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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.
*/
/* eslint-disable max-statements */
'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/abs' );
var copysign = require( '@stdlib/math/base/special/copysign' );
// VARIABLES //
var EPS = dlamch( 'E' );
// MAIN //
/**
* Computes the singular value decomposition of a 2x2 upper triangular matrix.
*
* ## Notes
*
* - `abs(SSMAX)` is the larger singular value.
* - `abs(SSMIN)` is the smaller singular value.
* - (`CSL`,`SNL`) and (`CSR`,`SNR`) are the left and right singular vectors for `abs(SSMAX)`.
*
* @private
* @param {number} F - the (0,0) element of matrix
* @param {number} G - the (0,1) element of matrix
* @param {number} H - the (1,1) element of matrix
* @param {Float64Array} out - output array containing `SSMIN`, `SSMAX`, `SNR`, `CSR`, `SNL`, and `CSL` 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( 6 );
*
* dlasv2( 2.0, 3.0, 4.0, out, 1, 0 );
* // out => <Float64Array>[ ~1.5513, ~5.1569, ~0.9665, ~0.2567, ~0.7497, ~0.6618 ]
*/
function dlasv2( F, G, H, out, strideOut, offsetOut ) {
var gasmal;
var ssmin;
var ssmax;
var tsign;
var PMAX;
var swap;
var clt;
var crt;
var csl;
var csr;
var idx;
var slt;
var snl;
var snr;
var srt;
var tmp;
var fa;
var ft;
var ga;
var gt;
var ha;
var ht;
var mm;
var tt;
var a;
var d;
var l;
var m;
var r;
var s;
var t;
ft = F;
fa = abs( ft );
ht = H;
ha = abs( ht );
/*
* PMAX points to the maximum absolute element of the matrix.
*
* PMAX = 1 if F is the largest in absolute value
* PMAX = 2 if G is the largest in absolute value
* PMAX = 3 if H is the largest in absolute value
*/
PMAX = 1;
swap = ha > fa;
if ( swap ) {
PMAX = 3;
tmp = ft;
ft = ht;
ht = tmp;
tmp = fa;
fa = ha;
ha = tmp;
// Now FA >= HA
}
gt = G;
ga = abs( gt );
if ( ga === 0.0 ) {
// Diagonal matrix
ssmin = ha;
ssmax = fa;
clt = 1.0;
crt = 1.0;
slt = 0.0;
srt = 0.0;
} else {
gasmal = true;
if ( ga > fa ) {
PMAX = 2;
if ( ( fa / ga ) < EPS ) {
// Case of very large GA
gasmal = false;
ssmax = ga;
if ( ha > 1.0 ) {
ssmin = fa / ( ga / ha );
} else {
ssmin = ( fa / ga ) * ha;
}
clt = 1.0;
slt = ht / gt;
srt = 1.0;
crt = ft / gt;
}
}
if ( gasmal === true ) {
// Normal case
d = fa - ha;
if ( d === fa ) {
// Copes with infinite F or H
l = 1.0;
} else {
l = d / fa;
}
// Note that 0 < l < 1
m = gt / ft;
// Note that abs( m ) < 1 / macheps
t = 2.0 - l;
// Note that T > 1
mm = m * m;
tt = t * t;
s = sqrt( tt + mm );
// Note that 1 < S < 1 + 1 / macheps
if ( l === 0.0 ) {
r = abs( m );
} else {
r = sqrt( ( l * l ) + mm );
}
// Note that 0 < R < 1 + 1 / macheps
a = 0.5 * ( s + r);
// Note that 1 < A < 1 + abs( m )
ssmin = ha / a;
ssmax = fa * a;
if ( mm === 0.0 ) {
// Note that M is very tiny
if ( l === 0.0 ) {
t = copysign( 2.0, ft ) * copysign( 1.0, gt );
} else {
t = ( ( gt / copysign( d, ft ) ) + ( m / t ) );
}
} else {
t = ( ( m / ( s + t ) ) + ( m / ( r + l ) ) ) * ( 1.0 + a );
}
l = sqrt( ( t * t ) + 4.0 );
crt = 2.0 / l;
srt = t / l;
clt = ( crt + ( srt * m ) ) / a;
slt = ( ht / ft ) * ( srt / a );
}
}
if ( swap ) {
csl = srt;
snl = crt;
csr = slt;
snr = clt;
} else {
csl = clt;
snl = slt;
csr = crt;
snr = srt;
}
// Correct signs of ssmax and ssmin
if ( PMAX === 1 ) {
tsign = copysign( 1.0, csr ) * copysign( 1.0, csl ) * copysign( 1.0, F );
}
if ( PMAX === 2 ) {
tsign = copysign( 1.0, snr ) * copysign( 1.0, csl ) * copysign( 1.0, G );
}
if ( PMAX === 3 ) {
tsign = copysign( 1.0, snr ) * copysign( 1.0, snl ) * copysign( 1.0, H );
}
ssmax = copysign( ssmax, tsign );
ssmin = copysign( ssmin, tsign * copysign( 1.0, F ) * copysign( 1.0, H ) );
idx = offsetOut;
out[ idx ] = ssmin;
idx += strideOut;
out[ idx ] = ssmax;
idx += strideOut;
out[ idx ] = snr;
idx += strideOut;
out[ idx ] = csr;
idx += strideOut;
out[ idx ] = snl;
idx += strideOut;
out[ idx ] = csl;
return out;
}
// EXPORTS //
module.exports = dlasv2;
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