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use super::*;
use crate::ATol;
use ::approx::AbsDiffEq;
impl AbsDiffEq for DecisionVariable {
type Epsilon = ATol;
fn default_epsilon() -> Self::Epsilon {
crate::ATol::default()
}
fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool {
// Must be same ID
if self.id != other.id {
return false;
}
// For different bounds, they are always different.
if !self.bound.abs_diff_eq(&other.bound, epsilon) {
return false;
}
// If kinds are same and bounds are same, they are equal.
if self.kind == other.kind {
return true;
}
// Hereafter, bounds are same, but kinds are different.
// We may consider them mathematically equal in several cases.
// We regard point bound Continuous[a, a] and Integer[a, a] are identical mathematically.
if let Some(lower) = self.bound.is_point(epsilon) {
// If both are point bounds and they are [0, 0], they are considered equal for any kind.
if lower.abs() < epsilon {
return true;
}
// If a != 0, binary, integer, continuous are considered equal,
// but semi-continuous and semi-integer are not because they can be a or 0.
return same_kind_class(
self.kind,
other.kind,
&[Kind::Binary, Kind::Integer, Kind::Continuous],
&[Kind::SemiContinuous, Kind::SemiInteger],
);
}
if self.bound.contains(0.0, epsilon) {
// Bound contains 0, so semi-integer and semi-continuous are equal to integer and continuous.
same_kind_class(
self.kind,
other.kind,
&[Kind::Binary, Kind::Integer, Kind::SemiInteger],
&[Kind::Continuous, Kind::SemiContinuous],
)
} else {
// Only binary and integer are considered equal.
matches!(
(self.kind, other.kind),
(Kind::Binary, Kind::Integer) | (Kind::Integer, Kind::Binary)
)
}
}
}
fn same_kind_class(a: Kind, b: Kind, class1: &[Kind], class2: &[Kind]) -> bool {
(class1.contains(&a) && class1.contains(&b)) || (class2.contains(&a) && class2.contains(&b))
}
#[cfg(test)]
mod tests {
use super::*;
use crate::{ATol, Bound, DecisionVariable, VariableID};
use ::approx::{assert_abs_diff_eq, assert_abs_diff_ne};
#[test]
fn test_different_ids_not_equal() {
// Variables with different IDs are never equal
let var1 = DecisionVariable::new(
VariableID::from(1),
Kind::Continuous,
Bound::new(0.0, 1.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
let var2 = DecisionVariable::new(
VariableID::from(2),
Kind::Continuous,
Bound::new(0.0, 1.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
assert_abs_diff_ne!(var1, var2);
}
#[test]
fn test_different_bounds_not_equal() {
// Variables with different bounds are not equal
let var1 = DecisionVariable::new(
VariableID::from(1),
Kind::Continuous,
Bound::new(0.0, 1.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
let var2 = DecisionVariable::new(
VariableID::from(1),
Kind::Continuous,
Bound::new(0.0, 2.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
assert_abs_diff_ne!(var1, var2);
}
#[test]
fn test_same_kind_and_bound_equal() {
// Variables with same ID, kind, and bounds are equal
let var1 = DecisionVariable::new(
VariableID::from(1),
Kind::Integer,
Bound::new(0.0, 10.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
let var2 = DecisionVariable::new(
VariableID::from(1),
Kind::Integer,
Bound::new(0.0, 10.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
assert_abs_diff_eq!(var1, var2);
}
#[test]
fn test_point_bound_continuous_integer_equal() {
// Continuous[a, a] and Integer[a, a] are equal for point bounds
let var1 = DecisionVariable::new(
VariableID::from(1),
Kind::Continuous,
Bound::new(5.0, 5.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
let var2 = DecisionVariable::new(
VariableID::from(1),
Kind::Integer,
Bound::new(5.0, 5.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
assert_abs_diff_eq!(var1, var2);
}
#[test]
fn test_point_bound_zero_all_kinds_equal() {
// For point bound [0, 0], all kinds are considered equal
let continuous = DecisionVariable::new(
VariableID::from(1),
Kind::Continuous,
Bound::new(0.0, 0.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
let integer = DecisionVariable::new(
