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# 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)

  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 : bool, 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