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* @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 Float64Array = require( '@stdlib/array/float64' );
var abs = require( '@stdlib/math/base/special/abs' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var cabs2 = require( '@stdlib/math/base/special/cabs2' );
var EPS = require( '@stdlib/constants/float64/eps' );
var Complex128 = require( '@stdlib/complex/float64/ctor' );
var real = require( '@stdlib/complex/float64/real' );
var imag = require( '@stdlib/complex/float64/imag' );
var cmul = require( '@stdlib/complex/float64/base/mul' );
var conj = require( '@stdlib/complex/float64/conj' );
// MAIN //
/**
* Constructs a Givens plane rotation.
*
* @param {Complex128} za - rotational elimination parameter
* @param {Complex128} zb - rotational elimination parameter
* @returns {Float64Array} output array
*
* @example
* var Complex128 = require( '@stdlib/complex/float64/ctor' );
*
* var za = new Complex128( 4.0, 3.0 );
* // returns <Complex128>
*
* var zb = new Complex128( 0.0, 0.0 );
* // returns <Complex128>
*
* var out = zrotg( za, zb );
* // out => <Float64Array>[ 4.0, 3.0, 1.0, 0.0, 0.0 ]
*/
function zrotg( za, zb ) {
var scalar;
var scale;
var temp;
var za2;
var zb2;
var out;
var c2;
var c;
var s;
var r;
var d;
out = new Float64Array( 5 );
s = new Complex128( 0.0, 0.0 );
r = new Complex128( 0.0, 0.0 );
if ( real( zb ) === 0.0 && imag( zb ) === 0.0 ) {
c = 1.0;
r = za;
} else if ( real( za ) === 0.0 && imag( za ) === 0.0 ) {
c = 0;
if ( real( zb ) === 0 ) {
r = abs( imag( zb ) );
s = conj( zb ) / r;
} else if ( imag( zb ) === 0 ) {
r = abs( real( zb ) );
s = conj( zb ) / r;
} else {
zb2 = cabs2( zb );
d = sqrt( zb2 );
s = conj( zb ) / d;
r = d;
}
} else {
za2 = cabs2( za );
zb2 = cabs2( zb );
c2 = za2 + zb2;
if ( za2 >= c2 * EPS ) {
c = sqrt( za2 / c2);
r = new Complex128( real( za ) / c, imag( za ) / c );
scale = 1 / sqrt(za2 * c2);
temp = new Complex128(real(za) * scale, imag(za) * scale);
s = cmul(conj(zb), temp);
} else {
d = sqrt( za2 * c2 );
c = za2 / d;
while ( c < EPS ) {
d *= 2;
c = za2 / d;
}
while ( c === 0.0 ) {
c = 1;
}
r = new Complex128( real( za ) / c, imag( za ) / c );
scalar = new Complex128( 1 / d, 0.0 );
s = cmul( conj( zb ), cmul( za, scalar ) );
}
}
za = r;
out[ 0 ] = real( za );
out[ 1 ] = imag( za );
out[ 2 ] = c;
out[ 3 ] = real( s );
out[ 4 ] = imag( s );
return out;
}
// EXPORTS //
module.exports = zrotg;
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