induced_norm¶

probnum.utils.linalg.induced_norm(v, A=None, axis=- 1)[source]¶

Induced norm \(\lVert v \rVert_A := \sqrt{v^T A v}\).

Computes the induced norm over the given axis of the array.

Parameters

v (np.ndarray) – Array.
A (Optional[Union[np.ndarray, linops.LinearOperator]]) – Symmetric positive (semi-)definite linear operator defining the geometry.
axis (int) – Specifies the axis along which to compute the vector norms.

Returns

Vector norm of v along the given axis.

Return type

norm