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* @license Apache-2.0
*
* Copyright (c) 2025 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 base = require( './base.js' );
// MAIN //
/**
* Generates a real elementary reflector `H` of order `N` such that applying `H` to a vector `[alpha; x]` zeros out `X`.
*
* ## Notes
*
* - `H` is a Householder matrix with the form `H = I - tau * [1; v] * [1, v^T]`, where `tau` is a scalar and `v` is a vector.
* - the input vector is `[alpha; x]`, where `alpha` is a scalar and `X` is a real `(n-1)`-element vector.
* - the result of applying `H` to `[alpha; x]` is `[beta; 0]`, with `beta` being a scalar and the rest of the vector zeroed.
* - if all elements of `X` are zero, then `tau = 0` and `H` is the identity matrix.
* - otherwise, `1 <= tau <= 2`
*
* @param {NonNegativeInteger} N - number of rows/columns of the elementary reflector `H`
* @param {Float64Array} X - overwritten by the vector `V` on exit, expects `N - 1` indexed elements
* @param {integer} incx - stride length for `X`
* @param {Float64Array} out - array to store `alpha` and `tau`, first indexed element stores `alpha` and the second indexed element stores `tau`
* @returns {void} overwrites the array `X` and `out` in place
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var X = new Float64Array( [ 2.0, 3.0, 4.0 ] );
* var out = new Float64Array( [ 4.0, 0.0 ] );
*
* dlarfg( 4, X, 1, out );
* // X => <Float64Array>[ ~0.19, ~0.28, ~0.37 ]
* // out => <Float64Array>[ ~-6.7, ~1.6 ]
*/
function dlarfg( N, X, incx, out ) {
base( N, X, incx, 0, out, 1, 0 );
}
// EXPORTS //
module.exports = dlarfg;
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