boundlab.zonoq.matmul#
Matrix products that keep the quadratic term symbolic.
For two linear zonotopes the product is exactly quadratic:
\[\Big(\sum_i A_i \varepsilon_i\Big)\Big(\sum_j B_j \varepsilon_j\Big)
= \sum_{ij} (A_i B_j)\, \varepsilon_i \varepsilon_j ,\]
so Matmul stores \(A_i B_j\) in a
Quad unchanged; only the linear-times-quadratic
and quadratic-times-quadratic cross terms (degree 3 and 4) are bounded into
interval noise.
Classes
ZonoQ × ZonoQ product: \(L_1 L_2\) exactly into the quadratic part; \(L Q\), \(Q L\) and \(Q Q\) terms box-bounded as noise (degree ≥ 3 has no representation here). |
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Matrix product for a ZonoQ with an independent Zono remainder. |