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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 accessors = require( './accessors.js' );
// MAIN //
/**
* Generates a companion matrix using alternative indexing semantics.
*
* @param {NonNegativeInteger} N - number of indexed elements in `x`
* @param {Collection} x - input array containing polynomial coefficients
* @param {integer} strideX - stride length for `x`
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @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 x = [ 1.0, 2.0, 3.0 ];
* var out = [ 0.0, 0.0, 0.0, 0.0 ];
*
* gcompanion( 3, x, 1, 0, out, 2, 1, 0 );
* // out => [ -2.0, -3.0, 1.0, 0.0 ]
*/
function gcompanion( N, x, strideX, offsetX, out, strideOut1, strideOut2, offsetOut ) { // eslint-disable-line max-len
var ox;
var oo;
var ix;
var io;
var ij;
var M;
var v;
var i;
var j;
if ( N <= 1 ) {
return out;
}
ox = arraylike2object( x );
oo = arraylike2object( out );
if ( ox.accessorProtocol || oo.accessorProtocol ) {
accessors( N, ox, strideX, offsetX, oo, strideOut1, strideOut2, offsetOut ); // eslint-disable-line max-len
return out;
}
M = N - 1;
// Cache the leading coefficient:
v = x[ offsetX ];
// Fill the first row with the remaining coefficients negated and normalized by the leading coefficient...
ix = offsetX + strideX;
io = offsetOut;
ij = io;
for ( j = 0; j < M; j++ ) {
out[ ij ] = -x[ ix ] / v;
ix += strideX;
ij += strideOut2;
}
// Fill the remaining rows with ones along the first subdiagonal and zeros elsewhere...
for ( i = 1; i < M; i++ ) {
io += strideOut1;
ij = io;
for ( j = 0; j < M; j++ ) {
if ( j === i-1 ) {
out[ ij ] = 1.0;
} else {
out[ ij ] = 0.0;
}
ij += strideOut2;
}
}
return out;
}
// EXPORTS //
module.exports = gcompanion;
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