@rayyamhk/matrix/lib/core/linear-equations/solve.js

A professional, comprehensive and high-performance library for you to manipulate matrices.

"use strict";

function _slicedToArray(arr, i) { return _arrayWithHoles(arr) || _iterableToArrayLimit(arr, i) || _unsupportedIterableToArray(arr, i) || _nonIterableRest(); }

function _nonIterableRest() { throw new TypeError("Invalid attempt to destructure non-iterable instance.\nIn order to be iterable, non-array objects must have a [Symbol.iterator]() method."); }

function _unsupportedIterableToArray(o, minLen) { if (!o) return; if (typeof o === "string") return _arrayLikeToArray(o, minLen); var n = Object.prototype.toString.call(o).slice(8, -1); if (n === "Object" && o.constructor) n = o.constructor.name; if (n === "Map" || n === "Set") return Array.from(o); if (n === "Arguments" || /^(?:Ui|I)nt(?:8|16|32)(?:Clamped)?Array$/.test(n)) return _arrayLikeToArray(o, minLen); }

function _arrayLikeToArray(arr, len) { if (len == null || len > arr.length) len = arr.length; for (var i = 0, arr2 = new Array(len); i < len; i++) { arr2[i] = arr[i]; } return arr2; }

function _iterableToArrayLimit(arr, i) { var _i = arr == null ? null : typeof Symbol !== "undefined" && arr[Symbol.iterator] || arr["@@iterator"]; if (_i == null) return; var _arr = []; var _n = true; var _d = false; var _s, _e; try { for (_i = _i.call(arr); !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"] != null) _i["return"](); } finally { if (_d) throw _e; } } return _arr; }

function _arrayWithHoles(arr) { if (Array.isArray(arr)) return arr; }

var _require = require('../../Error'),
    INVALID_MATRIX = _require.INVALID_MATRIX,
    NO_UNIQUE_SOLUTION = _require.NO_UNIQUE_SOLUTION,
    INVALID_SQUARE_MATRIX = _require.INVALID_SQUARE_MATRIX,
    SIZE_INCOMPATIBLE = _require.SIZE_INCOMPATIBLE;
/**
 * Solve system of linear equations Ax = y using LU decomposition.
 * If there is no unique solutions, an error is thrown.
 * @memberof Matrix
 * @static
 * @param {Matrix} L - Any n x n square Matrix
 * @param {Matrix} y - Any n x 1 Matrix
 * @returns {Matrix} n x 1 Matrix which is the solution of Ax = y
 */


function solve(A, b) {
  if (!(A instanceof this) || !(b instanceof this)) {
    throw new Error(INVALID_MATRIX);
  }

  if (!A.isSquare()) {
    throw new Error(INVALID_SQUARE_MATRIX);
  }

  var _A$size = A.size(),
      _A$size2 = _slicedToArray(_A$size, 2),
      aRow = _A$size2[0],
      aCol = _A$size2[1];

  var _b$size = b.size(),
      _b$size2 = _slicedToArray(_b$size, 2),
      bRow = _b$size2[0],
      bCol = _b$size2[1];

  if (aCol !== bRow || bCol !== 1) {
    throw new Error(SIZE_INCOMPATIBLE);
  }

  var EPSILON = 1 / (Math.pow(10, A._digit) * 2);

  var _this$LU = this.LU(A, true),
      _this$LU2 = _slicedToArray(_this$LU, 2),
      P = _this$LU2[0],
      LU = _this$LU2[1];

  var matrixLU = LU._matrix;
  var matrixB = b._matrix;

  for (var i = aRow - 1; i >= 0; i--) {
    if (Math.abs(matrixLU[i][i]) < EPSILON) {
      throw new Error(NO_UNIQUE_SOLUTION);
    }
  }

  var clonedVector = new Array(bRow);
  var coefficients = new Array(bRow);

  for (var _i2 = 0; _i2 < bRow; _i2++) {
    // eslint-disable-next-line prefer-destructuring
    clonedVector[_i2] = matrixB[P[_i2]][0];
  }

  for (var _i3 = 0; _i3 < aRow; _i3++) {
    var summation = 0;

    for (var j = 0; j < _i3; j++) {
      summation += coefficients[j] * matrixLU[_i3][j];
    }

    coefficients[_i3] = clonedVector[_i3] - summation;
  }

  for (var _i4 = aRow - 1; _i4 >= 0; _i4--) {
    var _summation = 0;

    for (var _j = _i4 + 1; _j < aRow; _j++) {
      _summation += matrixLU[_i4][_j] * clonedVector[_j];
    }

    clonedVector[_i4] = (coefficients[_i4] - _summation) / matrixLU[_i4][_i4];
  }

  for (var _i5 = 0; _i5 < bRow; _i5++) {
    coefficients[_i5] = [clonedVector[_i5]];
  }

  return new this(coefficients);
}

;
module.exports = solve;