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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 isnan = require( '@stdlib/math/base/assert/is-nan' );
var ln = require( '@stdlib/math/base/special/ln' );
var TWO_PI = require( '@stdlib/constants/float64/two-pi' );
var E = require( '@stdlib/constants/float64/e' );
// MAIN //
/**
* Returns the differential entropy for a normal distribution with mean `mu` and standard deviation `sigma`.
*
* @param {number} mu - mean
* @param {PositiveNumber} sigma - standard deviation
* @returns {number} entropy
*
* @example
* var y = entropy( 0.0, 1.0 );
* // returns ~1.419
*
* @example
* var y = entropy( 5.0, 3.0 );
* // returns ~2.518
*
* @example
* var y = entropy( NaN, 1.0 );
* // returns NaN
*
* @example
* var y = entropy( 0.0, NaN );
* // returns NaN
*
* @example
* var y = entropy( 0.0, 0.0 );
* // returns NaN
*/
function entropy( mu, sigma ) {
if (
isnan( mu ) ||
isnan( sigma ) ||
sigma <= 0.0
) {
return NaN;
}
return 0.5 * ln( TWO_PI * E * sigma*sigma );
}
// EXPORTS //
module.exports = entropy;
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