coords_array.js (1583B)
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 sqrt = require( '@stdlib/math/base/special/sqrt' ); 24 var exp = require( '@stdlib/math/base/special/exp' ); 25 var ln = require( '@stdlib/math/base/special/ln' ); 26 27 28 // VARIABLES // 29 30 // (R*phi(R) + Pr(X>=R))*sqrt(2\pi) 31 var V = 9.91256303526217e-3; 32 33 34 // MAIN // 35 36 /** 37 * Returns an array containing coordinates such that each rectangle has the same area. 38 * 39 * @private 40 * @param {PositiveInteger} N - number of rectangles 41 * @param {number} rTail - start of right tail 42 * @returns {NumberArray} coordinate array 43 * 44 * @example 45 * var X = coordsArray( 128, 3.44 ); 46 * // returns <Array> 47 */ 48 function coordsArray( N, rTail ) { 49 var X; 50 var f; 51 var i; 52 53 f = exp( -0.5 * rTail * rTail ); 54 55 X = []; 56 X.push( V/f ); // bottom block: V / f(R) 57 X.push( rTail ); 58 for ( i = 2; i < N; i++ ) { 59 X[ i ] = sqrt( -2.0 * ln( ( V/X[i-1] ) + f ) ); 60 f = exp( -0.5 * X[ i ] * X[ i ] ); 61 } 62 X.push( 0.0 ); 63 return X; 64 } 65 66 67 // EXPORTS // 68 69 module.exports = coordsArray;