feat: add lapack/base/dlartg

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Author: aayush0325

lib/node_modules/@stdlib/lapack/base/dlartg/lib/base.js

@@ -0,0 +1,114 @@
+/**
+* @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 sign = 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 //
+
+/**
+* Generates a plane rotation of a vector 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 representing the first component of the vector to be rotated
+* @param {NonNegativeInteger} offsetF - starting index for `F`
+* @param {Float64Array} G - single element array representing the second component of the vector to be rotated
+* @param {NonNegativeInteger} offsetG - starting index for `G`
+* @param {Float64Array} CS - single element array overwritten by the cosine of the rotation
+* @param {NonNegativeInteger} offsetCS - starting index for `CS`
+* @param {Float64Array} SN - single element array overwritten by the sine of the rotation
+* @param {NonNegativeInteger} offsetSN - starting index for `SN`
+* @param {Float64Array} R - single element array overwritten by the non-zero component of the rotated vector
+* @param {NonNegativeInteger} offsetR - starting index for `R`
+* @returns {void}
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var F = new Float64Array( [ 3.0 ] );
+* var G = new Float64Array( [ 4.0 ] );
+* var CS = new Float64Array( 1 );
+* var SN = new Float64Array( 1 );
+* var R = new Float64Array( 1 );
+*
+* dlartg( F, 0, G, 0, CS, 0, SN, 0, R, 0 );
+* // R => <Float64Array>[ 5.0 ]
+* // CS => <Float64Array>[ 0.6 ]
+* // SN => <Float64Array>[ 0.8 ]
+*/
+function dlartg( F, offsetF, G, offsetG, CS, offsetCS, SN, offsetSN, R, offsetR ) { // eslint-disable-line max-len
+	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 ) {
+		CS[ offsetCS ] = 1.0;
+		SN[ offsetSN ] = 0.0;
+		R[ offsetR ] = F[ offsetF ];
+	} else if ( F[ offsetF ] === 0.0 ) {
+		CS[ offsetCS ] = 0.0;
+		SN[ offsetSN ] = sign( 1.0, G[ offsetG ] );
+		R[ offsetR ] = g1;
+	} else if ( f1 > rtmin && f1 < rtmax && g1 > rtmin && g1 < rtmax ) {
+		d = sqrt( (F[ offsetF ]*F[ offsetF ]) + (G[ offsetG ]*G[ offsetG ]) );
+		CS[ offsetCS ] = f1 / d;
+		R[ offsetR ] = sign( d, F[ offsetF ] );
+		SN[ offsetSN ] = G[ offsetG ] / R[ offsetR ];
+	} else {
+		u = min( safmax, max( safmin, f1, g1 ) );
+		fs = F[ offsetF ] / u;
+		gs = G[ offsetG ] / u;
+		d = sqrt( (fs*fs) + (gs*gs) );
+		CS[ offsetCS ] = abs( fs ) / d;
+		R[ offsetR ] = sign( d, F[ offsetF ] );
+		SN[ offsetSN ] = gs / R[ offsetR ];
+		R[ offsetR ] *= u;
+	}
+}
+
+
+// EXPORTS //
+
+module.exports = dlartg;