simplex-trace 0.1.0

Exact-arithmetic simplex (primal, Big-M, two-phase) that records every tableau and pivot as data, with sensitivity analysis.
Documentation 
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//! Golden tests: every tableau of a few textbook problems, exactly as a student sees it.
//!
//! Expected tables were checked by hand against the textbooks. If one of these tests fails,
//! the presentation of the method changed — make sure that is intentional.

use simplex_trace::{Method, Options, Phase, Problem, Relation, Sense, Step, solve};

fn tableaus(problem: &Problem, method: Method) -> Vec<String> {
    let solution = solve(problem, method, &Options::default()).unwrap();
    solution.trace.tableaus().map(ToString::to_string).collect()
}

fn assert_tableaus(actual: Vec<String>, expected: &[&str]) {
    assert_eq!(actual.len(), expected.len(), "number of tableaus");
    for (i, (a, e)) in actual.iter().zip(expected).enumerate() {
        assert_eq!(a.trim_end(), e.trim(), "tableau {i}");
    }
}

/// Taha, *Operations Research: An Introduction*, Big-M and two-phase example:
/// min z = 4x1 + x2  s.t.  3x1 + x2 = 3,  4x1 + 3x2 >= 6,  x1 + 2x2 <= 4.
fn taha() -> Problem {
    Problem::minimize([4, 1])
        .subject_to([3, 1], Relation::Eq, 3)
        .subject_to([4, 3], Relation::Ge, 6)
        .subject_to([1, 2], Relation::Le, 4)
}

#[test]
fn taha_big_m() {
    assert_tableaus(
        tableaus(&taha(), Method::BigM),
        &[
            r"
basis |     x1 |     x2 | s2 | s3 | a1 | a2 | rhs
------+--------+--------+----+----+----+----+----
a1    |      3 |      1 |  0 |  0 |  1 |  0 |   3
a2    |      4 |      3 | -1 |  0 |  0 |  1 |   6
s3    |      1 |      2 |  0 |  1 |  0 |  0 |   4
z     | 7M - 4 | 4M - 1 | -M |  0 |  0 |  0 |  9M",
            r"
basis | x1 |         x2 | s2 | s3 |          a1 | a2 |    rhs
------+----+------------+----+----+-------------+----+-------
x1    |  1 |        1/3 |  0 |  0 |         1/3 |  0 |      1
a2    |  0 |        5/3 | -1 |  0 |        -4/3 |  1 |      2
s3    |  0 |        5/3 |  0 |  1 |        -1/3 |  0 |      3
z     |  0 | 5/3M + 1/3 | -M |  0 | -7/3M + 4/3 |  0 | 2M + 4",
            r"
basis | x1 | x2 |   s2 | s3 |       a1 |       a2 |  rhs
------+----+----+------+----+----------+----------+-----
x1    |  1 |  0 |  1/5 |  0 |      3/5 |     -1/5 |  3/5
x2    |  0 |  1 | -3/5 |  0 |     -4/5 |      3/5 |  6/5
s3    |  0 |  0 |    1 |  1 |        1 |       -1 |    1
z     |  0 |  0 |  1/5 |  0 | -M + 8/5 | -M - 1/5 | 18/5",
            r"
basis | x1 | x2 | s2 |   s3 |       a1 | a2 |  rhs
------+----+----+----+------+----------+----+-----
x1    |  1 |  0 |  0 | -1/5 |      2/5 |  0 |  2/5
x2    |  0 |  1 |  0 |  3/5 |     -1/5 |  0 |  9/5
s2    |  0 |  0 |  1 |    1 |        1 | -1 |    1
z     |  0 |  0 |  0 | -1/5 | -M + 7/5 | -M | 17/5",
        ],
    );
}

