gaussian-elimination.js

function gaussianElimination(matrix) {
    var pivot, base, col, div, mul, v, n, i, j;

    n = matrix.length;

    // Forward Elimination

    for (pivot = 0; pivot < n - 1; pivot++) {
        swap(matrix, pivot);
        base = matrix[pivot];
        div = base[pivot];

        if (div === 0) {
            continue;
        }

        for (i = pivot + 1; i < n; i++) {
            col = matrix[i];
            mul = col[pivot] / div;

            for (j = pivot; j <= n; j++) {
                col[j] -= mul * base[j];
            }
        }
    }

    // Back Substitution

    for (i = n - 1; i >= 0; i--) {
        col = matrix[i];
        v = col[n];

        for (j = i + 1; j < n; j++) {
            v -= col[j] * matrix[j][n];
        }

        div = col[i];
        col[n] = div ? v / div : 0;
    }

    return matrix.map(function(col) { return col[n]; });
}

function swap(matrix, pivot) {
    var target, max, v, n, i, tmp;

    n = matrix.length;
    target = pivot;
    max = matrix[pivot][pivot];

    for (i = pivot + 1; i < n; i++) {
        v = matrix[i][pivot];

        if (max === 0 || v / max > 1) {
            max = v;
            target = i;
        }
    }

    if (target !== pivot) {
        tmp = matrix[pivot];
        matrix[pivot] = matrix[target];
        matrix[target] = tmp;
    }
}