116 lines
3.1 KiB
Markdown
116 lines
3.1 KiB
Markdown
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@license Apache-2.0
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Copyright (c) 2018 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# abs2
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> Compute the squared [absolute value][absolute-value] of a complex number.
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<section class="intro">
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The [absolute value][absolute-value] of a complex number is defined as
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<!-- <equation class="equation" label="eq:absolute_value_complex" align="center" raw="|a + bi| = \sqrt{a^2 + b^2}" alt="Absolute value"> -->
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<div class="equation" align="center" data-raw-text="|a + bi| = \sqrt{a^2 + b^2}" data-equation="eq:absolute_value_complex">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@d4edb68b52a6c646be5683023c5a24890300727f/lib/node_modules/@stdlib/math/base/special/cabs2/docs/img/equation_absolute_value_complex.svg" alt="Absolute value">
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<br>
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</div>
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<!-- </equation> -->
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which corresponds to the length of a vector from the origin to a complex value plotted in the complex plane.
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var cabs2 = require( '@stdlib/math/base/special/cabs2' );
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```
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#### cabs2( re, im )
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Computes the squared [absolute value][absolute-value] of a `complex` number comprised of a **real** component `re` and an **imaginary** component `im`.
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```javascript
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var y = cabs2( 5.0, 3.0 );
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// returns 34.0
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- Be careful to avoid overflow and underflow.
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- Depending on the environment, this function _may_ have better performance than computing the [absolute value][absolute-value] of a `complex` number and then squaring. Hence, where appropriate, consider using `cabs2()` over [`cabs()`][@stdlib/math/base/special/cabs].
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var Complex128 = require( '@stdlib/complex/float64' );
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var randu = require( '@stdlib/random/base/randu' );
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var round = require( '@stdlib/math/base/special/round' );
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var real = require( '@stdlib/complex/real' );
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var imag = require( '@stdlib/complex/imag' );
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var cabs2 = require( '@stdlib/math/base/special/cabs2' );
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var re;
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var im;
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var z;
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var i;
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for ( i = 0; i < 100; i++ ) {
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re = round( randu()*100.0 ) - 50.0;
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im = round( randu()*100.0 ) - 50.0;
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z = new Complex128( re, im );
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console.log( 'cabs2(%s) = %d', z.toString(), cabs2( real(z), imag(z) ) );
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}
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```
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</section>
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<!-- /.examples -->
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<section class="links">
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[absolute-value]: https://en.wikipedia.org/wiki/Absolute_value
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[@stdlib/math/base/special/cabs]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/cabs
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</section>
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<!-- /.links -->
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