# jax.scipy.linalg.eigh_tridiagonal#

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

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.

• 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`.

• eigvals_only (`bool`) –

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]`.