# shrinkage::DualCertificate

Shrinkage for Rust · 0.3.0

[Source](<https://github.com/jolars/shrinkage/blob/eeafe449edce19d3c552a03060f681ae3891af74/src/screening.rs>)

```rust
pub struct DualCertificate
```

Original-problem certificate on the observation scale. 

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## Inherent implementation

[Source](<https://github.com/jolars/shrinkage/blob/eeafe449edce19d3c552a03060f681ae3891af74/src/screening.rs>)

```rust
impl DualCertificate
```

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### `dual_objective`

```rust
pub fn dual_objective(&self) -> f64
```

[Source](<https://github.com/jolars/shrinkage/blob/eeafe449edce19d3c552a03060f681ae3891af74/src/screening.rs>)

Dual objective `D(theta)` for the original, complete problem. 

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### `dual_vector`

```rust
pub fn dual_vector(&self) -> &[f64]
```

[Source](<https://github.com/jolars/shrinkage/blob/eeafe449edce19d3c552a03060f681ae3891af74/src/screening.rs>)

Feasible observation-scale dual vector `theta`, in training-row order. 

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### `duality_gap`

```rust
pub fn duality_gap(&self) -> f64
```

[Source](<https://github.com/jolars/shrinkage/blob/eeafe449edce19d3c552a03060f681ae3891af74/src/screening.rs>)

Conservatively padded `G(beta_0, beta, theta)` on the averaged-loss scale. 

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### `radius`

```rust
pub fn radius(&self) -> f64
```

[Source](<https://github.com/jolars/shrinkage/blob/eeafe449edce19d3c552a03060f681ae3891af74/src/screening.rs>)

Euclidean radius containing the optimal observation-scale dual vector. 

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## Implementation of Clone

[Source](<https://github.com/jolars/shrinkage/blob/eeafe449edce19d3c552a03060f681ae3891af74/src/screening.rs>)

```rust
impl Clone for DualCertificate
```

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### `clone`

```rust
fn clone(&self) -> Self
```

[Source](<https://github.com/jolars/shrinkage/blob/eeafe449edce19d3c552a03060f681ae3891af74/src/screening.rs>)

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## Implementation of Debug

[Source](<https://github.com/jolars/shrinkage/blob/eeafe449edce19d3c552a03060f681ae3891af74/src/screening.rs>)

```rust
impl Debug for DualCertificate
```

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### `fmt`

```rust
fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result
```

[Source](<https://github.com/jolars/shrinkage/blob/eeafe449edce19d3c552a03060f681ae3891af74/src/screening.rs>)

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## Implementation of Freeze

```rust
impl Freeze for DualCertificate
```

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## Implementation of RefUnwindSafe

```rust
impl RefUnwindSafe for DualCertificate
```

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## Implementation of Send

```rust
impl Send for DualCertificate
```

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## Implementation of Sync

```rust
impl Sync for DualCertificate
```

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## Implementation of Unpin

```rust
impl Unpin for DualCertificate
```

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## Implementation of UnsafeUnpin

```rust
impl UnsafeUnpin for DualCertificate
```

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## Implementation of UnwindSafe

```rust
impl UnwindSafe for DualCertificate
```

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## Implementation of Any

```rust
impl<T> Any for T where T: 'static + ?Sized
```

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## Implementation of Borrow

```rust
impl<T> Borrow<T> for T where T: ?Sized
```

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## Implementation of BorrowMut

```rust
impl<T> BorrowMut<T> for T where T: ?Sized
```

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## Implementation of ByRef

```rust
impl<T> ByRef<T> for T
```

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## Implementation of CastableFrom

```rust
impl<ST, DT> CastableFrom<ST, Initialized, Initialized> for DT where ST: ?Sized, DT: ?Sized
```

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## Implementation of CastableFrom

```rust
impl<ST, DT> CastableFrom<ST, Uninit, Uninit> for DT where ST: ?Sized, DT: ?Sized
```

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## Implementation of CloneToUninit

```rust
impl<T> CloneToUninit for T where T: Clone
```

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## Implementation of From

```rust
impl<T> From<T> for T
```

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## Implementation of Imply

```rust
impl<T, U> Imply<T> for U where T: ?Sized, U: ?Sized
```

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## Implementation of Into

```rust
impl<T, U> Into<U> for T where U: From<T>
```

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## Implementation of IntoEither

```rust
impl<T> IntoEither for T
```

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## Implementation of Pointable

```rust
impl<T> Pointable for T
```

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## Implementation of Read

```rust
impl<T> Read<Exclusive, BecauseExclusive> for T where T: ?Sized
```

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## Implementation of Same

```rust
impl<T> Same for T
```

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## Implementation of SupersetOf

```rust
impl<SS, SP> SupersetOf<SS> for SP where SS: SubsetOf<SP>
```

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## Implementation of ToOwned

```rust
impl<T> ToOwned for T where T: Clone
```

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## Implementation of TryFrom

```rust
impl<T, U> TryFrom<U> for T where U: Into<T>
```

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## Implementation of TryInto

```rust
impl<T, U> TryInto<U> for T where U: TryFrom<T>
```