700 lines
17 KiB
Markdown
700 lines
17 KiB
Markdown
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<!--
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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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<details>
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<summary>
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About stdlib...
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</summary>
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<p>We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.</p>
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<p>The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.</p>
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<p>When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.</p>
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<p>To join us in bringing numerical computing to the web, get started by checking us out on <a href="https://github.com/stdlib-js/stdlib">GitHub</a>, and please consider <a href="https://opencollective.com/stdlib">financially supporting stdlib</a>. We greatly appreciate your continued support!</p>
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</details>
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# Complex128
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[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->
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> 128-bit complex number.
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- Package usage documentation. -->
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<section class="installation">
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## Installation
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```bash
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npm install @stdlib/complex-float64-ctor
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```
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</section>
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<section class="usage">
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## Usage
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```javascript
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var Complex128 = require( '@stdlib/complex-float64-ctor' );
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```
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#### Complex128( real, imag )
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128-bit complex number constructor, where `real` and `imag` are the **real** and **imaginary** components, respectively.
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```javascript
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var z = new Complex128( 5.0, 3.0 );
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// returns <Complex128>
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```
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* * *
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## Properties
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#### Complex128.BYTES_PER_ELEMENT
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Size (in bytes) of each component.
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```javascript
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var nbytes = Complex128.BYTES_PER_ELEMENT;
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// returns 8
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```
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#### Complex128.prototype.BYTES_PER_ELEMENT
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Size (in bytes) of each component.
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```javascript
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var z = new Complex128( 5.0, 3.0 );
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var nbytes = z.BYTES_PER_ELEMENT;
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// returns 8
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```
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#### Complex128.prototype.byteLength
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Length (in bytes) of a complex number.
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```javascript
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var z = new Complex128( 5.0, 3.0 );
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var nbytes = z.byteLength;
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// returns 16
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```
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### Instance
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A `Complex128` instance has the following properties...
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#### re
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A **read-only** property returning the **real** component.
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```javascript
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var z = new Complex128( 5.0, 3.0 );
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var re = z.re;
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// returns 5.0
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```
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#### im
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A **read-only** property returning the **imaginary** component.
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```javascript
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var z = new Complex128( 5.0, -3.0 );
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var im = z.im;
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// returns -3.0
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```
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* * *
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## Methods
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### Accessor Methods
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These methods do **not** mutate a `Complex128` instance and, instead, return a complex number representation.
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#### Complex128.prototype.toString()
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Returns a `string` representation of a `Complex128` instance.
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```javascript
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var z = new Complex128( 5.0, 3.0 );
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var str = z.toString();
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// returns '5 + 3i'
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z = new Complex128( -5.0, -3.0 );
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str = z.toString();
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// returns '-5 - 3i'
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```
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#### Complex128.prototype.toJSON()
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Returns a [JSON][json] representation of a `Complex128` instance. [`JSON.stringify()`][mdn-json-stringify] implicitly calls this method when stringifying a `Complex128` instance.
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```javascript
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var z = new Complex128( 5.0, -3.0 );
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var o = z.toJSON();
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/*
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{
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"type": "Complex128",
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"re": 5.0,
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"im": -3.0
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}
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*/
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```
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To [revive][mdn-json-parse] a `Complex128` number from a [JSON][json] `string`, see [@stdlib/complex/float64/reviver][@stdlib/complex/float64/reviver].
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</section>
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<!-- /.usage -->
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* * *
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<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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## Notes
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- Both the **real** and **imaginary** components are stored as double-precision floating-point numbers.
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</section>
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<!-- /.notes -->
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* * *
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<!-- Package usage examples. -->
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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-ctor' );
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var z = new Complex128( 3.0, -2.0 );
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console.log( 'type: %s', typeof z );
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// => 'type: object'
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console.log( 'str: %s', z );
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// => 'str: 3 - 2i'
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console.log( 'real: %d', z.re );
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// => 'real: 3'
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console.log( 'imaginary: %d', z.im );
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// => 'imaginary: -2'
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console.log( 'JSON: %s', JSON.stringify( z ) );
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// => 'JSON: {"type":"Complex128","re":3,"im":-2}'
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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#include "stdlib/complex/float64/ctor.h"
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```
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#### stdlib_complex128_t
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An opaque type definition for a double-precision complex floating-point number.
