@rayyamhk/matrix/lib/core/linear-equations/backward.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 empty = require('../../util/empty');

var _require = require('../../Error'),
    INVALID_MATRIX = _require.INVALID_MATRIX,
    INVALID_UPPER_TRIANGULAR_MATRIX = _require.INVALID_UPPER_TRIANGULAR_MATRIX,
    INVALID_SQUARE_MATRIX = _require.INVALID_SQUARE_MATRIX,
    SIZE_INCOMPATIBLE = _require.SIZE_INCOMPATIBLE,
    NO_UNIQUE_SOLUTION = _require.NO_UNIQUE_SOLUTION;
/**
* Solve system of linear equations Ux = y using backward substitution,
* where U is an upper triangular matrix.
* If there is no unique solutions, an error is thrown.
* @memberof Matrix
* @static
* @param {Matrix} U - Any n x n upper triangular Matrix
* @param {Matrix} y - Any n x 1 Matrix
* @returns {Matrix} n x 1 Matrix which is the solution of Ux = y
*/


function backward(U, y) {
  if (!(U instanceof this) || !(y instanceof this)) {
    throw new Error(INVALID_MATRIX);
  }

  if (!U.isUpperTriangular()) {
    throw new Error(INVALID_UPPER_TRIANGULAR_MATRIX);
  }

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

  var size = U.size()[0];

  var _y$size = y.size(),
      _y$size2 = _slicedToArray(_y$size, 2),
      yrow = _y$size2[0],
      ycol = _y$size2[1];

  var matrixU = U._matrix;
  var matrixY = y._matrix;

  if (yrow !== size || ycol !== 1) {
    throw new Error(SIZE_INCOMPATIBLE);
  }

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

  for (var i = 0; i < size; i++) {
    if (Math.abs(matrixU[i][i]) < EPSILON) {
      throw new Error(NO_UNIQUE_SOLUTION);
    }
  }

  var coefficients = empty(size, 1);

  for (var _i2 = size - 1; _i2 >= 0; _i2--) {
    var summation = 0;

    for (var j = _i2 + 1; j < size; j++) {
      summation += coefficients[j][0] * matrixU[_i2][j];
    }

    coefficients[_i2][0] = (matrixY[_i2][0] - summation) / matrixU[_i2][_i2];
  }

  return new this(coefficients);
}

;
module.exports = backward;