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

Module « scipy.linalg »

Fonction eigh_tridiagonal - module scipy.linalg

Signature de la fonction eigh_tridiagonal

def eigh_tridiagonal(d, e, eigvals_only=False, select='a', select_range=None, check_finite=True, tol=0.0, lapack_driver='auto') 

Description

help(scipy.linalg.eigh_tridiagonal)

Solve eigenvalue problem for a real symmetric tridiagonal matrix.

Find eigenvalues `w` and optionally right eigenvectors `v` of ``a``::

    a v[:,i] = w[i] v[:,i]
    v.H v    = identity

For a real symmetric matrix ``a`` with diagonal elements `d` and
off-diagonal elements `e`.

Parameters
----------
d : ndarray, shape (ndim,)
    The diagonal elements of the array.
e : ndarray, shape (ndim-1,)
    The off-diagonal elements of the array.
eigvals_only : bool, optional
    Compute only the eigenvalues and no eigenvectors.
    (Default: calculate also eigenvectors)
select : {'a', 'v', 'i'}, optional
    Which eigenvalues to calculate

    ======  ========================================
    select  calculated
    ======  ========================================
    'a'     All eigenvalues
    'v'     Eigenvalues in the interval (min, max]
    'i'     Eigenvalues with indices min <= i <= max
    ======  ========================================
select_range : (min, max), optional
    Range of selected eigenvalues
check_finite : bool, optional
    Whether to check that the input matrix contains only finite numbers.
    Disabling may give a performance gain, but may result in problems
    (crashes, non-termination) if the inputs do contain infinities or NaNs.
tol : float
    The absolute tolerance to which each eigenvalue is required
    (only used when 'stebz' is the `lapack_driver`).
    An eigenvalue (or cluster) is considered to have converged if it
    lies in an interval of this width. If <= 0. (default),
    the value ``eps*|a|`` is used where eps is the machine precision,
    and ``|a|`` is the 1-norm of the matrix ``a``.
lapack_driver : str
    LAPACK function to use, can be 'auto', 'stemr', 'stebz', 'sterf',
    or 'stev'. When 'auto' (default), it will use 'stemr' if ``select='a'``
    and 'stebz' otherwise. When 'stebz' is used to find the eigenvalues and
    ``eigvals_only=False``, then a second LAPACK call (to ``?STEIN``) is
    used to find the corresponding eigenvectors. 'sterf' can only be
    used when ``eigvals_only=True`` and ``select='a'``. 'stev' can only
    be used when ``select='a'``.

Returns
-------
w : (M,) ndarray
    The eigenvalues, in ascending order, each repeated according to its
    multiplicity.
v : (M, M) ndarray
    The normalized eigenvector corresponding to the eigenvalue ``w[i]`` is
    the column ``v[:,i]``. Only returned if ``eigvals_only=False``.

Raises
------
LinAlgError
    If eigenvalue computation does not converge.

See Also
--------
eigvalsh_tridiagonal : eigenvalues of symmetric/Hermitian tridiagonal
    matrices
eig : eigenvalues and right eigenvectors for non-symmetric arrays
eigh : eigenvalues and right eigenvectors for symmetric/Hermitian arrays
eig_banded : eigenvalues and right eigenvectors for symmetric/Hermitian
    band matrices

Notes
-----
This function makes use of LAPACK ``S/DSTEMR`` routines.

Examples
--------
>>> import numpy as np
>>> from scipy.linalg import eigh_tridiagonal
>>> d = 3*np.ones(4)
>>> e = -1*np.ones(3)
>>> w, v = eigh_tridiagonal(d, e)
>>> A = np.diag(d) + np.diag(e, k=1) + np.diag(e, k=-1)
>>> np.allclose(A @ v - v @ np.diag(w), np.zeros((4, 4)))
True

Vous êtes un professionnel et vous avez besoin d'une formation ? Deep Learning avec Python
et Keras et Tensorflow Voir le programme détaillé