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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.
*/
/* eslint-disable max-len, max-params */
'use strict';
// MODULES //
var dlarf1f = require( '@stdlib/lapack/base/dlarf1f' ).ndarray;
var dscal = require( '@stdlib/blas/base/dscal' ).ndarray;
var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
// MAIN //
/**
* Generates an M-by-N real orthogonal matrix Q from the elementary reflectors returned by DGELQF/DGELQ2 (LQ factorization, unblocked).
*
* ## Notes
*
* - On entry, the i-th row of A must contain the vector which defines the elementary reflector H(i), for i = 1, 2, ..., K, as returned by `DGELQF` in the first K rows of its array argument A.
*
* - Q is defined as the product of K elementary reflectors:
*
* - Q = H(K) ... H(2) H(1), where each H(i) has the form `H(i) = I - tau(i)*v*v^T`, and v is stored as row i of the input matrix A.
*
* - On exit, A contains the M-by-N matrix Q.
*
* @private
* @param {NonNegativeInteger} M - number of rows of Q (0 <= M <= N)
* @param {NonNegativeInteger} N - number of columns of Q (N >= 0)
* @param {NonNegativeInteger} K - number of elementary reflectors (0 <= K <= M)
* @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 - scalar factors of reflectors (length K)
* @param {integer} strideTAU - stride for TAU
* @param {NonNegativeInteger} offsetTAU - starting index for TAU
* @param {Float64Array} WORK - workspace (length >= M)
* @param {integer} strideWORK - stride for WORK
* @param {NonNegativeInteger} offsetWORK - starting index for WORK
* @returns {integer} status code (0 = success)
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( 12 );
* var TAU = new Float64Array( 2 );
* var WORK = new Float64Array( 3 );
*
* var info = dorgl2( 3, 4, 2, A, 4, 1, 0, TAU, 1, 0, WORK, 1, 0 );
* // returns 0
* // A => <Float64Array>[ 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0 ]
* // WORK => <Float64Array>[ 0, 0, 0 ]
*/
function dorgl2( M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK ) {
var idx0;
var idx1;
var idx2;
var idx3;
var i;
var j;
var l;
// Initialize rows K+1..M to rows of the unit matrix
if ( K < M ) {
if ( isRowMajor( [ strideA1, strideA2 ] ) ) {
idx1 = offsetA + ( strideA1*K );
for ( l = K; l < M; l++ ) {
idx2 = idx1;
for ( j = 0; j < N; j++ ) {
A[ idx2 ] = 0;
idx2 += strideA2;
if ( j >= K && j < M ) {
A[ offsetA + ( j*( strideA1 + strideA2 ) ) ] = 1;
}
}
idx1 += strideA1;
}
} else { // column-major
idx1 = offsetA;
for ( j = 0; j < N; j++ ) {
idx2 = idx1 + ( K*strideA1 );
for ( l = K; l < M; l++ ) {
A[ idx2 ] = 0;
idx2 += strideA1;
}
if ( j >= K && j < M ) {
A[ idx1 + ( j*strideA1 ) ] = 1;
}
idx1 += strideA2;
}
}
}
idx0 = offsetTAU + ( strideTAU*( K - 1 ) ); // TAU( i )
idx1 = offsetA + ( ( K - 1 )*( strideA1 + strideA2 ) ); // A( i,i )
idx2 = offsetA + ( ( K - 1 )*strideA1 ); // A( i,0 )
for ( i = K - 1; i >= 0; i-- ) {
// Apply H(i) to A(i:m,i:n) from the right
if ( i < N - 1 ) {
if ( i < M - 1 ) {
dlarf1f( 'right', M - i - 1, N - i, A, strideA2, idx1, TAU[ idx0 ], A, strideA1, strideA2, idx1 + strideA1, WORK, strideWORK, offsetWORK );
}
dscal( N - i - 1, -TAU[ idx0 ], A, strideA2, idx1 + strideA2 );
}
A[ idx1 ] = 1 - TAU[ idx0 ];
// Set A(i,1:i-1) to zero
idx3 = idx2; // A( i,l )
for ( l = 0; l < i; l++ ) {
A[ idx3 ] = 0;
idx3 += strideA2;
}
idx0 -= strideTAU;
idx1 -= strideA1 + strideA2;
idx2 -= strideA1;
}
return 0;
}
// EXPORTS //
module.exports = dorgl2;
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