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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 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 cdiv = require( '@stdlib/complex/float64/base/div' );
var conj = require( '@stdlib/complex/float64/conj' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
// MAIN //
/**
* Constructs a Givens plane rotation.
*
* @param {Complex128} za - rotational elimination parameter
* @param {Complex128} zb - rotational elimination parameter
* @param {Float64Array} out - output array
* @param {integer} stride - index increment
* @param {NonNegativeInteger} offset - starting index
* @returns {Float64Array} output array
*
* @example
* var Complex128 = require( '@stdlib/complex/float64/ctor' );
*
* var za = new Complex128( 5.0, 6.0 );
* // returns <Complex128>
*
* var zb = new Complex128( 0.0, 0.0 );
* // returns <Complex128>
*
* var out = zrotg( za, zb, new Float64Array( 5 ), 1, 0 );
* // returns <Float64Array>[ 5.0, 6.0, 1.0, 0.0, 0.0 ]
*/
function zrotg(za, zb, out, stride, offset) {
var scalar;
var scale;
var temp;
var za2;
var zb2;
var c2;
var c;
var s;
var r;
var d;
// Handle NaN inputs - if either input is NaN (not a Complex128), return array of NaNs
if (typeof za === 'number' && isnan(za)) {
out[0] = NaN;
out[1] = NaN;
out[2] = NaN;
out[3] = NaN;
out[4] = NaN;
return out;
}
if (typeof zb === 'number' && isnan(zb)) {
out[0] = NaN;
out[1] = NaN;
out[2] = NaN;
out[3] = NaN;
out[4] = NaN;
return out;
}
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) {
d = abs(imag(zb));
r = new Complex128(d, 0.0);
s = cdiv(conj(zb), new Complex128(d, 0.0));
} else if (imag(zb) === 0) {
d = abs(real(zb));
r = new Complex128(d, 0.0);
s = cdiv(conj(zb), new Complex128(d, 0.0));
} else {
zb2 = cabs2(zb);
d = sqrt(zb2);
r = new Complex128(d, 0.0);
s = cdiv(conj(zb), new Complex128(d, 0.0));
}
} 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(c2);
temp = new Complex128(real(za) / sqrt(za2), imag(za) / sqrt(za2));
temp = new Complex128(real(temp) * scale, imag(temp) * 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[offset] = real(za);
out[offset + stride] = imag(za);
out[offset + (2 * stride)] = c;
out[offset + (3 * stride)] = real(s);
out[offset + (4 * stride)] = imag(s);
return out;
}
// EXPORTS //
module.exports = zrotg;
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