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```c
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stdlib_complex128_t z = stdlib_complex128( 5.0, 2.0 );
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```
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#### stdlib_complex128_parts_t
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An opaque type definition for a union for accessing the real and imaginary parts of a double-precision complex floating-point number.
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```c
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double real( const stdlib_complex128_t z ) {
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stdlib_complex128_parts_t v;
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// Assign a double-precision complex floating-point number:
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v.value = z;
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// Extract the real component:
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double re = v.parts[ 0 ];
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return re;
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}
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// ...
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// Create a complex number:
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stdlib_complex128_t z = stdlib_complex128( 5.0, 2.0 );
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// ...
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// Access the real component:
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double re = real( z );
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// returns 5.0
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```
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The union has the following members:
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- **value**: `stdlib_complex128_t` double-precision complex floating-point number.
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- **parts**: `double[]` array having the following elements:
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- **0**: `double` real component.
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- **1**: `double` imaginary component.
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#### stdlib_complex128( real, imag )
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Returns a double-precision complex floating-point number.
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```c
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stdlib_complex128_t z = stdlib_complex128( 5.0, 2.0 );
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```
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The function accepts the following arguments:
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- **real**: `[in] double` real component.
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- **imag**: `[in] double` imaginary component.
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```c
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stdlib_complex128_t stdlib_complex128( const double real, const double imag );
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```
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#### stdlib_complex128_from_float32( real )
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Converts a single-precision floating-point number to a double-precision complex floating-point number.
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```c
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stdlib_complex128_t z = stdlib_complex128_from_float32( 5.0f );
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```
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The function accepts the following arguments:
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- **real**: `[in] float` real component.
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```c
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stdlib_complex128_t stdlib_complex128_from_float32( const float real );
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```
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#### stdlib_complex128_from_float64( real )
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Converts a double-precision floating-point number to a double-precision complex floating-point number.
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```c
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stdlib_complex128_t z = stdlib_complex128_from_float64( 5.0 );
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```
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The function accepts the following arguments:
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- **real**: `[in] double` real component.
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```c
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stdlib_complex128_t stdlib_complex128_from_float64( const double real );
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```
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#### stdlib_complex128_from_complex64( z )
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Converts a single-precision complex floating-point number to a double-precision complex floating-point number.
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```c
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#include "stdlib/complex/float32/ctor.h"
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stdlib_complex64_t z1 = stdlib_complex64( 5.0f, 3.0f );
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stdlib_complex128_t z2 = stdlib_complex128_from_complex64( z1 );
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```
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The function accepts the following arguments:
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- **z**: `[in] stdlib_complex64_t` single-precision complex floating-point number.
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```c
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stdlib_complex128_t stdlib_complex128_from_complex64( const stdlib_complex64_t z );
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```
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#### stdlib_complex128_from_complex128( z )
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Converts (copies) a double-precision complex floating-point number to a double-precision complex floating-point number.
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```c
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stdlib_complex128_t z1 = stdlib_complex128( 5.0, 3.0 );
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stdlib_complex128_t z2 = stdlib_complex128_from_complex128( z1 );
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```
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The function accepts the following arguments:
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- **z**: `[in] stdlib_complex128_t` double-precision complex floating-point number.
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```c
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stdlib_complex128_t stdlib_complex128_from_complex128( const stdlib_complex128_t z );
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```
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#### stdlib_complex128_from_int8( real )
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Converts a signed 8-bit integer to a double-precision complex floating-point number.
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```c
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stdlib_complex128_t z = stdlib_complex128_from_int8( 5 );
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```
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The function accepts the following arguments:
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- **real**: `[in] int8_t` real component.
