Detect unbounded LPs in simplex instead of looping forever

[shehio]

Summary

simplex() does not terminate on an unbounded linear program, and matrix() writes through its arguments. Both paths were untested.

Unboundedness Is Never Detected

pick_row() performs the minimum-ratio test. When the pivot column holds no positive entry, no basic variable bounds the entering variable and the program is unbounded — but the function returned its initialiser, index = 0:

let index = 0;
for (let i = 0; i < n - 1; i++) {
    if (matrix[i][col] <= 0) { continue; }
    ...
}
return index;

simplex() then pivoted on row 0 on a non-positive element, check() never came back true, and the while loop spun forever.

Reproduced on develop — maximize x subject to −x + y ≤ 1:

$ node unbounded_check.js
calling simplex on unbounded LP...
EXIT=124   # killed by a 12s timeout; no output, no return

pick_row() now returns -1 when the column has no positive entry, and simplex() throws Error('The linear program is unbounded.'). The same LP now returns in milliseconds.

matrix() Mutated Its Caller's Arrays

It negated cT in place and assigned the assembled tableau row back into A[i], so a caller could not reuse or even inspect its own inputs afterwards. Measured on develop:

A before:  [[1,2],[1,1],[3,2]]
A after :  [[1,2,1,0,0,0,16],[1,1,0,1,0,0,9],[3,2,0,0,1,0,24]]
cT before: [40,30]
cT after : [-40,-30]

The rows are now built without writing back into A, and the objective is negated into a local via map. After the fix A, b and cT all compare equal to their original values.

Verification

The bundled Richland example is unchanged: P = 330, both through the test and through node src/linear-programming/simplex.js.

Suite: 34 tests / 10 suites before → 36 tests / 10 suites after, all passing. The two new cases are the unbounded LP and the input-mutation check.

Left Alone

n, m, last_row and last_col are module-level mutable state written by matrix() and read by every other function, so a tableau can only be solved while it is the most recently built one. That is a real latent hazard but it is orthogonal to these two fixes, so I have not touched it.

🤖 Generated with Claude Code

https://claude.ai/code/session_01THEv7BFJd31NjvBRehbZPL