gridcraft/crates/engine/src/cmd/solver/tests.rs

use gridcraft_core::{CellRef, Value};
use serde_json::json;

use crate::Session;

fn s() -> Session {
    let mut s = Session::new();
    s.new_workbook();
    s
}
fn n(s: &Session, a: &str) -> f64 {
    let d = s.doc().unwrap();
    d.wb.active().unwrap().value(CellRef::parse(a).unwrap()).as_f64().unwrap_or(f64::NAN)
}
/// The first saved-model name scoped to the active sheet.
fn saved(s: &Session) -> String {
    let d = s.doc().unwrap();
    d.wb.names.iter().find(|n| n.scope == Some(d.wb.active_sheet())).map(|n| n.name.clone()).unwrap_or_default()
}
fn set(s: &mut Session, cells: &[(&str, &str)]) {
    for (c, v) in cells {
        s.execute("cell.set", json!({"cell": c, "input": v})).unwrap();
    }
}

#[test]
fn simplex_solves_the_wyndor_glass_lp() {
    // Hillier & Lieberman's Wyndor Glass problem: max 3x + 5y, x ≤ 4, 2y ≤ 12, 3x + 2y ≤ 18
    // → x = 2, y = 6, Z = 36.
    let mut s = s();
    set(&mut s, &[("A1", "0"), ("A2", "0"), ("B1", "=3*A1+5*A2"), ("B2", "=2*A2"), ("B3", "=3*A1+2*A2")]);
    let r = s
        .execute(
            "data.solver",
            json!({"objective": "B1", "goal": "max", "variables": "A1:A2", "constraints": ["A1 <= 4", "B2 <= 12", {"lhs": "B3", "op": "<=", "rhs": 18}], "method": "simplex"}),
        )
        .unwrap();
    assert_eq!(r["status"], "optimal", "{r}");
    assert!((n(&s, "A1") - 2.0).abs() < 1e-9 && (n(&s, "A2") - 6.0).abs() < 1e-9);
    assert!((n(&s, "B1") - 36.0).abs() < 1e-9);
    // The model is saved as hidden names, survives XLSX and solves again from them.
    let names: Vec<String> = s.doc().unwrap().wb.names.iter().map(|n| n.name.clone()).collect();
    assert!(names.iter().any(|n| n == "solver_opt") && names.iter().any(|n| n == "solver_lhs3"));
    let b64 = s.execute("file.saveBytes", json!({"format": "xlsx"})).unwrap()["base64"].as_str().unwrap().to_string();
    s.execute("file.open", json!({"name": "m.xlsx", "base64": b64})).unwrap();
    set(&mut s, &[("A1", "0"), ("A2", "0")]);
    let m = s.execute("data.solver", json!({})).unwrap();
    assert_eq!(m["model"]["objective"], "B1");
    assert_eq!(m["model"]["method"], "simplex");
    let r = s.execute("data.solver", json!({"saved": true})).unwrap();
    assert_eq!(r["status"], "optimal");
    assert!((n(&s, "B1") - 36.0).abs() < 1e-9);
    // Minimise with keep: false leaves the cells alone.
    set(&mut s, &[("A1", "1"), ("A2", "1")]);
    let r = s.execute("data.solver", json!({"saved": true, "goal": "min", "keep": false})).unwrap();
    assert_eq!(r["objective"], 0.0);
    assert_eq!((n(&s, "A1"), n(&s, "A2")), (1.0, 1.0));
}

#[test]
fn integer_and_binary_constraints_use_branch_and_bound() {
    // max 5x + 4y, 6x + 4y ≤ 24, x + 2y ≤ 6: the LP optimum (3, 1.5) = 21; integers give
    // (4, 0) = 20.
    let mut s = s();
    set(&mut s, &[("B1", "=5*A1+4*A2"), ("B2", "=6*A1+4*A2"), ("B3", "=A1+2*A2")]);
    let base = json!({"objective": "B1", "variables": "A1:A2", "constraints": ["B2 <= 24", "B3 <= 6"], "method": "simplex"});
    let r = s.execute("data.solver", base.clone()).unwrap();
    assert!((r["objective"].as_f64().unwrap() - 21.0).abs() < 1e-9);
    let mut p = base.clone();
    p["constraints"].as_array_mut().unwrap().push(json!("A1:A2 int"));
    let r = s.execute("data.solver", p).unwrap();
    assert_eq!(r["status"], "optimal");
    assert_eq!((n(&s, "A1"), n(&s, "A2"), n(&s, "B1")), (4.0, 0.0, 20.0));
    // 0/1 knapsack: values 10, 13, 7, weights 5, 6, 4, capacity 10 → items 2 and 3 (20).
    set(&mut s, &[("D1", "=10*C1+13*C2+7*C3"), ("D2", "=5*C1+6*C2+4*C3")]);
    let r = s
        .execute("data.solver", json!({"objective": "D1", "variables": "C1:C3", "constraints": ["D2 <= 10", "C1:C3 bin"], "method": "simplex"}))
        .unwrap();
    assert_eq!(r["status"], "optimal");
    assert_eq!((n(&s, "C1"), n(&s, "C2"), n(&s, "C3"), n(&s, "D1")), (0.0, 1.0, 1.0, 20.0));
}

#[test]
fn grg_finds_smooth_optima() {
    // Largest rectangle with perimeter at most 20: a 5 × 5 square, area 25.
    let mut s = s();
    set(&mut s, &[("A1", "1"), ("A2", "1"), ("B1", "=A1*A2"), ("B2", "=2*A1+2*A2")]);
    let r = s.execute("data.solver", json!({"objective": "B1", "variables": "A1:A2", "constraints": ["B2 <= 20"]})).unwrap();
    assert_eq!(r["status"], "converged", "{r}");
    assert!((n(&s, "A1") - 5.0).abs() < 1e-3 && (n(&s, "A2") - 5.0).abs() < 1e-3, "{r}");
    // Unconstrained minimum of (x − 3)² + (y + 1)² at (3, −1) once negatives are allowed.
    set(&mut s, &[("C1", "0"), ("C2", "0"), ("D1", "=(C1-3)^2+(C2+1)^2")]);
    s.execute("data.solver", json!({"objective": "D1", "goal": "min", "variables": "C1:C2", "nonNegative": false})).unwrap();
    assert!((n(&s, "C1") - 3.0).abs() < 1e-4 && (n(&s, "C2") + 1.0).abs() < 1e-4);
    // Value Of: x³ = 8 → x = 2.
    set(&mut s, &[("E1", "1"), ("F1", "=E1^3")]);
    s.execute("data.solver", json!({"objective": "F1", "goal": "value", "value": 8, "variables": "E1"})).unwrap();
    assert!((n(&s, "E1") - 2.0).abs() < 1e-4);
}

#[test]
fn evolutionary_finds_the_global_minimum_of_non_smooth_and_multimodal_models() {
    let mut s = s();
    // |x − 3| + |y + 2| has a kink at its minimum (3, −2).
    set(&mut s, &[("A1", "0"), ("A2", "0"), ("B1", "=ABS(A1-3)+ABS(A2+2)")]);
    let p = json!({"objective": "B1", "goal": "min", "variables": "A1:A2", "constraints": ["A1:A2 >= -10", "A1:A2 <= 10"], "method": "evolutionary"});
    let r = s.execute("data.solver", p.clone()).unwrap();
    assert!(r["status"] == "converged" || r["status"] == "cannotImprove", "{r}");
    assert!((n(&s, "A1") - 3.0).abs() < 1e-6 && (n(&s, "A2") + 2.0).abs() < 1e-6, "{r}");
    // The same seed repeats the run exactly.
    set(&mut s, &[("A1", "0"), ("A2", "0")]);
    let again = s.execute("data.solver", p).unwrap();
    assert_eq!(again["values"], r["values"]);
    assert_eq!(again["evaluations"], r["evaluations"]);
    // Rastrigin's function 20 + Σ (x² − 10 cos 2πx) on [−5.12, 5.12]² has its global minimum 0
    // at the origin among many local minima; GRG from (3.3, −2.7) stops at a local one.
    set(&mut s, &[("C1", "3.3"), ("C2", "-2.7"), ("D1", "=20+C1^2-10*COS(2*PI()*C1)+C2^2-10*COS(2*PI()*C2)")]);
    let base = json!({"objective": "D1", "goal": "min", "variables": "C1:C2", "constraints": ["C1:C2 >= -5.12", "C1:C2 <= 5.12"]});
    s.execute("data.solver", base.clone()).unwrap();
    assert!(n(&s, "D1") > 0.5, "GRG is local: {}", n(&s, "D1"));
    set(&mut s, &[("C1", "3.3"), ("C2", "-2.7")]);
    let mut p = base.clone();
    p["method"] = json!("evolutionary");
    let r = s.execute("data.solver", p).unwrap();
    assert!(n(&s, "D1") < 1e-8 && n(&s, "C1").abs() < 1e-5 && n(&s, "C2").abs() < 1e-5, "{r}");
    // A stepped model: ROUND makes it flat almost everywhere; the minimum is at 7.2.
    set(&mut s, &[("E1", "0"), ("F1", "=ABS(ROUND(E1,0)-7)+ABS(E1-7.2)/100")]);
    s.execute("data.solver", json!({"objective": "F1", "goal": "min", "variables": "E1", "constraints": ["E1 <= 20"], "method": "evolutionary"}))
        .unwrap();
    assert!((n(&s, "E1") - 7.2).abs() < 1e-6, "{}", n(&s, "E1"));
}

#[test]
fn evolutionary_handles_integers_bounds_and_the_saved_model() {
    let mut s = s();
    // The 0/1 knapsack of the branch-and-bound test: items 2 and 3, value 20.
    set(&mut s, &[("D1", "=10*C1+13*C2+7*C3"), ("D2", "=5*C1+6*C2+4*C3")]);
    let p = json!({"objective": "D1", "variables": "C1:C3", "constraints": ["D2 <= 10", "C1:C3 bin"], "method": "evolutionary", "populationSize": 30, "randomSeed": 7});
    let r = s.execute("data.solver", p).unwrap();
    assert!(r["status"] == "converged" || r["status"] == "cannotImprove", "{r}");
    assert_eq!((n(&s, "C1"), n(&s, "C2"), n(&s, "C3"), n(&s, "D1")), (0.0, 1.0, 1.0, 20.0));
    // The method and its options are saved, survive XLSX and solve again.
    let b64 = s.execute("file.saveBytes", json!({"format": "xlsx"})).unwrap()["base64"].as_str().unwrap().to_string();
    s.execute("file.open", json!({"name": "e.xlsx", "base64": b64})).unwrap();
    let m = s.execute("data.solver", json!({})).unwrap();
    assert_eq!(m["model"]["method"], "evolutionary");
    assert_eq!((m["model"]["populationSize"].as_f64(), m["model"]["randomSeed"].as_f64()), (Some(30.0), Some(7.0)));
    set(&mut s, &[("C1", "0"), ("C2", "0"), ("C3", "0")]);
    s.execute("data.solver", json!({"saved": true})).unwrap();
    assert_eq!(n(&s, "D1"), 20.0);
    // Integer constraints: max x + y with x + 2y ≤ 7 on integers in [0, 10] → (7, 0).
    set(&mut s, &[("A1", "0"), ("A2", "0"), ("B1", "=A1+A2"), ("B2", "=A1+2*A2")]);
    let r = s
        .execute(
            "data.solver",
            json!({"objective": "B1", "variables": "A1:A2", "constraints": ["B2 <= 7", "A1:A2 <= 10", "A1:A2 int"], "method": "evolutionary"}),
        )
        .unwrap();
    assert_eq!((n(&s, "A1"), n(&s, "A2")), (7.0, 0.0), "{r}");
    // Every variable needs bounds unless requireBounds is off; then it searches around the start.
    set(&mut s, &[("E1", "1"), ("F1", "=ABS(E1-4)")]);
    let p = json!({"objective": "F1", "goal": "min", "variables": "E1", "method": "evolutionary"});
    assert!(s.execute("data.solver", p.clone()).is_err());
    let mut p = p;
    p["requireBounds"] = json!(false);
    s.execute("data.solver", p).unwrap();
    assert!((n(&s, "E1") - 4.0).abs() < 1e-6);
    // Infeasible constraints and a tiny budget are reported without changing the cells.
    set(&mut s, &[("E1", "1")]);
    let r = s
        .execute("data.solver", json!({"objective": "F1", "variables": "E1", "constraints": ["E1 <= 3", "F1 >= 10"], "method": "evolutionary"}))
        .unwrap();
    assert_eq!(r["status"], "infeasible", "{r}");
    let r = s
        .execute(
            "data.solver",
            json!({"objective": "F1", "variables": "E1", "constraints": ["E1 <= 3"], "method": "evolutionary", "maxEvaluations": 3}),
        )
        .unwrap();
    assert_eq!(r["status"], "iterationLimit", "{r}");
    assert_eq!(n(&s, "E1"), 1.0);
}

/// Text or number at `a1` on sheet `name`.
fn at(s: &Session, name: &str, a1: &str) -> Value {
    let d = s.doc().unwrap();
    d.wb.sheet(d.wb.sheet_index(name).unwrap()).unwrap().value(CellRef::parse(a1).unwrap())
}

/// The row of the first cell holding `text` on sheet `name`.
fn row_of(s: &Session, name: &str, text: &str) -> u32 {
    let d = s.doc().unwrap();
    let sh = d.wb.sheet(d.wb.sheet_index(name).unwrap()).unwrap();
    (0..60).find(|r| (0..8).any(|c| sh.value(CellRef::new(*r, c)) == Value::text(text))).unwrap()
}

