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Module « scipy.linalg »

Fonction eigvals_banded - module scipy.linalg

Signature de la fonction eigvals_banded

def eigvals_banded(a_band, lower=False, overwrite_a_band=False, select='a', select_range=None, check_finite=True) 

Description

help(scipy.linalg.eigvals_banded)

Solve real symmetric or complex Hermitian band matrix eigenvalue problem.

Find eigenvalues w of a::

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

The matrix a is stored in a_band either in lower diagonal or upper
diagonal ordered form:

    a_band[u + i - j, j] == a[i,j]        (if upper form; i <= j)
    a_band[    i - j, j] == a[i,j]        (if lower form; i >= j)

where u is the number of bands above the diagonal.

Example of a_band (shape of a is (6,6), u=2)::

    upper form:
    *   *   a02 a13 a24 a35
    *   a01 a12 a23 a34 a45
    a00 a11 a22 a33 a44 a55

    lower form:
    a00 a11 a22 a33 a44 a55
    a10 a21 a32 a43 a54 *
    a20 a31 a42 a53 *   *

Cells marked with * are not used.

Parameters
----------
a_band : (u+1, M) array_like
    The bands of the M by M matrix a.
lower : bool, optional
    Is the matrix in the lower form. (Default is upper form)
overwrite_a_band : bool, optional
    Discard data in a_band (may enhance performance)
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.

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

Examples
--------
>>> import numpy as np
>>> from scipy.linalg import eigvals_banded
>>> A = np.array([[1, 5, 2, 0], [5, 2, 5, 2], [2, 5, 3, 5], [0, 2, 5, 4]])
>>> Ab = np.array([[1, 2, 3, 4], [5, 5, 5, 0], [2, 2, 0, 0]])
>>> w = eigvals_banded(Ab, lower=True)
>>> w
array([-4.26200532, -2.22987175,  3.95222349, 12.53965359])

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