87 lines
2.3 KiB
JavaScript
87 lines
2.3 KiB
JavaScript
|
/**
|
||
|
|
* @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( './../../is-square-matrix' );
|
||
|
|
var floor = require( '@stdlib/math/base/special/floor' );
|
||
|
|
var isOdd = require( '@stdlib/math/base/assert/is-odd' );
|
||
|
|
|
||
|
|
|
||
|
|
// MAIN //
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Tests if a value is a skew-centrosymmetric matrix.
|
||
|
|
*
|
||
|
|
* ## Notes
|
||
|
|
*
|
||
|
|
* - The implementation must rely on manually checking that \\(M_{ij} = -M_{N-i-1,N-j-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-centrosymmetric matrix
|
||
|
|
*
|
||
|
|
* @example
|
||
|
|
* var ndarray = require( '@stdlib/ndarray/ctor' );
|
||
|
|
*
|
||
|
|
* var arr = ndarray( 'generic', [ 2, 1, -1, -2 ], [ 2, 2 ], [ 2, 1 ], 0, 'row-major' );
|
||
|
|
* var bool = isSkewCentrosymmetricMatrix( arr );
|
||
|
|
* // returns true
|
||
|
|
*
|
||
|
|
* bool = isSkewCentrosymmetricMatrix( [] );
|
||
|
|
* // returns false
|
||
|
|
*/
|
||
|
|
function isSkewCentrosymmetricMatrix( v ) { // eslint-disable-line id-length
|
||
|
|
var m1;
|
||
|
|
var M;
|
||
|
|
var N;
|
||
|
|
var n;
|
||
|
|
var i;
|
||
|
|
var j;
|
||
|
|
if ( !isSquareMatrix( v ) ) {
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
M = v.shape[ 0 ];
|
||
|
|
N = floor( M/2.0 ); // corresponds to a row index + 1
|
||
|
|
m1 = M - 1;
|
||
|
|
for ( i = 0; i < N; i++ ) {
|
||
|
|
n = m1 - i;
|
||
|
|
for ( j = 0; j < M; j++ ) {
|
||
|
|
if ( v.get( i, j ) !== -v.get( n, m1-j ) ) {
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if ( isOdd( M ) ) {
|
||
|
|
// Only need to examine the first half of the row (including the center element) due to symmetry...
|
||
|
|
for ( j = 0; j <= N; j++ ) {
|
||
|
|
if ( v.get( i, j ) !== -v.get( N, m1-j ) ) {
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
// EXPORTS //
|
||
|
|
|
||
|
|
module.exports = isSkewCentrosymmetricMatrix;
|