#[test]
fn answer_and_limits_reports_describe_the_wyndor_glass_solution() {
    // Wyndor Glass with labels: doors and windows across, the three plants' hours down.
    let mut s = s();
    s.execute(
        "range.setValues",
        json!({"range": "A1", "values": [[null, "Doors", "Windows", "Used", "Available"], ["Batches", 0, 0, null, null], ["Plant 1", 1, 0, null, 4], ["Plant 2", 0, 2, null, 12], ["Plant 3", 3, 2, null, 18], ["Profit", 3, 5, null, null]]}),
    )
    .unwrap();
    for r in 3..=6 {
        set(&mut s, &[(&format!("D{r}"), &format!("=SUMPRODUCT(B{r}:C{r},$B$2:$C$2)"))]);
    }
    let solved = s
        .execute(
            "data.solver",
            json!({"objective": "D6", "variables": "B2:C2", "constraints": ["D3:D5 <= E3:E5"], "method": "simplex", "reports": ["answer", "limits"]}),
        )
        .unwrap();
    assert_eq!(solved["status"], "optimal", "{solved}");
    assert_eq!(solved["reports"], json!(["Answer Report 1", "Limits Report 1"]));
    assert_eq!(solved["original"], json!({"B2": 0.0, "C2": 0.0}));
    let d = s.doc().unwrap();
    let names: Vec<&str> = d.wb.sheets.iter().map(|x| x.name.as_str()).collect();
    assert_eq!(names, ["Answer Report 1", "Limits Report 1", "Sheet1"]);
    assert_eq!(d.wb.active().unwrap().name, "Sheet1", "the model's sheet stays active");
    assert_eq!(saved(&s), "solver_opt", "the saved model follows its sheet");
    let a = "Answer Report 1";
    assert_eq!(at(&s, a, "A1"), Value::text("GridCraft Answer Report"));
    // Objective: $D$6 "Profit Used", from 0 to 36.
    let r = row_of(&s, a, "$D$6");
    assert_eq!(at(&s, a, &format!("C{}", r + 1)), Value::text("Profit Used"));
    assert_eq!((at(&s, a, &format!("D{}", r + 1)), at(&s, a, &format!("E{}", r + 1))), (Value::number(0.0), Value::number(36.0)));
    // Variables: doors 0 → 2, windows 0 → 6, continuous.
    let r = row_of(&s, a, "$B$2") + 1;
    assert_eq!(at(&s, a, &format!("C{r}")), Value::text("Batches Doors"));
    assert_eq!(at(&s, a, &format!("E{r}")), Value::number(2.0));
    assert_eq!(at(&s, a, &format!("F{r}")), Value::text("Contin"));
    assert_eq!(at(&s, a, &format!("E{}", r + 1)), Value::number(6.0));
    // Constraints: plant 1 has 2 hours to spare; plants 2 and 3 are binding.
    let r = row_of(&s, a, "$D$3") + 1;
    assert_eq!(at(&s, a, &format!("E{r}")), Value::text("$D$3<=$E$3"));
    assert_eq!((at(&s, a, &format!("F{r}")), at(&s, a, &format!("G{r}"))), (Value::text("Not Binding"), Value::number(2.0)));
    for k in 1..=2 {
        assert_eq!((at(&s, a, &format!("F{}", r + k)), at(&s, a, &format!("G{}", r + k))), (Value::text("Binding"), Value::number(0.0)));
    }
    // Limits with the other variable held: doors 0..2 (profit 30..36), windows 0..6 (6..36).
    let l = "Limits Report 1";
    let r = row_of(&s, l, "$B$2") + 1;
    let row = |r: u32| ["D", "E", "F", "G", "H"].map(|c| at(&s, l, &format!("{c}{r}")).as_f64().unwrap());
    assert_eq!(row(r), [2.0, 0.0, 30.0, 2.0, 36.0]);
    assert_eq!(row(r + 1), [6.0, 0.0, 6.0, 6.0, 36.0]);
    // data.solverReport writes reports from the saved model and a given solution.
    let out = s.execute("data.solverReport", json!({"reports": ["answer"], "values": {"B2": 2, "C2": 6}, "original": {"B2": 1, "C2": 1}})).unwrap();
    assert_eq!(out["sheets"], json!(["Answer Report 2"]));
    let r = row_of(&s, "Answer Report 2", "$D$6") + 1;
    assert_eq!(at(&s, "Answer Report 2", &format!("D{r}")), Value::number(8.0));
    // Undo removes the reports and keeps the solution; refused requests write nothing.
    s.execute("edit.undo", json!({})).unwrap();
    assert_eq!(s.doc().unwrap().wb.sheets.len(), 3);
    for p in [
        json!({}),
        json!({"reports": []}),
        json!({"reports": "answer"}),
        json!({"reports": ["population"]}),
        json!({"reports": ["answer"], "values": {"Z9": 1}}),
        json!({"reports": ["answer"], "values": {"B2": "x"}}),
        json!({"reports": ["limits"], "constraints": ["D3:D5 <= E3:E5", "B2:C2 int"]}),
        json!({"reports": ["limits"], "method": "evolutionary", "constraints": ["D3:D5 <= E3:E5", "B2:C2 <= 10"]}),
    ] {
        assert!(s.execute("data.solverReport", p.clone()).is_err(), "{p}");
    }
    assert_eq!(s.doc().unwrap().wb.sheets.len(), 3);
    // With the solve, its reports and the saved model undone (one step), the result still
    // describes the solution.
    s.execute("edit.undo", json!({})).unwrap();
    assert_eq!((s.doc().unwrap().wb.sheets.len(), n(&s, "B2")), (1, 0.0));
    let mut p = solved.clone();
    p["reports"] = json!(["answer"]);
    assert_eq!(s.execute("data.solverReport", p).unwrap()["sheets"], json!(["Answer Report 1"]));
    let r = row_of(&s, "Answer Report 1", "$B$2") + 1;
    assert_eq!(at(&s, "Answer Report 1", &format!("E{r}")), Value::number(2.0));
}

#[test]
fn refused_solver_reports_preserve_the_document_and_history() {
    for (protected, method, constraints, reports, error) in [
        (true, "simplex", json!(["A1 <= 4"]), json!(["answer"]), "workbook is protected"),
        (false, "simplex", json!(["A1 <= 4", "A1 int"]), json!(["answer", "limits"]), "integer or binary"),
        (false, "evolutionary", json!(["A1 <= 4"]), json!(["answer", "limits"]), "Simplex LP and GRG"),
        (false, "simplex", json!(["A1 <= 4", "A1 int"]), json!(["answer", "sensitivity"]), "integer or binary"),
        (false, "evolutionary", json!(["A1 <= 4"]), json!(["sensitivity"]), "Simplex LP and GRG"),
    ] {
        for (keep, save) in [(true, true), (false, true), (true, false), (false, false)] {
            let mut s = s();
            set(&mut s, &[("A1", "1"), ("B1", "=2*A1")]);
            s.execute("data.solver", json!({"objective": "B1", "variables": "A1", "constraints": ["A1 <= 2"], "method": "simplex", "keep": false}))
                .unwrap();
            set(&mut s, &[("C1", "redo")]);
            s.execute("edit.undo", json!({})).unwrap();
            let d = s.doc_mut().unwrap();
            std::sync::Arc::make_mut(&mut d.wb).protected_structure = protected;
            d.saved = d.wb.clone();
            let before = d.clone();
            let journal = s.journal.clone();
            let err = s
                .execute(
                    "data.solver",
                    json!({"objective": "B1", "variables": "A1", "constraints": constraints, "method": method,
                        "reports": reports, "keep": keep, "saveModel": save}),
                )
                .unwrap_err();
            assert!(err.to_string().contains(error), "{err}");
            let d = s.doc().unwrap();
            assert!(std::sync::Arc::ptr_eq(&d.wb, &before.wb), "{method}: keep={keep}, save={save}: {err}");
            assert!(!d.is_dirty());
            assert_eq!(d.revision, before.revision);
            assert_eq!(d.selection, before.selection);
            assert_eq!(d.sheet_selections, before.sheet_selections);
            for (after, before) in [(&d.undo, &before.undo), (&d.redo, &before.redo)] {
                assert_eq!(after.len(), before.len());
                for (a, b) in after.iter().zip(before) {
                    assert!(std::sync::Arc::ptr_eq(&a.wb, &b.wb));
                    assert_eq!((&a.label, &a.selection), (&b.label, &b.selection));
                }
            }
            assert_eq!(s.journal, journal);
        }
    }
}

#[test]
fn solver_reports_and_optional_solution_and_model_share_one_undo() {
    for (keep, save) in [(true, true), (false, true), (true, false), (false, false)] {
        let mut s = s();
        set(&mut s, &[("A1", "1"), ("B1", "=2*A1")]);
        let before = s.doc().unwrap().clone();
        let out = s
            .execute(
                "data.solver",
                json!({"objective": "B1", "variables": "A1", "constraints": ["A1 <= 4"], "method": "simplex",
                    "reports": ["answer"], "keep": keep, "saveModel": save}),
            )
            .unwrap();
        assert_eq!(out["status"], "optimal");
        assert_eq!(out["reports"], json!(["Answer Report 1"]));
        assert_eq!(out["model"]["objective"], "Sheet1!B1");
        assert_eq!(n(&s, "A1"), if keep { 4.0 } else { 1.0 });
        assert_eq!(saved(&s), if save { "solver_opt" } else { "" });
        assert_eq!(s.doc().unwrap().undo.len(), before.undo.len() + 1);
        assert_eq!(s.doc().unwrap().wb.active().unwrap().name, "Sheet1");
        let r = row_of(&s, "Answer Report 1", "$A$1") + 1;
        assert_eq!(at(&s, "Answer Report 1", &format!("E{r}")), Value::number(4.0));
        s.execute("edit.undo", json!({})).unwrap();
        assert!(std::sync::Arc::ptr_eq(&s.doc().unwrap().wb, &before.wb));
        s.execute("edit.redo", json!({})).unwrap();
        assert_eq!(s.doc().unwrap().wb.sheets.len(), 2);
        assert_eq!(n(&s, "A1"), if keep { 4.0 } else { 1.0 });
    }
}

#[test]
fn solver_reports_keep_row_autofit_on_the_model_sheet() {
    let mut s = s();
    set(&mut s, &[("A1", "1"), ("B1", "=2*A1")]);
    s.execute("home.columnWidth", json!({"cols": "A:A", "width": 30})).unwrap();
    s.execute("home.wrapText", json!({"range": "A1", "on": true})).unwrap();
    let before = s.doc().unwrap().wb.active().unwrap().row_height(0);
    s.execute(
        "data.solver",
        json!({"objective": "B1", "variables": "A1", "constraints": ["A1 <= 1000000"], "method": "simplex", "reports": ["answer"]}),
    )
    .unwrap();
    let sh = s.doc().unwrap().wb.active().unwrap();
    assert_eq!(sh.name, "Sheet1");
    assert_eq!(sh.value(CellRef::new(0, 0)), Value::number(1_000_000.0));
    assert!(sh.row_height(0) > before, "the solved wrapped number must re-fit its row after the report shifts its sheet");
    s.execute("edit.undo", json!({})).unwrap();
    assert_eq!(s.doc().unwrap().wb.active().unwrap().row_height(0), before);
}

#[test]
fn solver_report_insertion_keeps_variable_edit_guards() {
    for array in [false, true] {
        let mut s = s();
        set(&mut s, &[("A2", "1"), ("B1", "=2*A2")]);
        let error = if array {
            s.execute("selection.set", json!({"range": "A1:A2"})).unwrap();
            s.execute("cell.set", json!({"input": "=1", "array": true})).unwrap();
            "part of an array"
        } else {
            s.execute("review.protectSheet", json!({})).unwrap();
            "protected sheet"
        };
        let before = s.doc().unwrap().clone();
        let err = s
            .execute(
                "data.solver",
                json!({"objective": "B1", "variables": "A2", "constraints": ["A2 <= 4"], "method": "simplex", "reports": ["answer"]}),
            )
            .unwrap_err();
        assert!(err.to_string().contains(error), "{err}");
        let d = s.doc().unwrap();
        assert!(std::sync::Arc::ptr_eq(&d.wb, &before.wb));
        assert_eq!(d.undo.len(), before.undo.len());
        assert_eq!(d.sheet_selections, before.sheet_selections);
    }
}

/// The numbers from column D on in the row below the one holding `text` on report `name`.
fn report_row(s: &Session, name: &str, text: &str, cols: &[&str]) -> Vec<f64> {
    let r = row_of(s, name, text) + 1;
    cols.iter().map(|c| at(s, name, &format!("{c}{r}")).as_f64().unwrap()).collect()
}

fn close(got: &[f64], want: &[f64], tol: f64) -> bool {
    got.len() == want.len() && got.iter().zip(want).all(|(g, w)| (g - w).abs() <= tol * (1.0 + w.abs()))
}

#[test]
fn sensitivity_report_gives_the_wyndor_glass_shadow_prices_and_ranges() {
    // Hillier & Lieberman's Wyndor Glass sensitivity analysis: shadow prices 0, 1.5 and 1
    // for the three plants; plant 1's hours may fall by 2 and rise without limit, plants 2's
    // and 3's by 6 either way; the doors' profit 3 may range over 0..7.5, the windows' 5 over
    // 2 and up.
    let mut s = s();
    s.execute(
        "range.setValues",
        json!({"range": "A1", "values": [[null, "Doors", "Windows", "Used", "Available"], ["Batches", 0, 0, null, null], ["Plant 1", 1, 0, null, 4], ["Plant 2", 0, 2, null, 12], ["Plant 3", 3, 2, null, 18], ["Profit", 3, 5, null, null]]}),
    )
    .unwrap();
    for r in 3..=6 {
        set(&mut s, &[(&format!("D{r}"), &format!("=SUMPRODUCT(B{r}:C{r},$B$2:$C$2)"))]);
    }
    let solved = s
        .execute(
            "data.solver",
            json!({"objective": "D6", "variables": "B2:C2", "constraints": ["D3:D5 <= E3:E5"], "method": "simplex", "reports": ["sensitivity"]}),
        )
        .unwrap();
    assert_eq!(solved["reports"], json!(["Sensitivity Report 1"]), "{solved}");
    let rep = "Sensitivity Report 1";
    assert_eq!(at(&s, rep, "A1"), Value::text("GridCraft Sensitivity Report"));
    let r = row_of(&s, rep, "Reduced Cost");
    assert_eq!(at(&s, rep, &format!("F{}", r + 1)), Value::text("Objective Coefficient"));
    let cols = ["D", "E", "F", "G", "H"];
    // Final value, reduced cost, objective coefficient, allowable increase and decrease.
    assert!(close(&report_row(&s, rep, "$B$2", &cols)[1..], &[0.0, 3.0, 4.5, 3.0], 1e-9));
    assert!(close(&report_row(&s, rep, "$C$2", &cols), &[6.0, 0.0, 5.0, 1e30, 3.0], 1e-9));
    // Final value, shadow price, right side, allowable increase and decrease.
    assert!(close(&report_row(&s, rep, "$D$3", &cols), &[2.0, 0.0, 4.0, 1e30, 2.0], 1e-9));
    assert!(close(&report_row(&s, rep, "$D$4", &cols), &[12.0, 1.5, 12.0, 6.0, 6.0], 1e-9));
    assert!(close(&report_row(&s, rep, "$D$5", &cols), &[18.0, 1.0, 18.0, 6.0, 6.0], 1e-9));
    // A minimisation with `>=` rows: min 2x + 3y, x + y ≥ 4, x + 3y ≥ 6 → (3, 1), cost 9.
    // The duals 1.5 and 0.5 solve u + v = 2, u + 3v = 3; the basis holds for 2 ≤ b₁ ≤ 6,
    // 4 ≤ b₂ ≤ 12, 1 ≤ c₁ ≤ 3 and 2 ≤ c₂ ≤ 6.
    set(&mut s, &[("H1", "0"), ("H2", "0"), ("I1", "=2*H1+3*H2"), ("I2", "=H1+H2"), ("I3", "=H1+3*H2")]);
    let r = s
        .execute(
            "data.solver",
            json!({"objective": "I1", "goal": "min", "variables": "H1:H2", "constraints": ["I2 >= 4", "I3 >= 6"], "method": "simplex", "reports": ["sensitivity"]}),
        )
        .unwrap();
    let rep = r["reports"][0].as_str().unwrap().to_string();
    assert!(close(&report_row(&s, &rep, "$H$1", &cols), &[3.0, 0.0, 2.0, 1.0, 1.0], 1e-9), "{r}");
    assert!(close(&report_row(&s, &rep, "$H$2", &cols), &[1.0, 0.0, 3.0, 3.0, 1.0], 1e-9));
    assert!(close(&report_row(&s, &rep, "$I$2", &cols), &[4.0, 1.5, 4.0, 2.0, 2.0], 1e-9));
    assert!(close(&report_row(&s, &rep, "$I$3", &cols), &[6.0, 0.5, 6.0, 6.0, 2.0], 1e-9));
    // A variable held at zero has a reduced cost: min 2x + 3y with x + y ≥ 4 alone uses
    // only x; y would add 3 − 2 = 1 per unit.
    let r = s
        .execute(
            "data.solver",
            json!({"objective": "I1", "goal": "min", "variables": "H1:H2", "constraints": ["I2 >= 4"], "method": "simplex", "reports": ["sensitivity"]}),
        )
        .unwrap();
    let rep = r["reports"][0].as_str().unwrap().to_string();
    assert!(close(&report_row(&s, &rep, "$H$2", &cols), &[0.0, 1.0, 3.0, 1e30, 1.0], 1e-9), "{r}");
    // Integer models, the Evolutionary method and Value Of goals have no Sensitivity report.
    s.execute("data.solver", json!({"objective": "D6", "variables": "B2:C2", "constraints": ["D3:D5 <= E3:E5"], "method": "simplex"})).unwrap();
    for p in [
        json!({"reports": ["sensitivity"], "constraints": ["D3:D5 <= E3:E5", "B2:C2 int"]}),
        json!({"reports": ["sensitivity"], "method": "evolutionary", "constraints": ["D3:D5 <= E3:E5", "B2:C2 <= 10"]}),
        json!({"reports": ["sensitivity"], "goal": "value", "value": 30}),
    ] {
        assert!(s.execute("data.solverReport", p.clone()).is_err(), "{p}");
    }
    // data.solver refuses a Value Of goal's Sensitivity report before it changes anything.
    set(&mut s, &[("B2", "1"), ("C2", "1")]);
    let undo = s.doc().unwrap().undo.len();
    let p = json!({"objective": "D6", "goal": "value", "value": 30, "variables": "B2:C2", "constraints": ["D3:D5 <= E3:E5"], "method": "simplex", "reports": ["sensitivity"]});
    let err = s.execute("data.solver", p).unwrap_err();
    assert!(err.to_string().contains("maximise or minimise"), "{err}");
    assert_eq!((at(&s, "Sheet1", "B2"), at(&s, "Sheet1", "C2")), (Value::number(1.0), Value::number(1.0)));
    assert_eq!(s.doc().unwrap().undo.len(), undo);
}

