@rayyamhk/matrix/lib/core/decompositions/LU.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;
/**
 * Calculates the LUP decomposition of the Matrix,
 * where L is lower triangular matrix which diagonal entries are always 1,
 * U is upper triangular matrix, and P is permutation matrix.<br><br>
 * 
 * It is implemented using Gaussian Elimination with Partial Pivoting in order to
 * reduce the error caused by floating-point arithmetic.<br><br>
 * 
 * Note that if optimized is true, P is a Permutation Array and both L and U are merged
 * into one matrix in order to improve performance.
 * @memberof Matrix
 * @static
 * @param {Matrix} A - Any matrix
 * @param {boolean} [optimized=false] - Returns [P, LU] if it is true, [P, L, U] if it is false
 * @returns {Matrix[]} The LUP decomposition of Matrix
 */


function LU(A) {
  var optimized = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : false;

  if (!(A instanceof this)) {
    throw new Error(INVALID_MATRIX);
  }

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

  var size = Math.min(row, col);
  var EPSILON = 1 / (Math.pow(10, A._digit) * 2);
  var permutation = initPermutation(row);

  var copy = this.clone(A)._matrix;

  for (var i = 0; i < row - 1; i++) {
    var currentCol = Math.min(i, col); // apply Partial Pivoting

    PartialPivoting(copy, permutation, currentCol, row, col);
    var ith = permutation[i];
    var pivot = copy[ith][currentCol];

    if (Math.abs(pivot) < EPSILON) {
      continue;
    }

    for (var j = i + 1; j < row; j++) {
      var jth = permutation[j];
      var entry = copy[jth][currentCol];

      if (Math.abs(entry) >= EPSILON) {
        var factor = entry / pivot;

        for (var k = currentCol; k < col; k++) {
          copy[jth][k] -= factor * copy[ith][k];
        }

        copy[jth][currentCol] = factor;
      }
    }
  }

  var result = new Array(row);

  for (var _i2 = 0; _i2 < row; _i2++) {
    result[_i2] = copy[permutation[_i2]];
  }

  if (optimized) {
    return [permutation, new this(result)];
  }

  var P = this.generate(row, row, function (i, j) {
    var idx = permutation[i];

    if (j === idx) {
      return 1;
    }

    return 0;
  });
  var L = this.generate(row, size, function (i, j) {
    if (i === j) {
      return 1;
    }

    if (i < j) {
      return 0;
    }

    return result[i][j];
  });
  var U = this.generate(size, col, function (i, j) {
    if (i > j) {
      return 0;
    }

    return result[i][j];
  });
  return [P, L, U];
}

;

function initPermutation(size) {
  var permutation = new Array(size);

  for (var i = 0; i < size; i++) {
    permutation[i] = i;
  }

  return permutation;
}

function PartialPivoting(matrix, permutation, pos, row, col) {
  var currentCol = Math.min(pos, col);
  var maxIdx = pos;
  var max = Math.abs(matrix[permutation[pos]][currentCol]);

  for (var i = pos + 1; i < row; i++) {
    var value = Math.abs(matrix[permutation[i]][currentCol]);

    if (value > max) {
      maxIdx = i;
      max = value;
    }
  }

  var t = permutation[pos];
  permutation[pos] = permutation[maxIdx];
  permutation[maxIdx] = t;
}

module.exports = LU;