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)

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 : 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)

eigvals_only : boolean

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

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

max_ev : integer

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

In doubt, leave this parameter untouched.

Returns :

w : array, shape (M,)

The eigenvalues, in ascending order, each repeated according to its multiplicity.

v : double or complex double array, shape (M, M)

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

Raises LinAlgError if eigenvalue computation does not converge :

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