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```c
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stdlib_complex128_t stdlib_complex128_from_int8( const int8_t real );
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```
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#### stdlib_complex128_from_uint8( real )
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Converts an unsigned 8-bit integer to a double-precision complex floating-point number.
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```c
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stdlib_complex128_t z = stdlib_complex128_from_uint8( 5 );
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```
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The function accepts the following arguments:
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- **real**: `[in] uint8_t` real component.
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```c
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stdlib_complex128_t stdlib_complex128_from_uint8( const uint8_t real );
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```
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#### stdlib_complex128_from_int16( real )
|
||
|
|
|
||
|
|
Converts a signed 16-bit integer to a double-precision complex floating-point number.
|
||
|
|
|
||
|
|
```c
|
||
|
|
stdlib_complex128_t z = stdlib_complex128_from_int16( 5 );
|
||
|
|
```
|
||
|
|
|
||
|
|
The function accepts the following arguments:
|
||
|
|
|
||
|
|
- **real**: `[in] int16_t` real component.
|
||
|
|
|
||
|
|
```c
|
||
|
|
stdlib_complex128_t stdlib_complex128_from_int16( const int16_t real );
|
||
|
|
```
|
||
|
|
|
||
|
|
#### stdlib_complex128_from_uint16( real )
|
||
|
|
|
||
|
|
Converts an unsigned 16-bit integer to a double-precision complex floating-point number.
|
||
|
|
|
||
|
|
```c
|
||
|
|
stdlib_complex128_t z = stdlib_complex128_from_uint16( 5 );
|
||
|
|
```
|
||
|
|
|
||
|
|
The function accepts the following arguments:
|
||
|
|
|
||
|
|
- **real**: `[in] uint16_t` real component.
|
||
|
|
|
||
|
|
```c
|
||
|
|
stdlib_complex128_t stdlib_complex128_from_uint16( const uint16_t real );
|
||
|
|
```
|
||
|
|
|
||
|
|
#### stdlib_complex128_from_int32( real )
|
||
|
|
|
||
|
|
Converts a signed 32-bit integer to a double-precision complex floating-point number.
|
||
|
|
|
||
|
|
```c
|
||
|
|
stdlib_complex128_t z = stdlib_complex128_from_int32( 5 );
|
||
|
|
```
|
||
|
|
|
||
|
|
The function accepts the following arguments:
|
||
|
|
|
||
|
|
- **real**: `[in] int32_t` real component.
|
||
|
|
|
||
|
|
```c
|
||
|
|
stdlib_complex128_t stdlib_complex128_from_int32( const int32_t real );
|
||
|
|
```
|
||
|
|
|
||
|
|
#### stdlib_complex128_from_uint32( real )
|
||
|
|
|
||
|
|
Converts an unsigned 32-bit integer to a double-precision complex floating-point number.
|
||
|
|
|
||
|
|
```c
|
||
|
|
stdlib_complex128_t z = stdlib_complex128_from_uint32( 5 );
|
||
|
|
```
|
||
|
|
|
||
|
|
The function accepts the following arguments:
|
||
|
|
|
||
|
|
- **real**: `[in] uint32_t` real component.
|
||
|
|
|
||
|
|
```c
|
||
|
|
stdlib_complex128_t stdlib_complex128_from_uint32( const uint32_t real );
|
||
|
|
```
|
||
|
|
|
||
|
|
#### stdlib_complex128_to_complex64( z )
|
||
|
|
|
||
|
|
Converts a double-precision complex floating-point number to a single-precision complex floating-point number.
|
||
|
|
|
||
|
|
```c
|
||
|
|
#include "stdlib/complex/float32/ctor.h"
|
||
|
|
|
||
|
|
stdlib_complex128_t z1 = stdlib_complex128( 5.0, 3.0 );
|
||
|
|
stdlib_complex64_t z2 = stdlib_complex128_to_complex64( z1 );
|
||
|
|
```
|
||
|
|
|
||
|
|
The function accepts the following arguments:
|
||
|
|
|
||
|
|
- **z**: `[in] stdlib_complex64_t` double-precision complex floating-point number.
