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* @license Apache-2.0
*
* Copyright (c) 2018 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 max = require( '@stdlib/math/base/special/max' );
var FLOAT64_BIGGEST = require( '@stdlib/constants/float64/max' );
var FLOAT64_SMALLEST = require( '@stdlib/constants/float64/smallest-normal' );
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' );
// VARIABLES //
var LARGE_THRESHOLD = FLOAT64_BIGGEST * 0.5;
var SMALL_THRESHOLD = FLOAT64_SMALLEST * ( 2.0 / EPS );
var RECIP_EPS_SQR = 2.0 / ( EPS * EPS );
// MAIN //
/**
* Computes the inverse of a double-precision complex floating-point number.
*
* ## References
*
* - Baudin, Michael, and Robert L. Smith. 2012. "A Robust Complex Division in Scilab." _arXiv_ abs/1210.4539 \[cs.MS\] (October): 1–25. <https://arxiv.org/abs/1210.4539>.
*
* @param {Complex128} z - complex number
* @returns {Complex128} result
*
* @example
* var Complex128 = require( '@stdlib/complex/float64/ctor' );
* var real = require( '@stdlib/complex/float64/real' );
* var imag = require( '@stdlib/complex/float64/imag' );
*
* var v = cinv( new Complex128( 2.0, 4.0 ) );
* // returns <Complex128>
*
* var re = real( v );
* // returns 0.1
*
* var im = imag( v );
* // returns -0.2
*/
function cinv( z ) {
var ab;
var re;
var im;
var s;
var r;
var t;
re = real( z );
im = imag( z );
ab = max( abs(re), abs(im) );
s = 1.0;
if ( ab >= LARGE_THRESHOLD ) {
re *= 0.5;
im *= 0.5;
s *= 0.5;
} else if ( ab <= SMALL_THRESHOLD ) {
re *= RECIP_EPS_SQR;
im *= RECIP_EPS_SQR;
s *= RECIP_EPS_SQR;
}
if ( abs( im ) <= abs( re ) ) {
r = im / re;
t = 1.0 / ( re + (im*r) );
re = t;
im = -r * t;
} else {
r = re / im;
t = 1.0 / ( im + (re*r) );
re = r * t;
im = -t;
}
re *= s;
im *= s;
return new Complex128( re, im );
}
// EXPORTS //
module.exports = cinv;
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