1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
|
/**
* @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.
*
*
* ## Notice
*
* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_64_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified for JavaScript.
*
* ```text
* Copyright John Maddock 2006-7, 2013-14.
* Copyright Paul A. Bristow 2007, 2013-14.
* Copyright Nikhar Agrawal 2013-14.
* Copyright Christopher Kormanyos 2013-14.
*
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt)
* ```
*/
'use strict';
// MODULES //
var abs = require( './../../../../base/special/abs' );
var floor = require( './../../../../base/special/floor' );
var gamma = require( './../../../../base/special/gamma' );
var factorial = require( './../../../../base/special/factorial' );
var gammaDeltaRatioLanczos = require( './gamma_delta_ratio_lanczos.js' );
// VARIABLES //
var MAX_FACTORIAL = 170; // TODO: consider moving to pkg
// MAIN //
/**
* Computes the ratio of two gamma functions.
*
* ## Notes
*
* - Specifically, the function evaluates
*
* ```tex
* \frac{ \Gamma( z ) }{ \Gamma( z + \delta ) }
* ```
*
* @param {number} z - first gamma parameter
* @param {number} delta - difference
* @returns {number} gamma ratio
*
* @example
* var y = gammaDeltaRatio( 2.0, 3.0 );
* // returns ~0.042
*
* @example
* var y = gammaDeltaRatio( 4.0, 0.5 );
* // returns ~0.516
*
* @example
* var y = gammaDeltaRatio( 100.0, 0.0 );
* // returns 1.0
*/
function gammaDeltaRatio( z, delta ) {
var result;
var idelta;
var iz;
if ( z <= 0.0 || z + delta <= 0.0 ) {
// This isn't very sophisticated, or accurate, but it does work:
return gamma( z ) / gamma( z + delta );
}
idelta = floor( delta );
if ( idelta === delta ) {
iz = floor( z );
if ( iz === z ) {
// As both `z` and `delta` are integers, see if we can use a table lookup:
if ( z <= MAX_FACTORIAL && ( z + delta <= MAX_FACTORIAL ) ) {
return factorial( iz - 1.0 ) / factorial( idelta + iz - 1.0 );
}
}
if ( abs(delta) < 20.0 ) {
// As `delta` is a small integer, we can use a finite product:
if ( delta === 0.0 ) {
return 1.0;
}
if ( delta < 0.0 ) {
z -= 1.0;
result = z;
delta += 1.0;
while ( delta !== 0.0 ) {
z -= 1.0;
result *= z;
delta += 1.0;
}
return result;
}
result = 1.0 / z;
delta -= 1.0;
while ( delta !== 0.0 ) {
z += 1.0;
result /= z;
delta -= 1.0;
}
return result;
}
}
return gammaDeltaRatioLanczos( z, delta );
}
// EXPORTS //
module.exports = gammaDeltaRatio;
|
