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| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 | 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 17x 17x 17x 17x 17x 17x 13x 13x 4x 17x 6x 6x 15x 2x 2x 15x 6x 2x 17x 1x 1x 1x 1x 1x | /**
* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
// MODULES //
var isSquareMatrix = require( '@stdlib/assert/is-square-matrix' );
// MAIN //
/**
* Tests if a value is a skew-persymmetric matrix.
*
* ## Notes
*
* - 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.
* - Worst case scenario: O(N^2).
*
* @param {*} v - value to test
* @returns {boolean} boolean indicating if a value is a skew-persymmetric matrix
*
* @example
* var ndarray = require( '@stdlib/ndarray/ctor' );
*
* var arr = ndarray( 'generic', [ 1, 0, 0, -1 ], [ 2, 2 ], [ 2, 1 ], 0, 'row-major' );
* var bool = isSkewPersymmetricMatrix( arr );
* // returns true
*
* bool = isSkewPersymmetricMatrix( [] );
* // returns false
*/
function isSkewPersymmetricMatrix( v ) {
var M;
var n;
var i;
var j;
if ( !isSquareMatrix( v ) ) {
return false;
}
M = v.shape[ 0 ] - 1;
for ( i = 0; i < M; i++ ) {
n = M - i;
for ( j = 0; j <= n; j++ ) {
if ( v.get( i, j ) !== -v.get( M-j, n ) ) {
return false;
}
}
}
return true;
}
// EXPORTS //
module.exports = isSkewPersymmetricMatrix;
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