88 lines
2.3 KiB
JavaScript
88 lines
2.3 KiB
JavaScript
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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2018 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var isSquareMatrix = require( './../../is-square-matrix' );
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var floor = require( '@stdlib/math/base/special/floor' );
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var isOdd = require( '@stdlib/math/base/assert/is-odd' );
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// MAIN //
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/**
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* Tests if a value is a centrosymmetric matrix.
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*
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* ## Notes
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*
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* - 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.
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* - Worst case scenario: O(N^2).
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*
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* @param {*} v - value to test
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* @returns {boolean} boolean indicating if a value is a centrosymmetric matrix
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*
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* @example
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* var ndarray = require( '@stdlib/ndarray/ctor' );
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*
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* var arr = ndarray( 'generic', [ 2, 1, 1, 2 ], [ 2, 2 ], [ 2, 1 ], 0, 'row-major' );
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*
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* var bool = isCentrosymmetricMatrix( arr );
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* // returns true
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*
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* bool = isCentrosymmetricMatrix( [] );
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* // returns false
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*/
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function isCentrosymmetricMatrix( v ) {
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var m1;
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var M;
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var N;
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var n;
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var i;
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var j;
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if ( !isSquareMatrix( v ) ) {
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return false;
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}
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M = v.shape[ 0 ];
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N = floor( M/2.0 ); // corresponds to a row index + 1
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m1 = M - 1;
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for ( i = 0; i < N; i++ ) {
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n = m1 - i;
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for ( j = 0; j < M; j++ ) {
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if ( v.get( i, j ) !== v.get( n, m1-j ) ) {
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return false;
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}
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}
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}
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if ( isOdd( M ) ) {
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// Only need to examine the first half of the row (up until the center element) due to symmetry...
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for ( j = 0; j < N; j++ ) {
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if ( v.get( i, j ) !== v.get( N, m1-j ) ) {
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return false;
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}
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}
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}
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return true;
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}
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// EXPORTS //
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module.exports = isCentrosymmetricMatrix;
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