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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 cospi = require( '@stdlib/math/base/special/cospi' );
// MAIN //
/**
* Returns a function for evaluating the probability density function (PDF) for a raised cosine distribution.
*
* @param {number} mu - location parameter
* @param {NonNegativeNumber} s - scale parameter
* @returns {Function} PDF
*
* @example
* var pdf = factory( 0.0, 3.0 );
* var y = pdf( 2.0 );
* // returns ~0.083
*
* y = pdf( 5.0 );
* // returns 0.0
*/
function factory( mu, s ) {
if ( isnan( mu ) || isnan( s ) || s < 0.0 ) {
return constantFunction( NaN );
}
if ( s === 0.0 ) {
return degenerate( mu );
}
return pdf;
/**
* Evaluates the probability density function (PDF) for a raised cosine distribution.
*
* @private
* @param {number} x - input value
* @returns {number} evaluated PDF
*
* @example
* var y = pdf( -1.2 );
* // returns <number>
*/
function pdf( x ) {
var c;
var z;
if ( isnan( x ) ) {
return NaN;
}
if (
x < mu - s ||
x > mu + s
) {
return 0.0;
}
z = ( x - mu ) / s;
// `1 + cos(pi*z)` cancels near the edges of the support (`z = -1` and `z = 1`); `1 + cos(pi*z) = 2*cos(pi*z/2)^2` has no subtraction:
c = cospi( z / 2.0 );
return ( c * c ) / s;
}
}
// EXPORTS //
module.exports = factory;
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