#[test]
fn taha_two_phase() {
    assert_tableaus(
        tableaus(&taha(), Method::TwoPhase),
        &[
            // Phase 1: minimize r = a1 + a2.
            r"
basis | x1 | x2 | s2 | s3 | a1 | a2 | rhs
------+----+----+----+----+----+----+----
a1    |  3 |  1 |  0 |  0 |  1 |  0 |   3
a2    |  4 |  3 | -1 |  0 |  0 |  1 |   6
s3    |  1 |  2 |  0 |  1 |  0 |  0 |   4
r     |  7 |  4 | -1 |  0 |  0 |  0 |   9",
            r"
basis | x1 |  x2 | s2 | s3 |   a1 | a2 | rhs
------+----+-----+----+----+------+----+----
x1    |  1 | 1/3 |  0 |  0 |  1/3 |  0 |   1
a2    |  0 | 5/3 | -1 |  0 | -4/3 |  1 |   2
s3    |  0 | 5/3 |  0 |  1 | -1/3 |  0 |   3
r     |  0 | 5/3 | -1 |  0 | -7/3 |  0 |   2",
            r"
basis | x1 | x2 |   s2 | s3 |   a1 |   a2 | rhs
------+----+----+------+----+------+------+----
x1    |  1 |  0 |  1/5 |  0 |  3/5 | -1/5 | 3/5
x2    |  0 |  1 | -3/5 |  0 | -4/5 |  3/5 | 6/5
s3    |  0 |  0 |    1 |  1 |    1 |   -1 |   1
r     |  0 |  0 |    0 |  0 |   -1 |   -1 |   0",
            // Phase 2: artificial columns dropped, real objective priced out.
            r"
basis | x1 | x2 |   s2 | s3 |  rhs
------+----+----+------+----+-----
x1    |  1 |  0 |  1/5 |  0 |  3/5
x2    |  0 |  1 | -3/5 |  0 |  6/5
s3    |  0 |  0 |    1 |  1 |    1
z     |  0 |  0 |  1/5 |  0 | 18/5",
            r"
basis | x1 | x2 | s2 |   s3 |  rhs
------+----+----+----+------+-----
x1    |  1 |  0 |  0 | -1/5 |  2/5
x2    |  0 |  1 |  0 |  3/5 |  9/5
s2    |  0 |  0 |  1 |    1 |    1
z     |  0 |  0 |  0 | -1/5 | 17/5",
        ],
    );
}

/// Hillier & Lieberman, Wyndor Glass Co.: max z = 3x1 + 5x2.
#[test]
fn hillier_wyndor() {
    let problem = Problem::maximize([3, 5])
        .subject_to([1, 0], Relation::Le, 4)
        .subject_to([0, 2], Relation::Le, 12)
        .subject_to([3, 2], Relation::Le, 18);
    assert_tableaus(
        tableaus(&problem, Method::Simplex),
        &[
            r"
basis | x1 | x2 | s1 | s2 | s3 | rhs
------+----+----+----+----+----+----
s1    |  1 |  0 |  1 |  0 |  0 |   4
s2    |  0 |  2 |  0 |  1 |  0 |  12
s3    |  3 |  2 |  0 |  0 |  1 |  18
z     | -3 | -5 |  0 |  0 |  0 |   0",
            r"
basis | x1 | x2 | s1 |  s2 | s3 | rhs
------+----+----+----+-----+----+----
s1    |  1 |  0 |  1 |   0 |  0 |   4
x2    |  0 |  1 |  0 | 1/2 |  0 |   6
s3    |  3 |  0 |  0 |  -1 |  1 |   6
z     | -3 |  0 |  0 | 5/2 |  0 |  30",
            r"
basis | x1 | x2 | s1 |   s2 |   s3 | rhs
------+----+----+----+------+------+----
s1    |  0 |  0 |  1 |  1/3 | -1/3 |   2
x2    |  0 |  1 |  0 |  1/2 |    0 |   6
x1    |  1 |  0 |  0 | -1/3 |  1/3 |   2
z     |  0 |  0 |  0 |  3/2 |    1 |  36",
        ],
    );
}

#[test]
fn snapshots_carry_sense_label_and_optimality() {
    let solution = solve(&taha(), Method::TwoPhase, &Options::default()).unwrap();
    let mut seen = Vec::new();
    for step in &solution.trace.steps {
        if let Step::Tableau {
            phase, snapshot, ..
        } = step
        {
            let expected = match phase {
                Phase::One => (Sense::Minimize, "r"),
                _ => (Sense::Minimize, "z"),
            };
            assert_eq!(
                (snapshot.sense, snapshot.objective_label.as_str()),
                expected
            );
            seen.push((*phase, snapshot.is_optimal()));
        }
    }
    // Only the last tableau of each phase is optimal.
    assert_eq!(
        seen,
        [
            (Phase::One, false),
            (Phase::One, false),
            (Phase::One, true),
            (Phase::Two, false),
            (Phase::Two, true),
        ]
    );
}

#[test]
fn maximization_phase_two_keeps_max_sense() {
    // max 2x1 + 3x2  s.t.  x1 + x2 >= 2,  x1 + 2x2 <= 6
    let problem = Problem::maximize([2, 3])
        .subject_to([1, 1], Relation::Ge, 2)
        .subject_to([1, 2], Relation::Le, 6);
    let solution = solve(&problem, Method::TwoPhase, &Options::default()).unwrap();
    for step in &solution.trace.steps {
        if let Step::Tableau {
            phase, snapshot, ..
        } = step
        {
            let sense = if *phase == Phase::One {
                Sense::Minimize
            } else {
                Sense::Maximize
            };
            assert_eq!(snapshot.sense, sense);
        }
    }
    assert!(solution.trace.tableaus().last().unwrap().is_optimal());
}