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* @license Apache-2.0
*
* Copyright (c) 2025 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 format = require( '@stdlib/string/format' );
var base = require( './base.js' );
// MAIN //
/**
* Computes the scalar multiple of the first column of `K` where `K = (H - Z1)*(H - Z2)` for a 2-by-2 or a 3-by-3 matrix `H` using alternative indexing semantics and where `Z1 = z1*I`, `Z2 = z2*I`, `z1 = a + bi`, `z2 = c + di`, and `I` is the identity matrix.
*
* ## Notes
*
* - It is expected that either `sr1 = sr2` and `si1 + si2 = 0` or `si1 = si2 = 0` (i.e., they represent complex conjugate values).
* - This is useful for starting double implicit shift bulges in the QR algorithm.
* - `V` should have at least `N` indexed elements.
*
* @param {PositiveInteger} N - number of row/columns in `H`
* @param {Float64Array} H - input matrix
* @param {integer} strideH1 - stride of the first dimension of `H`
* @param {integer} strideH2 - stride of the second dimension of `H`
* @param {NonNegativeInteger} offsetH - index offset for `H`
* @param {number} sr1 - real part of the first conjugate complex shift
* @param {number} si1 - imaginary part of the first conjugate complex shift
* @param {number} sr2 - real part of the second conjugate complex shift
* @param {number} si2 - imaginary part of the second conjugate complex shift
* @param {Float64Array} V - output array
* @param {integer} strideV - stride length for `V`
* @param {NonNegativeInteger} offsetV - index offset for `V`
* @throws {RangeError} first argument must be either 2 or 3
* @returns {Float64Array} `V`
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var H = new Float64Array( [ 1.0, 3.0, 2.0, 2.0, 4.0, 6.0, 0.0, 5.0, 7.0 ] ); // => [ [ 1.0, 3.0, 2.0 ], [ 2.0, 4.0, 6.0 ], [ 0.0, 5.0, 7.0 ] ]
* var V = new Float64Array( 3 );
*
* var out = dlaqr1( 3, H, 3, 1, 0, 1.5, 0.0, 2.5, 0.0, V, 1, 0 );
* // returns <Float64Array>[ ~1.93, ~0.57, ~2.86 ]
*/
function dlaqr1( N, H, strideH1, strideH2, offsetH, sr1, si1, sr2, si2, V, strideV, offsetV ) { // eslint-disable-line max-len, max-params
if ( N !== 2 && N !== 3 ) {
throw new RangeError( format( 'invalid argument. First argument must be either %d or %d. Value: `%d`.', 2, 3, N ) );
}
return base( N, H, strideH1, strideH2, offsetH, sr1, si1, sr2, si2, V, strideV, offsetV ); // eslint-disable-line max-len
}
// EXPORTS //
module.exports = dlaqr1;
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