# cr.sparse.opt.indicator_l1_ball¶

cr.sparse.opt.indicator_l1_ball(q=1.0, b=None, A=None)[source]

Returns an indicator function for the closed l1 ball $$\| A x - b \|_1 \leq q$$

Parameters
• q (float) – Radius of the ball

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

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

Returns

An indicator function

The indicator function is defined as:

(1)$\begin{split}I(x) = \begin{cases} 0 & \text{if } \| A x - b \|_1 \leq q \\ \infty & \text{otherwise} \end{cases}\end{split}$

Special cases:

• indicator_l1_ball() returns the l1 unit ball $$\| x \|_1 \leq 1$$.

• indicator_l1_ball(q) returns the l1 ball $$\| x \|_1 \leq q$$.

• indicator_l1_ball(q, b=b) returns the l1 ball at center $$b$$, $$\| x - b\|_1 \leq q$$.

Notes:

• If center $$b \in \RR^m$$ is unspecified, we assume the center to be at origin.

• If radius $$q$$ is unspecified, we assume the radius to be 1.

• If the matrix $$A$$ is unspecified, we assume $$A$$ to be the identity matrix $$I \in \RR^{n \times n}$$.