VariableID::from(1),
Kind::Integer,
Bound::new(0.0, 0.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
let binary = DecisionVariable::new(
VariableID::from(1),
Kind::Binary,
Bound::new(0.0, 0.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
let semi_continuous = DecisionVariable::new(
VariableID::from(1),
Kind::SemiContinuous,
Bound::new(0.0, 0.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
let semi_integer = DecisionVariable::new(
VariableID::from(1),
Kind::SemiInteger,
Bound::new(0.0, 0.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
// All combinations should be equal
assert_abs_diff_eq!(continuous, integer);
assert_abs_diff_eq!(continuous, binary);
assert_abs_diff_eq!(continuous, semi_continuous);
assert_abs_diff_eq!(continuous, semi_integer);
assert_abs_diff_eq!(integer, semi_integer);
}
#[test]
fn test_point_bound_nonzero_semi_not_equal() {
// For point bound [a, a] where a != 0, semi-continuous/semi-integer
// are not equal to continuous/integer/binary
let continuous = DecisionVariable::new(
VariableID::from(1),
Kind::Continuous,
Bound::new(5.0, 5.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
let semi_continuous = DecisionVariable::new(
VariableID::from(1),
Kind::SemiContinuous,
Bound::new(5.0, 5.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
assert_abs_diff_ne!(continuous, semi_continuous);
}
#[test]
fn test_bound_contains_zero_semi_equal() {
// When bound contains 0, semi-integer equals integer and semi-continuous equals continuous
let integer = DecisionVariable::new(
VariableID::from(1),
Kind::Integer,
Bound::new(-5.0, 5.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
let semi_integer = DecisionVariable::new(
VariableID::from(1),
Kind::SemiInteger,
Bound::new(-5.0, 5.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
let continuous = DecisionVariable::new(
VariableID::from(1),
Kind::Continuous,
Bound::new(-5.0, 5.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
let semi_continuous = DecisionVariable::new(
VariableID::from(1),
Kind::SemiContinuous,
Bound::new(-5.0, 5.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
assert_abs_diff_eq!(integer, semi_integer);
assert_abs_diff_eq!(continuous, semi_continuous);
// Test binary-integer equality with compatible bounds
// Binary is always [0, 1], so test with integer that has same bound
let binary = DecisionVariable::new(
VariableID::from(1),
Kind::Binary,
Bound::new(0.0, 1.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
let integer_01 = DecisionVariable::new(
VariableID::from(1),
Kind::Integer,
Bound::new(0.0, 1.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
assert_abs_diff_eq!(binary, integer_01);
}
#[test]
fn test_point_bound_nonzero_all_basic_kinds_equal() {
// For point bound [a, a] where a != 0, binary, integer, and continuous are all equal
// This is according to the logic in lines 36-43 of the implementation
let binary = DecisionVariable::new(
VariableID::from(1),
Kind::Binary,
Bound::new(1.0, 1.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
let integer = DecisionVariable::new(
VariableID::from(1),
Kind::Integer,
Bound::new(1.0, 1.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
let continuous = DecisionVariable::new(
VariableID::from(1),
Kind::Continuous,
Bound::new(1.0, 1.0).unwrap(),
None,
ATol::default(),
)
.unwrap();
// For point bound [1,1] (not zero), binary, integer, and continuous are all equal
assert_abs_diff_eq!(binary, integer);
assert_abs_diff_eq!(binary, continuous);
assert_abs_diff_eq!(integer, continuous);
}
#[test]
fn test_tolerance_in_point_bound() {
// Test that tolerance is considered for point bounds
let var1 = DecisionVariable::new(
VariableID::from(1),
Kind::Continuous,
Bound::new(1.0, 1.0 + 1e-10).unwrap(),
None,
ATol::default(),
)
.unwrap();
let var2 = DecisionVariable::new(
VariableID::from(1),
Kind::Integer,
Bound::new(1.0, 1.0 + 1e-10).unwrap(),
None,
ATol::default(),
)
.unwrap();
// Should be equal with default tolerance
assert_abs_diff_eq!(var1, var2);
}
}