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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 Pascal matrix using alternative indexing semantics.
*
* @param {string} uplo - specifies whether to fill the lower or upper triangular part of `out`
* @param {NonNegativeInteger} N - order of the Pascal 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 ];
*
* gpascal( 'symmetric', 3, out, 3, 1, 0 );
* // out => [ 1.0, 1.0, 1.0, 1.0, 2.0, 3.0, 1.0, 3.0, 6.0 ]
*
* @example
* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
*
* gpascal( 'lower', 3, out, 3, 1, 0 );
* // out => [ 1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 2.0, 1.0 ]
*
* @example
* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
*
* gpascal( 'upper', 3, out, 3, 1, 0 );
* // out => [ 1.0, 1.0, 1.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ]
*/
function gpascal( uplo, N, out, strideOut1, strideOut2, offsetOut ) {
var oo;
var io;
var v;
var i;
var j;
if ( N <= 0 ) {
return out;
}
oo = arraylike2object( out );
if ( oo.accessorProtocol ) {
accessors( uplo, N, oo, strideOut1, strideOut2, offsetOut );
return out;
}
if ( uplo === 'symmetric' ) {
io = offsetOut;
for ( i = 0; i < N; i++ ) {
v = 1.0;
out[ io ] = v;
for ( j = 1; j < N; j++ ) {
v *= ( i + j ) / j;
out[ io + (j*strideOut2) ] = v;
}
io += strideOut1;
}
return out;
}
if ( uplo === 'lower' ) {
io = offsetOut;
for ( i = 0; i < N; i++ ) {
v = 1.0;
out[ io ] = v;
for ( j = 1; j <= i; j++ ) {
v *= ( i - j + 1 ) / j;
out[ io + (j*strideOut2) ] = v;
}
for ( j = i + 1; j < N; j++ ) {
out[ io + (j*strideOut2) ] = 0.0;
}
io += strideOut1;
}
return out;
}
// uplo === 'upper'
io = offsetOut;
for ( i = 0; i < N; i++ ) {
for ( j = 0; j < i; j++ ) {
out[ io + (j*strideOut2) ] = 0.0;
}
v = 1.0;
out[ io + (i*strideOut2) ] = v;
for ( j = i + 1; j < N; j++ ) {
v *= j / ( j - i );
out[ io + (j*strideOut2) ] = v;
}
io += strideOut1;
}
return out;
}
// EXPORTS //
module.exports = gpascal;
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