#[test]
fn simplex_sensitivity_ranges_of_a_redundant_equality_are_zero() {
    // max x with x = 2 and 2x = 4: the second row repeats the first, so any change to either
    // right side alone has no solution, and both ranges of each row are 0. With x = 2 alone the
    // right side may rise without limit and fall by 2 (to x = 0).
    let mut s = s();
    set(&mut s, &[("A1", "0"), ("B1", "=A1"), ("C1", "=A1"), ("C2", "=2*A1")]);
    let cols = ["D", "F", "G", "H"];
    let r = s
        .execute(
            "data.solver",
            json!({"objective": "B1", "variables": "A1", "constraints": ["C1 = 2", "C2 = 4"], "method": "simplex", "reports": ["sensitivity"]}),
        )
        .unwrap();
    let rep = r["reports"][0].as_str().unwrap().to_string();
    assert!(close(&report_row(&s, &rep, "$C$1", &cols), &[2.0, 2.0, 0.0, 0.0], 1e-9), "{:?}", report_row(&s, &rep, "$C$1", &cols));
    assert!(close(&report_row(&s, &rep, "$C$2", &cols), &[4.0, 4.0, 0.0, 0.0], 1e-9), "{:?}", report_row(&s, &rep, "$C$2", &cols));
    // The redundant row doesn't restrict the objective coefficient: x = 2 stays the only
    // solution whatever its profit.
    assert!(close(&report_row(&s, &rep, "$A$1", &["D", "F", "G", "H"]), &[2.0, 1.0, 1e30, 1e30], 1e-9));
    let r = s
        .execute(
            "data.solver",
            json!({"objective": "B1", "variables": "A1", "constraints": ["C1 = 2"], "method": "simplex", "reports": ["sensitivity"]}),
        )
        .unwrap();
    let rep = r["reports"][0].as_str().unwrap().to_string();
    assert!(close(&report_row(&s, &rep, "$C$1", &cols), &[2.0, 2.0, 1e30, 2.0], 1e-9), "{:?}", report_row(&s, &rep, "$C$1", &cols));
}

#[test]
fn simplex_sensitivity_report_needs_an_optimal_point() {
    // Wyndor Glass: (2, 6) is the optimum (36). (0, 0) is feasible but not optimal; (4, 4.8)
    // reaches 36 but breaks plant 3's hours (21.6 > 18).
    let mut s = s();
    s.execute(
        "range.setValues",
        json!({"range": "A1", "values": [[null, "Doors", "Windows", "Used", "Available"], ["Batches", 0, 0, null, null], ["Plant 1", 1, 0, null, 4], ["Plant 2", 0, 2, null, 12], ["Plant 3", 3, 2, null, 18], ["Profit", 3, 5, null, null]]}),
    )
    .unwrap();
    for r in 3..=6 {
        set(&mut s, &[(&format!("D{r}"), &format!("=SUMPRODUCT(B{r}:C{r},$B$2:$C$2)"))]);
    }
    let model = json!({"objective": "D6", "variables": "B2:C2", "constraints": ["D3:D5 <= E3:E5"], "method": "simplex"});
    let report = |b: f64, c: f64| json!({"reports": ["sensitivity"], "model": model, "values": {"B2": b, "C2": c}});
    for (b, c) in [(0.0, 0.0), (4.0, 4.8)] {
        let before = s.doc().unwrap().clone();
        let err = s.execute("data.solverReport", report(b, c)).unwrap_err();
        assert!(err.to_string().contains("not optimal"), "({b}, {c}): {err}");
        assert!(std::sync::Arc::ptr_eq(&s.doc().unwrap().wb, &before.wb));
    }
    let r = s.execute("data.solverReport", report(2.0, 6.0)).unwrap();
    assert_eq!(r["sheets"], json!(["Sensitivity Report 1"]), "{r}");
}

#[test]
fn simplex_sensitivity_report_describes_the_vertex_the_solver_returns() {
    // max x + y with x + y <= 4, x <= 3, y <= 3: every point from (3, 1) to (1, 3) is optimal,
    // but the ranges belong to one vertex. The vertex Simplex LP returns is reported (from
    // several starting values, as Solver Results passes the solve's result on); the other vertex
    // and the midpoint are refused.
    let model = json!({"objective": "D1", "variables": "A1:A2", "constraints": ["C1 <= 4", "A1 <= 3", "A2 <= 3"], "method": "simplex"});
    let mut found = Vec::new();
    for (x, y) in [("0", "0"), ("0.1", "0.7"), ("2.9", "0.3"), ("1", "1"), ("-5", "12.25")] {
        let mut s = s();
        set(&mut s, &[("A1", x), ("A2", y), ("C1", "=A1+A2"), ("D1", "=A1+A2")]);
        let mut p = model.clone();
        p["keep"] = json!(false);
        let r = s.execute("data.solver", p).unwrap();
        assert_eq!(r["status"], "optimal", "{r}");
        let rep = s.execute("data.solverReport", json!({"reports": ["sensitivity"], "model": r["model"], "values": r["values"]})).unwrap();
        assert_eq!(rep["sheets"], json!(["Sensitivity Report 1"]), "from ({x}, {y}): {rep}");
        found.push((r["values"]["A1"].as_f64().unwrap(), r["values"]["A2"].as_f64().unwrap()));
    }
    let (vx, vy) = found[0];
    assert!(found.iter().all(|v| *v == (vx, vy)), "{found:?}");
    let other = if vx == 3.0 { (1.0, 3.0) } else { (3.0, 1.0) };
    assert!([(3.0, 1.0), (1.0, 3.0)].contains(&(vx, vy)), "{found:?}");
    let mut s = s();
    set(&mut s, &[("A1", "0"), ("A2", "0"), ("C1", "=A1+A2"), ("D1", "=A1+A2")]);
    for (x, y) in [other, (2.0, 2.0)] {
        let before = s.doc().unwrap().clone();
        let err = s.execute("data.solverReport", json!({"reports": ["sensitivity"], "model": model, "values": {"A1": x, "A2": y}})).unwrap_err();
        assert!(err.to_string().contains("another optimal solution"), "({x}, {y}): {err}");
        assert!(std::sync::Arc::ptr_eq(&s.doc().unwrap().wb, &before.wb));
        // data.solver's Skip mode (as Solver Results passes) skips only the Sensitivity report.
        let r = s
            .execute(
                "data.solverReport",
                json!({"reports": ["answer", "sensitivity"], "model": model, "values": {"A1": x, "A2": y}, "skipNotOptimal": true}),
            )
            .unwrap();
        assert_eq!(r["skippedReports"][0]["report"], "sensitivity", "{r}");
        assert_eq!(r["sheets"].as_array().map(Vec::len), Some(1), "{r}");
    }
    let r = s.execute("data.solverReport", json!({"reports": ["sensitivity"], "model": model, "values": {"A1": vx, "A2": vy}})).unwrap();
    assert!(r["sheets"][0].as_str().unwrap().starts_with("Sensitivity Report"), "{r}");
}

#[test]
fn simplex_sensitivity_report_repeats_the_solve_from_its_start_values() {
    // max 0.1x + 0.1y with 0.1x + 0.1y <= 0.4, 0.7x + 0.7y <= 2.8, x <= 3, y <= 3: the optimum is
    // not unique, and the difference coefficients of these formulas differ in their last bits
    // with the point they are taken at. From these starts the solve returns (3, 1) or (1, 3);
    // linearised at that solution instead, the report's solve broke the tie the other way and
    // refused the solve's own values. Built from the same start values, the program is the
    // same to the bit, so each solve's own report is written.
    let model =
        json!({"objective": "D1", "variables": "A1:A2", "constraints": ["C1 <= 0.4", "E1 <= 2.8", "A1 <= 3", "A2 <= 3"], "method": "simplex"});
    let formulas = [("C1", "=A1*0.1+A2*0.1"), ("D1", "=A1*0.1+A2*0.1"), ("E1", "=A1*0.7+A2*0.7")];
    let program = |s: &Session, x: &[f64]| {
        let m = super::parse_model(s, &model).unwrap();
        let prob = super::build_problem(&m);
        let mut ev = super::Evaluator {
            trial: super::Trial::new(s.doc().unwrap()),
            sheet: m.sheet,
            vars: m.vars.clone(),
            objective: m.objective,
            rows: prob.rows.clone(),
            evals: 0,
            budget: 100,
            target: None,
        };
        let p = super::lp::simplex_program(&mut ev, m.goal, x).unwrap();
        let bits = |v: &[f64]| v.iter().map(|x| x.to_bits()).collect::<Vec<u64>>();
        let rows: Vec<(Vec<u64>, u64)> = p.rows.iter().map(|(a, _, b)| (bits(a), b.to_bits())).collect();
        (bits(&p.cf), bits(&p.c), rows, p.work)
    };
    let mut vertices = Vec::new();
    for (x, y) in [("-3", "-5"), ("-3", "2.42"), ("-3", "6.13"), ("-3", "9.84"), ("-3", "13.55"), ("0.37", "0.3"), ("2.55", "-1.2")] {
        let mut s = s();
        set(&mut s, &[("A1", x), ("A2", y)]);
        set(&mut s, &formulas);
        let start: Vec<f64> = [x, y].iter().map(|v| v.parse().unwrap()).collect();
        let before = program(&s, &start);
        let r = s.execute("data.solver", model.clone()).unwrap();
        assert_eq!(r["status"], "optimal", "{r}");
        // The program the report builds after the solve (cells now at the solution) from the
        // solve's `original`, as Solver Results passes it, equals the solve's.
        let original: Vec<f64> = ["A1", "A2"].iter().map(|c| r["original"][c].as_f64().unwrap()).collect();
        assert_eq!(original, start);
        assert_eq!(program(&s, &original), before, "from ({x}, {y})");
        let rep = s
            .execute("data.solverReport", json!({"reports": ["sensitivity"], "model": r["model"], "values": r["values"], "original": r["original"]}))
            .unwrap();
        assert_eq!(rep["sheets"], json!(["Sensitivity Report 1"]), "from ({x}, {y}): {rep}");
        let v = (r["values"]["A1"].as_f64().unwrap(), r["values"]["A2"].as_f64().unwrap());
        vertices.push(if v.0 > v.1 { "(3, 1)" } else { "(1, 3)" });
    }
    // Both vertices occur, so the starts exercise the tie.
    assert!(vertices.contains(&"(3, 1)") && vertices.contains(&"(1, 3)"), "{vertices:?}");
}

#[test]
fn simplex_sensitivity_report_refuses_a_point_that_beats_the_optimum() {
    // min 1E+9·A1 with A1 ≥ 0: the optimum is 0. A1 = -1E-7 is outside the bound by less than
    // the precision, yet its objective is -100, far from the optimum.
    let mut s = s();
    set(&mut s, &[("A1", "0"), ("B1", "=1E+9*A1")]);
    let model = json!({"objective": "B1", "goal": "min", "variables": "A1", "constraints": ["A1 <= 5"], "method": "simplex"});
    let before = s.doc().unwrap().clone();
    let err = s.execute("data.solverReport", json!({"reports": ["sensitivity"], "model": model, "values": {"A1": -1e-7}})).unwrap_err();
    assert!(err.to_string().contains("not optimal"), "{err}");
    assert!(std::sync::Arc::ptr_eq(&s.doc().unwrap().wb, &before.wb));
    let r = s.execute("data.solverReport", json!({"reports": ["sensitivity"], "model": model, "values": {"A1": 0}})).unwrap();
    assert_eq!(r["sheets"], json!(["Sensitivity Report 1"]), "{r}");
}

#[test]
fn sensitivity_report_of_a_nonlinear_model_gives_lagrange_multipliers() {
    // The largest rectangle with perimeter at most 20: the area (P/4)² grows by P/8 = 2.5 per
    // unit of perimeter, and both reduced gradients are 0.
    let mut s = s();
    set(&mut s, &[("A1", "1"), ("A2", "1"), ("B1", "=A1*A2"), ("B2", "=2*A1+2*A2")]);
    let r =
        s.execute("data.solver", json!({"objective": "B1", "variables": "A1:A2", "constraints": ["B2 <= 20"], "reports": ["sensitivity"]})).unwrap();
    let rep = "Sensitivity Report 1";
    assert_eq!(r["reports"], json!([rep]), "{r}");
    assert_eq!(at(&s, rep, &format!("E{}", row_of(&s, rep, "$A$1"))), Value::text("Reduced Gradient"));
    assert!(close(&report_row(&s, rep, "$A$1", &["D", "E"]), &[5.0, 0.0], 1e-4));
    assert!(close(&report_row(&s, rep, "$B$2", &["D", "E"]), &[20.0, 2.5], 1e-4));
    // min (x + 1)² + (y − 2)² with x + y ≤ 1 and x, y ≥ 0: (0, 1). The constraint's
    // multiplier is −2; x sits at its bound, where raising it costs 2(x + 1) + 2 = 4.
    set(&mut s, &[("C1", "0.5"), ("C2", "0.5"), ("D1", "=(C1+1)^2+(C2-2)^2"), ("D2", "=C1+C2")]);
    let r = s
        .execute(
            "data.solver",
            json!({"objective": "D1", "goal": "min", "variables": "C1:C2", "constraints": ["D2 <= 1"], "reports": ["sensitivity"]}),
        )
        .unwrap();
    let rep = r["reports"][0].as_str().unwrap().to_string();
    assert!(close(&report_row(&s, &rep, "$C$1", &["D", "E"]), &[0.0, 4.0], 1e-4), "{r}");
    assert!(close(&report_row(&s, &rep, "$C$2", &["D", "E"]), &[1.0, 0.0], 1e-4));
    assert!(close(&report_row(&s, &rep, "$D$2", &["D", "E"]), &[1.0, -2.0], 1e-4));
}

#[test]
fn nonlinear_sensitivity_report_needs_an_optimal_point() {
    let mut s = s();
    set(&mut s, &[("A1", "1"), ("B1", "=A1^2")]);
    set(&mut s, &[("C1", "0"), ("D1", "=(C1-2)^2")]);
    set(&mut s, &[("E1", "1"), ("E2", "1"), ("F1", "=E1*E2"), ("F2", "=2*E1+2*E2")]);
    set(&mut s, &[("G1", "0"), ("G2", "1"), ("H1", "=(G1+1)^2+(G2-2)^2"), ("H2", "=G1+G2")]);
    let square = json!({"objective": "B1", "goal": "min", "variables": "A1", "constraints": ["A1 <= 5"]});
    let shifted = json!({"objective": "D1", "goal": "min", "variables": "C1", "constraints": ["C1 <= 5"]});
    let rectangle = json!({"objective": "F1", "variables": "E1:E2", "constraints": ["F2 <= 20"]});
    let bounded = json!({"objective": "H1", "goal": "min", "variables": "G1:G2", "constraints": ["H2 <= 1"]});
    let report = |model: &serde_json::Value, values: serde_json::Value| json!({"reports": ["sensitivity"], "model": model, "values": values});
    for (model, values, why) in [
        // min A1² at A1 = 1: the free variable's reduced gradient is 2, not 0.
        (&square, json!({"A1": 1}), "free gradient"),
        // The rectangle at 6 × 6 has a larger area than the optimum but a perimeter of 24 > 20.
        (&rectangle, json!({"E1": 6, "E2": 6}), "infeasible"),
        // At 4 × 6 the perimeter binds, but its multiplier can't explain the gradient (6, 4).
        (&rectangle, json!({"E1": 4, "E2": 6}), "unexplained gradient"),
        // min (C1 − 2)² at the bound C1 = 0: raising C1 lowers the objective.
        (&shifted, json!({"C1": 0}), "wrong-way bound"),
        // (1, 0) in the bounded model: the binding row's multiplier would be +4, the wrong sign
        // for a `<=` row when minimising, so the row is dropped and the gradient is unexplained.
        (&bounded, json!({"G1": 1, "G2": 0}), "wrong-sign multiplier"),
    ] {
        let before = s.doc().unwrap().clone();
        let err = s.execute("data.solverReport", report(model, values)).unwrap_err();
        assert!(err.to_string().contains("not optimal"), "{why}: {err}");
        let d = s.doc().unwrap();
        assert!(std::sync::Arc::ptr_eq(&d.wb, &before.wb), "{why}");
        assert_eq!((d.undo.len(), d.redo.len()), (before.undo.len(), before.redo.len()), "{why}");
    }
    // The optima are still reported.
    for (k, (model, values)) in
        [(&square, json!({"A1": 0})), (&shifted, json!({"C1": 2})), (&rectangle, json!({"E1": 5, "E2": 5})), (&bounded, json!({"G1": 0, "G2": 1}))]
            .into_iter()
            .enumerate()
    {
        let r = s.execute("data.solverReport", report(model, values)).unwrap();
        assert_eq!(r["sheets"], json!([format!("Sensitivity Report {}", k + 1)]), "{r}");
    }
}

