feat: add lapack/base/dlartg

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Author: aayush0325

lib/node_modules/@stdlib/lapack/base/dlaqr1/lib/base.js

@@ -0,0 +1,125 @@
+/**
+* @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 abs = require( '@stdlib/math/base/special/fast/abs' );
+
+
+// MAIN //
+
+/**
+* Given a 2-by-2 or a 3-by-3 matrix, this function sets `V` to a scalar multiple of the first column of `K` where `K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)`.
+*
+* ## 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.
+* -   `H` should be an upper hessenberg matrix if it's a 3-by-3 matrix.
+* -   `V` should have at least `N` indexed elements.
+*
+* @private
+* @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`
+* @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-params, max-len
+	var h21s;
+	var h31s;
+	var h11;
+	var h12;
+	var h13;
+	var h21;
+	var h22;
+	var h23;
+	var h31;
+	var h32;
+	var h33;
+	var iv;
+	var s;
+	var i;
+
+	h11 = offsetH;
+	h12 = offsetH + strideH2;
+	h21 = offsetH + strideH1;
+	h22 = h21 + strideH2;
+
+	if ( N === 2 ) {
+		s = abs( H[ h11 ] - sr2 ) + abs( si2 ) + abs( H[ h21 ] );
+		if ( s === 0.0 ) {
+			V[ offsetV ] = 0.0;
+			V[ strideV + offsetV ] = 0.0;
+			return V;
+		}
+		h21s = H[ h21 ] / s;
+		V[ offsetV ] = ( h21s * H[ h12 ] ) + ( ( H[ h11 ]-sr1 ) * ( ( H[ h11 ]-sr2 ) / s ) ) - ( si1*( si2 / s ) ); // eslint-disable-line max-len
+		V[ offsetV + strideV ] = h21s*( H[ h11 ]+H[ h22 ]-sr1-sr2 );
+		return V;
+	}
+
+	h13 = h12 + strideH2;
+	h31 = h21 + strideH1;
+	h33 = h22 + strideH1 + strideH2;
+	h23 = h22 + strideH2;
+	h32 = h22 + strideH1;
+
+	s = abs( H[ h11 ]-sr2 ) + abs( si2 ) + abs( H[ h21 ] ) + abs( H[ h31 ] );
+	if ( s === 0.0 ) {
+		iv = offsetV;
+		for ( i = 0; i < 3; i++ ) {
+			V[ iv ] = 0.0;
+			iv += strideV;
+		}
+		return V;
+	}
+	h21s = H[ h21 ] / s;
+	h31s = H[ h31 ] / s;
+	iv = offsetV;
+	V[ iv ] = (( H[ h11 ]-sr1 )*( ( H[ h11 ]-sr2 ) / s )) - (si1*( si2 / s )) + ((H[ h12 ]*h21s) + (H[ h13 ]*h31s)); // eslint-disable-line max-len
+	iv += strideV;
+	V[ iv ] = (h21s*( H[ h11 ]+H[ h22 ]-sr1-sr2 )) + (H[ h23 ]*h31s);
+	iv += strideV;
+	V[ iv ] = (h31s*( H[ h11 ]+H[ h33 ]-sr1-sr2 )) + (h21s*H[ h32 ]);
+	return V;
+}
+
+
+// EXPORTS //
+
+module.exports = dlaqr1;