expand_entries()

static CubicOperator.expand_entries(Gc)

Given \(\tilde{\G}\in\RR^{a \times r(r+1)(r+2)/6}\), construct the matrix \(\Ghat\in\RR^{a\times r^3}\) such that \(\Ghat[\qhat\otimes\qhat\otimes\qhat] = \tilde{\G}[\qhat\,\hat{\otimes}\,\qhat\,\hat{\otimes}\,\qhat]\) for all \(\qhat\in\RR^{r}\) where \(\cdot\hat{\otimes}\cdot\hat{\otimes}\cdot\) is the compressed cubic Kronecker product (see ckron()).

Parameters:

Gc(a, r(r+1)(r+2)/2) ndarray

Matrix that acts on the compressed cubic Kronecker product.

Returns:

G(a, r^3) ndarray

Matrix that acts on the full cubic Kronecker product.

Examples

>>> from opinf.operators import CubicOperator
>>> r = 20
>>> Gtilde = np.random.random((r, r * (r + 1) * (r + 2)/ 6))
>>> Gtilde.shape
(20, 1540)
>>> G = CubicOperator.expand_entries(Gtilde)
>>> G.shape
(20, 8000)
>>> q = np.random.random(r)
>>> Gq3 = G @ np.kron(q, np.kron(q, q))
>>> np.allclose(Gq2, Gtilde @ CubicOperator.ckron(q))
True
>>> np.all(CubicOperator.compress_entries(G) == Gtilde)
True