#[test]
fn solver_writes_the_other_reports_when_the_run_stops_before_an_optimum() {
    // Rosenbrock's function from (-1.2, 1) with 60 evaluations: the run stops at the limit with
    // a solution that is not the optimum (1, 1). The solve applies and the Answer report is
    // written; the Sensitivity report is left out with its reason.
    let mut s = s();
    set(&mut s, &[("A1", "-1.2"), ("A2", "1"), ("B1", "=(1-A1)^2+100*(A2-A1^2)^2")]);
    let undo = s.doc().unwrap().undo.len();
    let r = s
        .execute(
            "data.solver",
            json!({"objective": "B1", "goal": "min", "variables": "A1:A2", "nonNegative": false, "maxEvaluations": 60, "reports": ["answer", "sensitivity"]}),
        )
        .unwrap();
    assert_eq!(r["status"], "iterationLimit", "{r}");
    assert_eq!(r["changed"], true);
    assert_eq!(n(&s, "A1"), r["values"]["A1"].as_f64().unwrap());
    assert_eq!(r["reports"], json!(["Answer Report 1"]), "{r}");
    assert_eq!(r["skippedReports"][0]["report"], "sensitivity", "{r}");
    assert!(r["skippedReports"][0]["reason"].as_str().unwrap().contains("optimal"), "{r}");
    assert_eq!(s.doc().unwrap().undo.len(), undo + 1);
    // A solve that reaches the optimum still writes the Sensitivity report and skips nothing.
    let r = s
        .execute("data.solver", json!({"objective": "B1", "goal": "min", "variables": "A1:A2", "nonNegative": false, "reports": ["sensitivity"]}))
        .unwrap();
    assert_eq!(r["status"], "converged", "{r}");
    assert_eq!(r["reports"], json!(["Sensitivity Report 1"]), "{r}");
    assert!(r.get("skippedReports").is_none(), "{r}");
}

#[test]
fn solver_report_can_skip_a_sensitivity_report_the_values_do_not_support() {
    // min A1² at A1 = 1 is not an optimum. Called directly, data.solverReport refuses it; with
    // skipNotOptimal (as Solver Results passes) the Answer report is still written.
    let mut s = s();
    set(&mut s, &[("A1", "1"), ("B1", "=A1^2")]);
    let model = json!({"objective": "B1", "goal": "min", "variables": "A1", "constraints": ["A1 <= 5"]});
    let p = |reports: serde_json::Value, skip: bool| json!({"reports": reports, "model": model, "values": {"A1": 1}, "skipNotOptimal": skip});
    let err = s.execute("data.solverReport", p(json!(["answer", "sensitivity"]), false)).unwrap_err();
    assert!(err.to_string().contains("not optimal"), "{err}");
    let undo = s.doc().unwrap().undo.len();
    let r = s.execute("data.solverReport", p(json!(["answer", "sensitivity"]), true)).unwrap();
    assert_eq!(r["sheets"], json!(["Answer Report 1"]), "{r}");
    assert!(r["skippedReports"][0]["reason"].as_str().unwrap().contains("not optimal"), "{r}");
    assert_eq!(s.doc().unwrap().undo.len(), undo + 1);
    // With nothing left to write, nothing changes and no Undo step is added.
    let before = s.doc().unwrap().clone();
    let r = s.execute("data.solverReport", p(json!(["sensitivity"]), true)).unwrap();
    assert_eq!(r["sheets"], json!([]), "{r}");
    let d = s.doc().unwrap();
    assert!(std::sync::Arc::ptr_eq(&d.wb, &before.wb));
    assert_eq!((d.undo.len(), d.redo.len()), (before.undo.len(), before.redo.len()));
    // A model with no Sensitivity report is still refused, skipNotOptimal or not.
    let err = s.execute("data.solverReport", json!({"reports": ["answer", "sensitivity"], "model": {"objective": "B1", "variables": "A1", "constraints": ["A1 <= 5", "A1 int"]}, "skipNotOptimal": true})).unwrap_err();
    assert!(err.to_string().contains("integer or binary"), "{err}");
    // In a workbook whose structure is protected, a request whose only report is skipped
    // writes no sheet, so it succeeds; one that would write a sheet is still refused.
    let d = s.doc_mut().unwrap();
    std::sync::Arc::make_mut(&mut d.wb).protected_structure = true;
    let before = s.doc().unwrap().clone();
    let r = s.execute("data.solverReport", p(json!(["sensitivity"]), true)).unwrap();
    assert_eq!(r["sheets"], json!([]), "{r}");
    assert!(r["skippedReports"][0]["reason"].as_str().unwrap().contains("not optimal"), "{r}");
    let err = s.execute("data.solverReport", p(json!(["answer", "sensitivity"]), true)).unwrap_err();
    assert!(err.to_string().contains("protected"), "{err}");
    // A request that must write a sheet is refused before its reports are built, so an
    // integer model's Limits report gives the protection message, not the report's own refusal.
    let int_model = json!({"objective": "B1", "variables": "A1", "constraints": ["A1 <= 5", "A1 int"]});
    let err = s.execute("data.solverReport", json!({"reports": ["limits"], "model": int_model, "values": {"A1": 1}})).unwrap_err();
    assert!(err.to_string().contains("protected"), "{err}");
    let d = s.doc().unwrap();
    assert!(std::sync::Arc::ptr_eq(&d.wb, &before.wb));
    assert_eq!((d.undo.len(), d.redo.len()), (before.undo.len(), before.redo.len()));
}

#[test]
fn a_sensitivity_refusal_of_the_model_comes_before_any_report_is_built() {
    // The refusals that apply to the model (integer or binary constraints, the Evolutionary
    // method, a Value Of goal) are checked before any report is built, in both modes and from
    // both commands: a Limits report listed first would otherwise run its two optimisations per
    // variable, and data.solver its whole solve, for an error. An integer model asking for
    // limits and sensitivity gets the Sensitivity refusal, not the Limits report's, which the
    // report loop reached first; a Value Of model, whose Limits report is not refused, gets the
    // Sensitivity refusal with no sheet written and the workbook as it was.
    let mut s = s();
    set(&mut s, &[("A1", "1"), ("B1", "=2*A1")]);
    let before = s.doc().unwrap().clone();
    let int_model = json!({"objective": "B1", "variables": "A1", "constraints": ["A1 <= 5", "A1 int"]});
    let value_model = json!({"objective": "B1", "goal": "value", "value": 4, "variables": "A1", "constraints": ["A1 <= 5"]});
    for (model, values, why) in
        [(&int_model, json!({"A1": 1}), "The Sensitivity report doesn't apply"), (&value_model, json!({"A1": 2}), "maximise or minimise")]
    {
        for skip in [false, true] {
            let p = json!({"reports": ["limits", "sensitivity"], "model": model, "values": values, "skipNotOptimal": skip});
            let err = s.execute("data.solverReport", p).unwrap_err();
            assert!(err.to_string().contains(why), "{skip}: {err}");
        }
    }
    let p = json!({"objective": "B1", "variables": "A1", "constraints": ["A1 <= 5", "A1 int"], "method": "simplex", "reports": ["limits", "sensitivity"]});
    let err = s.execute("data.solver", p).unwrap_err();
    assert!(err.to_string().contains("The Sensitivity report doesn't apply"), "{err}");
    let d = s.doc().unwrap();
    assert!(std::sync::Arc::ptr_eq(&d.wb, &before.wb));
    assert_eq!((d.undo.len(), d.redo.len()), (before.undo.len(), before.redo.len()));
}

#[test]
fn nonlinear_sensitivity_with_too_many_binding_constraints_is_refused_without_change() {
    // 80 binding rows on two free variables pass the work limit (lowered in tests); 40 don't.
    let mut s = s();
    set(&mut s, &[("A1", "5"), ("A2", "5"), ("B1", "=A1*A2")]);
    for r in 1..=80 {
        set(&mut s, &[(&format!("D{r}"), "=A1+A2")]);
    }
    let report = |rows: u32| json!({"reports": ["sensitivity"], "model": {"objective": "B1", "variables": "A1:A2", "constraints": [format!("D1:D{rows} <= 10")]}});
    let before = s.doc().unwrap().clone();
    let err = s.execute("data.solverReport", report(80)).unwrap_err();
    assert!(err.to_string().contains("too many binding constraints"), "{err}");
    let d = s.doc().unwrap();
    assert!(std::sync::Arc::ptr_eq(&d.wb, &before.wb));
    assert_eq!((d.undo.len(), d.redo.len()), (before.undo.len(), before.redo.len()));
    let r = s.execute("data.solverReport", report(40)).unwrap();
    assert_eq!(r["sheets"], json!(["Sensitivity Report 1"]), "{r}");
}

#[test]
fn sensitivity_applies_agrees_with_the_report() {
    let mut s = s();
    set(&mut s, &[("A1", "1"), ("B1", "=3*A1")]);
    for (extra, ok) in [
        (json!({}), true),
        (json!({"goal": "min"}), true),
        (json!({"method": "grg"}), true),
        (json!({"goal": "value", "value": 3}), false),
        (json!({"constraints": ["A1 <= 4", "A1 int"]}), false),
        (json!({"constraints": ["A1 <= 4", {"lhs": "A1", "op": "bin"}]}), false),
        (json!({"method": "evolutionary"}), false),
    ] {
        let mut p = json!({"objective": "B1", "variables": "A1", "constraints": ["A1 <= 4"], "method": "simplex", "keep": false});
        for (k, v) in extra.as_object().unwrap() {
            p[k] = v.clone();
        }
        assert_eq!(super::sensitivity_applies(&p), ok, "{p}");
        let r = s.execute("data.solver", p.clone()).unwrap();
        assert_eq!(super::sensitivity_applies(&r["model"]), ok, "{p}");
        let rep = s.execute("data.solverReport", json!({"reports": ["sensitivity"], "model": r["model"], "values": r["values"]}));
        assert_eq!(rep.is_ok(), ok, "{p}: {rep:?}");
    }
}

/// How many cells of sheet `name` hold `text`.
fn count_of(s: &Session, name: &str, text: &str) -> usize {
    let d = s.doc().unwrap();
    let sh = d.wb.sheet(d.wb.sheet_index(name).unwrap()).unwrap();
    (0..60).flat_map(|r| (0..8).map(move |c| (r, c))).filter(|(r, c)| sh.value(CellRef::new(*r, *c)) == Value::text(text)).count()
}

#[test]
fn sensitivity_report_is_the_same_whatever_constant_the_objective_adds() {
    // A constant in the objective changes no price: max 1E9 + x with x ≤ 10 (a row) has the
    // same report as max x with x ≤ 10. At x = 10 the row's shadow price is 1 (one more unit
    // of right side adds one to the objective); x is basic, with reduced cost 0 and
    // coefficient 1, which may rise without limit and fall by 1 (to 0, where the slack ties);
    // the right side 10 may rise without limit and fall by 10 (to x = 0). A tolerance taken
    // from the objective's value (1E-9 · 1E9 = 1) wrote the shadow price as 0.
    let mut s = s();
    set(&mut s, &[("A1", "0"), ("B1", "=1000000000+A1"), ("C1", "=A1"), ("E1", "0"), ("F1", "=E1"), ("G1", "=E1")]);
    let cols = ["D", "E", "F", "G", "H"];
    let mut rows = Vec::new();
    for (obj, var, con, v, c) in [("B1", "A1", "C1", "$A$1", "$C$1"), ("F1", "E1", "G1", "$E$1", "$G$1")] {
        let p = json!({"objective": obj, "variables": var, "constraints": [format!("{con} <= 10")], "method": "simplex", "reports": ["sensitivity"]});
        let r = s.execute("data.solver", p).unwrap();
        assert_eq!(r["status"], "optimal", "{r}");
        let rep = r["reports"][0].as_str().unwrap().to_string();
        rows.push((report_row(&s, &rep, v, &cols), report_row(&s, &rep, c, &cols)));
    }
    assert!(close(&rows[0].0, &[10.0, 0.0, 1.0, 1e30, 1.0], 1e-9), "{rows:?}");
    assert!(close(&rows[0].1, &[10.0, 1.0, 10.0, 1e30, 10.0], 1e-9), "{rows:?}");
    assert_eq!(rows[0], rows[1]);
}

#[test]
fn nonlinear_sensitivity_report_is_the_same_whatever_constant_the_objective_adds() {
    // min 1E6 + (x − 3)² with x ≤ 2.75 has the same report as min (x − 3)² with x ≤ 2.75. At
    // x = 2.75 the objective's gradient is 2(2.75 − 3) = −0.5. As a bound on the variable cell
    // (no constraint row) it is x's reduced gradient, −0.5; as a row y = x ≤ 2.75 it is the
    // row's Lagrange multiplier, −0.5 (∇f = λ∇y with ∇y = 1), and x's reduced gradient is 0.
    // A tolerance taken from the objective's value (1E-6 · 1E6 = 1) wrote both as 0. The
    // difference gradients of the model with the constant lose about four digits to rounding,
    // so the figures agree to 1E-3.
    let mut s = s();
    set(&mut s, &[("A1", "0"), ("B1", "=1000000+(A1-3)^2"), ("C1", "=A1"), ("E1", "0"), ("F1", "=(E1-3)^2"), ("G1", "=E1")]);
    let mut figures = Vec::new();
    for (obj, var, con, v, c) in [("B1", "A1", "C1", "$A$1", "$C$1"), ("F1", "E1", "G1", "$E$1", "$G$1")] {
        let solve = |s: &mut Session, bound: String| {
            let p = json!({"objective": obj, "goal": "min", "variables": var, "constraints": [bound], "reports": ["sensitivity"]});
            let r = s.execute("data.solver", p).unwrap();
            assert_eq!(r["status"], "converged", "{r}");
            r["reports"][0].as_str().unwrap().to_string()
        };
        let rep = solve(&mut s, format!("{var} <= 2.75"));
        let at_bound = report_row(&s, &rep, v, &["D", "E"]);
        assert_eq!(count_of(&s, &rep, c), 0, "a bound has no constraint row");
        let rep = solve(&mut s, format!("{con} <= 2.75"));
        figures.push((at_bound, report_row(&s, &rep, v, &["D", "E"]), report_row(&s, &rep, c, &["D", "E"])));
    }
    let (at_bound, free, row) = &figures[0];
    assert!(close(at_bound, &[2.75, -0.5], 1e-3), "{figures:?}");
    assert!(close(free, &[2.75, 0.0], 1e-3), "{figures:?}");
    assert!(close(row, &[2.75, -0.5], 1e-3), "{figures:?}");
    assert!(close(&figures[1].0, at_bound, 1e-3) && close(&figures[1].1, free, 1e-3) && close(&figures[1].2, row, 1e-3), "{figures:?}");
}

