Masking Function

Function Form

$$y=\text{masking}(x,mask)=x\cdot mask=\{\begin{array}{ll}x,& mask\\ \\ 0,& \mathrm{\neg }mask\end{array}$$

where $mask\in \{0,1\}$.

Constants

$$m=max(|x|)$$

Additional Variables

$y^{\prime }\in \mathbb{R}$: Represents the masked value.

Derived Symbol

$$y=y^{\prime }$$

Mathematical Model

$$\begin{array}{rl}\text{s.t.}& y^{\prime }\le x+m\cdot (1-mask)\\ \\ & y^{\prime }\ge x-m\cdot (1-mask)\\ \\ & y^{\prime }\le m\cdot mask\\ \\ & y^{\prime }\ge -m\cdot mask\\ \end{array}$$

Code Example

kotlin

import kotlinx.coroutines.*
import fuookami.ospf.kotlin.utils.math.*
import fuookami.ospf.kotlin.core.frontend.variable.*
import fuookami.ospf.kotlin.core.frontend.expression.polynomial.*
import fuookami.ospf.kotlin.core.frontend.expression.symbol.linear_function.*
import fuookami.ospf.kotlin.core.frontend.inequality.*
import fuookami.ospf.kotlin.core.frontend.model.mechanism.*
import fuookami.ospf.kotlin.core.backend.plugins.scip.*

val x = RealVar("x")
x.range.leq(Flt64.two)
x.range.geq(-Flt64.three)
val mask = BinVar("mask")
val masking = MaskingFunction(
    x = x,
    mask = mask,
    name = "masking"
)
val solver = ScipLinearSolver()

val model1 = LinearMetaModel()
model1.add(x)
model1.add(mask)
model1.add(masking)
model1.minimize(masking)

val result1 = runBlocking { solver(model1) }
assert(result1.value!!.obj eq -Flt64.three)
assert(result1.value!!.solution[0] eq -Flt64.three)
assert(result1.value!!.solution[1] eq Flt64.one)

val model2 = LinearMetaModel()
model2.add(x)
model2.add(mask)
model2.add(masking)
model2.addConstraint(mask eq false)
model2.minimize(masking)

val result2 = runBlocking { solver(model2) }
assert(result2.value!!.obj eq Flt64.zero)

Complete Implementation Reference:

• Kotlin

Complete Example Reference:

• Kotlin