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Module « scipy.linalg »

Fonction eigvalsh_tridiagonal - module scipy.linalg

Signature de la fonction eigvalsh_tridiagonal

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

Description

help(scipy.linalg.eigvalsh_tridiagonal)

Solve eigenvalue problem for a real symmetric tridiagonal matrix.

Find eigenvalues `w` 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.
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 ``lapack_driver='stebz'``).
    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. 'sterf' and 'stev' can only be used when
    ``select='a'``.

Returns
-------
w : (M,) ndarray
    The eigenvalues, in ascending order, each repeated according to its
    multiplicity.

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

See Also
--------
eigh_tridiagonal : eigenvalues and right eiegenvectors for
    symmetric/Hermitian tridiagonal matrices

Examples
--------
>>> import numpy as np
>>> from scipy.linalg import eigvalsh_tridiagonal, eigvalsh
>>> d = 3*np.ones(4)
>>> e = -1*np.ones(3)
>>> w = eigvalsh_tridiagonal(d, e)
>>> A = np.diag(d) + np.diag(e, k=1) + np.diag(e, k=-1)
>>> w2 = eigvalsh(A)  # Verify with other eigenvalue routines
>>> np.allclose(w - w2, np.zeros(4))
True

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