#[test]
fn simplex_sensitivity_keeps_a_small_price_beside_a_large_coefficient() {
    // max 1E9·x + y with x ≤ 1 and y ≤ 1 as rows and x, y ≥ 0: (1, 1). Both rows bind, the
    // basis is {x, y} with B = I, so the shadow prices are the coefficients, 1E9 and 1, and both
    // reduced costs are 0. x's coefficient may rise without limit and fall by 1E9 (to 0, where
    // its row's slack ties), y's without limit and by 1. Each right side may rise without limit
    // (the other row doesn't involve the variable) and fall by 1 (to 0). The second row's price
    // is the single term 1 · 1, so the first row's coefficient 1E9 is no rounding error in it; a
    // noise level taken from the largest coefficient (1E-9 · 1E9 = 1) wrote it as 0.
    let mut s = s();
    set(&mut s, &[("A1", "0"), ("A2", "0"), ("B1", "=1000000000*A1+A2"), ("C1", "=A1"), ("C2", "=A2")]);
    let p = json!({"objective": "B1", "variables": "A1:A2", "constraints": ["C1 <= 1", "C2 <= 1"], "method": "simplex", "reports": ["sensitivity"]});
    let r = s.execute("data.solver", p).unwrap();
    assert_eq!(r["status"], "optimal", "{r}");
    let rep = r["reports"][0].as_str().unwrap().to_string();
    let cols = ["D", "E", "F", "G", "H"];
    let row = |c: &str| report_row(&s, &rep, c, &cols);
    assert!(close(&row("$A$1"), &[1.0, 0.0, 1e9, 1e30, 1e9], 1e-9), "{:?}", row("$A$1"));
    assert!(close(&row("$A$2"), &[1.0, 0.0, 1.0, 1e30, 1.0], 1e-9), "{:?}", row("$A$2"));
    assert!(close(&row("$C$1"), &[1.0, 1e9, 1.0, 1e30, 1.0], 1e-9), "{:?}", row("$C$1"));
    assert!(close(&row("$C$2"), &[1.0, 1.0, 1.0, 1e30, 1.0], 1e-9), "{:?}", row("$C$2"));
}

#[test]
fn simplex_sensitivity_keeps_a_small_reduced_cost_beside_a_large_coefficient() {
    // max 1E9·x + y − z with x ≤ 1 and y ≤ 1 as rows and x, y, z ≥ 0 (z's bound is the only
    // constraint on it): (1, 1, 0). z is nonbasic at zero with reduced cost −1 − 0 = −1 (no
    // row involves it): its coefficient must rise by 1 before z is made, so the Allowable
    // Increase is 1 and the Allowable Decrease 1E+30, as for a maximum's variable at zero in
    // `simplex_sensitivity_gives_the_dakota_furniture_report`. The other rows are those of
    // `simplex_sensitivity_keeps_a_small_price_beside_a_large_coefficient`. The reduced cost
    // is the coefficient alone, so x's coefficient 1E9 is no rounding error in it; a noise
    // level taken from the largest coefficient wrote it as 0.
    let mut s = s();
    set(&mut s, &[("A1", "0"), ("A2", "0"), ("A3", "0"), ("B1", "=1000000000*A1+A2-A3"), ("C1", "=A1"), ("C2", "=A2")]);
    let p = json!({"objective": "B1", "variables": "A1:A3", "constraints": ["C1 <= 1", "C2 <= 1"], "method": "simplex", "reports": ["sensitivity"]});
    let r = s.execute("data.solver", p).unwrap();
    assert_eq!(r["status"], "optimal", "{r}");
    let rep = r["reports"][0].as_str().unwrap().to_string();
    let cols = ["D", "E", "F", "G", "H"];
    let row = |c: &str| report_row(&s, &rep, c, &cols);
    assert!(close(&row("$A$1"), &[1.0, 0.0, 1e9, 1e30, 1e9], 1e-9), "{:?}", row("$A$1"));
    assert!(close(&row("$A$2"), &[1.0, 0.0, 1.0, 1e30, 1.0], 1e-9), "{:?}", row("$A$2"));
    assert!(close(&row("$A$3"), &[0.0, -1.0, -1.0, 1.0, 1e30], 1e-9), "{:?}", row("$A$3"));
    assert!(close(&row("$C$1"), &[1.0, 1e9, 1.0, 1e30, 1.0], 1e-9), "{:?}", row("$C$1"));
    assert!(close(&row("$C$2"), &[1.0, 1.0, 1.0, 1e30, 1.0], 1e-9), "{:?}", row("$C$2"));
}

#[test]
fn nonlinear_sensitivity_keeps_a_small_multiplier_beside_a_large_gradient() {
    // The model of `simplex_sensitivity_keeps_a_small_price_beside_a_large_coefficient` under
    // GRG Nonlinear: at (1, 1) both rows bind; with ∇f = (1E9, 1) and unit row gradients the
    // Lagrange multipliers are 1E9 and 1, and both reduced gradients are 0. The second row's
    // multiplier is the single term 1 · 1, so the gradient's large first component is no
    // rounding error in it; a noise level taken from the gradient's size (1E-6 · 1E9 = 1000)
    // wrote it as 0. The difference gradient of y is the difference of two values near 1E9,
    // where the last place is 2⁻²² ≈ 2.4E-7: the step 1E-6 rounds to 4 places, 9.54E-7, so
    // df_y ≈ 0.954 and the multiplier is checked to 0.1. The nonlinear method stops on this
    // model from (0, 0) with "unbounded", so the report is asked for at the optimum (1, 1).
    let mut s = s();
    set(&mut s, &[("A1", "0"), ("A2", "0"), ("B1", "=1000000000*A1+A2"), ("C1", "=A1"), ("C2", "=A2")]);
    let model = json!({"objective": "B1", "variables": "A1:A2", "constraints": ["C1 <= 1", "C2 <= 1"]});
    let r = s.execute("data.solverReport", json!({"reports": ["sensitivity"], "model": model, "values": {"A1": 1, "A2": 1}})).unwrap();
    let rep = r["sheets"][0].as_str().unwrap().to_string();
    let row = |c: &str| report_row(&s, &rep, c, &["D", "E"]);
    assert!(close(&row("$A$1"), &[1.0, 0.0], 1e-3), "{:?}", row("$A$1"));
    assert!(close(&row("$A$2"), &[1.0, 0.0], 1e-3), "{:?}", row("$A$2"));
    assert!(close(&row("$C$1"), &[1.0, 1e9], 1e-3), "{:?}", row("$C$1"));
    assert!(close(&row("$C$2"), &[1.0, 1.0], 0.1), "{:?}", row("$C$2"));
}

#[test]
fn nonlinear_sensitivity_keeps_a_small_reduced_gradient_beside_a_large_gradient() {
    // The model of `simplex_sensitivity_keeps_a_small_reduced_cost_beside_a_large_coefficient`
    // under GRG Nonlinear: z sits at its bound 0, where its reduced gradient is its own
    // gradient −1 (no row involves it); a noise level taken from the gradient's size (1000)
    // wrote it as 0. Its difference gradient is one-sided at the bound, over the step 1E-6
    // from a value near 1E9 that rounds as in
    // `nonlinear_sensitivity_keeps_a_small_multiplier_beside_a_large_gradient`: about −0.954,
    // checked to 0.1. As there, the report is asked for at the optimum (1, 1, 0).
    let mut s = s();
    set(&mut s, &[("A1", "0"), ("A2", "0"), ("A3", "0"), ("B1", "=1000000000*A1+A2-A3"), ("C1", "=A1"), ("C2", "=A2")]);
    let model = json!({"objective": "B1", "variables": "A1:A3", "constraints": ["C1 <= 1", "C2 <= 1"]});
    let r = s.execute("data.solverReport", json!({"reports": ["sensitivity"], "model": model, "values": {"A1": 1, "A2": 1, "A3": 0}})).unwrap();
    let rep = r["sheets"][0].as_str().unwrap().to_string();
    let row = |c: &str| report_row(&s, &rep, c, &["D", "E"]);
    assert!(close(&row("$A$1"), &[1.0, 0.0], 1e-3), "{:?}", row("$A$1"));
    assert!(close(&row("$A$2"), &[1.0, 0.0], 1e-3), "{:?}", row("$A$2"));
    assert!(close(&row("$A$3"), &[0.0, -1.0], 0.1), "{:?}", row("$A$3"));
    assert!(close(&row("$C$1"), &[1.0, 1e9], 1e-3), "{:?}", row("$C$1"));
    assert!(close(&row("$C$2"), &[1.0, 1.0], 0.1), "{:?}", row("$C$2"));
}

#[test]
fn nonlinear_sensitivity_refuses_a_point_that_is_not_optimal_in_a_small_variable() {
    // max 1E9·x + y with x ≤ 1 and y ≤ 1 as rows, at (1, 0.5): the second row doesn't bind, y
    // is free and its reduced gradient is its own gradient, about 1 (0.954 with the rounding
    // in `nonlinear_sensitivity_keeps_a_small_multiplier_beside_a_large_gradient`), so raising
    // y to 1 gains 0.5 and the point is not optimal: the report is refused and the workbook
    // left as it was. A stationarity tolerance taken from the largest gradient component
    // (1E-3 · 1E9 = 1E6) accepted the point and wrote the report. The optimum (1, 1) is
    // reported.
    let mut s = s();
    set(&mut s, &[("A1", "0"), ("A2", "0"), ("B1", "=1000000000*A1+A2"), ("C1", "=A1"), ("C2", "=A2")]);
    let model = json!({"objective": "B1", "variables": "A1:A2", "constraints": ["C1 <= 1", "C2 <= 1"]});
    let report = |values: serde_json::Value| json!({"reports": ["sensitivity"], "model": model, "values": values});
    let before = s.doc().unwrap().clone();
    let err = s.execute("data.solverReport", report(json!({"A1": 1, "A2": 0.5}))).unwrap_err();
    assert!(err.to_string().contains("not optimal"), "{err}");
    let d = s.doc().unwrap();
    assert!(std::sync::Arc::ptr_eq(&d.wb, &before.wb));
    assert_eq!((d.undo.len(), d.redo.len()), (before.undo.len(), before.redo.len()));
    let r = s.execute("data.solverReport", report(json!({"A1": 1, "A2": 1}))).unwrap();
    assert_eq!(r["sheets"], json!(["Sensitivity Report 1"]), "{r}");
}

#[test]
fn nonlinear_sensitivity_refuses_a_point_that_breaks_a_small_row_beside_a_large_one() {
    // max y − (x − 2)² with x ≤ 1E9 and y ≤ 1 as rows: (2, 1). At (2, 1.0001) the second row
    // is over by 1E-4, more than ten times the constraint precision of its own right side
    // (1E-5 · (1 + 1) = 2E-5), so the point is infeasible and the report is refused; it is
    // stationary (x's gradient is 0 and the row, within the binding tolerance, explains y's),
    // so feasibility alone decides. A feasibility tolerance relative to the largest constant
    // right side (1E-5 · 1E9 = 1E4) accepted the point. The optimum (2, 1) is reported.
    let mut s = s();
    set(&mut s, &[("A1", "0"), ("A2", "0"), ("B1", "=A2-(A1-2)^2"), ("C1", "=A1"), ("C2", "=A2")]);
    let model = json!({"objective": "B1", "variables": "A1:A2", "constraints": ["C1 <= 1000000000", "C2 <= 1"]});
    let report = |values: serde_json::Value| json!({"reports": ["sensitivity"], "model": model, "values": values});
    let before = s.doc().unwrap().clone();
    let err = s.execute("data.solverReport", report(json!({"A1": 2, "A2": 1.0001}))).unwrap_err();
    assert!(err.to_string().contains("not optimal"), "{err}");
    let d = s.doc().unwrap();
    assert!(std::sync::Arc::ptr_eq(&d.wb, &before.wb));
    assert_eq!((d.undo.len(), d.redo.len()), (before.undo.len(), before.redo.len()));
    let r = s.execute("data.solverReport", report(json!({"A1": 2, "A2": 1}))).unwrap();
    assert_eq!(r["sheets"], json!(["Sensitivity Report 1"]), "{r}");
    assert!(close(&report_row(&s, "Sensitivity Report 1", "$C$2", &["D", "E"]), &[1.0, 1.0], 1e-3), "{r}");
}

#[test]
fn simplex_sensitivity_of_a_variable_at_its_upper_bound() {
    // max 3x + 2y with x + y ≤ 4 (a row), x ≤ 3 and y ≤ 5 (bounds on the variable cells, which
    // have no row in the Constraints table): x = 3, y = 1, objective 11. The row's shadow price
    // is y's coefficient 2 (y is basic in it). x, held at its upper bound, has reduced cost
    // 3 − 1·2 = 1: one more unit of its bound adds 1. This is the convention of Frontline's
    // "Excel Solver - Interpreting the Sensitivity Report" (solver.com): a variable's dual
    // value is nonzero only at a bound, measures the objective's change per unit increase in
    // the variable, and a bound on a variable cell has no row in the Constraints section, its
    // reduced cost standing for the bound's shadow price. Its coefficient may rise without limit
    // and fall by 1 (to 2, a tie with y): for a maximum's variable at its upper bound the
    // Allowable Increase is 1E+30 and the Allowable Decrease the reduced cost, the mirror
    // image of a variable at zero (`simplex_sensitivity_gives_the_dakota_furniture_report`).
    // y's coefficient may rise by 1 (to 3, a tie with x) and fall by 2 (to 0, where the row's
    // slack ties). The right side 4 may rise by 4 (y reaches its bound 5 at 8) and fall by 1
    // (y reaches 0 at 3).
    let mut s = s();
    set(&mut s, &[("A1", "0"), ("A2", "0"), ("B1", "=3*A1+2*A2"), ("C1", "=A1+A2")]);
    let p = json!({"objective": "B1", "variables": "A1:A2", "constraints": ["C1 <= 4", "A1 <= 3", "A2 <= 5"], "method": "simplex", "reports": ["sensitivity"]});
    let r = s.execute("data.solver", p).unwrap();
    assert_eq!(r["status"], "optimal", "{r}");
    let rep = r["reports"][0].as_str().unwrap().to_string();
    let cols = ["D", "E", "F", "G", "H"];
    let row = |c: &str| report_row(&s, &rep, c, &cols);
    assert!(close(&row("$A$1"), &[3.0, 1.0, 3.0, 1e30, 1.0], 1e-9), "{:?}", row("$A$1"));
    assert!(close(&row("$A$2"), &[1.0, 0.0, 2.0, 1.0, 2.0], 1e-9), "{:?}", row("$A$2"));
    assert!(close(&row("$C$1"), &[4.0, 2.0, 4.0, 4.0, 1.0], 1e-9), "{:?}", row("$C$1"));
    assert_eq!((count_of(&s, &rep, "$A$1"), count_of(&s, &rep, "$A$2"), count_of(&s, &rep, "$C$1")), (1, 1, 1));
}

#[test]
fn simplex_sensitivity_of_a_minimum_with_a_greater_row_and_a_bound() {
    // min 2x + 3y with x + y ≥ 5 (a row) and x ≤ 2 (a bound): x = 2, y = 3, cost 13. The row's
    // shadow price is 3: one more unit of right side costs one more y. x, at its upper bound,
    // has reduced cost 2 − 1·3 = −1 (one more unit of its bound saves 1). Its coefficient may
    // rise by 1 (to 3, a tie with y) and fall without limit: for a minimum's variable at its
    // upper bound the Allowable Increase is the reduced cost's size and the Allowable Decrease
    // 1E+30, the mirror image of a minimum's variable at zero (the reduced cost 1 with
    // Allowable Increase 1E+30 and Allowable Decrease 1 in
    // `sensitivity_report_gives_the_wyndor_glass_shadow_prices_and_ranges`). y's coefficient
    // may rise without limit (x can take no more) and fall by 1 (to 2, a tie with x). The right
    // side 5 may rise without limit and fall by 3 (y reaches 0 at 2).
    let mut s = s();
    set(&mut s, &[("A1", "0"), ("A2", "0"), ("B1", "=2*A1+3*A2"), ("C1", "=A1+A2")]);
    let p = json!({"objective": "B1", "goal": "min", "variables": "A1:A2", "constraints": ["C1 >= 5", "A1 <= 2"], "method": "simplex", "reports": ["sensitivity"]});
    let r = s.execute("data.solver", p).unwrap();
    assert_eq!(r["status"], "optimal", "{r}");
    let rep = r["reports"][0].as_str().unwrap().to_string();
    let cols = ["D", "E", "F", "G", "H"];
    let row = |c: &str| report_row(&s, &rep, c, &cols);
    assert!(close(&row("$A$1"), &[2.0, -1.0, 2.0, 1.0, 1e30], 1e-9), "{:?}", row("$A$1"));
    assert!(close(&row("$A$2"), &[3.0, 0.0, 3.0, 1e30, 1.0], 1e-9), "{:?}", row("$A$2"));
    assert!(close(&row("$C$1"), &[5.0, 3.0, 5.0, 1e30, 3.0], 1e-9), "{:?}", row("$C$1"));
}