|
||
|
|
|
||
|
|
```c
|
||
|
|
stdlib_complex64_t stdlib_complex128_to_complex64( const stdlib_complex128_t z );
|
||
|
|
```
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.usage -->
|
||
|
|
|
||
|
|
<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
|
||
|
|
|
||
|
|
<section class="notes">
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.notes -->
|
||
|
|
|
||
|
|
<!-- C API usage examples. -->
|
||
|
|
|
||
|
|
<section class="examples">
|
||
|
|
|
||
|
|
### Examples
|
||
|
|
|
||
|
|
```c
|
||
|
|
#include "stdlib/complex/float64/ctor.h"
|
||
|
|
#include <stdint.h>
|
||
|
|
#include <stdio.h>
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Return the real component of a double-precision complex floating-point number.
|
||
|
|
*
|
||
|
|
* @param z complex number
|
||
|
|
* @return real component
|
||
|
|
*/
|
||
|
|
static double real( const stdlib_complex128_t z ) {
|
||
|
|
stdlib_complex128_parts_t v;
|
||
|
|
|
||
|
|
// Assign a double-precision complex floating-point number:
|
||
|
|
v.value = z;
|
||
|
|
|
||
|
|
// Extract the real component:
|
||
|
|
double re = v.parts[ 0 ];
|
||
|
|
|
||
|
|
return re;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Return the imaginary component of a double-precision complex floating-point number.
|
||
|
|
*
|
||
|
|
* @param z complex number
|
||
|
|
* @return imaginary component
|
||
|
|
*/
|
||
|
|
static double imag( const stdlib_complex128_t z ) {
|
||
|
|
stdlib_complex128_parts_t v;
|
||
|
|
|
||
|
|
// Assign a double-precision complex floating-point number:
|
||
|
|
v.value = z;
|
||
|
|
|
||
|
|
// Extract the imaginary component:
|
||
|
|
double im = v.parts[ 1 ];
|
||
|
|
|
||
|
|
return im;
|
||
|
|
}
|
||
|
|
|
||
|
|
int main( void ) {
|
||
|
|
const stdlib_complex128_t x[] = {
|
||
|
|
stdlib_complex128( 5.0, 2.0 ),
|
||
|
|
stdlib_complex128( -2.0, 1.0 ),
|
||
|
|
stdlib_complex128( 0.0, -0.0 ),
|
||
|
|
stdlib_complex128( 0.0/0.0, 0.0/0.0 )
|
||
|
|
};
|
||
|
|
|
||
|
|
stdlib_complex128_t v;
|
||
|
|
int i;
|
||
|
|
for ( i = 0; i < 4; i++ ) {
|
||
|
|
v = x[ i ];
|
||
|
|
printf( "%lf + %lfi\n", real( v ), imag( v ) );
|
||
|
|
}
|
||
|
|
}
|
||
|
|
```
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.examples -->
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.c -->
|
||
|
|
|
||
|
|
<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
|
||
|
|
|
||
|
|
<section class="references">
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.references -->
|
||
|
|
|
||
|
|
<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
|
||
|
|
|
||
|
|
<section class="related">
|
||
|
|
|
||
|
|
* * *
|
||
|
|
|
||
|
|
## See Also
|
||
|
|
|
||
|
|
- <span class="package-name">[`@stdlib/complex-cmplx`][@stdlib/complex/cmplx]</span><span class="delimiter">: </span><span class="description">create a complex number.</span>
|
||
|
|
- <span class="package-name">[`@stdlib/complex-float32/ctor`][@stdlib/complex/float32/ctor]</span><span class="delimiter">: </span><span class="description">64-bit complex number.</span>
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.related -->
|
||
|
|
|
||
|
|
<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
|
||
|
|
|
||
|
|
|
||
|
|
<section class="main-repo" >
|
||
|
|
|
||
|
|
* * *
|
||
|
|
|
||
|
|
## Notice
|
||
|
|
|
||
|
|
This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
|
||
|
|
|
||
|
|
For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].
|
||
|
|
|
||
|
|
#### Community
|
||
|
|
|
||
|
|
[![Chat][chat-image]][chat-url]
|
||
|
|
|
||
|
|
---
|
||
|
|
|
||
|
|
## License
|
||
|
|
|
||
|
|
See [LICENSE][stdlib-license].
|
||
|
|
|
||
|
|
|
||
|
|
## Copyright
|
||
|
|
|
||
|
|
Copyright © 2016-2024. The Stdlib [Authors][stdlib-authors].
