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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 min = require( '@stdlib/math/base/special/min' );
var floor = require( '@stdlib/math/base/special/floor' );
var dgeqr2 = require( './dgeqr2.js' );
var dlarfb = require( './dlarfb.js' );
var dlarft = require( './dlarft.js' );
// MAIN //
/**
* Compute a QR factorization of a real M-by-N matrix `A`.
*
* ## Notes
*
* - On exit, the elements on and above the diagonal of the array contain the `min(M,N)-by-N` upper trapezoidal matrix `R` (`R` is upper triangular if `m >= n`).
* - On exit, the elements below the diagonal, with the array `TAU`, represent the orthogonal matrix `Q` as a product of `min(m,n)` elementary reflectors.
* - `LWORK >= 1`, if `MIN(M,N) = 0`, and `LWORK >= N`, otherwise. For optimum performance `LWORK >= N*NB`, where `NB` is the optimal blocksize.
* - If `LWORK = -1`, then a workspace query is assumed; the routine only calculates the optimal size of the `WORK` array, returns this value as the first entry of the `WORK` array
*
* @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`
* @param {NonNegativeInteger} LWORK - dimension of the array `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( 4 );
*
* dgeqrf( 3, 4, A, 1, 3, 0, TAU, 1, 0, WORK, 1, 0, 4 );
* // A => <Float64Array>[ ~-10.344, ~0.441, ~0.793, ~-11.794, ~0.947, ~0.919, ~-13.244, ~1.894, ~0.0, ~-14.694, ~2.842, ~0.0 ]
* // TAU => <Float64Array>[ ~1.097, ~1.084, 0.0 ]
* // WORK => <Float64Array>[ 4.0, ~-2.842, ~17.046, 0.0 ]
*/
function dgeqrf( M, N, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK ) { // eslint-disable-line stdlib/jsdoc-doctest-decimal-point, max-len, max-params
var ldwork;
var lquery;
var inctau;
var lwkopt;
var nbmin;
var inca;
var taui;
var aii;
var iws;
var ib;
var nb;
var nx;
var i;
var k;
k = min( M, N );
nb = 32; // The optimal block size derived from fortran LAPACK call `ilaenv( 1, 'DGEQRF', ' ', m, n, -1, -1 )`
lquery = ( LWORK === -1 );
if ( lquery ) {
if ( k === 0 ) {
lwkopt = 1;
} else {
lwkopt = N * nb;
}
WORK[ offsetWORK ] = lwkopt;
return 0;
}
// Quick return if possible
if ( k === 0 ) {
WORK[ offsetWORK ] = 1;
return 0;
}
nbmin = 2;
nx = 0;
iws = N;
if ( nb > 1 && nb < k ) {
// Determine when to cross over from blocked to unblocked code.
nx = 128; // The crossover point derived from fortran LAPACK call `ilaenv( 3, 'DGEQRF', ' ', m, n, -1, -1 )`
if ( nx < k ) {
// Determine if workspace is large enough for blocked code.
ldwork = N;
iws = ldwork * nb;
if ( LWORK < iws ) {
// Not enough workspace to use optimal NB: reduce NB and determine the minimum value of NB.
nb = floor( LWORK / ldwork );
nbmin = 2; // The minimal block size derived from fortran LAPACK call `ilaenv( 2, 'DGEQRF', ' ', m, n, -1, -1 )`
}
}
}
inca = nb * ( strideA1 + strideA2 );
inctau = nb * strideTAU;
aii = offsetA; // Index of A(i,i)
taui = offsetTAU; // Index of TAU(i)
if ( nb >= nbmin && nb < k && nx < k ) {
// Use blocked code initially
for ( i = 0; i < k - nx; i += nb ) {
ib = min( k - i, nb );
// Compute the QR factorization of the current block A(i:m,i:i+ib-1)
dgeqr2( M - i, ib, A, strideA1, strideA2, aii, TAU, strideTAU, taui, WORK, strideWORK, offsetWORK );
if ( i + ib < N ) {
// Form the triangular factor of the block reflector: H = H(i) H(i+1) . . . H(i+ib-1)
dlarft( 'forward', 'columns', M - i, ib, A, strideA1, strideA2, aii, TAU, strideTAU, taui, WORK, 1, N, offsetWORK );
// Apply H**T to A(i:m,i+ib:n) from the left
dlarfb( 'left', 'transpose', 'forward', 'columns', M - i, N - i - ib, ib, A, strideA1, strideA2, aii, WORK, 1, N, offsetWORK, A, strideA1, strideA2, aii + ( ib * strideA2 ), WORK, 1, ldwork, offsetWORK + ( ib * strideWORK ) );
}
aii += inca;
taui += inctau;
}
} else {
i = 0;
}
// Use unblocked code to factor the last or only block
if ( i <= k - 1 ) {
dgeqr2( M - i, N - i, A, strideA1, strideA2, aii, TAU, strideTAU, taui, WORK, strideWORK, offsetWORK );
}
WORK[ offsetWORK ] = iws;
return 0;
}
// EXPORTS //
module.exports = dgeqrf;
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