jax.scipy.linalg.hankel

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jax.scipy.linalg.hankel#

jax.scipy.linalg.hankel(c, r=None)[source]#

Construct a Hankel matrix.

JAX implementation of scipy.linalg.hankel().

A Hankel matrix has constant anti-diagonals: H[i, j] = v[i + j], where v = concatenate([c, r[1:]]). Notice this implies that r[0] is ignored.

Parameters:

  • c (ArrayLike) – array of shape (..., N) specifying the first column.

  • r (ArrayLike | None) – (optional) array of shape (..., M) specifying the last row. Leading dimensions must be broadcast-compatible with those of c. If not specified, r defaults to zeros_like(c).

Returns:

A Hankel matrix of shape (..., N, M).

Return type:

Array

Examples

>>> c = jnp.array([1, 2, 3])
>>> jax.scipy.linalg.hankel(c)
Array([[1, 2, 3],
       [2, 3, 0],
       [3, 0, 0]], dtype=int32)

>>> r = jnp.array([999, 4, 5, 6]) # Note r[0] is ignored
>>> jax.scipy.linalg.hankel(c, r)
Array([[1, 2, 3, 4],
       [2, 3, 4, 5],
       [3, 4, 5, 6]], dtype=int32)

For N-dimensional c and/or r, the result is a batch of Hankel matrices.

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