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scipy.linalg.eigvals_banded

scipy.linalg.eigvals_banded(a_band, lower=False, overwrite_a_band=False, select='a', select_range=None)

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 : array, shape (u+1, M)

The bands of the M by M matrix a.

lower : boolean

Is the matrix in the lower form. (Default is upper form)

overwrite_a_band: :

Discard data in a_band (may enhance performance)

select: {‘a’, ‘v’, ‘i’} :

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)

Range of selected eigenvalues

Returns :

w : array, shape (M,)

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

eigvals

eigenvalues of general arrays

eigh

eigenvalues and right eigenvectors for symmetric/Hermitian arrays

eig

eigenvalues and right eigenvectors for non-symmetric arrays