cr.sparse.opt.indicator_affine

cr.sparse.opt.indicator_affine(A, b=0)

Returns an indicator function for the linear system \(A x = b\)

Parameters

• A (jax.numpy.ndarray) – A matrix \(A \in \RR^{m \times n}\)

• b (jax.numpy.ndarray) – A vector \(b \in \RR^{m}\)

Returns

An indicator function

The indicator function is defined as:

(1)\[\begin{split}I(x) = \begin{cases} 0 & \text{if } A x = b \\ \infty & \text{otherwise} \end{cases}\end{split}\]

The convex set \(C\) is an affine space which is the solution set of system of linear equations \(A x = b\). It is parallel to the null space of \(A\).