@rayyamhk/matrix/lib/core/structure/isSkewSymmetric.js

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

"use strict";

/**
 * Determines whether a square Matrix is skew symmetric or not.<br><br>
 * 
 * Skew symmetric Matrix is a square Matrix whose transpose equals its negative.<br><br>
 * 
 * The result is cached.
 * @memberof Matrix
 * @instance
 * @param {number} [digit=8] - Number of significant digits
 * @returns {boolean} Returns true if the square Matrix is skew symmetric
 */
function isSkewSymmetric() {
  var digit = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : this._digit;

  if (this._isSkewSymmetric !== undefined) {
    return this._isSkewSymmetric;
  }

  if (!this.isSquare()) {
    this._isSkewSymmetric = false;
    return false;
  }

  var A = this._matrix;
  var EPSILON = 1 / (Math.pow(10, digit) * 2);
  var size = A.length;

  if (size === 0) {
    this._isSkewSymmetric = true;
    return true; // []
  }

  for (var i = 0; i < size; i++) {
    for (var j = 0; j < i; j++) {
      if (Math.abs(A[i][j] + A[j][i]) >= EPSILON) {
        this._isSkewSymmetric = false;
        return false;
      }
    }
  }

  this._isSkewSymmetric = true;
  return true;
}

;
module.exports = isSkewSymmetric;