg »

Fonction cdf2rdf - module scipy.linalg

Signature de la fonction cdf2rdf

def cdf2rdf(w, v) 

Description

help(scipy.linalg.cdf2rdf)

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 @ vr

continues to hold, where ``X`` is the original array for which ``w`` and
``v`` are the eigenvalues and eigenvectors.

.. versionadded:: 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
--------
eig : Eigenvalues and right eigenvectors for non-symmetric arrays
rsf2csf : Convert real Schur form to complex Schur form

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.

.. versionadded:: 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]])

Vous êtes un professionnel et vous avez besoin d'une formation ? RAG (Retrieval-Augmented Generation)
et Fine Tuning d'un LLM Voir le programme détaillé