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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 sqrt = require( '@stdlib/math/base/special/sqrt' );
var accessors = require( './accessors.js' );
// MAIN //
/**
* Generates a Helmert matrix using alternative indexing semantics.
*
* @param {boolean} full - boolean indicating whether to include the first row
* @param {NonNegativeInteger} N - order of the Helmert 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`
* @returns {Collection} output matrix
*
* @example
* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
*
* ghelmert( true, 3, out, 3, 1, 0 );
* // out => [ ~0.577, ~0.577, ~0.577, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
*
* @example
* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
*
* ghelmert( false, 3, out, 3, 1, 0 );
* // out => [ ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
*/
function ghelmert( full, N, out, strideOut1, strideOut2, offsetOut ) {
var do1;
var oo;
var io;
var v;
var i;
var j;
if ( N <= 0 || ( !full && N <= 1 ) ) {
return out;
}
oo = arraylike2object( out );
if ( oo.accessorProtocol ) {
accessors( full, N, oo, strideOut1, strideOut2, offsetOut );
return out;
}
do1 = strideOut1 - ( N*strideOut2 );
io = offsetOut;
// If full, write the first row with all elements equal to 1/sqrt(N)...
if ( full ) {
v = 1.0 / sqrt( N );
for ( j = 0; j < N; j++ ) {
out[ io ] = v;
io += strideOut2;
}
io += do1;
}
// For the remaining rows, compute the sub-diagonal Helmert rows...
for ( i = 1; i < N; i++ ) {
v = 1.0 / sqrt( i * (i+1) );
for ( j = 0; j < i; j++ ) {
out[ io ] = v;
io += strideOut2;
}
out[ io ] = -i * v;
io += strideOut2;
for ( j = i + 1; j < N; j++ ) {
out[ io ] = 0.0;
io += strideOut2;
}
io += do1;
}
return out;
}
// EXPORTS //
module.exports = ghelmert;
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