Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 | 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 25x 25x 25x 25x 25x 25x 25x 25x 25x 25x 25x 25x 25x 25x 25x 25x 25x 25x 25x 10x 10x 5x 5x 5x 5x 25x 5x 5x 5x 5x 5x 5x 15x 10x 10x 5x 5x 5x 5x 5x 5x 5x 5x 5x 5x 5x 10x 25x 25x 25x 25x 3x 3x 3x 3x 3x | /**
* @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;
|