#[test]
fn simplex_sensitivity_gives_the_dakota_furniture_report() {
    // Winston, Operations Research: Applications and Algorithms, the Dakota Furniture problem:
    // max 60x₁ + 30x₂ + 20x₃ (desks, tables, chairs) with 8x₁ + 6x₂ + x₃ ≤ 48 (lumber),
    // 4x₁ + 2x₂ + 1.5x₃ ≤ 20 (finishing) and 2x₁ + 1.5x₂ + 0.5x₃ ≤ 8 (carpentry): x = (2, 0, 8),
    // revenue 280. For the basis {s₁, x₃, x₁} the rows of B⁻¹ are (1, 2, −8), (0, 2, −4) and
    // (0, −0.5, 1.5), so the basic values are B⁻¹b = (24, 8, 2) and the shadow prices
    // c_B·B⁻¹ = (0, 20, 60)·B⁻¹ = (0, 10, 10). Tables, at zero, have reduced cost
    // 30 − (6·0 + 2·10 + 1.5·10) = −5: their price must rise by 5 before they are made, so the
    // Allowable Increase is 5 and the Allowable Decrease 1E+30, as Excel's report shows a
    // maximum's variable at zero. A change Δ in a basic variable's coefficient moves each
    // nonbasic reduced cost by Δ times that variable's row of the final tableau; the tables'
    // column there is B⁻¹(6, 2, 1.5) = (−2, −2, 1.25) and the slacks' columns are B⁻¹'s. Desks
    // (row 3): −5 − 1.25Δ ≤ 0, −10 + 0.5Δ ≤ 0 and −10 − 1.5Δ ≤ 0 hold for −4 ≤ Δ ≤ 20. Chairs
    // (row 2): −5 + 2Δ ≤ 0, −10 − 2Δ ≤ 0 and −10 + 4Δ ≤ 0 hold for −5 ≤ Δ ≤ 2.5. A right side
    // moves the basic values along its column of B⁻¹: lumber (24 + Δ, 8, 2) ≥ 0 for Δ ≥ −24;
    // finishing (24 + 2Δ, 8 + 2Δ, 2 − 0.5Δ) ≥ 0 for −4 ≤ Δ ≤ 4; carpentry
    // (24 − 8Δ, 8 − 4Δ, 2 + 1.5Δ) ≥ 0 for −4/3 ≤ Δ ≤ 2.
    let mut s = s();
    set(
        &mut s,
        &[
            ("A1", "0"),
            ("A2", "0"),
            ("A3", "0"),
            ("B1", "=60*A1+30*A2+20*A3"),
            ("C1", "=8*A1+6*A2+A3"),
            ("C2", "=4*A1+2*A2+1.5*A3"),
            ("C3", "=2*A1+1.5*A2+0.5*A3"),
        ],
    );
    let p = json!({"objective": "B1", "variables": "A1:A3", "constraints": ["C1 <= 48", "C2 <= 20", "C3 <= 8"], "method": "simplex", "reports": ["sensitivity"]});
    let r = s.execute("data.solver", p).unwrap();
    assert_eq!(r["status"], "optimal", "{r}");
    assert_eq!(r["objective"], 280.0, "{r}");
    let rep = r["reports"][0].as_str().unwrap().to_string();
    let cols = ["D", "E", "F", "G", "H"];
    let row = |c: &str| report_row(&s, &rep, c, &cols);
    assert!(close(&row("$A$1"), &[2.0, 0.0, 60.0, 20.0, 4.0], 1e-9), "{:?}", row("$A$1"));
    assert!(close(&row("$A$2"), &[0.0, -5.0, 30.0, 5.0, 1e30], 1e-9), "{:?}", row("$A$2"));
    assert!(close(&row("$A$3"), &[8.0, 0.0, 20.0, 2.5, 5.0], 1e-9), "{:?}", row("$A$3"));
    assert!(close(&row("$C$1"), &[24.0, 0.0, 48.0, 1e30, 24.0], 1e-9), "{:?}", row("$C$1"));
    assert!(close(&row("$C$2"), &[20.0, 10.0, 20.0, 4.0, 4.0], 1e-9), "{:?}", row("$C$2"));
    assert!(close(&row("$C$3"), &[8.0, 10.0, 8.0, 2.0, 4.0 / 3.0], 1e-9), "{:?}", row("$C$3"));
}

#[test]
fn nonlinear_sensitivity_signs_follow_the_goal() {
    // A Lagrange multiplier is the derivative of the optimal objective with respect to the
    // row's right side, and a reduced gradient that with respect to the variable's bound,
    // whichever way the goal points. Frontline's "Excel Solver - Interpreting the Sensitivity
    // Report" (solver.com) names a binding constraint's dual value its Lagrange multiplier and a
    // variable's its reduced gradient, each the objective's change per unit increase in the
    // constraint's bound or the variable, valid at the optimal point alone for a nonlinear
    // model.
    // min (x − 3)² + (y − 1)² with x + y ≤ b: the point of the line nearest (3, 1) is
    // (2.5, 0.5) at b = 3, f*(b) = (4 − b)²/2 and df*/db = −(4 − b) = −1, the multiplier;
    // maximising the negated objective reaches the same point with multiplier +1. Both
    // variables are interior, so their reduced gradients are 0.
    let mut s = s();
    set(&mut s, &[("A1", "0"), ("A2", "0"), ("B1", "=(A1-3)^2+(A2-1)^2"), ("B2", "=0-(A1-3)^2-(A2-1)^2"), ("C1", "=A1+A2")]);
    for (obj, goal, lambda) in [("B1", "min", -1.0), ("B2", "max", 1.0)] {
        set(&mut s, &[("A1", "0"), ("A2", "0")]);
        let p = json!({"objective": obj, "goal": goal, "variables": "A1:A2", "constraints": ["C1 <= 3"], "reports": ["sensitivity"]});
        let r = s.execute("data.solver", p).unwrap();
        let rep = r["reports"][0].as_str().unwrap().to_string();
        assert!(close(&report_row(&s, &rep, "$A$1", &["D", "E"]), &[2.5, 0.0], 1e-3), "{goal}: {r}");
        assert!(close(&report_row(&s, &rep, "$A$2", &["D", "E"]), &[0.5, 0.0], 1e-3), "{goal}: {r}");
        assert!(close(&report_row(&s, &rep, "$C$1", &["D", "E"]), &[3.0, lambda], 1e-3), "{goal}: {r}");
    }
    // max −(x + 1)² − (y − 2)² with x + y ≤ 1 and x, y ≥ 0 mirrors the minimum in
    // `sensitivity_report_of_a_nonlinear_model_gives_lagrange_multipliers`: at (0, 1) the
    // multiplier is +2 (−2 there) and x's reduced gradient −4 (4 there), since raising x from
    // its bound lowers the maximum by 2(x + 1) + 2 = 4 per unit.
    set(&mut s, &[("D1", "0.5"), ("D2", "0.5"), ("E1", "=0-(D1+1)^2-(D2-2)^2"), ("E2", "=D1+D2")]);
    let p = json!({"objective": "E1", "goal": "max", "variables": "D1:D2", "constraints": ["E2 <= 1"], "reports": ["sensitivity"]});
    let r = s.execute("data.solver", p).unwrap();
    let rep = r["reports"][0].as_str().unwrap().to_string();
    assert!(close(&report_row(&s, &rep, "$D$1", &["D", "E"]), &[0.0, -4.0], 1e-3), "{r}");
    assert!(close(&report_row(&s, &rep, "$D$2", &["D", "E"]), &[1.0, 0.0], 1e-3), "{r}");
    assert!(close(&report_row(&s, &rep, "$E$2", &["D", "E"]), &[1.0, 2.0], 1e-3), "{r}");
}

fn formula(s: &Session, a1: &str) -> String {
    let d = s.doc().unwrap();
    d.wb.active().unwrap().cell(CellRef::parse(a1).unwrap()).and_then(|c| c.formula.as_ref()).map(|f| f.text.clone()).unwrap_or_default()
}

#[test]
fn save_and_load_model_round_trip_through_cells() {
    let mut s = s();
    set(&mut s, &[("B1", "=5*A1+4*A2"), ("B2", "=6*A1+4*A2"), ("B3", "=A1+2*A2"), ("C2", "24")]);
    let model = json!({"objective": "B1", "variables": "A1:A2", "constraints": ["B2 <= C2", "B3 <= 6", "A1:A2 int", "A2 bin", "A1 >= 1"], "method": "simplex"});
    s.execute("data.solver", model.clone()).unwrap();
    let out = s.execute("data.solverSaveModel", json!({"to": "H1"})).unwrap();
    assert_eq!(out["range"], "H1:H8");
    let rows: Vec<String> = (1..=8).map(|r| formula(&s, &format!("H{r}"))).collect();
    assert_eq!(
        rows,
        [
            "MAX($B$1)",
            "COUNT($A$1:$A$2)",
            "AND($B$2<=$C$2)",
            "AND($B$3<=6)",
            "AND($A$1:$A$2=INT($A$1:$A$2))",
            "AND(($A$2=0)+($A$2=1))",
            "AND($A$1>=1)",
            "{2,1,100,0.075,0,1,0.0001,50,20000,0}",
        ]
    );
    // The constraint cells show whether each constraint holds at the solution (4, 0).
    assert_eq!(at(&s, "Sheet1", "H3"), Value::Bool(true));
    assert_eq!(at(&s, "Sheet1", "H2"), Value::number(2.0));
    // Reset All removes the model; Load Model restores it from the range or its first cell.
    assert_eq!(s.execute("data.solverReset", json!({})).unwrap()["removed"].as_u64().map(|n| n > 0), Some(true));
    assert!(s.execute("data.solver", json!({})).unwrap()["model"].is_null());
    assert_eq!(s.execute("data.solverReset", json!({})).unwrap()["removed"], 0);
    for from in ["H1:H8", "H1"] {
        let loaded = s.execute("data.solverLoadModel", json!({"from": from})).unwrap();
        assert_eq!(loaded["model"]["objective"], "B1", "{loaded}");
        assert_eq!(loaded["model"]["constraints"], json!(["B2 <= C2", "B3 <= 6", "A1:A2 int", "A2 bin", "A1 >= 1"]));
        assert_eq!(loaded["model"]["method"], "simplex");
    }
    set(&mut s, &[("A1", "0"), ("A2", "0")]);
    let r = s.execute("data.solver", json!({"saved": true})).unwrap();
    assert_eq!((r["status"].as_str(), n(&s, "A1"), n(&s, "A2")), (Some("optimal"), 4.0, 0.0), "{r}");
    // A Value Of goal and the Evolutionary options survive too; an explicit model is saved
    // as given.
    let evo = json!({"objective": "B1", "goal": "value", "value": -2.5, "variables": "A1:A2", "constraints": ["A1:A2 <= 10"], "nonNegative": false, "method": "evolutionary", "populationSize": 40, "randomSeed": 3, "requireBounds": false});
    assert_eq!(s.execute("data.solverSaveModel", json!({"to": "J10", "model": evo})).unwrap()["range"], "J10:J13");
    assert_eq!(formula(&s, "J10"), "$B$1=-2.5");
    let m = s.execute("data.solverLoadModel", json!({"from": "J10:J13"})).unwrap()["model"].clone();
    assert_eq!((m["goal"].as_str(), m["value"].as_f64(), m["nonNegative"].as_bool()), (Some("value"), Some(-2.5), Some(false)), "{m}");
    assert_eq!((m["method"].as_str(), m["populationSize"].as_f64(), m["randomSeed"].as_f64()), (Some("evolutionary"), Some(40.0), Some(3.0)));
    assert_eq!(m["requireBounds"], false);
    // Each command is one undo step.
    s.execute("edit.undo", json!({})).unwrap();
    assert_eq!(s.execute("data.solver", json!({})).unwrap()["model"]["method"], "simplex");
    // Refused: no model or no target, overlapping the model, off the sheet, ranges that
    // hold no model, other sheets and oversized ranges.
    set(&mut s, &[("L1", "=1+1"), ("L2", "=SUM(A1:A2)")]);
    for (cmd, p) in [
        ("data.solverSaveModel", json!({})),
        ("data.solverSaveModel", json!({"to": "A1"})),
        ("data.solverSaveModel", json!({"to": "B3"})),
        ("data.solverSaveModel", json!({"to": "A1048575"})),
        ("data.solverSaveModel", json!({"to": "H1", "model": {"objective": "B1", "variables": "A1,A2", "constraints": ["A1,A2 <= 3"]}})),
        ("data.solverSaveModel", json!({"to": "H1", "model": "B1"})),
        ("data.solverLoadModel", json!({})),
        ("data.solverLoadModel", json!({"from": "L1:L2"})),
        ("data.solverLoadModel", json!({"from": "Z1"})),
        ("data.solverLoadModel", json!({"from": "H2:H8"})),
        ("data.solverLoadModel", json!({"from": "H1:H1048576"})),
        ("data.solverLoadModel", json!({"from": "Nope!H1"})),
    ] {
        assert!(s.execute(cmd, p.clone()).is_err(), "{cmd} {p}");
    }
    s.execute("data.solverReset", json!({})).unwrap();
    assert!(s.execute("data.solverSaveModel", json!({"to": "H1"})).is_err(), "no model to save");
}

#[test]
fn reset_all_masks_a_workbook_level_model_and_keeps_other_sheets_models() {
    let mut s = s();
    set(&mut s, &[("A1", "1"), ("B1", "=2*A1")]);
    s.execute("home.insertSheet", json!({"name": "Two"})).unwrap();
    s.execute("sheet.activate", json!({"sheet": "Sheet1"})).unwrap();
    let (one, two) = {
        let wb = &s.doc().unwrap().wb;
        (wb.sheet_index("Sheet1").unwrap(), wb.sheet_index("Two").unwrap())
    };
    // A model saved as workbook-level names, which every sheet reads.
    {
        let d = s.doc_mut().unwrap();
        let wb = std::sync::Arc::make_mut(&mut d.wb);
        for (name, formula) in [
            ("solver_opt", "Sheet1!$B$1"),
            ("solver_adj", "Sheet1!$A$1"),
            ("solver_typ", "1"),
            ("solver_num", "0"),
            ("solver_eng", "2"),
            ("solver_ssz", "500"),
        ] {
            wb.names.push(gridcraft_model::DefinedName {
                name: name.into(),
                scope: None,
                formula: formula.into(),
                comment: String::new(),
                hidden: true,
            });
        }
    }
    let model = |s: &Session, sheet: usize| super::saved_model(&s.doc().unwrap().wb, sheet);
    assert_eq!(model(&s, one).map(|m| m["objective"].clone()), Some(json!("B1")));
    // Reset All empties this sheet's model, which the dialog then shows, and no other sheet's.
    let r = s.execute("data.solverReset", json!({})).unwrap();
    assert_eq!(model(&s, one), None, "{r}");
    assert_eq!(r["masked"], true, "{r}");
    assert!(s.execute("data.solver", json!({})).unwrap()["model"].is_null());
    assert_eq!(model(&s, two).map(|m| m["objective"].clone()), Some(json!("B1")));
    assert_eq!(s.doc().unwrap().wb.names.iter().filter(|n| n.scope.is_none()).count(), 6);
    // Undo brings the model back with its options; the mask survives XLSX.
    s.execute("edit.undo", json!({})).unwrap();
    assert_eq!(model(&s, one).and_then(|m| m["populationSize"].as_f64()), Some(500.0));
    s.execute("edit.redo", json!({})).unwrap();
    assert_eq!(model(&s, one), None);
    let b64 = s.execute("file.saveBytes", json!({"format": "xlsx"})).unwrap()["base64"].as_str().unwrap().to_string();
    s.execute("file.open", json!({"name": "r.xlsx", "base64": b64})).unwrap();
    s.execute("sheet.activate", json!({"sheet": "Sheet1"})).unwrap();
    assert_eq!(model(&s, one), None);
    assert!(model(&s, two).is_some());
    // A model saved on the sheet replaces the mask and is read alone: the workbook-level
    // population size doesn't leak into it.
    s.execute("data.solver", json!({"objective": "B1", "variables": "A1", "constraints": ["A1 <= 3"], "method": "simplex"})).unwrap();
    let m = model(&s, one).unwrap();
    assert_eq!((m["objective"].as_str(), m["populationSize"].as_f64()), (Some("B1"), Some(100.0)), "{m}");
    assert_eq!(s.execute("data.solverReset", json!({})).unwrap()["masked"], true);
    assert_eq!(model(&s, one), None);
}

