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* @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' );
var floor = require( '@stdlib/math/base/special/floor' );
var isOdd = require( '@stdlib/math/base/assert/is-odd' );
// MAIN //
/**
* Tests if a value is a 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 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 = isCentrosymmetricMatrix( arr );
* // returns true
*
* bool = isCentrosymmetricMatrix( [] );
* // returns false
*/
function isCentrosymmetricMatrix( v ) {
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 (up until 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 = isCentrosymmetricMatrix;
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