rayleigh-cdf:瑞利分布累积分布函数（CDF）

Cumulative Distribution Function === [![NPM version][npm-image]][npm-url] [![Build Status][travis-image]][travis-url] [![Coverage Status][codecov-image]][codecov-url] [![Dependencies][dependencies-image]][dependencies-url] > [Rayleigh](https://en.wikipedia.org/wiki/Rayleigh_distribution) distribution [cumulative distribution function](https://en.wikipedia.org/wiki/Cumulative_distribution_function). The [cumulative distribution function](https://en.wikipedia.org/wiki/Cumulative_distribution_function) for a [Rayleigh](https://en.wikipedia.org/wiki/Rayleigh_distribution) random variable is <div class="equation" align="center" data-raw-text="F(x;\sigma) = \begin{cases} 0 &amp; \text{ for } x < 0 \\ 1 - e^{-x^2/2\sigma^2} &amp; \text{ for } x \ge 0 \end{cases} " data-equation="eq:cdf"> <img src="https://cdn.rawgit.com/distributions-io/rayleigh-cdf/dc9d27df02622b24a327b54d839c83bb3be3f327/docs/img/eqn.svg" alt="Cumulative distribution function for a Rayleigh distribution."> <br> </div> where `sigma` is the scale parameter. ## Installation ``` bash $ npm install distributions-rayleigh-cdf ``` For use in the browser, use [browserify](https://github.com/substack/node-browserify). ## Usage ``` javascript var cdf = require( 'distributions-rayleigh-cdf' ); ``` #### cdf( x[, options] ) Evaluates the [cumulative distribution function](https://en.wikipedia.org/wiki/Cumulative_distribution_function) for the [Rayleigh](https://en.wikipedia.org/wiki/Rayleigh_distribution) distribution. `x` may be either a [`number`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number), an [`array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array), a [`typed array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays), or a [`matrix`](https://github.com/dstructs/matrix). ``` javascript var matrix = require( 'dstructs-matrix' ), mat, out, x, i; out = cdf( 1 ); // returns ~0.393 x = [ -1, 0, 1, 2, 3 ]; out = cdf( x ); // returns [ 0, 0, ~0.393, ~0.865, ~0.989 ] x = new Float32Array( x ); out = cdf( x ); // returns Float64Array( [0,0,~0.393,~0.865,~0.989] ) x = new Float32Array( 6 ); for ( i = 0; i < 6; i++ ) { x[ i ] = i; } mat = matrix( x, [3,2], 'float32' ); /* [ 0 1 2 3 3 5 ] */ out = cdf( mat ); /* [ 0 ~0.393 ~0.865 ~0.989 ~1 ~1 ] */ ``` The function accepts the following `options`: * __sigma__: scale parameter. Default: `1`. * __accessor__: accessor `function` for accessing `array` values. * __dtype__: output [`typed array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays) or [`matrix`](https://github.com/dstructs/matrix) data type. Default: `float64`. * __copy__: `boolean` indicating if the `function` should return a new data structure. Default: `true`. * __path__: [deepget](https://github.com/kgryte/utils-deep-get)/[deepset](https://github.com/kgryte/utils-deep-set) key path. * __sep__: [deepget](https://github.com/kgryte/utils-deep-get)/[deepset](https://github.com/kgryte/utils-deep-set) key path separator. Default: `'.'`. A [Rayleigh](https://en.wikipedia.org/wiki/Rayleigh_distribution) distribution is a function of one parameter: `sigma`(scale parameter). By default, `sigma` is equal to `1`. To adjust it, set the corresponding option. ``` javascript var x = [ -1, 0, 1, 2, 3 ]; var out = cdf( x, { 'sigma': 7 }); // returns [ 0, 0, ~0.0102, ~0.04, ~0.0877 ] ``` For non-numeric `arrays`, provide an accessor `function` for accessing `array` values. ``` javascript var data = [ [0,-1], [1,0], [2,1], [3,2], [4,3], ]; function getValue( d, i ) { return d[ 1 ]; } var out = cdf( data, { 'accessor': getValue }); // returns [ 0, 0, ~0.393, ~0.865, ~0.989 ] ``` To [deepset](https://github.com/kgryte/utils-deep-set) an object `array`, provide a key path and, optionally, a key path separator. ``` javascript var data = [ {'x':[0,-4]}, {'x':[1,-2]}, {'x':[2,0]}, {'x':[3,2]}, {'x':[4,4]}, ]; var out = cdf( data, { 'path': 'x/1', 'sep': '/' }); /* [ {'x':[0,0]}, {'x':[1,0]}, {'x':[2,~0.393]}, {'x':[3,~0.865]}, {'x':[4,~0.989]}, ] */ var bool = ( data === out ); // returns true ``` By default, when provided a [`typed array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays) or [`matrix`](https://github.com/dstructs/matrix), the output data structure is `float64` in order to preserve precision. To specify a different data type, set the `dtype` option (see [`matrix`](https://github.com/dstructs/matrix) for a list of acceptable data types). ``` javascript var x, out; x = new Float64Array( [-1,0,1,2,3] ); out = cdf( x, { 'dtype': 'float32' }); // returns Float32Array( [0,0,~0.393,~0.865,~0.989] ) // Works for plain arrays, as well... out = cdf( [-1,0,1,2,3], { 'dtype': 'float32' }); // returns Float32Array( [0,0,~0.393,~0.865,~0.989] ) ``` By default, the function returns a new data structure. To mutate the input data structure (e.g., when input values can be discarded or when optimizing memory usage), set the `copy` option to `false`. ``` javascript var bool, mat, out, x, i; x = [ -1, 0, 1, 2, 3 ]; out = cdf( x, { 'copy': false }); // returns [ 0, 0, ~0.0102, ~0.04, ~0.0877 ] bool = ( x === out ); // returns true x = new Float32Array( 6 ); for ( i = 0; i < 6; i++ ) { x[ i ] = i; } mat = matrix( x, [3,2], 'float32' ); /* [ 0 1 2 3 3 5 ] */ out = cdf( mat, { 'copy': false }); /* [ 0 ~0.393 ~0.865 ~0.989 ~1 ~1 ] */ bool = ( mat === out ); // returns true ``` ## Notes * If an element is __not__ a numeric value, the evaluated [cumulative distribution function](https://en.wikipedia.org/wiki/Cumulative_distribution_function) is `NaN`. ``` javascript var data, out; out = cdf( null ); // returns NaN out = cdf( true ); // returns NaN out = cdf( {'a':'b'} ); // returns NaN out = cdf( [ true, null, [] ] ); // returns [ NaN, NaN, NaN ] function getValue( d, i ) { return d.x; } data = [ {'x':true}, {'x':[]}, {'x':{}}, {'x':null} ]; out = cdf( data, { 'accessor': getValue }); // returns [ NaN, NaN, NaN, NaN ] out = cdf( data, { 'path': 'x' }); /* [ {'x':NaN}, {'x':NaN}, {'x':NaN, {'x':NaN} ] */ ``` ## Examples ``` javascript var cdf = require( 'distributions-rayleigh-cdf' ), matrix = require( 'dstructs-matrix' ); var data, mat, out, tmp, i; // Plain arrays... data = new Array( 10 ); for ( i = 0; i < data.length; i++ ) { data[ i ] = i / 2; } out = cdf( data ); // Object arrays (accessors)... function getValue( d ) { return d.x; } for ( i = 0; i < data.length; i++ ) { data[ i ] = { 'x': data[ i ] }; } out = cdf( data, { 'accessor': getValue }); // Deep set arrays... for ( i = 0; i < data.length; i++ ) { data[ i ] = { 'x': [ i, data[ i ].x ] }; } out = cdf( data, { 'path': 'x/1', 'sep': '/' }); // Typed arrays... data = new Float32Array( 10 ); for ( i = 0; i < data.length; i++ ) { data[ i ] = i / 2; } out = cdf( data ); // Matrices... mat = matrix( data, [5,2], 'float32' ); out = cdf( mat ); // Matrices (custom output data type)... out = cdf( mat, { 'dtype': 'uint8' }); ``` To run the example code from the top-level application directory, ``` bash $ node ./examples/index.js ``` ## Tests ### Unit Unit tests use the [Mocha](http://mochajs.org/) test framework with [Chai](http://chaijs.com) assertions. To run the tests, execute the following command in the top-level application directory: ``` bash $ make test ``` All new feature development should have corresponding unit tests to validate correct functionality. ### Test Coverage This repository uses [Istanbul](https://github.com/gotwarlost/istanbul) as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory: ``` bash $ make test-cov ``` Istanbul creates a `./reports/coverage` directory. To access an HTML version of the report, ``