#[test]
fn saving_a_shorter_model_over_a_longer_one_clears_the_rest() {
    let mut s = s();
    set(&mut s, &[("B1", "=5*A1+4*A2"), ("B2", "=6*A1+4*A2"), ("B3", "=A1+2*A2"), ("H9", "=1+1")]);
    let long = json!({"objective": "B1", "variables": "A1:A2", "constraints": ["B2 <= 24", "B3 <= 6", "A1 <= 3", "A2 <= 3"]});
    let short = json!({"objective": "B1", "variables": "A1:A2", "constraints": ["B2 <= 24"]});
    assert_eq!(s.execute("data.solverSaveModel", json!({"to": "H1", "model": long})).unwrap()["range"], "H1:H7");
    assert_eq!(s.execute("data.solverSaveModel", json!({"to": "H1", "model": short, "overwrite": true})).unwrap()["range"], "H1:H4");
    // The old model's last rows are cleared; a formula below it stays.
    for r in 5..=7 {
        assert_eq!(formula(&s, &format!("H{r}")), "", "H{r}");
    }
    assert_eq!(formula(&s, "H9"), "1+1");
    let loaded = s.execute("data.solverLoadModel", json!({"from": "H1"})).unwrap();
    assert_eq!(loaded["model"]["constraints"], json!(["B2 <= 24"]), "{loaded}");
    // Reading down from one cell stops at the options row even with formulas right below it.
    set(&mut s, &[("H5", "=2+2")]);
    let loaded = s.execute("data.solverLoadModel", json!({"from": "H1"})).unwrap();
    assert_eq!(loaded["model"]["constraints"], json!(["B2 <= 24"]), "{loaded}");
    // Saving over cells that hold no model leaves the cells below them as they are.
    assert_eq!(s.execute("data.solverSaveModel", json!({"to": "H8", "model": short, "overwrite": true})).unwrap()["range"], "H8:H11");
    assert_eq!(formula(&s, "H5"), "2+2");
}

#[test]
fn save_model_asks_before_it_replaces_data_and_is_one_undo_step() {
    let mut s = s();
    set(&mut s, &[("B1", "=5*A1+4*A2"), ("B2", "=6*A1+4*A2"), ("H2", "kept"), ("H3", "=1+1")]);
    let model = json!({"objective": "B1", "variables": "A1:A2", "constraints": ["B2 <= 24"]});
    // A value or a formula in the column: refused, the sheet unchanged, the cell named.
    let e = s.execute("data.solverSaveModel", json!({"to": "H1", "model": model.clone()})).unwrap_err().to_string();
    assert!(e.contains(crate::cmd::analysis::OVERWRITE_ERROR) && e.contains("H1:H4") && e.contains("H2"), "{e}");
    assert_eq!((at(&s, "Sheet1", "H2"), formula(&s, "H3"), formula(&s, "H1")), (Value::text("kept"), "1+1".into(), String::new()));
    // So is a model saved there before, and `overwrite` only as a true boolean.
    assert!(s.execute("data.solverSaveModel", json!({"to": "J10", "model": model.clone()})).is_ok());
    for overwrite in [json!(null), json!(false), json!("true"), json!(1)] {
        let e = s.execute("data.solverSaveModel", json!({"to": "J10", "model": model.clone(), "overwrite": overwrite})).unwrap_err();
        assert!(e.to_string().contains(crate::cmd::analysis::OVERWRITE_ERROR), "{overwrite}: {e}");
    }
    // overwrite: true replaces the data in one undo step, which brings it all back.
    let out = s.execute("data.solverSaveModel", json!({"to": "H1", "model": model, "overwrite": true})).unwrap();
    assert_eq!(out["range"], "H1:H4");
    assert_eq!((formula(&s, "H1"), formula(&s, "H2"), formula(&s, "H3")), ("MAX($B$1)".into(), "COUNT($A$1:$A$2)".into(), "AND($B$2<=24)".into()));
    s.execute("edit.undo", json!({})).unwrap();
    assert_eq!(
        (at(&s, "Sheet1", "H2"), formula(&s, "H3"), formula(&s, "H1"), formula(&s, "H4")),
        (Value::text("kept"), "1+1".into(), String::new(), String::new())
    );
    assert_eq!(formula(&s, "J10"), "MAX($B$1)");
    s.execute("edit.redo", json!({})).unwrap();
    assert_eq!(formula(&s, "H2"), "COUNT($A$1:$A$2)");
}

#[test]
fn saving_and_resetting_a_model_keep_the_users_own_solver_names() {
    let mut s = s();
    set(&mut s, &[("A1", "0"), ("B1", "=ABS(A1-3)"), ("C1", "100")]);
    let name = |name: &str, scope: Option<usize>, formula: &str, hidden: bool| gridcraft_model::DefinedName {
        name: name.into(),
        scope,
        formula: formula.into(),
        comment: String::new(),
        hidden,
    };
    {
        let d = s.doc_mut().unwrap();
        let wb = std::sync::Arc::make_mut(&mut d.wb);
        // The user's own names, on the sheet and the workbook, and Excel's Solver names the
        // model replaces.
        wb.names.push(name("solver_budget", Some(0), "Sheet1!$C$1", false));
        wb.names.push(name("Solver_Lhs_Total", Some(0), "Sheet1!$C$1", false));
        wb.names.push(name("solver_budget", None, "Sheet1!$C$1", false));
        wb.names.push(name("solver_lin", Some(0), "2", true));
        wb.names.push(name("solver_lhs12", Some(0), "Sheet1!$A$1", true));
    }
    let names = |s: &Session| -> Vec<String> {
        let mut v: Vec<String> = s.doc().unwrap().wb.names.iter().map(|n| format!("{}@{:?}", n.name, n.scope)).collect();
        v.sort();
        v
    };
    let mine = ["Solver_Lhs_Total@Some(0)", "solver_budget@None", "solver_budget@Some(0)"];
    let model = json!({"objective": "B1", "goal": "min", "variables": "A1", "constraints": ["A1 <= 4"], "method": "simplex"});
    s.execute("data.solver", model.clone()).unwrap();
    let after = names(&s);
    assert!(mine.iter().all(|n| after.contains(&n.to_string())), "{after:?}");
    assert!(!after.iter().any(|n| n.starts_with("solver_lin") || n.starts_with("solver_lhs12")), "{after:?}");
    // Load Model saves the model again; Reset All removes it and nothing else.
    s.execute("data.solverSaveModel", json!({"to": "H1"})).unwrap();
    s.execute("data.solverLoadModel", json!({"from": "H1"})).unwrap();
    assert!(mine.iter().all(|n| names(&s).contains(&n.to_string())), "{:?}", names(&s));
    let model_names = names(&s).len() - mine.len();
    let r = s.execute("data.solverReset", json!({})).unwrap();
    assert_eq!((r["removed"].as_u64(), r["masked"].as_bool()), (Some(model_names as u64), Some(false)), "{r}");
    assert_eq!(names(&s), mine);
    assert!(s.execute("data.solver", json!({})).unwrap()["model"].is_null());
}

#[test]
fn save_model_refuses_a_place_where_the_options_cannot_spill() {
    let mut s = s();
    set(&mut s, &[("B1", "=ABS(A1-3)"), ("H24", "=SEQUENCE(1,3)"), ("K30", "=SEQUENCE(3)"), ("M50", "=SEQUENCE(3)")]);
    // Tables whose empty data rows meet an options row: one in its way, one holding the
    // options cell.
    for range in ["T59:U62", "W69:W71"] {
        s.execute("insert.table", json!({"range": range, "header": true})).unwrap();
    }
    let model = json!({"objective": "B1", "goal": "min", "variables": "A1", "constraints": ["F4 <= 5"]});
    let save = |s: &mut Session, to: &str| s.execute("data.solverSaveModel", json!({"to": to, "model": model.clone()}));
    // The options row (H4) spills into I4:Q4: a value in its last cell is in the way.
    set(&mut s, &[("Q4", "x")]);
    let e = save(&mut s, "H1").unwrap_err().to_string();
    assert!(e.contains("I4:Q4") && e.contains("Q4 isn't empty"), "{e}");
    assert_eq!((formula(&s, "H1"), formula(&s, "H4")), (String::new(), String::new()));
    assert!(s.execute("data.solver", json!({})).unwrap()["model"].is_null());
    // With the row clear the options spill, and saving again at the same cell replaces them.
    set(&mut s, &[("Q4", "")]);
    for overwrite in [false, true] {
        let p = json!({"to": "H1", "model": model.clone(), "overwrite": overwrite});
        assert_eq!(s.execute("data.solverSaveModel", p).unwrap()["range"], "H1:H4");
        assert_eq!(
            (at(&s, "Sheet1", "H4"), at(&s, "Sheet1", "I4"), at(&s, "Sheet1", "O4"), at(&s, "Sheet1", "Q4")),
            (Value::number(1.0), Value::number(1.0), Value::number(50.0), Value::number(0.0))
        );
    }
    // Refused: in the options row, a formula (H24), another formula's spilled values (K31,
    // from K30), a cell of the model (F4), merged cells, a table and the sheet's last columns;
    // a column over another formula's spilled values (I24 of H24:J24, M51 of M50:M52) or with
    // its options cell in a table.
    s.execute("home.mergeCells", json!({"range": "S8:T9"})).unwrap();
    for (to, why) in [
        ("G21", "H24 isn't empty"),
        ("J28", "K31 holds the values of another formula"),
        ("E1", "F4 is a cell of the model"),
        ("R5", "merged"),
        ("S57", "T60:AB60, but a table is in the way"),
        ("XFA1", "need 10 cells"),
        ("I21", "cover I24, which holds the values of another formula"),
        ("M51", "cover M51, which holds the values of another formula"),
        ("W67", "X70:AF70, but a table is in the way"),
    ] {
        let e = save(&mut s, to).unwrap_err().to_string();
        assert!(e.contains(why), "{to}: {e}");
        assert_eq!(formula(&s, to), "", "{to}");
    }
    assert_eq!(
        (at(&s, "Sheet1", "J24"), at(&s, "Sheet1", "K32"), at(&s, "Sheet1", "M52")),
        (Value::number(3.0), Value::number(3.0), Value::number(3.0))
    );
}

#[test]
fn load_model_refuses_a_range_with_a_cell_without_a_formula() {
    let mut s = s();
    set(&mut s, &[("B1", "=5*A1+4*A2"), ("B2", "=6*A1+4*A2"), ("B3", "=A1+2*A2")]);
    let model = json!({"objective": "B1", "variables": "A1:A2", "constraints": ["B2 <= 24", "B3 <= 6", "A1 <= 3"], "method": "simplex"});
    assert_eq!(s.execute("data.solverSaveModel", json!({"to": "H1", "model": model})).unwrap()["range"], "H1:H6");
    // A range with empty cells after the model loads it.
    let loaded = s.execute("data.solverLoadModel", json!({"from": "H1:H9"})).unwrap();
    assert_eq!(loaded["model"]["constraints"], json!(["B2 <= 24", "B3 <= 6", "A1 <= 3"]), "{loaded}");
    s.execute("data.solverReset", json!({})).unwrap();
    // A constraint overwritten by a constant would drop that constraint; a gap before the
    // options row would drop the options. Both are refused, naming the cell.
    for (cell, input) in [("H4", "7"), ("H5", "")] {
        let before = formula(&s, cell);
        set(&mut s, &[(cell, input)]);
        let e = s.execute("data.solverLoadModel", json!({"from": "H1:H6"})).unwrap_err().to_string();
        assert!(e.contains(cell), "{e}");
        assert!(s.execute("data.solver", json!({})).unwrap()["model"].is_null(), "{cell}");
        set(&mut s, &[(cell, &format!("={before}"))]);
    }
    assert!(s.execute("data.solverLoadModel", json!({"from": "H1:H6"})).is_ok());
}

#[test]
fn load_model_refuses_a_model_cut_short_and_keeps_the_old_one() {
    let mut s = s();
    set(&mut s, &[("B1", "=5*A1+4*A2"), ("B2", "=6*A1+4*A2"), ("B3", "=A1+2*A2")]);
    let model = json!({"objective": "B1", "variables": "A1:A2", "constraints": ["B2 <= 24", "B3 <= 6", "A1 <= 3"], "method": "simplex"});
    s.execute("data.solver", model).unwrap();
    assert_eq!(s.execute("data.solverSaveModel", json!({"to": "H1"})).unwrap()["range"], "H1:H6");
    let kept = |s: &mut Session| {
        let m = s.execute("data.solver", json!({})).unwrap()["model"].clone();
        assert_eq!((m["constraints"].clone(), m["method"].clone()), (json!(["B2 <= 24", "B3 <= 6", "A1 <= 3"]), json!("simplex")), "{m}");
    };
    // A constraint cleared (H4), the options row cleared (H6) or replaced by a constant: from
    // the first cell or as a range, the rows above the gap are not loaded as the whole model.
    for (cell, input) in [("H4", ""), ("H6", ""), ("H6", "7")] {
        let before = formula(&s, cell);
        set(&mut s, &[(cell, input)]);
        for from in ["H1", "H1:H6", "H1:H9"] {
            let e = s.execute("data.solverLoadModel", json!({"from": from})).unwrap_err().to_string();
            assert!(e.contains("complete model") || e.contains(cell), "{cell} {from}: {e}");
            kept(&mut s);
        }
        set(&mut s, &[(cell, &format!("={before}"))]);
    }
    // An options row cut short or edited by hand: fewer than the eight values Save Model
    // writes, or a value that isn't a number (among the eight, after them or after the sixteenth).
    let options = formula(&s, "H6");
    for row in [
        "={1}",
        "={2,1,100,0.075,0,1,0.0001}",
        "={2,1,100,0.075,0,1,\"x\",50}",
        "={2,TRUE,100,0.075,0,1,0.0001,50}",
        "={2,1,100,0.075,0,1,0.0001,50,\"x\"}",
        "={2,1,100,0.075,0,1,0.0001,50,9,10,11,12,13,14,15,16,\"x\"}",
    ] {
        set(&mut s, &[("H6", row)]);
        for from in ["H1", "H1:H6"] {
            let e = s.execute("data.solverLoadModel", json!({"from": from})).unwrap_err().to_string();
            assert!(e.contains("complete model"), "{row} {from}: {e}");
            kept(&mut s);
        }
    }
    // More values than eight (as a later version may write) still load.
    set(&mut s, &[("H6", &format!("={}", options.trim_end_matches('}').to_string() + ",7,8}"))]);
    assert!(s.execute("data.solverLoadModel", json!({"from": "H1"})).is_ok());
    kept(&mut s);
    set(&mut s, &[("H6", &format!("={options}"))]);
    // The gap is named when reading down from one cell.
    set(&mut s, &[("H4", "")]);
    let e = s.execute("data.solverLoadModel", json!({"from": "H1"})).unwrap_err().to_string();
    assert!(e.contains("H4 holds no formula"), "{e}");
    s.execute("edit.undo", json!({})).unwrap();
    assert!(s.execute("data.solverLoadModel", json!({"from": "H1"})).is_ok());
    kept(&mut s);
}

