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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 the first `NB` rows and columns of a real general matrix `A` to upper or lower bi-diagonal form by an orthogonal transformation `Q**T*A*P`.
*
* ## Notes
*
* - If `M >= N`,
*
* - `A` is reduced to upper bi-diagonal form.
* - Elements on and below the diagonal in the first `NB` columns, with the array `TAUQ`, represent the orthogonal matrix `Q` as a product of elementary reflectors.
* - Elements above the diagonal in the first `NB` rows, with the array `TAUP`, represent the orthogonal matrix `P` as a product of elementary reflectors.
*
* - If `M < N`,
*
* - `A` is reduced to lower bi-diagonal form.
* - Elements below the diagonal in the first `NB` columns, with the array `TAUQ`, represent the orthogonal matrix `Q` as a product of elementary reflectors.
* - Elements on and above the diagonal in the first `NB` rows, 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 {integer} NB - number of leading rows and columns of `A` to reduce
* @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 - real diagonal elements (length `NB`)
* @param {Float64Array} E - real off-diagonal elements (length `NB`)
* @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} X - output matrix
* @param {integer} LDX - stride of the first dimension of `X` (a.k.a., leading dimension of the matrix `X`)
* @param {Float64Array} Y - output matrix
* @param {integer} LDY - stride of the first dimension of `Y` (a.k.a., leading dimension of the matrix `Y`)
* @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} sixth argument must be greater than or equal to max(1,N)
* @throws {RangeError} twelfth argument must be greater than or equal to max(1,NB)
* @throws {RangeError} fourteenth argument must be greater than or equal to max(1,NB)
* @returns {void}
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
* var D = new Float64Array( [ 0.0 ] );
* var E = new Float64Array( [ 0.0 ] );
* var TAUQ = new Float64Array( [ 0.0 ] );
* var TAUP = new Float64Array( [ 0.0 ] );
* var X = new Float64Array( [ 0.0, 0.0, 0.0 ] );
* var Y = new Float64Array( [ 0.0, 0.0 ] );
*
* dlabrd( 'column-major', 3, 2, 1, A, 3, D, E, TAUQ, TAUP, X, 3, Y, 2 );
* // A => <Float64Array>[ 1.0, ~0.422, ~0.633, 1.0, 5.0, 6.0 ]
* // D => <Float64Array>[ ~-3.742 ]
* // E => <Float64Array>[ ~-8.552 ]
* // TAUQ => <Float64Array>[ ~1.267 ]
* // TAUP => <Float64Array>[ 0.0 ]
* // X => <Float64Array>[ ~12.552, 0.0, 0.0 ]
* // Y => <Float64Array>[ 0.0, ~12.552 ]
*/
function dlabrd( order, M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y, LDY ) { // eslint-disable-line max-params
var sA1;
var sA2;
var sX1;
var sX2;
var sY1;
var sY2;
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 ) ) {
sA1 = 1;
sA2 = LDA;
sX1 = 1;
sX2 = LDX;
sY1 = 1;
sY2 = LDY;
} else { // order === 'row-major'
if ( LDA < max( 1, N ) ) {
throw new RangeError( format( 'invalid argument. Sixth argument must be greater than or equal to max(1,%d). Value: `%d`.', N, LDA ) );
}
if ( LDX < max( 1, NB ) ) {
throw new RangeError( format( 'invalid argument. Twelfth argument must be greater than or equal to max(1,%d). Value: `%d`.', NB, LDX ) );
}
if ( LDY < max( 1, NB ) ) {
throw new RangeError( format( 'invalid argument. Fourteenth argument must be greater than or equal to max(1,%d). Value: `%d`.', NB, LDY ) );
}
sA1 = LDA;
sA2 = 1;
sX1 = LDX;
sX2 = 1;
sY1 = LDY;
sY2 = 1;
}
return base( M, N, NB, A, sA1, sA2, 0, D, 1, 0, E, 1, 0, TAUQ, 1, 0, TAUP, 1, 0, X, sX1, sX2, 0, Y, sY1, sY2, 0 ); // eslint-disable-line max-len
}
// EXPORTS //
module.exports = dlabrd;
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