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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 cospi = require( '@stdlib/math/base/special/cospi' );
var ln = require( '@stdlib/math/base/special/ln' );
var NINF = require( '@stdlib/constants/float64/ninf' );
var PINF = require( '@stdlib/constants/float64/pinf' );
// MAIN //
/**
* Evaluates the natural logarithm of the probability density function (PDF) for a raised cosine distribution with location parameter `mu` and scale parameter `s` at a value `x`.
*
* @param {number} x - input value
* @param {number} mu - location parameter
* @param {NonNegativeNumber} s - scale parameter
* @returns {number} evaluated logPDF
*
* @example
* var y = logpdf( 2.0, 0.0, 3.0 );
* // returns ~-2.485
*
* @example
* var y = logpdf( 1.5, 4.0, 4.0 );
* // returns ~-2.562
*
* @example
* var y = logpdf( NaN, 0.0, 1.0 );
* // returns NaN
*
* @example
* var y = logpdf( 0.0, NaN, 1.0 );
* // returns NaN
*
* @example
* var y = logpdf( 0.0, 0.0, NaN );
* // returns NaN
*
* @example
* // Negative scale parameter:
* var y = logpdf( 2.0, 0.0, -1.0 );
* // returns NaN
*
* @example
* var y = logpdf( 2.0, 8.0, 0.0 );
* // returns -Infinity
*
* @example
* var y = logpdf( 8.0, 8.0, 0.0 );
* // returns Infinity
*/
function logpdf( x, mu, s ) {
var z;
if (
isnan( x ) ||
isnan( mu ) ||
isnan( s ) ||
s < 0.0
) {
return NaN;
}
if ( s === 0.0 ) {
return ( x === mu ) ? PINF : NINF;
}
if (
x < mu - s ||
x > mu + s
) {
return NINF;
}
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:
return ( 2.0 * ln( cospi( z / 2.0 ) ) ) - ln( s );
}
// EXPORTS //
module.exports = logpdf;
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