# Masked
`Masked` excludes selected coefficients from a supported penalty. Let $m_j$ be one for penalized coordinates and zero for excluded coordinates. Then
$$
R_{\mathrm{masked}}(\beta) = R(m \odot \beta).
$$
In the Rust mask, `true` means **unpenalized**, while `false` retains the penalty. The mask has one entry per coefficient and never includes intercepts.
## Constraint region
`Masked::new(vec![true, false], L1::new(1.0))` gives $|\beta_2| \leq 1$. The first coordinate is free, so the region is unbounded horizontally. See the [plot conventions](<./#read-the-constraint-plots>).
## Use the wrapper
```rust
use shrinkage::{L1, Masked, Penalty, ProximalPenalty};
fn main() -> Result<(), Box> {
let penalty = Masked::new(vec![true, false], L1::new(0.5));
assert_eq!(penalty.value(&[100.0, -2.0])?, 1.0);
let mut shrunk = [0.0; 2];
penalty.prox(&[100.0, -2.0], 1.0, &mut shrunk)?;
assert_eq!(shrunk, [100.0, -1.5]);
Ok(())
}
```
The proximal map copies excluded inputs unchanged and solves the restricted penalty exactly. L1, ridge, and elastic net implement the required `RestrictedProximalPenalty` capability. `Scaled` preserves it. Coupled penalties cannot be masked merely by restoring coefficients after an unrestricted prox.
Use [proximal gradient](<../reference/solvers/proximal-gradient>) and compose the wrapper inside [AxisPenalty]() when needed. The wrapper does not supply the coordinate capability required by IRLS.
API: [`shrinkage::Masked`]() and [`shrinkage::RestrictedProximalPenalty`]().