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bundles / scipy 1.17.1 / scipy / linalg / _decomp / eig

function

scipy.linalg._decomp:eig

source: /scipy/linalg/_decomp.py :114

Signature

def   eig ( a ,  b = None ,  left = False ,  right = True ,  overwrite_a = False ,  overwrite_b = False ,  check_finite = True ,  homogeneous_eigvals = False )

Summary

Solve an ordinary or generalized eigenvalue problem of a square matrix.

Extended Summary

Find eigenvalues w and right or left eigenvectors of a general matrix 

a   vr[:,i] = w[i]        b   vr[:,i]
a.H vl[:,i] = w[i].conj() b.H vl[:,i]

where .H is the Hermitian conjugation.

The documentation is written assuming array arguments are of specified "core" shapes. However, array argument(s) of this function may have additional "batch" dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see linalg_batch for details. Note that calls with zero-size batches are unsupported and will raise a ValueError.

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. Default is None, identity matrix is assumed.

left : bool, optional

Whether to calculate and return left eigenvectors. Default is False.

right : bool, optional

Whether to calculate and return right eigenvectors. Default is True.

overwrite_a : bool, optional

Whether to overwrite a; may improve performance. Default is False.

overwrite_b : bool, optional

Whether to overwrite b; may improve performance. Default is False.

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. The shape is (M,) unless homogeneous_eigvals=True.

vl : (M, M) double or complex ndarray

The left eigenvector corresponding to the eigenvalue w[i] is the column vl[:,i]. Only returned if left=True. The left eigenvector is not normalized.

vr : (M, M) double or complex ndarray

The normalized right eigenvector corresponding to the eigenvalue w[i] is the column vr[:,i]. Only returned if right=True.

Raises

: LinAlgError

If eigenvalue computation does not converge.

Examples

import numpy as np
from scipy import linalg
a = np.array([[0., -1.], [1., 0.]])
linalg.eigvals(a)
✓
b = np.array([[0., 1.], [1., 1.]])
linalg.eigvals(a, b)
✓
a = np.array([[3., 0., 0.], [0., 8., 0.], [0., 0., 7.]])
linalg.eigvals(a, homogeneous_eigvals=True)
✓
a = np.array([[0., -1.], [1., 0.]])
linalg.eigvals(a) == linalg.eig(a)[0]
✓
linalg.eig(a, left=True, right=False)[1] # normalized left eigenvector
linalg.eig(a, left=False, right=True)[1] # normalized right eigenvector
✗

See also

eig_banded

eigenvalues and right eigenvectors for symmetric/Hermitian band matrices

eigh

Eigenvalues and right eigenvectors for symmetric/Hermitian arrays.

eigh_tridiagonal

eigenvalues and right eigenvectors for symmetric/Hermitian tridiagonal matrices

eigvals

eigenvalues of general arrays

Aliases

  • scipy.linalg.eig

Referenced by

Other packages