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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 sqrt = require( '@stdlib/math/base/special/sqrt' );
// MAIN //
/**
* Returns the median of a triangular distribution.
*
* @param {number} a - minimum support
* @param {number} b - maximum support
* @param {number} c - mode
* @returns {number} median
*
* @example
* var v = median( 0.0, 1.0, 0.5 );
* // returns 0.5
*
* @example
* var v = median( 4.0, 12.0, 9.0 );
* // returns ~8.472
*
* @example
* var v = median( -4.0, 4.0, -1.0 );
* // returns ~-0.472
*
* @example
* var v = median( 1.0, -0.1, 0.5 );
* // returns NaN
*
* @example
* var v = median( 0.0, 1.0, 2.0 );
* // returns NaN
*
* @example
* var v = median( NaN, 4.0, 2.0 );
* // returns NaN
*
* @example
* var v = median( 0.0, NaN, 2.0 );
* // returns NaN
*
* @example
* var v = median( 0.0, 4.0, NaN );
* // returns NaN
*/
function median( a, b, c ) {
if (
isnan( a ) ||
isnan( b ) ||
isnan( c ) ||
!( a <= c && c <= b )
) {
return NaN;
}
if ( c >= ( a+b ) / 2.0 ) {
return a + sqrt( 0.5 * ( b-a ) * ( c-a ) );
}
return b - sqrt( 0.5 * ( b-a ) * ( b-c ) );
}
// EXPORTS //
module.exports = median;
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