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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 */
'use strict';
// MODULES //
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` using alternative indexing semantics.
*
* ## 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 {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} 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} D - real diagonal elements (length `NB`)
* @param {integer} strideD - stride length for `D`
* @param {NonNegativeInteger} offsetD - starting index for `D`
* @param {Float64Array} E - real off-diagonal elements (length `NB`)
* @param {integer} strideE - stride length for `E`
* @param {NonNegativeInteger} offsetE - starting index for `E`
* @param {Float64Array} TAUQ - scalars factors of the elementary reflectors that represent the orthogonal matrix `Q` (length `NB`)
* @param {integer} strideTAUQ - stride length for `TAUQ`
* @param {NonNegativeInteger} offsetTAUQ - starting index for `TAUQ`
* @param {Float64Array} TAUP - scalars factors of the elementary reflectors that represent the orthogonal matrix `P` (length `NB`)
* @param {integer} strideTAUP - stride length for `TAUP`
* @param {NonNegativeInteger} offsetTAUP - starting index for `TAUP`
* @param {Float64Array} X - output matrix
* @param {integer} strideX1 - stride of the first dimension of `X`
* @param {integer} strideX2 - stride of the second dimension of `X`
* @param {NonNegativeInteger} offsetX - starting index for `X`
* @param {Float64Array} Y - output matrix
* @param {integer} strideY1 - stride of the first dimension of `Y`
* @param {integer} strideY2 - stride of the second dimension of `Y`
* @param {NonNegativeInteger} offsetY - starting index for `Y`
* @throws {TypeError} first argument must be a valid order
* @throws {RangeError} second argument must be a non-negative integer
* @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( 3, 2, 1, A, 1, 3, 0, D, 1, 0, E, 1, 0, TAUQ, 1, 0, TAUP, 1, 0, X, 1, 3, 0, Y, 1, 2, 0 );
* // 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( M, N, NB, A, strideA1, strideA2, offsetA, D, strideD, offsetD, E, strideE, offsetE, TAUQ, strideTAUQ, offsetTAUQ, TAUP, strideTAUP, offsetTAUP, X, strideX1, strideX2, offsetX, Y, strideY1, strideY2, offsetY ) { // eslint-disable-line max-params
if ( M < 0 ) {
throw new RangeError( format( 'invalid argument. First argument must be a nonnegative integer. Value: `%d`.', M ) );
}
if ( N < 0 ) {
throw new RangeError( format( 'invalid argument. Second argument must be a nonnegative integer. Value: `%d`.', N ) );
}
return base( M, N, NB, A, strideA1, strideA2, offsetA, D, strideD, offsetD, E, strideE, offsetE, TAUQ, strideTAUQ, offsetTAUQ, TAUP, strideTAUP, offsetTAUP, X, strideX1, strideX2, offsetX, Y, strideY1, strideY2, offsetY );
}
// EXPORTS //
module.exports = dlabrd;
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