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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 isColumnMajor = require( '@stdlib/ndarray/base/assert/is-column-major-string' );
var max = require( '@stdlib/math/base/special/max' );
var format = require( '@stdlib/string/format' );
var base = require( './base.js' );
// MAIN //
/**
* Reduces a general real `M-by-N` matrix `A` to upper or lower bi-diagonal form `B` by an orthogonal transformation `Q**T * A * P = B`.
*
* ## Notes
*
* - If `M >= N`,
*
* - `B` is upper bi-diagonal form.
* - The diagonal and the first superdiagonal are overwritten with the upper bi-diagonal matrix `B`.
* - Elements below the diagonal, with the array `TAUQ`, represent the orthogonal matrix `Q` as a product of elementary reflectors.
* - Elements above the first super-diagonal, with the array `TAUP`, represent the orthogonal matrix `P` as a product of elementary reflectors.
*
* - If `M < N`,
*
* - `B` is lower bi-diagonal form.
* - The diagonal and the first sub-diagonal are overwritten with the lower bi-diagonal matrix `B`.
* - Elements below the first sub-diagonal, with the array `TAUQ`, represent the orthogonal matrix `Q` as a product of elementary reflectors.
* - Elements on and above the diagonal, with the array `TAUP`, represent the orthogonal matrix `P` as a product of elementary reflectors.
*
* @param {string} order - storage layout
* @param {NonNegativeInteger} M - number of rows in `A`
* @param {NonNegativeInteger} N - number of columns in `A`
* @param {Float64Array} A - input matrix
* @param {integer} LDA - stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`)
* @param {Float64Array} D - diagonal elements of the bi-diagonal matrix `B` (length `min(M,N)`)
* @param {Float64Array} E - off-diagonal elements of the bi-diagonal matrix `B` (length `min(M,N)-1`)
* @param {Float64Array} TAUQ - scalars factors of the elementary reflectors that represent the orthogonal matrix `Q` (length `NB`)
* @param {Float64Array} TAUP - scalars factors of the elementary reflectors that represent the orthogonal matrix `P` (length `NB`)
* @param {Float64Array} WORK - workspace array (length >= `max(1,LWORK)`)
* @param {integer} LWORK - length of WORK array
* @throws {TypeError} first argument must be a valid order
* @throws {RangeError} second argument must be a non-negative integer
* @throws {RangeError} third argument must be a non-negative integer
* @throws {RangeError} fifth argument must be valid LDA value
* @returns {integer} status code
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 4.0, -1.0, 2.5, 7.0, 8.5, -2.0 ] );
* var D = new Float64Array( [ 0.0, 0.0 ] );
* var E = new Float64Array( [ 0.0 ] );
* var TAUQ = new Float64Array( [ 0.0, 0.0 ] );
* var TAUP = new Float64Array( [ 0.0, 0.0 ] );
* var WORK = new Float64Array( 100 );
*
* dgebrd( 'column-major', 3, 2, A, 3, D, E, TAUQ, TAUP, WORK, 100 );
* // A => <Float64Array>[ ~-4.822, ~-0.113, ~0.283, ~-3.007, ~-10.78, ~-0.237 ]
* // D => <Float64Array>[ ~-4.822, ~-10.78 ]
* // E => <Float64Array>[ ~-3.007 ]
* // TAUQ => <Float64Array>[ ~1.83, ~1.894 ]
* // TAUP => <Float64Array>[ 0.0, 0.0 ]
* // WORK[ 0 ] => 3.0
*/
function dgebrd( order, M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK ) { // eslint-disable-line max-params, stdlib/jsdoc-doctest-decimal-point
var sA1;
var sA2;
if ( !isLayout( order ) ) {
throw new TypeError( format( 'invalid argument. First argument must be a valid order. Value: `%s`.', order ) );
}
if ( M < 0 ) {
throw new RangeError( format( 'invalid argument. Second argument must be a nonnegative integer. Value: `%d`.', M ) );
}
if ( N < 0 ) {
throw new RangeError( format( 'invalid argument. Third argument must be a nonnegative integer. Value: `%d`.', N ) );
}
if ( isColumnMajor( order ) ) {
if ( LDA < max( 1, M ) ) {
throw new RangeError( format( 'invalid argument. Fifth argument must be greater than or equal to max(1,%d). Value: `%d`.', M, LDA ) );
}
sA1 = 1;
sA2 = LDA;
} else { // order === 'row-major'
if ( LDA < max( 1, N ) ) {
throw new RangeError( format( 'invalid argument. Fifth argument must be greater than or equal to max(1,%d). Value: `%d`.', N, LDA ) );
}
sA1 = LDA;
sA2 = 1;
}
return base( M, N, A, sA1, sA2, 0, D, 1, 0, E, 1, 0, TAUQ, 1, 0, TAUP, 1, 0, WORK, 1, 0, LWORK ); // eslint-disable-line max-len
}
// EXPORTS //
module.exports = dgebrd;
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