main.js (1913B)
1 /** 2 * @license Apache-2.0 3 * 4 * Copyright (c) 2018 The Stdlib Authors. 5 * 6 * Licensed under the Apache License, Version 2.0 (the "License"); 7 * you may not use this file except in compliance with the License. 8 * You may obtain a copy of the License at 9 * 10 * http://www.apache.org/licenses/LICENSE-2.0 11 * 12 * Unless required by applicable law or agreed to in writing, software 13 * distributed under the License is distributed on an "AS IS" BASIS, 14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 15 * See the License for the specific language governing permissions and 16 * limitations under the License. 17 */ 18 19 'use strict'; 20 21 // MODULES // 22 23 var isSquareMatrix = require( './../../is-square-matrix' ); 24 25 26 // MAIN // 27 28 /** 29 * Tests if a value is a skew-persymmetric matrix. 30 * 31 * ## Notes 32 * 33 * - The implementation must rely on manually checking that \\(M_{ij} = -M_{N-j-1,N-i-1}\\), and, while element access is deterministic, no way exists to prevent cache misses outside of reordering the underlying matrix elements, thus incurring a larger performance penalty than just "jumping around" in a single pass. 34 * - Worst case scenario: O(N^2). 35 * 36 * @param {*} v - value to test 37 * @returns {boolean} boolean indicating if a value is a skew-persymmetric matrix 38 * 39 * @example 40 * var ndarray = require( '@stdlib/ndarray/ctor' ); 41 * 42 * var arr = ndarray( 'generic', [ 1, 0, 0, -1 ], [ 2, 2 ], [ 2, 1 ], 0, 'row-major' ); 43 * var bool = isSkewPersymmetricMatrix( arr ); 44 * // returns true 45 * 46 * bool = isSkewPersymmetricMatrix( [] ); 47 * // returns false 48 */ 49 function isSkewPersymmetricMatrix( v ) { 50 var M; 51 var n; 52 var i; 53 var j; 54 if ( !isSquareMatrix( v ) ) { 55 return false; 56 } 57 M = v.shape[ 0 ] - 1; 58 for ( i = 0; i < M; i++ ) { 59 n = M - i; 60 for ( j = 0; j <= n; j++ ) { 61 if ( v.get( i, j ) !== -v.get( M-j, n ) ) { 62 return false; 63 } 64 } 65 } 66 return true; 67 } 68 69 70 // EXPORTS // 71 72 module.exports = isSkewPersymmetricMatrix;