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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 dlamch = require( '@stdlib/lapack/base/dlamch' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var abs = require( '@stdlib/math/base/special/fast/abs' );
var hypot = require( '@stdlib/math/base/special/fast/hypot' );
var copysign = require( '@stdlib/math/base/special/copysign' );
var min = require( '@stdlib/math/base/special/fast/min' );
var max = require( '@stdlib/math/base/special/fast/max' );
// VARIABLES //
var safmin = dlamch( 'safe minimum' );
var safmax = 1.0 / safmin;
var rtmin = sqrt( safmin );
var rtmax = sqrt( safmax / 2.0 );
// MAIN //
/**
* Constructs a Givens rotation of a two-dimensional vector that zeros out the second component.
*
* For a two-dimensional vector ( f, g ) it computes the sine `S`, cosine `C` and the resultant `R` such that the following equation is satisfied:
*
* ```tex
* \(\begin{bmatrix} C & S \\ -S & C \end{bmatrix} \begin{bmatrix} F \\ G \end{bmatrix} = \begin{bmatrix} R \\ 0 \end{bmatrix}\)
* ```
*
* @private
* @param {Float64Array} F - single element array containing the first component of the vector to be rotated
* @param {NonNegativeInteger} offsetF - index of the element in `F`
* @param {Float64Array} G - single element array containing the second component of the vector to be rotated
* @param {NonNegativeInteger} offsetG - index of the element in `G`
* @param {Float64Array} C - single element array which is overwritten by the cosine of the rotation
* @param {NonNegativeInteger} offsetC - index of the element in `C`
* @param {Float64Array} S - single element array which is overwritten by the sine of the rotation
* @param {NonNegativeInteger} offsetS - index of the element in `S`
* @param {Float64Array} R - single element array which is overwritten by the length of the rotated vector
* @param {NonNegativeInteger} offsetR - index of the element in `R`
* @returns {void}
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var F = new Float64Array( [ 3.0 ] );
* var G = new Float64Array( [ 4.0 ] );
* var C = new Float64Array( 1 );
* var S = new Float64Array( 1 );
* var R = new Float64Array( 1 );
*
* dlartg( F, 0, G, 0, C, 0, S, 0, R, 0 );
* // R => <Float64Array>[ 5.0 ]
* // C => <Float64Array>[ 0.6 ]
* // S => <Float64Array>[ 0.8 ]
*/
function dlartg( F, offsetF, G, offsetG, C, offsetC, S, offsetS, R, offsetR ) {
var f1;
var g1;
var fs;
var gs;
var u;
var d;
f1 = abs( F[ offsetF ] );
g1 = abs( G[ offsetG ] );
if ( G[ offsetG ] === 0.0 ) {
C[ offsetC ] = 1.0;
S[ offsetS ] = 0.0;
R[ offsetR ] = F[ offsetF ];
} else if ( F[ offsetF ] === 0.0 ) {
C[ offsetC ] = 0.0;
S[ offsetS ] = copysign( 1.0, G[ offsetG ] );
R[ offsetR ] = g1;
} else if ( f1 > rtmin && f1 < rtmax && g1 > rtmin && g1 < rtmax ) {
d = hypot( F[ offsetF ], G[ offsetG ] );
C[ offsetC ] = f1 / d;
R[ offsetR ] = copysign( d, F[ offsetF ] );
S[ offsetS ] = G[ offsetG ] / R[ offsetR ];
} else {
u = min( safmax, max( safmin, max( f1, g1 ) ) );
fs = F[ offsetF ] / u;
gs = G[ offsetG ] / u;
d = hypot( fs, gs );
C[ offsetC ] = abs( fs ) / d;
R[ offsetR ] = copysign( d, F[ offsetF ] );
S[ offsetS ] = gs / R[ offsetR ];
R[ offsetR ] *= u;
}
}
// EXPORTS //
module.exports = dlartg;
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