jax.scipy.linalg.eigh_tridiagonal

jax.scipy.linalg.eigh_tridiagonal(d, e, *, eigvals_only=False, select='a', select_range=None, tol=None)

Solve eigenvalue problem for a real symmetric tridiagonal matrix.

LAX-backend implementation of scipy.linalg._decomp.eigh_tridiagonal().

Original docstring below.

Find eigenvalues w and optionally right eigenvectors v of a:

a v[:,i] = w[i] v[:,i]
v.H v    = identity

For a real symmetric matrix a with diagonal elements d and off-diagonal elements e.

Parameters:

• d (ndarray, shape (ndim,)) – The diagonal elements of the array.

• e (ndarray, shape (ndim-1,)) – The off-diagonal elements of the array.

• eigvals_only (bool, optional) – Compute only the eigenvalues and no eigenvectors. (Default: calculate also eigenvectors)

• 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

• tol (float) – The absolute tolerance to which each eigenvalue is required (only used when ‘stebz’ is the lapack_driver). An eigenvalue (or cluster) is considered to have converged if it lies in an interval of this width. If <= 0. (default), the value eps*|a| is used where eps is the machine precision, and |a| is the 1-norm of the matrix a.

Return type:

Array

Returns:

• w ((M,) ndarray) – The eigenvalues, in ascending order, each repeated according to its multiplicity.

• v ((M, M) ndarray) – The normalized eigenvector corresponding to the eigenvalue w[i] is the column v[:,i]. Only returned if eigvals_only=False.