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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 isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
var accessors = require( './accessors.js' );
// MAIN //
/**
* Generates a Fiedler 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, 4.0 ];
* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
*
* gfiedlerCompanion( 4, x, 1, 0, out, 3, 1, 0 );
* // out => [ -2.0, -3.0, 1.0, 1.0, 0.0, 0.0, 0.0, -4.0, 0.0 ]
*/
function gfiedlerCompanion( N, x, strideX, offsetX, out, strideOut1, strideOut2, offsetOut ) { // eslint-disable-line max-len
var so1;
var so2;
var ox;
var oo;
var ds;
var ix;
var io;
var ij;
var M;
var d;
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;
// As a zero matrix is symmetric, when filling the output matrix with zeros, we can swap the strides so that the innermost loop always moves over contiguous memory, thus ensuring cache optimal traversal...
if ( isRowMajor( [ strideOut1, strideOut2 ] ) ) {
so1 = strideOut1;
so2 = strideOut2;
} else { // column-major
so1 = strideOut2;
so2 = strideOut1;
}
// Fill the matrix with zeros...
io = offsetOut;
for ( i = 0; i < M; i++ ) {
ij = io;
for ( j = 0; j < M; j++ ) {
out[ ij ] = 0.0;
ij += so2;
}
io += so1;
}
// Cache the leading coefficient:
v = x[ offsetX ];
// Resolve the step size for moving along a matrix diagonal, skipping every other element:
ds = 2 * ( strideOut1 + strideOut2 );
// Set the first element to the negated and normalized second coefficient...
ix = offsetX + strideX;
out[ offsetOut ] = -x[ ix ] / v;
// Write the remaining negated and normalized coefficients, alternating between positions along the first super- and subdiagonals...
io = offsetOut + strideOut2;
d = 2 * strideOut1;
for ( i = 1; i < M; i++ ) {
ix += strideX;
out[ io ] = -x[ ix ] / v;
io += d;
// Toggle the step between the first super- and subdiagonals:
d = ds - d;
}
// Write a one as the first element of the first subdiagonal...
if ( M > 1 ) {
out[ offsetOut+strideOut1 ] = 1.0;
}
// Write ones, alternating with zeros, along the second superdiagonal...
io = offsetOut + ( 2*strideOut2 );
for ( i = 2; i < M; i += 2 ) {
out[ io ] = 1.0;
io += ds;
}
// Write ones, alternating with zeros, along the second subdiagonal...
io = offsetOut + ( 3*strideOut1 ) + strideOut2;
for ( i = 3; i < M; i += 2 ) {
out[ io ] = 1.0;
io += ds;
}
return out;
}
// EXPORTS //
module.exports = gfiedlerCompanion;
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