3x3-equation-solver/lib/index.js

Solves systems of 3 equations with three unknowns.

"use strict";

/**
 * Solver
 * Solves the system of equations.
 *
 * @name Solver
 * @function
 * @param {Array} input An array of arrays containing the coeficients and the results. Example:
 *
 *    ```js
 *    [
 *        3,  1, -5, 5
 *      , 4,  2,  7, 19
 *      , 5, -4,  1, 6
 *    ]
 *    ```
 * @param {Boolean} raw If it is true, the return value will be an object like described below. Otherwise, the result array will be returned.
 * @return {Object|Array} The actual result (if `raw` is not true) or an object containing the following fields:
 *
 *  - `result` (Array): An array of three values containing the unknown values.
 *  - `coefficients` (Array): An array of arrays containing the coefficients.
 *  - `results` (Array): The equation results.
 *  - `determinant` (Number): The determinant value.
 *  - `determinants` (Array): The unknown determinants.
 *  - `solved` (Boolean): If `true`, that means the system has a solution, otherwise.
 */
function Solver(input, raw) {

  var a = input[0][0],
      b = input[0][1],
      c = input[0][2],
      d = input[1][0],
      e = input[1][1],
      f = input[1][2],
      g = input[2][0],
      h = input[2][1],
      i = input[2][2],
      s1 = input[0][3],
      s2 = input[1][3],
      s3 = input[2][3],
      dd = a * e * i + d * h * c + b * f * g - g * e * c - d * b * i - a * h * f,
      solved = true;

  if (!dd) {
    solved = false;
  }

  var dx = s1 * e * i + s2 * h * c + b * f * s3 - s3 * e * c - s2 * b * i - s1 * h * f,
      dy = a * s2 * i + d * s3 * c + s1 * f * g - g * s2 * c - d * s1 * i - a * s3 * f,
      dz = a * e * s3 + d * h * s1 + b * s2 * g - g * e * s1 - d * b * s3 - a * h * s2,
      x = dx / dd,
      y = dy / dd,
      z = dz / dd;

  if (raw) {
    return {
      result: [x, y, z],
      results: [s1, s2, s3],
      coefficients: [[a, b, c], [d, e, f], [g, h, i]],
      determinant: dd,
      determinants: [dx, dy, dz],
      solved: solved
    };
  }

  return [x, y, z];
}

module.exports = Solver;