#[test]
fn load_model_reads_a_bounded_column_and_refuses_malformed_cells() {
    let mut s = s();
    set(&mut s, &[("B1", "=ABS(A1-3)")]);
    let put = |s: &mut Session, col: u32, rows: std::ops::Range<u32>, f: &dyn Fn(u32) -> String| {
        let d = s.doc_mut().unwrap();
        let sh = std::sync::Arc::make_mut(&mut std::sync::Arc::make_mut(&mut d.wb).sheets[0]);
        for r in rows {
            sh.set_cell(CellRef::new(r, col), gridcraft_model::Cell::formula(gridcraft_model::Formula::new(&f(r))));
        }
    };
    // A column of formulas far longer than any model: read from its first cell, the read stops
    // after the most rows a model takes and the column is refused; as a range, it is refused
    // before any cell is read.
    put(&mut s, 15, 0..5_000, &|r| format!("{r}+1"));
    for from in ["P1", "P1:P5000", "P1:P1048576", "A1:XFD1048576"] {
        assert!(s.execute("data.solverLoadModel", json!({"from": from})).is_err(), "{from}");
    }
    // Malformed and hostile cells and ranges: an error each, never a panic, no model.
    let bad = ["AND(", "{", "{1e400,2", "MAX(Nope!A1)", "COUNT($A$1:$A$2", "AND($B$1<=", "MAX($B$1)&\"x\""];
    put(&mut s, 17, 0..bad.len() as u32, &|r| bad[r as usize].to_string());
    put(&mut s, 18, 0..1, &|_| format!("AND({})", "(".repeat(10_000)));
    for r in 1..=bad.len() {
        assert!(s.execute("data.solverLoadModel", json!({"from": format!("R{r}")})).is_err(), "R{r}");
    }
    for from in ["S1", "", ":", "P1:", "H0", "Sheet9!H1", "'Sheet1'!R1:R7", "R7:R1"] {
        assert!(s.execute("data.solverLoadModel", json!({"from": from})).is_err(), "{from}");
    }
    assert!(s.execute("data.solverLoadModel", json!({"from": 7})).is_err());
    assert!(s.execute("data.solver", json!({})).unwrap()["model"].is_null());
}

#[test]
fn load_model_keeps_the_evolutionary_convergence_and_generations() {
    let mut s = s();
    set(&mut s, &[("B1", "=ABS(A1-3)")]);
    let evo = json!({"objective": "B1", "goal": "min", "variables": "A1", "constraints": ["A1 <= 4"], "method": "evolutionary", "convergence": 0.001, "generationsWithoutImprovement": 20});
    s.execute("data.solverSaveModel", json!({"to": "H1", "model": evo})).unwrap();
    let m = s.execute("data.solverLoadModel", json!({"from": "H1"})).unwrap()["model"].clone();
    assert_eq!((m["convergence"].as_f64(), m["generationsWithoutImprovement"].as_f64()), (Some(0.001), Some(20.0)), "{m}");
    // They survive XLSX; Excel's time limit (solver_mni, in seconds) isn't written or read.
    let b64 = s.execute("file.saveBytes", json!({"format": "xlsx"})).unwrap()["base64"].as_str().unwrap().to_string();
    s.execute("file.open", json!({"name": "c.xlsx", "base64": b64})).unwrap();
    let m = s.execute("data.solver", json!({})).unwrap()["model"].clone();
    assert_eq!((m["convergence"].as_f64(), m["generationsWithoutImprovement"].as_f64()), (Some(0.001), Some(20.0)), "{m}");
    assert!(!s.doc().unwrap().wb.names.iter().any(|n| n.name == "solver_mni"));
    // Reset All removes the GridCraft name with the rest.
    s.execute("data.solverReset", json!({})).unwrap();
    assert!(s.doc().unwrap().wb.names.iter().all(|n| n.scope != Some(0)));
}

#[test]
fn solver_options_are_saved_with_the_model() {
    let mut s = s();
    set(&mut s, &[("B1", "=10*A1+13*A2"), ("B2", "=5*A1+6*A2")]);
    let p = json!({"objective": "B1", "variables": "A1:A2", "constraints": ["B2 <= 10", "A1:A2 bin"], "method": "evolutionary", "maxEvaluations": "3000", "integerOptimality": 5, "convergence": 0.001, "generationsWithoutImprovement": 20, "mutationRate": "0.1"});
    let r = s.execute("data.solver", p).unwrap();
    assert!(r["evaluations"].as_u64().unwrap() <= 3001, "{r}");
    // The solve's own result gives whole numbers as integers too.
    for k in ["maxEvaluations", "integerOptimality", "generationsWithoutImprovement", "populationSize", "randomSeed"] {
        assert!(r["model"][k].is_i64() || r["model"][k].is_u64(), "{k}: {r}");
    }
    // The options survive XLSX in the hidden names, as given or as text.
    let b64 = s.execute("file.saveBytes", json!({"format": "xlsx"})).unwrap()["base64"].as_str().unwrap().to_string();
    s.execute("file.open", json!({"name": "o.xlsx", "base64": b64})).unwrap();
    let m = s.execute("data.solver", json!({})).unwrap()["model"].clone();
    let f = |k: &str| m[k].as_f64();
    assert_eq!((f("maxEvaluations"), f("integerOptimality"), f("convergence")), (Some(3000.0), Some(5.0), Some(0.001)), "{m}");
    assert_eq!((f("generationsWithoutImprovement"), f("mutationRate")), (Some(20.0), Some(0.1)));
    // Whole numbers read back as integers, so the Solver dialog shows 3000 and not 3000.0.
    for k in ["maxEvaluations", "integerOptimality", "generationsWithoutImprovement", "populationSize", "randomSeed"] {
        assert!(m[k].is_i64(), "{k}: {m}");
    }
    assert_eq!(m["maxEvaluations"].to_string(), "3000");
    // Out-of-range options are clamped, not refused.
    let r = s.execute("data.solver", json!({"saved": true, "maxEvaluations": "1e300", "integerOptimality": -4})).unwrap();
    assert_eq!((r["model"]["maxEvaluations"].as_f64(), r["model"]["integerOptimality"].as_f64()), (Some(200_000.0), Some(0.0)));
}

#[test]
fn excel_iteration_and_time_limits_are_not_read_as_gridcraft_options() {
    let mut s = s();
    set(&mut s, &[("A1", "0"), ("B1", "=ABS(A1-3)")]);
    let model = json!({"objective": "B1", "goal": "min", "variables": "A1", "constraints": ["A1 <= 4"], "method": "evolutionary"});
    s.execute("data.solver", model.clone()).unwrap();
    let names = |s: &Session| -> Vec<String> {
        let d = s.doc().unwrap();
        d.wb.names.iter().filter(|n| n.scope == Some(0)).map(|n| n.name.clone()).collect()
    };
    // GridCraft's evaluation limit and generations go under its own names, not Excel's.
    let saved = names(&s);
    assert!(saved.iter().all(|n| n != "solver_itr" && n != "solver_mni"), "{saved:?}");
    assert!(saved.iter().any(|n| n == "gridcraft_solver_evals") && saved.iter().any(|n| n == "gridcraft_solver_stall"), "{saved:?}");
    // Excel's own limits, as a workbook from Excel holds them: 100 iterations, 30 seconds.
    {
        let d = s.doc_mut().unwrap();
        let wb = std::sync::Arc::make_mut(&mut d.wb);
        wb.names.retain(|n| !n.name.starts_with("gridcraft_"));
        for (name, formula) in [("solver_itr", "100"), ("solver_mni", "30")] {
            wb.names.push(gridcraft_model::DefinedName {
                name: name.into(),
                scope: Some(0),
                formula: formula.into(),
                comment: String::new(),
                hidden: true,
            });
        }
    }
    let m = s.execute("data.solver", json!({})).unwrap()["model"].clone();
    assert!(m["maxEvaluations"].is_null() && m["generationsWithoutImprovement"].is_null(), "{m}");
    set(&mut s, &[("A1", "0")]);
    let r = s.execute("data.solver", json!({"saved": true})).unwrap();
    assert!(r["evaluations"].as_u64().unwrap() > 100, "{r}");
    assert!((n(&s, "A1") - 3.0).abs() < 1e-3, "{r}");
    // Saving again replaces GridCraft's names; Reset All removes them with the rest. Simplex
    // LP refuses the nonlinear ABS model, but the model is saved before the solve.
    let r = s.execute(
        "data.solver",
        json!({"objective": "B1", "goal": "min", "variables": "A1", "constraints": ["A1 <= 4"], "method": "simplex", "maxEvaluations": 700, "keep": false}),
    );
    let m = super::saved_model(&s.doc().unwrap().wb, 0).unwrap();
    assert_eq!((m["method"].as_str(), m["maxEvaluations"].as_f64()), (Some("simplex"), Some(700.0)), "{m} {r:?}");
    let saved = names(&s);
    assert_eq!(
        saved.iter().filter(|n| n.starts_with("gridcraft_")).collect::<Vec<_>>(),
        ["gridcraft_solver_evals", "gridcraft_solver_stall"],
        "{saved:?}"
    );
    s.execute("data.solver", model).unwrap();
    s.execute("data.solverReset", json!({})).unwrap();
    assert!(names(&s).is_empty(), "{:?}", names(&s));
}

#[test]
fn integer_optimality_reads_a_percent_sign_as_percent() {
    let mut s = s();
    set(&mut s, &[("B1", "=3*A1")]);
    for (given, want) in [(json!("5%"), 5.0), (json!(" 2.5 % "), 2.5), (json!("5"), 5.0), (json!(5), 5.0), (json!("150%"), 100.0)] {
        let p = json!({"objective": "B1", "variables": "A1", "constraints": ["A1 <= 4", "A1 int"], "method": "simplex", "integerOptimality": given});
        let r = s.execute("data.solver", p).unwrap();
        assert_eq!(r["model"]["integerOptimality"].as_f64(), Some(want), "{given}: {r}");
    }
    // Percents whose fraction is not exact in binary read back as given, from the solve's
    // result and from the saved model.
    for given in [7.0, 29.0, 0.1] {
        let p = json!({"objective": "B1", "variables": "A1", "constraints": ["A1 <= 4", "A1 int"], "method": "simplex", "integerOptimality": given});
        let r = s.execute("data.solver", p).unwrap();
        assert_eq!(r["model"]["integerOptimality"].as_f64(), Some(given), "{r}");
        let m = s.execute("data.solver", json!({})).unwrap()["model"].clone();
        assert_eq!(m["integerOptimality"].as_f64(), Some(given), "{m}");
    }
}

#[test]
fn evolutionary_options_survive_a_solve_with_another_method() {
    let mut s = s();
    set(&mut s, &[("B1", "=3*A1")]);
    let p = json!({"objective": "B1", "variables": "A1", "constraints": ["A1 <= 4"], "method": "grg", "populationSize": 40, "mutationRate": 0.2, "randomSeed": 7, "convergence": 0.001, "generationsWithoutImprovement": 25, "requireBounds": false});
    let r = s.execute("data.solver", p).unwrap();
    assert_eq!(r["model"]["populationSize"].as_f64(), Some(40.0), "{r}");
    // The saved model keeps them for the next time the method is Evolutionary.
    let m = s.execute("data.solver", json!({})).unwrap()["model"].clone();
    let f = |k: &str| m[k].as_f64();
    assert_eq!((f("populationSize"), f("mutationRate"), f("randomSeed")), (Some(40.0), Some(0.2), Some(7.0)), "{m}");
    assert_eq!((f("convergence"), f("generationsWithoutImprovement"), m["requireBounds"].as_bool()), (Some(0.001), Some(25.0), Some(false)));
}

#[test]
fn limits_report_of_a_nonlinear_model() {
    // The largest rectangle with perimeter at most 20 (5 × 5): with the height held at 5, the
    // width ranges over 0..5, the area over 0..25.
    let mut s = s();
    set(&mut s, &[("A1", "1"), ("A2", "1"), ("B1", "=A1*A2"), ("B2", "=2*A1+2*A2")]);
    let r = s.execute("data.solver", json!({"objective": "B1", "variables": "A1:A2", "constraints": ["B2 <= 20"], "reports": ["limits"]})).unwrap();
    assert_eq!(r["reports"], json!(["Limits Report 1"]), "{r}");
    let l = "Limits Report 1";
    let r = row_of(&s, l, "$A$1") + 1;
    let got: Vec<f64> = ["E", "F", "G", "H"].iter().map(|c| at(&s, l, &format!("{c}{r}")).as_f64().unwrap()).collect();
    for (g, want) in got.iter().zip([0.0, 0.0, 5.0, 25.0]) {
        assert!((g - want).abs() < 1e-3, "{got:?}");
    }
}

#[test]
fn infeasible_unbounded_and_nonlinear_models_are_reported() {
    let mut s = s();
    set(&mut s, &[("A1", "1"), ("B1", "=2*A1")]);
    for method in ["simplex", "grg"] {
        let r =
            s.execute("data.solver", json!({"objective": "B1", "variables": "A1", "constraints": ["A1 >= 5", "B1 <= 6"], "method": method})).unwrap();
        assert_eq!(r["status"], "infeasible", "{method}: {r}");
        assert_eq!(r["changed"], false);
        assert_eq!(n(&s, "A1"), 1.0, "an infeasible model leaves the cells alone");
    }
    let r = s.execute("data.solver", json!({"objective": "B1", "variables": "A1", "method": "simplex"})).unwrap();
    assert_eq!(r["status"], "unbounded");
    let r = s.execute("data.solver", json!({"objective": "B1", "variables": "A1", "method": "grg", "maxEvaluations": 5000})).unwrap();
    assert!(r["status"] == "unbounded" || r["status"] == "iterationLimit", "{r}");
    set(&mut s, &[("A1", "1"), ("C1", "=A1^2")]);
    let r = s.execute("data.solver", json!({"objective": "C1", "goal": "min", "variables": "A1", "method": "simplex"})).unwrap();
    assert_eq!(r["status"], "notLinear");
}

#[test]
fn hostile_models_are_refused_without_panicking() {
    let mut s = s();
    let r = s.execute("data.solver", json!({})).unwrap();
    assert!(r["model"].is_null());
    assert!(s.take_ui_requests().iter().any(|q| matches!(q, crate::UiRequest::Dialog(n, _) if n == "solver")));
    set(&mut s, &[("B1", "=SUM(A1:A1000)"), ("C1", "5")]);
    for p in [
        json!({"objective": "B1", "variables": "A1:A1000"}),
        json!({"objective": "B1", "variables": "A1:XFD1048576"}),
        json!({"objective": "C1", "variables": "A1"}),
        json!({"objective": "B1:B2", "variables": "A1"}),
        json!({"objective": "B1", "variables": "B1"}),
        json!({"objective": "B1", "variables": "A1", "goal": "sideways"}),
        json!({"objective": "B1", "variables": "A1", "goal": "value"}),
        json!({"objective": "B1", "variables": "A1", "method": "evolutionary"}),
        json!({"objective": "B1", "variables": "A1", "method": "annealing"}),
        json!({"objective": "B1", "variables": "A1", "constraints": ["A1 ?? 3"]}),
        json!({"objective": "B1", "variables": "A1", "constraints": "A1 <= 3"}),
        json!({"objective": "B1", "variables": "A1", "constraints": ["A1:A3 <= C1:C2"]}),
        json!({"objective": "B1", "variables": "A1", "constraints": ["C1 int"]}),
        json!({"objective": "B1", "variables": "A1", "constraints": ["A1:A1048576 <= 1"]}),
        json!({"objective": "B1", "variables": "A1", "constraints": vec![json!("A1 <= 1"); 1001]}),
        json!({"objective": "Nope!B1", "variables": "A1"}),
    ] {
        assert!(s.execute("data.solver", p.clone()).is_err(), "{p}");
    }
    // Huge evaluation requests are capped, and a model erroring everywhere doesn't panic.
    set(&mut s, &[("D1", "=1/0+A1")]);
    let r = s.execute("data.solver", json!({"objective": "D1", "variables": "A1", "maxEvaluations": 1e300})).unwrap();
    assert_ne!(r["status"], "converged");
}