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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)

  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 ab either in lower diagonal or upper diagonal ordered form:

  > ab[u + i - j, j] == a[i,j] (if upper form; i <= j) ab[ i - j, j] == a[i,j] (if lower form; i >= j)

  Example of ab (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 (M, u+1) Banded matrix whose eigenvalues to calculate 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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