@rayyamhk/matrix/lib/core/properties/norm.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 Matrix = require('../..');

var _require = require('../../Error'),
    INVALID_P_NORM = _require.INVALID_P_NORM;
/**
 * Calculates the Matrix norm of any Matrix with respect to the choice of norm.<br><br>
 * 
 * 1-norm: Maximum absolute column sum of the Matrix.<br>
 * 2-norm: The largest singular value of Matrix.<br>
 * Infinity-norm: Maximum absolute row sum of the Matrix.<br>
 * Frobenius-norm: Euclidean norm invloving all entries.<br><br>
 * 
 * The norms are not cached.
 * @memberof Matrix
 * @instance
 * @param {(1|2|Infinity|'F')} p - The choice of Matrix norm
 * @returns {number} The norm of the Matrix.
 */


function norm() {
  var p = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : 2;

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

  if (p !== 1 && p !== 2 && p !== Infinity && p !== 'F') {
    throw new Error(INVALID_P_NORM);
  }

  var matrix = this._matrix;
  var result = 0;

  if (p === 1) {
    // max of column sum
    for (var j = 0; j < col; j++) {
      var columnSum = 0;

      for (var i = 0; i < row; i++) {
        columnSum += Math.abs(matrix[i][j]);
      }

      if (columnSum > result) {
        result = columnSum;
      }
    }

    return result;
  } // largest singular value


  if (p === 2) {
    var transpose = Matrix.transpose(this);
    var M = Matrix.multiply(transpose, this);
    var eigenvalues = M.eigenvalues();

    for (var _i2 = 0; _i2 < eigenvalues.length; _i2++) {
      var value = eigenvalues[_i2].getModulus();

      if (value > result) {
        result = value;
      }
    }

    return Math.sqrt(result);
  }

  if (p === Infinity) {
    // max of row sum
    for (var _i3 = 0; _i3 < row; _i3++) {
      var rowSum = 0;

      for (var _j = 0; _j < col; _j++) {
        rowSum += Math.abs(matrix[_i3][_j]);
      }

      if (rowSum > result) {
        result = rowSum;
      }
    }

    return result;
  } // F


  for (var _i4 = 0; _i4 < row; _i4++) {
    for (var _j2 = 0; _j2 < col; _j2++) {
      result += Math.pow(matrix[_i4][_j2], 2);
    }
  }

  return Math.sqrt(result);
}

;
module.exports = norm;