main.js (1689B)
1 /** 2 * @license Apache-2.0 3 * 4 * Copyright (c) 2018 The Stdlib Authors. 5 * 6 * Licensed under the Apache License, Version 2.0 (the "License"); 7 * you may not use this file except in compliance with the License. 8 * You may obtain a copy of the License at 9 * 10 * http://www.apache.org/licenses/LICENSE-2.0 11 * 12 * Unless required by applicable law or agreed to in writing, software 13 * distributed under the License is distributed on an "AS IS" BASIS, 14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 15 * See the License for the specific language governing permissions and 16 * limitations under the License. 17 */ 18 19 'use strict'; 20 21 // MODULES // 22 23 var isnan = require( './../../../../base/assert/is-nan' ); 24 var isint = require( './../../../../base/assert/is-integer' ); 25 26 27 // MAIN // 28 29 /** 30 * Evaluates a normalized Hermite polynomial. 31 * 32 * @param {NonNegativeInteger} n - nonnegative polynomial degree 33 * @param {number} x - evaluation point 34 * @returns {number} function value 35 * 36 * @example 37 * var v = normhermitepoly( 1, 0.5 ); 38 * // returns 0.5 39 * 40 * @example 41 * var v = normhermitepoly( 0, 0.5 ); 42 * // returns 1.0 43 * 44 * @example 45 * var v = normhermitepoly( 2, 0.5 ); 46 * // returns -0.75 47 * 48 * @example 49 * var v = normhermitepoly( -1, 0.5 ); 50 * // returns NaN 51 */ 52 function normhermitepoly( n, x ) { 53 var y1; 54 var y2; 55 var y3; 56 var i; 57 58 if ( isnan( n ) || isnan( x ) || n < 0 || !isint( n ) ) { 59 return NaN; 60 } 61 if ( n === 0 ) { 62 // `x` is completely canceled from the expression: 63 return 1.0; 64 } 65 if ( n === 1 ) { 66 return x; 67 } 68 y2 = 1.0; 69 y3 = 0.0; 70 for ( i = n; i > 1; i-- ) { 71 y1 = (x*y2) - (i*y3); 72 y3 = y2; 73 y2 = y1; 74 } 75 return (x*y2) - y3; 76 } 77 78 79 // EXPORTS // 80 81 module.exports = normhermitepoly;