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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 base = require( './base.js' );
// MAIN //
/**
* Computes the Schur factorization of a real 2-by-2 nonsymmetric matrix `A` in standard form using alternative indexing semantics.
*
* Given a real 2×2 matrix:
*
* ```tex
* \begin{bmatrix}
* A & B \\
* C & D
* \end{bmatrix}
* ```
*
* this routine computes an orthogonal matrix:
*
* ```tex
* \begin{bmatrix}
* \text{CS} & \text{SN} \\
* -\text{SN} & \text{CS}
* \end{bmatrix}
* ```
*
* such that the matrix is reduced to Schur (quasi-triangular) form:
*
* ```tex
* \begin{bmatrix}
* \text{AA} & \text{BB} \\
* \text{CC} & \text{DD}
* \end{bmatrix}
* ```
*
* where either:
*
* - `CC` = 0, `AA` and `DD` are the real eigenvalues of the matrix.
* - `AA` = `DD` and `BB * CC` < 0, `AA + sqrt( BB * CC )` and `AA - sqrt( BB * CC )` are the complex conjugate eigenvalues.
*
* @param {Float64Array} A - array containing the element A(1,1)
* @param {NonNegativeInteger} offsetA - index in `A` of the element A(1,1)
* @param {Float64Array} B - array containing the element A(1,2)
* @param {NonNegativeInteger} offsetB - index in `B` of the element A(1,2)
* @param {Float64Array} C - array containing the element A(2,1)
* @param {NonNegativeInteger} offsetC - index in `C` of the element A(2,1)
* @param {Float64Array} D - array containing the element A(2,2)
* @param {NonNegativeInteger} offsetD - index in `D` of the element A(2,2)
* @param {Float64Array} RT1R - output array for the real part of the first eigenvalue
* @param {NonNegativeInteger} offsetRT1R - index in `RT1R` at which to store the value
* @param {Float64Array} RT1I - output array for the imaginary part of the first eigenvalue
* @param {NonNegativeInteger} offsetRT1I - index in `RT1I` at which to store the value
* @param {Float64Array} RT2R - output array for the real part of the second eigenvalue
* @param {NonNegativeInteger} offsetRT2R - index in `RT2R` at which to store the value
* @param {Float64Array} RT2I - output array for the imaginary part of the second eigenvalue
* @param {NonNegativeInteger} offsetRT2I - index in `RT2I` at which to store the value
* @param {Float64Array} CS - output array for cosine of the rotation
* @param {NonNegativeInteger} offsetCS - index in `CS` at which to store the value
* @param {Float64Array} SN - output array for sine of the rotation
* @param {NonNegativeInteger} offsetSN - index in `SN` at which to store the value
* @returns {void}
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 4.0 ] );
* var B = new Float64Array( [ -5.0 ] );
* var C = new Float64Array( [ 2.0 ] );
* var D = new Float64Array( [ -3.0 ] );
* var RT1R = new Float64Array( 1 );
* var RT1I = new Float64Array( 1 );
* var RT2R = new Float64Array( 1 );
* var RT2I = new Float64Array( 1 );
* var CS = new Float64Array( 1 );
* var SN = new Float64Array( 1 );
*
* dlanv2( A, 0, B, 0, C, 0, D, 0, RT1R, 0, RT1I, 0, RT2R, 0, RT2I, 0, CS, 0, SN, 0 );
* // A => <Float64Array>[ 2.0 ]
* // B => <Float64Array>[ -7.0 ]
* // C => <Float64Array>[ 0.0 ]
* // D => <Float64Array>[ -1.0 ]
* // RT1R => <Float64Array>[ 2.0 ]
* // RT1I => <Float64Array>[ 0.0 ]
* // RT2R => <Float64Array>[ -1.0 ]
* // RT2I => <Float64Array>[ 0.0 ]
* // CS => <Float64Array>[ ~0.93 ]
* // SN => <Float64Array>[ ~0.34 ]
*/
function dlanv2( A, offsetA, B, offsetB, C, offsetC, D, offsetD, RT1R, offsetRT1R, RT1I, offsetRT1I, RT2R, offsetRT2R, RT2I, offsetRT2I, CS, offsetCS, SN, offsetSN ) { // eslint-disable-line max-len, max-params
return base( A, offsetA, B, offsetB, C, offsetC, D, offsetD, RT1R, offsetRT1R, RT1I, offsetRT1I, RT2R, offsetRT2R, RT2I, offsetRT2I, CS, offsetCS, SN, offsetSN ); // eslint-disable-line max-len
}
// EXPORTS //
module.exports = dlanv2;
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