Press n or j to go to the next uncovered block, b, p or k for the previous block.
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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 isLayout = require( '@stdlib/blas/base/assert/is-layout' );
var format = require( '@stdlib/string/format' );
var max = require( '@stdlib/math/base/special/fast/max' );
var min = require( '@stdlib/math/base/special/min' );
var base = require( './base.js' );
// MAIN //
/**
* Generates one of the real orthogonal matrices `Q` or `P^T` determined by `DGEBRD` when reducing a real matrix `A` to bidiagonal form: `A = Q * B * P^T`.
*
* ## Notes
*
* - `Q` and `P^T` are defined as products of elementary reflectors `H(i)` or `G(i)` respectively.
*
* - If `vect = 'Q'`,
*
* - `A` is assumed to have been an `M-by-K` matrix, and `Q` is of order `M`.
* - if `m >= k`, `Q = H(1) H(2) . . . H(k)` and `dorgbr` returns the first `n` columns of `Q`, where `m >= n >= k`.
* - if `m < k`, `Q = H(1) H(2) . . . H(m-1)` and `dorgbr` returns `Q` as an `M-by-M` matrix.
*
* - If `vect = 'P'`,
*
* - `A` is assumed to have been a `K-by-N` matrix, and `P^T` is of order `N`.
* - if `k < n`, `P^T = G(k) . . . G(2) G(1)` and `dorgbr` returns the first `m` rows of `P^T`, where `n >= m >= k`.
* - if `k >= n`, `P^T = G(n-1) . . . G(2) G(1)` and `dorgbr` returns `P^T` as an `N-by-N` matrix.
*
* - `WORK` must have length, `LWORK >= max(1,min(M,N))`. For optimum performance `LWORK >= min(M,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, and no error message related to `LWORK` is issued.
*
* @param {string} order - storage layout
* @param {string} vect - specifies whether the matrix `Q` or the matrix `P^T` is returned in `A`
* @param {NonNegativeInteger} M - number of rows of `Q` or `P^T`
* @param {NonNegativeInteger} N - number of columns of `Q` or `P^T`
* @param {NonNegativeInteger} K - number of elementary reflectors
* @param {Float64Array} A - input/output matrix
* @param {integer} LDA - stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`)
* @param {Float64Array} TAU - scalar factors of elementary reflectors
* @param {Float64Array} WORK - workspace array
* @param {NonNegativeInteger} LWORK - dimension of the array `WORK`
* @throws {TypeError} first argument must be a valid order
* @throws {TypeError} second argument must be either `'Q'` or `'P'`
* @throws {RangeError} third argument must be a non-negative integer
* @throws {RangeError} fourth argument must be a non-negative integer satisfying the constraints for the given `vect` argument
* @throws {RangeError} fifth argument must be a non-negative integer
* @throws {RangeError} seventh argument must be a valid `LDA` value
* @throws {RangeError} tenth argument must be a valid `LWORK` value
* @returns {integer} status code
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1, 0.2, -0.1, 0.3, 0, 1, 0.4, -0.2, 0, 0, 1, 0.5 ] );
* var TAU = new Float64Array( [ 1.3, 0.9, 1.1 ] );
* var WORK = new Float64Array( 10 );
*
* var info = dorgbr( 'column-major', 'Q', 4, 3, 3, A, 4, TAU, WORK, 10 );
* // A => <Float64Array>[ -0.3, -0.26, 0.13, -0.39, -0.143, 0.0714, -0.3457, 0.1371, ~0.21, ~-0.021, ~-0.146, ~-0.474 ]
* // info => 0
* // WORK[ 0 ] => 64
*/
function dorgbr( order, vect, M, N, K, A, LDA, TAU, WORK, LWORK ) { // eslint-disable-line stdlib/jsdoc-doctest-decimal-point
var wantq;
var sa1;
var sa2;
if ( !isLayout( order ) ) {
throw new TypeError( format( 'invalid argument. First argument must be a valid order. Value: `%s`.', order ) );
}
if ( vect !== 'Q' && vect !== 'P' ) {
throw new TypeError( format( 'invalid argument. Second argument must be either `\'Q\'` or `\'P\'`. Value: `%s`.', vect ) );
}
wantq = ( vect === 'Q' );
if ( M < 0 ) {
throw new RangeError( format( 'invalid argument. Third argument must be a nonnegative integer. Value: `%d`.', M ) );
}
if ( wantq ) {
if ( N < min( M, K ) || N > M ) {
throw new RangeError( format( 'invalid argument. Fourth argument must be greater than or equal to `min(M,K)` and smaller than or equal to `M`. Value: `%d`.', N ) );
}
} else if ( N < M || M < min( N, K ) ) {
throw new RangeError( format( 'invalid argument. Fourth argument must be greater than or equal to `M`, and `M` must be greater than or equal to `min(N,K)`. Value: `%d`.', N ) );
}
if ( K < 0 ) {
throw new RangeError( format( 'invalid argument. Fifth argument must be a nonnegative integer. Value: `%d`.', K ) );
}
if ( order === 'column-major' ) {
if ( LDA < max( 1, M ) ) {
throw new RangeError( format( 'invalid argument. Seventh argument must be greater than or equal to `max(1,M)`. Value: `%d`.', LDA ) );
}
sa1 = 1;
sa2 = LDA;
} else { // row-major
if ( LDA < max( 1, N ) ) {
throw new RangeError( format( 'invalid argument. Seventh argument must be greater than or equal to `max(1,N)`. Value: `%d`.', LDA ) );
}
sa1 = LDA;
sa2 = 1;
}
if ( LWORK < max( 1, min( M, N ) ) && LWORK !== -1 ) {
throw new RangeError( format( 'invalid argument. Tenth argument must be greater than or equal to `max(1,min(M,N))` except when equal to -1. Value: `%d`.', LWORK ) );
}
return base( vect, M, N, K, A, sa1, sa2, 0, TAU, 1, 0, WORK, 1, 0, LWORK );
}
// EXPORTS //
module.exports = dorgbr;
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