SciPy

scipy.linalg.eig_banded

scipy.linalg.eig_banded(a_band, lower=False, eigvals_only=False, overwrite_a_band=False, select='a', select_range=None, max_ev=0, check_finite=True)[source]

Solve real symmetric or complex hermitian band matrix eigenvalue problem.

Find eigenvalues w and optionally right eigenvectors v 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)

eigvals_only : bool, optional

Compute only the eigenvalues and no eigenvectors. (Default: calculate also eigenvectors)

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

max_ev : int, optional

For select==’v’, maximum number of eigenvalues expected. For other values of select, has no meaning.

In doubt, leave this parameter untouched.

check_finite : boolean, 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.

v : (M, M) float or complex ndarray

The normalized eigenvector corresponding to the eigenvalue w[i] is the column v[:,i].

Raises LinAlgError if eigenvalue computation does not converge :