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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 dlarf1f = require( '@stdlib/lapack/base/dlarf1f' ).ndarray;
var Float64Array = require( '@stdlib/array/float64' );
var min = require( '@stdlib/math/base/special/min' );
var dlarfg = require( './dlarfg.js' );
// MAIN //
/**
* Computes an LQ factorization of a real M-by-N matrix `A = L * Q`, using Householder reflections (unblocked algorithm).
*
* ## Notes
*
* - On exit, the elements on and below the diagonal of A contain the M-by-min(M,N) lower trapezoidal matrix `L`.
* - The elements above the diagonal, with the array `TAU`, represent the orthogonal matrix `Q` as a product of elementary reflectors.
*
* @private
* @param {NonNegativeInteger} M - number of rows in `A`
* @param {NonNegativeInteger} N - number of columns in `A`
* @param {Float64Array} A - input/output matrix
* @param {integer} strideA1 - stride of the first dimension of `A`
* @param {integer} strideA2 - stride of the second dimension of `A`
* @param {NonNegativeInteger} offsetA - starting index for `A`
* @param {Float64Array} TAU - output array of scalar factors (length min(M,N))
* @param {integer} strideTAU - stride for TAU
* @param {NonNegativeInteger} offsetTAU - starting index for TAU
* @param {Float64Array} WORK - workspace array (length >= M)
* @param {integer} strideWORK - stride for WORK
* @param {NonNegativeInteger} offsetWORK - starting index for WORK
* @returns {integer} status code
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 12 ] );
* var TAU = new Float64Array( 3 );
* var work = new Float64Array( 3 );
*
* dgelq2( 3, 4, A, 1, 3, 0, TAU, 1, 0, work, 1, 0 );
* // A => <Float64Array>[ ~-5.477, ~-12.78, ~-20.083, ~0.309, ~-3.266, ~-6.532, ~0.463, ~-0.327, ~0, ~0.618, ~-0.789, ~0.618 ]
* // TAU => <Float64Array>[ ~1.183, ~1.156, ~1.447 ]
* // work => <Float64Array>[ ~6.532, ~24.593, 0 ]
*/
function dgelq2( M, N, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK ) { // eslint-disable-line stdlib/jsdoc-doctest-decimal-point, max-len, max-params
var taui;
var aii;
var out;
var K;
var i;
K = min( M, N );
out = new Float64Array( 2 );
aii = offsetA; // Index of A(i,i)
taui = offsetTAU; // Index of TAU(i)
for ( i = 0; i < K; i++ ) {
// Generate elementary reflector H(i) to annihilate A(i, i+1:N-1)
out[ 0 ] = A[ aii ];
dlarfg( N - i, A, strideA2, aii + ( min( 1, N - 1 - i ) * strideA2 ), out, 1, 0 );
A[ aii ] = out[ 0 ];
TAU[ taui ] = out[ 1 ];
if ( i < M - 1 ) {
// Apply H(i) to A(i+1:M-1, i:N-1) from the right
dlarf1f( 'right', M - i - 1, N - i, A, strideA2, aii, TAU[ taui ], A, strideA1, strideA2, aii + strideA1, WORK, strideWORK, offsetWORK);
}
aii += strideA1 + strideA2;
taui += strideTAU;
}
return 0;
}
// EXPORTS //
module.exports = dgelq2;
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