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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 constantFunction = require( '@stdlib/utils/constant-function' );
var degenerate = require( '@stdlib/stats/base/dists/degenerate/pdf' ).factory;
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var exp = require( '@stdlib/math/base/special/exp' );
var pow = require( '@stdlib/math/base/special/pow' );
var ln = require( '@stdlib/math/base/special/ln' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var FLOAT64_SMALLEST_NORMAL = require( '@stdlib/constants/float64/smallest-normal' );
// MAIN //
/**
* Returns a function for evaluating the probability density function (PDF) for a Rayleigh distribution with scale parameter `sigma`.
*
* @param {NonNegativeNumber} sigma - scale parameter
* @returns {Function} PDF
*
* @example
* var pdf = factory( 0.5 );
* var y = pdf( 1.0 );
* // returns ~0.541
*
* y = pdf( 0.1 );
* // returns ~0.392
*/
function factory( sigma ) {
var normal;
var s2i;
var lns;
var s2;
if ( isnan( sigma ) || sigma < 0.0 ) {
return constantFunction( NaN );
}
if ( sigma === 0.0 ) {
return degenerate( 0.0 );
}
s2 = pow( sigma, 2.0 );
s2i = 1.0 / s2;
normal = ( s2 >= FLOAT64_SMALLEST_NORMAL && 2.0 * s2 < PINF );
lns = ln( sigma );
return pdf;
/**
* Evaluates the probability density function (PDF) for a Rayleigh distribution.
*
* @private
* @param {number} x - input value
* @returns {number} evaluated PDF
*
* @example
* var y = pdf( 2.3 );
* // returns <number>
*/
function pdf( x ) {
var x2;
var r;
var q;
if ( isnan( x ) ) {
return NaN;
}
if ( x < 0.0 || x === PINF ) {
return 0.0;
}
x2 = pow( x, 2.0 );
q = s2i * x;
if ( normal && x2 < PINF && q >= FLOAT64_SMALLEST_NORMAL ) {
return q * exp( -x2 / ( 2.0 * s2 ) );
}
// For `sigma` or `x` far from `1`, forming `sigma^2` or `x^2` overflows or underflows, so evaluate via the ratio `x/sigma` instead...
r = x / sigma;
q = r / sigma;
if ( q < PINF ) {
return q * exp( -0.5 * r * r );
}
// `x/sigma^2` overflows only for a tiny `sigma`, where the exponential decides the result:
return exp( ( ln( r ) - lns ) - ( 0.5 * r * r ) );
}
}
// EXPORTS //
module.exports = factory;
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