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.stdlib -->
|
||
|
|
|
||
|
|
<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
|
||
|
|
|
||
|
|
<section class="links">
|
||
|
|
|
||
|
|
[npm-image]: http://img.shields.io/npm/v/@stdlib/complex-float64-ctor.svg
|
||
|
|
[npm-url]: https://npmjs.org/package/@stdlib/complex-float64-ctor
|
||
|
|
|
||
|
|
[test-image]: https://github.com/stdlib-js/complex-float64-ctor/actions/workflows/test.yml/badge.svg?branch=v0.0.3
|
||
|
|
[test-url]: https://github.com/stdlib-js/complex-float64-ctor/actions/workflows/test.yml?query=branch:v0.0.3
|
||
|
|
|
||
|
|
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/complex-float64-ctor/main.svg
|
||
|
|
[coverage-url]: https://codecov.io/github/stdlib-js/complex-float64-ctor?branch=main
|
||
|
|
|
||
|
|
<!--
|
||
|
|
|
||
|
|
[dependencies-image]: https://img.shields.io/david/stdlib-js/complex-float64-ctor.svg
|
||
|
|
[dependencies-url]: https://david-dm.org/stdlib-js/complex-float64-ctor/main
|
||
|
|
|
||
|
|
-->
|
||
|
|
|
||
|
|
[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg
|
||
|
|
[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im
|
||
|
|
|
||
|
|
[stdlib]: https://github.com/stdlib-js/stdlib
|
||
|
|
|
||
|
|
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
|
||
|
|
|
||
|
|
[umd]: https://github.com/umdjs/umd
|
||
|
|
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
|
||
|
|
|
||
|
|
[deno-url]: https://github.com/stdlib-js/complex-float64-ctor/tree/deno
|
||
|
|
[deno-readme]: https://github.com/stdlib-js/complex-float64-ctor/blob/deno/README.md
|
||
|
|
[umd-url]: https://github.com/stdlib-js/complex-float64-ctor/tree/umd
|
||
|
|
[umd-readme]: https://github.com/stdlib-js/complex-float64-ctor/blob/umd/README.md
|
||
|
|
[esm-url]: https://github.com/stdlib-js/complex-float64-ctor/tree/esm
|
||
|
|
[esm-readme]: https://github.com/stdlib-js/complex-float64-ctor/blob/esm/README.md
|
||
|
|
[branches-url]: https://github.com/stdlib-js/complex-float64-ctor/blob/main/branches.md
|
||
|
|
|
||
|
|
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/complex-float64-ctor/main/LICENSE
|
||
|
|
|
||
|
|
[json]: http://www.json.org/
|
||
|
|
|
||
|
|
[mdn-json-stringify]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/JSON/stringify
|
||
|
|
|
||
|
|
[mdn-json-parse]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/JSON/parse
|
||
|
|
|
||
|
|
[@stdlib/complex/float64/reviver]: https://www.npmjs.com/package/@stdlib/complex-float64-reviver
|
||
|
|
|
||
|
|
<!-- <related-links> -->
|
||
|
|
|
||
|
|
[@stdlib/complex/cmplx]: https://www.npmjs.com/package/@stdlib/complex-cmplx
|
||
|
|
|
||
|
|
[@stdlib/complex/float32/ctor]: https://www.npmjs.com/package/@stdlib/complex-float32-ctor
|
||
|
|
|
||
|
|
<!-- </related-links> -->
|
||
|
|
|
||
|
|
</section>
|
||
|
|
|
||
|
|
<!-- /.links -->
|