`scipy.linalg._decomp:eigvals`

source: /scipy/linalg/_decomp.py :841

Signature

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

Summary

Compute eigenvalues from an ordinary or generalized eigenvalue problem.

Extended Summary

Find eigenvalues of a general matrix

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

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. 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

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)

✓

Aliases

scipy.linalg.eigvals