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Module « scipy.linalg »

Fonction eigvals - module scipy.linalg

Signature de la fonction eigvals

def eigvals(a, b=None, overwrite_a=False, check_finite=True, homogeneous_eigvals=False) 

Description

help(scipy.linalg.eigvals)

Compute eigenvalues from an ordinary or generalized eigenvalue problem.

Find eigenvalues of a general matrix::

    a   vr[:,i] = w[i]        b   vr[:,i]

Parameters
----------
a : (M, M) array_like
    A complex or real matrix whose eigenvalues and eigenvectors
    will be computed.
b : (M, M) array_like, optional
    Right-hand side matrix in a generalized eigenvalue problem.
    If omitted, identity matrix is assumed.
overwrite_a : bool, optional
    Whether to overwrite data in a (may improve performance)
check_finite : bool, optional
    Whether to check that the input matrices contain 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.
homogeneous_eigvals : bool, optional
    If True, return the eigenvalues in homogeneous coordinates.
    In this case ``w`` is a (2, M) array so that::

        w[1,i] a vr[:,i] = w[0,i] b vr[:,i]

    Default is False.

Returns
-------
w : (M,) or (2, M) double or complex ndarray
    The eigenvalues, each repeated according to its multiplicity
    but not in any specific order. The shape is (M,) unless
    ``homogeneous_eigvals=True``.

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

See Also
--------
eig : eigenvalues and right eigenvectors of general arrays.
eigvalsh : eigenvalues of symmetric or Hermitian arrays
eigvals_banded : eigenvalues for symmetric/Hermitian band matrices
eigvalsh_tridiagonal : eigenvalues of symmetric/Hermitian tridiagonal
    matrices

Examples
--------
>>> import numpy as np
>>> from scipy import linalg
>>> a = np.array([[0., -1.], [1., 0.]])
>>> linalg.eigvals(a)
array([0.+1.j, 0.-1.j])

>>> b = np.array([[0., 1.], [1., 1.]])
>>> linalg.eigvals(a, b)
array([ 1.+0.j, -1.+0.j])

>>> a = np.array([[3., 0., 0.], [0., 8., 0.], [0., 0., 7.]])
>>> linalg.eigvals(a, homogeneous_eigvals=True)
array([[3.+0.j, 8.+0.j, 7.+0.j],
       [1.+0.j, 1.+0.j, 1.+0.j]])

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