Press n or j to go to the next uncovered block, b, p or k for the previous block.
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* @license Apache-2.0
*
* Copyright (c) 2026 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 sqrt = require( '@stdlib/math/base/special/sqrt' );
var abs = require( '@stdlib/math/base/special/abs' );
var max = require( '@stdlib/math/base/special/max' );
var min = require( '@stdlib/math/base/special/min' );
var abs2 = require( '@stdlib/math/base/special/abs2' );
// MAIN //
/**
* Computes the singular values of a `2x2` upper triangular matrix.
*
* @private
* @param {number} F - the (0,0) element of a `2x2` matrix
* @param {number} G - the (0,1) element of a `2x2` matrix
* @param {number} H - the (1,1) element of a `2x2` matrix
* @param {Float64Array} out - output array containing the smaller and larger singular values respectively
* @param {integer} strideOut - stride length for `out`
* @param {NonNegativeInteger} offsetOut - starting index of `out`
* @returns {Float64Array} output array
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var out = new Float64Array( 2 );
* dlas2( 1.0, 2.0, 3.0, out, 1, 0 );
* // out => <Float64Array>[ ~0.822, ~3.65 ]
*/
function dlas2( F, G, H, out, strideOut, offsetOut ) {
var ssmax;
var ssmin;
var fhmn;
var fhmx;
var as;
var at;
var au;
var fa;
var ga;
var ha;
var c;
fa = abs( F );
ga = abs( G );
ha = abs( H );
fhmn = min( fa, ha );
fhmx = max( fa, ha );
if ( fhmn === 0.0 ) {
ssmin = 0.0;
if ( fhmx === 0.0 ) {
ssmax = ga;
} else {
ssmax = max( fhmx, ga ) * sqrt( 1.0 + abs2( min( fhmx, ga ) / max( fhmx, ga ) ) );
}
} else if ( ga < fhmx ) {
as = 1.0 + ( fhmn / fhmx );
at = ( fhmx - fhmn ) / fhmx;
au = abs2( ga / fhmx );
c = 2.0 / ( sqrt( ( as * as ) + au ) + sqrt( ( at * at ) + au ) );
ssmin = fhmn * c;
ssmax = fhmx / c;
} else {
au = fhmx / ga;
if ( au === 0.0 ) {
// Avoid possible harmful underflow if exponent range asymmetric.
ssmin = ( fhmn * fhmx ) / ga;
ssmax = ga;
} else {
as = 1.0 + ( fhmn / fhmx );
at = ( fhmx - fhmn ) / fhmx;
c = 1.0 / ( sqrt( 1.0 + abs2( as * au ) ) + sqrt( 1.0 + abs2( at * au ) ) );
ssmin = ( fhmn * c ) * au;
ssmin += ssmin;
ssmax = ga / ( c + c );
}
}
out[ offsetOut ] = ssmin;
out[ offsetOut + strideOut ] = ssmax;
return out;
}
// EXPORTS //
module.exports = dlas2;
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