Press n or j to go to the next uncovered block, b, p or k for the previous block.
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* @license Apache-2.0
*
* Copyright (c) 2026 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 arraylike2object = require( '@stdlib/array/base/arraylike2object' );
var isPow2 = require( '@stdlib/math/base/assert/uint32-is-pow2' );
var format = require( '@stdlib/string/format' );
var accessors = require( './accessors.js' );
// MAIN //
/**
* Generates a Hadamard matrix using alternative indexing semantics.
*
* @param {NonNegativeInteger} N - number of rows and columns of the output matrix
* @param {Collection} out - output array
* @param {integer} strideOut1 - stride length for the first dimension of `out`
* @param {integer} strideOut2 - stride length for the second dimension of `out`
* @param {NonNegativeInteger} offsetOut - starting index for `out`
* @throws {RangeError} first argument must be a power of two
* @returns {Collection} output matrix
*
* @example
* var out = [ 0.0, 0.0, 0.0, 0.0 ];
*
* ghadamard( 2, out, 2, 1, 0 );
* // out => [ 1.0, 1.0, 1.0, -1.0 ]
*/
function ghadamard( N, out, strideOut1, strideOut2, offsetOut ) {
var oo;
var io;
var ij;
var d1;
var d2;
var v;
var n;
var i;
var j;
if ( N <= 0 ) {
return out;
}
if ( !isPow2( N ) ) {
throw new RangeError( format( 'invalid argument. First argument must be a power of two. Value: `%d`.', N ) );
}
oo = arraylike2object( out );
if ( oo.accessorProtocol ) {
accessors( N, oo, strideOut1, strideOut2, offsetOut );
return out;
}
// Seed the top-left quadrant with the 1x1 Hadamard matrix:
out[ offsetOut ] = 1.0;
// Perform iterative doubling, copying the current n-by-n leading submatrix to the three remaining quadrants of the 2n-by-2n leading submatrix, with the bottom-right quadrant having flipped signs...
for ( n = 1; n < N; n *= 2 ) {
d1 = n * strideOut1;
d2 = n * strideOut2;
io = offsetOut;
for ( i = 0; i < n; i++ ) {
ij = io;
for ( j = 0; j < n; j++ ) {
v = out[ ij ];
out[ ij+d2 ] = v;
out[ ij+d1 ] = v;
out[ ij+d1+d2 ] = -v;
ij += strideOut2;
}
io += strideOut1;
}
}
return out;
}
// EXPORTS //
module.exports = ghadamard;
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