distributions-rayleigh-entropy

Entropy
===
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> Rayleigh distribution entropy.

The entropy for a Rayleigh random variable is

where gamma is the Euler–Mascheroni constant and sigma > 0 is the scale parameter of the distribution.

Installation

`` bash
$ npm install distributions-rayleigh-entropy
`

For use in the browser, use browserify.

Usage

` javascript
var entropy = require( 'distributions-rayleigh-entropy' );
`

#### entropy( sigma[, opts] )

Computes the entropy for a Rayleigh distribution with parameter sigma. sigma may be either a number, an array, a typed array, or a matrix.

` javascript
var matrix = require( 'dstructs-matrix' ),
data,
mat,
out,
i;

out = entropy( 0.5 );
// returns ~0.249

sigma = [ 0.5, 1, 2, 4 ];
out = entropy( sigma );

// returns [ ~0.249, ~0.942, ~1.635, ~2.328 ]

sigma = new Float32Array( sigma );
out = entropy( sigma );
// returns Float64Array( [~0.249,~0.942,~1.635,~2.328] )

sigma = matrix( [ 0.5, 1, 2, 4 ], [2,2] );
/*
[ 0.5 1
2 4 ]
*/

out = entropy( sigma );
/*
[ ~0.249 ~0.942
~1.635 ~2.328 ]
*/
`

The function accepts the following options:

* __accessor__: accessor function for accessing array values.
* __dtype__: output typed array or matrix data type. Default: float64.
* __copy__: boolean indicating if the function should return a new data structure. Default: true.
* __path__: deepget/deepset key path.
* __sep__: deepget/deepset key path separator. Default: '.'.

For non-numeric arrays, provide an accessor function for accessing array values.

` javascript
var sigma = [
[0,0.5],
[1,1],
[2,2],
[3,4]
];

function getValue( d, i ) {
return d[ 1 ];
}

var out = entropy( sigma, {
'accessor': getValue
});
// returns [ ~0.249, ~0.942, ~1.635, ~2.328 ]
`

To deepset an object array, provide a key path and, optionally, a key path separator.

` javascript
var sigma = [
{'x':[9,0.5]},
{'x':[9,1]},
{'x':[9,2]},
{'x':[9,4]}
];

var out = entropy( sigma, {
'path': 'x|1',
'sep': '|'
});
/*
[
{'x':[9,~0.249]},
{'x':[9,~0.942]},
{'x':[9,~1.635]},
{'x':[9,~2.328]},
]
*/

var bool = ( data === out );
// returns true
`

By default, when provided a typed array or matrix, the output data structure is float64 in order to preserve precision. To specify a different data type, set the dtype option (see matrix for a list of acceptable data types).

` javascript
var sigma, out;

sigma = new Float64Array( [ 0.5,1,2,4 ] );

out = entropy( sigma, {
'dtype': 'int32'
});
// returns Int32Array( [ 0,0,1,2 ] )

// Works for plain arrays, as well...
out = entropy( [0.5,1,2,4], {
'dtype': 'int32'
});
// returns Int32Array( [ 0,0,1,2 ] )
`

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 sigma,
bool,
mat,
out,
i;

sigma = [ 0.5, 1, 2, 4 ];

out = entropy( sigma, {
'copy': false
});
// returns [ ~0.249, ~0.942, ~1.635, ~2.328 ]

bool = ( data === out );
// returns true

mat = matrix( [ 0.5, 1, 2, 4 ], [2,2] );
/*
[ 0.5 1
2 4 ]
*/

out = entropy( mat, {
'copy': false
});
/*
[ ~0.249 ~0.942
~1.635 ~2.328 ]
*/

bool = ( mat === out );
// returns true
`

Notes

* If an element is __not__ a positive number, the entropy is NaN.

` javascript
var sigma, out;

out = entropy( -1 );
// returns NaN

out = entropy( 0 );
// returns NaN

out = entropy( null );
// returns NaN

out = entropy( true );
// returns NaN

out = entropy( {'a':'b'} );
// returns NaN

out = entropy( [ true, null, [] ] );
// returns [ NaN, NaN, NaN ]

function getValue( d, i ) {
return d.x;
}
sigma = [
{'x':true},
{'x':[]},
{'x':{}},
{'x':null}
];

out = entropy( sigma, {
'accessor': getValue
});
// returns [ NaN, NaN, NaN, NaN ]

out = entropy( sigma, {
'path': 'x'
});
/*
[
{'x':NaN},
{'x':NaN},
{'x':NaN,
{'x':NaN}
]
*/
`

* Be careful when providing a data structure which contains non-numeric elements and specifying an integer output data type, as NaN values are cast to 0.

` javascript
var out = entropy( [ true, null, [] ], {
'dtype': 'int8'
});
// returns Int8Array( [0,0,0] );
`

Examples

` javascript
var matrix = require( 'dstructs-matrix' ),
entropy = require( 'distributions-rayleigh-entropy' );

var sigma,
mat,
out,
tmp,
i;

// Plain arrays...
sigma = new Array( 10 );
for ( i = 0; i < sigma.length; i++ ) {
sigma[ i ] = i + 1;
}
out = entropy( sigma );

// Object arrays (accessors)...
function getValue( d ) {
return d.x;
}
for ( i = 0; i < sigma.length; i++ ) {
sigma[ i ] = {
'x': sigma[ i ]
};
}
out = entropy( sigma, {
'accessor': getValue
});

// Deep set arrays...
for ( i = 0; i < sigma.length; i++ ) {
sigma[ i ] = {
'x': [ i, sigma[ i ].x ]
};
}
out = entropy( sigma, {
'path': 'x/1',
'sep': '/'
});

// Typed arrays...
sigma = new Float64Array( 10 );
for ( i = 0; i < sigma.length; i++ ) {
sigma[ i ] = i + 1;
}
out = entropy( sigma );

// Matrices...
mat = matrix( sigma, [5,2], 'float64' );
out = entropy( mat );

// Matrices (custom output data type)...
out = entropy( mat, {
'dtype': 'uint8'
});
`

To run the example code from the top-level application directory,

` bash
$ node ./examples/index.js
`

Tests

$3

Unit tests use the Mocha test framework with Chai 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.

$3

This repository uses 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,

` bash
$ make view-cov
``

---

License

MIT license.

Copyright

Copyright © 2015. The Compute.io Authors.

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[npm-url]: https://npmjs.org/package/distributions-rayleigh-entropy

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[travis-url]: https://travis-ci.org/distributions-io/rayleigh-entropy

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[codecov-url]: https://codecov.io/github/distributions-io/rayleigh-entropy?branch=master

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[dependencies-url]: https://david-dm.org/distributions-io/rayleigh-entropy

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[dev-dependencies-url]: https://david-dm.org/dev/distributions-io/rayleigh-entropy

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[github-issues-url]: https://github.com/distributions-io/rayleigh-entropy/issues