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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 isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
var accessors = require( './accessors.js' );
// MAIN //
/**
* Generates a circulant matrix using alternative indexing semantics.
*
* @param {NonNegativeInteger} N - number of indexed elements in `c`
* @param {Collection} c - first column of the matrix
* @param {integer} strideC - stride length for `c`
* @param {NonNegativeInteger} offsetC - starting index for `c`
* @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 c = [ 1.0, 2.0, 3.0 ];
* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
*
* gcirculant( 3, c, 1, 0, out, 3, 1, 0 );
* // out => [ 1.0, 3.0, 2.0, 2.0, 1.0, 3.0, 3.0, 2.0, 1.0 ]
*/
function gcirculant( N, c, strideC, offsetC, out, strideOut1, strideOut2, offsetOut ) { // eslint-disable-line max-len
var do0;
var do1;
var oo;
var oc;
var io;
var co;
var ol;
var i0;
var i1;
if ( N <= 0 ) {
return out;
}
oc = arraylike2object( c );
oo = arraylike2object( out );
if ( oc.accessorProtocol || oo.accessorProtocol ) {
accessors( N, oc, strideC, offsetC, oo, strideOut1, strideOut2, offsetOut ); // eslint-disable-line max-len
return out;
}
// Note on variable naming convention: S#, do#, io, i# where # corresponds to the loop number, with `0` being the innermost loop...
if ( isRowMajor( [ strideOut1, strideOut2 ] ) ) {
// Row-first iteration (inner loop walks columns):
do0 = strideOut2;
do1 = strideOut1 - ( N * strideOut2 );
ol = offsetC + ( ( N - 1 ) * strideC );
io = offsetOut;
for ( i1 = 0; i1 < N; i1++ ) {
// Diagonal and lower triangle: c[i1], c[i1-1], ..., c[0]
co = offsetC + ( i1 * strideC );
for ( i0 = 0; i0 <= i1; i0++ ) {
out[ io ] = c[ co ];
co -= strideC;
io += do0;
}
// Upper triangle: c[N-1], c[N-2], ..., c[i1+1]
co = ol;
for ( i0 = i1 + 1; i0 < N; i0++ ) {
out[ io ] = c[ co ];
co -= strideC;
io += do0;
}
io += do1;
}
} else {
// Column-first iteration (inner loop walks rows):
do0 = strideOut1;
do1 = strideOut2 - ( N * strideOut1 );
io = offsetOut;
for ( i1 = 0; i1 < N; i1++ ) {
// Upper triangle: c[N-i1], c[N-i1+1], ..., c[N-1]
co = offsetC + ( ( N - i1 ) * strideC );
for ( i0 = 0; i0 < i1; i0++ ) {
out[ io ] = c[ co ];
co += strideC;
io += do0;
}
// Diagonal and lower triangle: c[0], c[1], ..., c[N-1-i1]
co = offsetC;
for ( i0 = i1; i0 < N; i0++ ) {
out[ io ] = c[ co ];
co += strideC;
io += do0;
}
io += do1;
}
}
return out;
}
// EXPORTS //
module.exports = gcirculant;
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