jax.scipy.linalg.fiedler_companion

jax.scipy.linalg.fiedler_companion(a)

Construct a Fiedler companion matrix.

JAX implementation of scipy.linalg.fiedler_companion().

Given polynomial coefficients \(a = [a_0, a_1, \ldots, a_{n}]\) with \(a_0 \neq 0\), this constructs a pentadiagonal matrix whose eigenvalues coincide with the roots of the polynomial. The result is similar to companion() but with a sparser, banded structure.

Parameters:

a (ArrayLike) – array of shape (..., N) specifying the polynomial coefficients in descending order. The last axis must have nonzero length. For N == 1 an empty (0, 0) matrix is returned along that slice.

Raises:

ValueError – if the last axis of a has length zero.

Returns:

A Fiedler companion matrix of shape (..., N - 1, N - 1).

Return type:

Array

Note

Unlike scipy.linalg.fiedler_companion(), this function does not check at runtime that a[..., 0] is non-zero; if the leading coefficient is zero, the result will contain inf or nan entries.

Examples

>>> a = jnp.array([1., -16., 86., -176., 105.])
>>> jax.scipy.linalg.fiedler_companion(a)
Array([[ 16., -86.,   1.,   0.],
       [  1.,   0.,   0.,   0.],
       [  0., 176.,   0., -105.],
       [  0.,   1.,   0.,   0.]], dtype=float32)